The Ascent of Science

The Ascent of Science

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The Ascent of Science

Brian L. Silver

A Solomon Press Book

OXFORD UNIVERSITY PRES S

OXFORD UNIVERSITY PRESS

Oxford Ne w York Athens Aucklan d Bangko k Bogot a Bomba y Buenos Aires Calcutt a Cap e Town Da r es Salaam Delh i Florence Hon g Kong Istanbu l Karach i Kuala Lumpur Madra s Madri d Melbourn e Mexico City Nairob i Pari s Singapor e Taipei Toky o Toront o Warsa w and associated companie s in Berlin Ibada n

Copyright © 1998 by Oxford University Press First published b y Oxford University Press First issued a s an Oxford University Press Paperback, 2000 198 Madison Avenue, New York, New York 1001 6 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication ma y be reproduced, stored in a retrieval system, or transmitted, in any form o r means, electronic, mechanical, photocopying , recording, or otherwise, without the prior permission o f Oxford University Press. Library of Congress Cataloging-in-Publication Data Silver, Brian L. The ascent of science / Brian L. Silver. p. cm. "A Solomon Press book." Includes bibliographical reference s and index. ISBN 0-19-511699-2 (hbk); ISBN 0-19-513427-3 (pbk) 1. Science—History. 2. Science—Philosophy. 3. Thought an d thinking—History. I. Title. Q125.S5425 1998 303.48'3—dc2 1 97—1543 0 987654321 Printed in the United State s of America on acid-free pape r

This book is for Sharon, who knows the reasons that reason cannot know

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Contents

Acknowledgments i Preface xii i Introduction x v

x

Part One

1. Newto n Gets It Completely Wrong 3 2. I Believe 1 1 Part Two

3. Thoma s Aquinas versus Neil Armstrong 2 9 4. Th e Second La w 3 7 5. Predictin g Catastrophe 4 2 6. Fro m Newton to De Sade: The Partial Triumph of Reason 5 7. Fro m Rousseau to Blake: The Revolt against Reason 6 8 Part Three

8. Lodestone , Amber, and Lightning 8 9. Belie f and Action 10 3

1

Part Four

10. Th e Demise of Alchemy 11 3 11. Th e Nineteenth Centur y 12 1 12. Th e Material Trinity: The Atom 13 13. Th e Stuf f o f Existence 14 9 14. Scipio' s Dream 16 9

5

Part Five

15. Makin g Waves 18 3 16. Th e Ubiquity of Motion 20 1 17. Energ y 20 9 18. Entropy : Intimations o f Mortality 21 19. Chao s 23 3

5

0

Part Six

20. Th e Slo w Birth of Biology 25 3 21. I n a Monastery Garden 26 2 22. Evolutio n 26 8 23. Th e Descent of Man 28 2 24. Th e Gene Machine 29 2 25. Th e Lords of Nature? 30 7 26. Life : The Molecular Battle 319 27. Th e Origi n of Life? Tak e Your Choice 33

9

Part Seven

28. Th 29. Ne 30. Th 31. Th

e Inexplicable Quantum 35 7 w Ways of Thinking 37 1 e Lan d of Paradox 37 8 e Elementary Particles 40 1

Part Eight

32. Relativit y 41 7 33. Cosmolog y 44 2 34. Th e Cosmos and Peeping Tom 45 1 35. Th e Impossibility o f Creation 46 3 Part Nine

36. Th e Tree of Death 47 9 37. "What the Devil Does It All Mean?" 48 Part Ten

38. Th e Future 50

9

Annotated Bibliography 51 Index 51 9

3

8

Acknowledgments

It is a pleasure to acknowledge the help given me by the staf f of the Oxfor d University Press i n Ne w York, especiall y the encouragement , friendliness , an d construc tive professionalism of Kirk Jensen and Helen Mules.

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Please read before opening bottle.

The nineteenth-century Belgian mathematician and statistician Adolphe Quetelet, in his Treatise on Man and the Development of His Faculties, An Essay on Social Physics, defined "1'homme moyen." I have never met an average man, but I frequently meet his far more charismatic brother: 1'homme moyen sensuel. The French is usually puritanically translated int o English as "the average man," thus, with Anglo-Saxon squeamishness, sidestepping the Gallic "sensual." We shall leave him with his hormones and call him "HMS." HMS remembers little or nothing of the math and science that he learned at school, he is suspicious o f jargon, he is more streetwise than the average scientist, he is worried about the futur e o f this planet, he may like a glass of single-malt whisky to finish off the day . Above all, he is curious. In about 50 percent of cases he is in fact she. It is primarily to such readers, to HMS, that this book is addressed.

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Preface That which we know is a little thing; that which we do not kno w i s immense. —Pierre-Simon de Laplace

Science, man' s greates t intellectua l adventure , ha s rocke d hi s fait h an d engen dered dreams of a material Utopia. At its most abstract, science shades into philos ophy; at its most practical, it cure s disease . It has ease d ou r live s an d threatene d our existence . It aspires, but i n som e very basic way s fails, t o understand th e an t and th e Creation , the infinitesima l atom and th e mind-bludgeonin g immensit y of the cosmos. It has laid its hand o n the shoulder s o f poets and politicians , philoso phers an d charlatans . It s beauty i s ofte n apparen t onl y t o the initiated , it s peril s are generall y misunderstood , it s importanc e ha s bee n bot h over - an d underesti mated, an d it s fallibility , and tha t o f those wh o creat e it, i s ofte n glosse d over or malevolently exaggerated. The attempt to explain th e physical univers e has been characterized by perpetual conflict . Establishe d theorie s hav e continuall y bee n modifie d o r violentl y overthrown, an d a s i n th e histor y o f ar t an d music , innovation s ten d t o b e ridiculed onl y to become, in time, the ne w dogma . The struggle between old an d new has rarely been dignified . Scientists come in many colors, of which th e green of jealousy and th e purpl e of rage are fashionable shades. The essenc e of scientific history has been conflict . This book presents science as a series o f ideas that changed the cours e not onl y of science itself but ofte n o f whole areas of human thought . Science, of course, has its practical benefits, but they will not be our primary concern. This is not a book about nonstick fryin g pans . We will be looking at ideas—admiring their beauty, occasionally standing awestruc k befor e th e tower s o f imagination, but alway s being prepared t o doubt ; alway s being awar e no t onl y o f the ingenuit y but als o o f the deep limitations, and the repeatedly demonstrable inertia, of the human mind. Science, b y it s nature , i s changeable . Ther e i s alway s som e scientist , some where, who is disproving an explanation that another scientist has proposed. Usually these shifts o f interpretation leave the fabri c o f society undisturbed. Occasionally, however, real revolutions tear down part o f our system of established beliefs . Thus, i n th e seventeent h century , scienc e presente d u s wit h a mechanica l uni verse, a giant inexorable clock. Three centuries later , physics ha s cu t som e of the levers tha t bind caus e to effec t an d ha s le d us int o a shadowy maze where we affect th e univers e by the ac t of observing it and ar e ignorant of the tru e meaning of our most basic concepts. Some see the fragilit y o f scientific theory as an indication of a basic inability of science t o explai n th e universe . Bu t scientific change i s almos t alway s accompanied b y a n increas e i n ou r abilit y t o rationalize an d predic t th e cours e o f nature. Newton could explain far more than Aristotle, Einstein far more than Newton. Science frequentl y stumbles , but i t get s u p an d carrie s on . Th e roa d i s long. As we

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Preface

come to the en d of this century , it is prudent t o recall that a t the en d o f the ninet tenth centur y the general opinion amongs t physicists was that nothing of any great importance remained to be done in physics. An d then came radioactivity, X-rays, the discovery of the electron and the nucleus, a couple of hundred ne w fundamen tal particles , quantu m mechanic s an d relativity , antimatter , dar k matter , blac k holes, chaos, the Big Bang, and s o on. Biology has been no less prolific. At the en d of the twentieth centur y there are again voices proclaiming the imminent arriva l of a theory of everything, a complete explanation of the Creatio n and workings of the cosmos. Maybe. Science is not a harmless intellectual pastime . In the last two centuries we have moved fro m bein g simply observer s of nature t o being , in a modest bu t growing way, its controller . Concomitantly, we have occasionall y disturbe d th e balance of nature in ways that we did not always understand. Scienc e has to be watched. The layman ca n n o longe r affor d t o stan d t o on e side , ignoran t o f the meanin g o f advances that wil l determin e th e kin d o f world tha t hi s childre n wil l inhabit—an d the kin d o f children tha t h e wil l have . Scienc e ha s becom e par t o f the huma n race's way o f conceiving of and manipulatin g it s future . Th e manipulatio n o f the future i s not a question to be lef t t o philosophers. Th e answer s ca n affec t th e na tional budget, the health of your next child, and the long-term prospects for life on this planet . This book is a report o f the scientifi c campaign up t o now. It is not a history of science but rather an account o f the majo r battles, the frequentl y eccentric generals, an d th e way s i n whic h scienc e ha s deepl y influence d man's pictur e o f the world and of himself. I t is not a final summing-up . We know that we ar e far fro m a rea l understandin g o f nature. W e press on . Michelangelo' s divin e disconten t gives us no rest. And althoug h the histor y o f science may be a trail littere d wit h broken theories and discarde d concepts, science i s also a triumph o f reason, luck, and abov e al l imagination . Ther e ar e fe w mor e successful , exciting , o r strang e journeys.

Introduction This is a material world and I am a material girl. —Madonna

The Argentin e writer Jorge Luis Borges tells a tale o f a man curse d no t onl y with the abilit y to remember ever y leaf, ever y wave, every pattern o f shadows tha t h e has eve r seen but als o with the inabilit y t o realize that differen t leave s are united by the concep t "leaf" or that the myriad shifting shapes of the waves are all examples o f the on e ide a o f "wave. " Thi s extrem e fragmentation of experience i s th e antithesis of man's inheren t nee d to find unifyin g themes i n nature. The great scientists have ofte n bee n those who sa w such themes where other s failed, wh o saw wave under the waves. But if genius is, by definition, the possessio n o f a tiny elite, how i s the average man to satisfactorily comprehend tha t which too k genius to reveal? In some notorious cases , such a s quantum mechanics, it is a fact that many scientists ca n only form a blurred imag e of what th e exper t sees more or less clearly , and i t is hardly encouraging that thos e expert s ar e fighting t o clarif y som e of the mos t basic con cepts of science. Nevertheless, the vast majority of science is intelligible to the vast majority o f high schoo l graduates. The truth i s that many o f the grea t discoveries were made by someone who happened t o have a torch to illuminate th e darkness. The torc h wa s th e miracle: what was reveale d wa s ofte n simple—beautifull y so . However, it also remains true that at the borders of our knowledge we run into real complexity, into questions that challenge our ability to define the nature of reality. Thus the very foundations o f quantum mechanics, the centra l theory that w e use to describe the physical universe, are the subjec t of deep controversy. We don't really understan d quantu m mechanics . W e ar e lik e driver s wh o hav e learne d t o drive a Rolls-Royce without bein g tol d much abou t th e working s o f the interna l combustion engine. The car works wonderfully, but we're not sure why. It gets worse: we don't really know what "matter " is. A child thinks of matter as being somethin g lik e clay . A particl e physicis t migh t tel l yo u tha t matte r i s a "bunching u p o f a field," but if we are honest we have to admit that "matter" is little more than on e of the concept s that allow s us to deal with what ou r senses report of what we call the externa l world. As the seventeenth-century French scientist and philosopher Gassendi wrote: "Man establishes a system of signs, of names, which permi t hi m t o identif y thing s perceive d an d t o communicat e wit h othe r men." So before w e se t out , we shoul d fac e th e facts . Ou r capacity to predic t th e be havior o f the physical worl d i s ofte n amazing ; the theorie s which allo w us t o account fo r the behavio r o f matter, i n term s o f a fe w basic concepts, rank with th e highest achievements o f the human imagination . An d we can be thankful that, in tackling practical problems, the theories of science work very well for a huge range of questions . Bu t when i t come s t o fundamentals , we se e through a glass darkly;

__xvi Introductio

n

there is more faith involve d in science than many scientists woul d be prepared to admit. The Objectives One purpose of this book is to set science in its social perspective. Scientific ideas have affected th e relationship o f man t o society, his idea s of God, and hi s imag e of himself. Scienc e ha s influence d th e wa y peopl e writ e poetr y an d th e wa y the y paint pictures. In the hands o f bigots, it has provided a theoretical justification for the sterilizatio n o f some human beings and the enslavemen t o f others. Science, a s a source of ideas, is a major characte r in the human drama. The other aim of this book is to explain fo r the layma n the basic meaning of the great breakthroughs in science and to point out the chain o f imagination that link s the Creation with the movements o f the planets and the formation of the chemica l elements, that binds th e evolutio n o f man t o the en d o f the universe . A s far as the purely scientifi c conten t o f th e boo k i s concerned , w e ca n classif y everythin g under one of three headings: matter, change, or field. Matter I a m writin g thes e word s o n a flower-fringe d balcon y overlookin g the Mediter ranean. The sun blazes. My snow-white cat , "Schwarz," stretches in the Sun . Thi s morning I revel in being a material being in a material world. My infinitesima l slice o f the univers e contain s an apparen t infinit y o f shapes, colors, textures, sounds , smells , an d substances . Matte r has endles s expressions . Matter appears to be the source of everything that we know. We are material beings . Onl y a puritan lik e Bernar d Shaw coul d as k his audi ence t o believe i n a world populate d b y disembodie d vortices . Shaw' s projected scenario doesn' t explai n ho w ou r air y descendant s wil l b e capabl e o f thinking. There is no evidence for thought existin g independently of matter, living matter. If we want t o begin to comprehend th e universe , ou r starting poin t mus t b e a n un derstanding o f matter—its forms, it s organization , its movement, and it s transfor mations. As a counterweight to my paean of praise for matter, it is only fair to record that there hav e bee n extrem e idealist s wh o hav e questione d whethe r th e materia l world o f beer and ho t dog s has an y objectiv e reality whatsoever. Th e eighteenth century Iris h philosophe r Bisho p George Berkeley , in hi s Treatise Concerning the Principles of Human Knowledge, suggests that the physical universe is nothing but a constant perception in God's mind. If you are a follower of Berkeley, I am willing to respect you r belief, but I ask that i n return you be prepared to admit that God's perception is infinitely worth studying—which is one of the object s of this book. We will com e to the conclusio n tha t Beethove n and Scotlan d ar e constructe d from a menagerie of subatomic particle s strange r than th e inhabitant s o f any me dieval bestiary. We will meet forces tha t ar e pathetically wea k and other s that are hideously powerful . An d we will mee t th e weak and th e powerfu l huma n being s who have constructed, an d quarreled over, these concepts .

Introduction | Change

Matter is the flesh of the universe; chemical an d nuclear change is its soul. As you read thes e words , yo u ar e kep t aliv e b y th e microscopi c chemica l change s that characterize the livin g cell. Molecular change may not be the meanin g of life, bu t life woul d cease without it . It would certainl y sto p withou t nuclea r change . It is the apocalypti c fusion o f nuclei i n the Su n that releases the staggering amounts of energy tha t maintai n lif e o n thi s planet . Withou t th e Sun' s radiatio n th e Eart h would cool , th e wind s woul d die , th e Eart h would la y silent , barren , an d dark . Now turn off the stars. Without a n appreciatio n of material change , we canno t understan d th e natur e of the Creation , of life, o f evolution, of our environmen t an d th e threats to that environment. And w e will fin d tha t som e changes appea r to defin e th e directio n of time itself. Fields There appear s to be more than matte r i n th e universe . An appl e fall s t o Earth, a nail is dragged toward a magnet. What we observe is motion. If you hold the appl e or grasp the nai l and attemp t to sto p that motion , the n you ca n fee l th e actio n of what we cal l a force. Ye t there i s n o apparent physica l connection , n o stretche d spring, between Earth and the apple, or between the magnet and the nail. We use a convention to describe what is happening. We say that there is a gravitational (or magnetic) force actin g on the apple (or the nail), because the apple is in a gravitationa l field, an d th e nai l i s i n a magnetic field. Th e wor d field suggest s that there are invisible entities surroundin g the Earth and the magnet, entities created by the Earth and the magnet but having a life of their own. Fields have become an essentia l par t o f our descriptio n of the universe ; on e of the way s i n whic h w e tal k o f ligh t i s t o cal l i t a n electromagneti c field . Som e physicists tal k of matter as being the "manifestation " of a field. Part of this book is about fields . A Note on the Observer There is someone who i s living my life. And I know nothing about him. —Luigi Pirandello, diary

Say to yourself: "I am reading this book." Who is "I" ? Is it that part o f you whic h you imagin e to be outside the material universe ? Not matter, not field ? A n ineffa ble something localized somewhere i n your head, and quietl y chattin g with you? What is consciousness? A tremendous amount of research has enabled us to map the microscopic structure of the brain . No one has eve r found a n "I " in there. If "I" exist, "I" have been extraordinarily elusive . Descartes, in som e of his writings , assume d tha t th e soul was not locate d in spac e at all, but elsewher e h e localize d i t in the pinea l gland, which sits i n the brain. It fails t o appear under th e microscope. Our failure i s understandable i f "I" is a function o f the brain , not a n occupant . We would laug h at someone who took his car engine to pieces in order to find its "power. "

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xviii Introductio

n

So ho w d o "I " fi t int o ou r schem e o f things? "I " has , u p t o now , refuse d t o be categorize d as matter, change, o r field. Ye t "I" a m part o f the universe , "I " a m the observer; without "me " ther e would be no science. I s there somethin g besides matter, change , and fields ? I doubt it . Bu t i n sayin g s o I am relying on faith , no t reason. This book has nothing to say about consciousness. Rea d other books, go to conferences. You will find that there are many theories. This is always a bad sign .

I •

In which, among other things, we will look at the fallibility of science and of scientists, and ask if anyone can be trusted.

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1

Newton Gets It Completely Wrong

Matter, in the everyda y world, conies in three forms: solid , liquid , and gas . Gas is the simples t for m o f matter, the for m tha t we understand best. We live in a gas, in fact, a mixture of gases—air. The way that scientist s se e gases is not th e wa y tha t our eyes see them. In fact our eyes don't see air at all, but it is typical of science that it starts of f with th e somewha t thi n evidenc e of the sense s an d the n proceeds , by experiment an d hypothesis, to build a model that explains th e properties o f whatever syste m w e ar e intereste d in . On e of the mos t successfu l models i s tha t con structed to explain the behavior of gases. The key to the understanding of gases is to believe i n th e microscopi c motio n o f the bit s o f matter o f which a gas is composed—the molecules. Newton got this wrong, and we can profit fro m seein g both why he thought that he was right and why we think that he wasn't. I am going to ask the reader to accept certain facts o n faith. Thi s is not a disreputable cop-out . W e al l d o i t ever y day . Scientist s certainl y d o it—w e hav e n o choice. I am a physical chemist . Th e onl y way that I can intelligentl y apprehen d modern genetics, fo r example, i s by taking certai n things for granted and using my reason to build on them. This blind fait h i n what I read in reviews or selected research papers is not to be likened t o an unquestioning belie f in flyin g saucers . No one has demonstrate d the existence of flying saucers in a manner that would satisfy eithe r a sloppy scientis t o r a critical layman . In this book I will, unless specifi cally stated, use only facts that have been accepted as such by the international scientific community . Where a fact is in reality only a hypothesis I shall say so, and I will tell you when I think that I'm on shaky ground. It is quite possible that some of rny so-called facts will sooner or later turn out to be fiction—I am not the pope. For the moment all I ask is unqualified acceptance. This sounds like the spiel of a secondhand ca r salesman, but if you don't believe something in this book, you can go to standar d textbooks . If you questio n thei r validity , yo u ca n tak e a specialize d course o f lectures . I f doub t remains , follo w you r doubt ; yo u ma y b e th e nex t Galileo. Molecules In this chapter, and elsewhere in this book, the word molecule will make many appearances. What is a molecule? For the moment think of it this way: Take a glass of water an d divid e it s content s int o fou r cups ; yo u will stil l cal l th e substanc e i n each cup "water. " No w take one of the fou r cup s an d divid e the water i n i t into a thousand droplets . Each drop is still recognizably water. Take one of these droplets and divide it into a million droplets , each one visible only under a microscope. All tests, physical or chemical, will verify tha t each dro p is a sample of water. Can we

4j

The Ascent of Science

Figure 1.1. The approximate shapes of th e molecule s o f wate r (H 2O), oxygen (O2), and ozone (O3).

go on with this game indefinitely? There have been those in the past who thought so, who believed that matter was a continuum, an infinitely divisible Jell-o. Today we know that the game stops somewhere. There comes a stage when th e piece s of water, if split, divid e int o fragment s that ar e very definitely not water . It's a little like splitting u p a crowd of demonstrators; there comes a time when you get down to individuals who, if split up, are no longer people. The smallest entity that still has the right to be called water is termed a molecule of water . Loo k a t Figure 1.1 . Mos t of you wil l recal l tha t wate r i s als o know n a s H2O, which i s just a shorthand way of saying that eac h molecule of water consists of two hydrogen atoms and on e oxygen atom. (The word atom also needs more explanation, and we will return to it later on.) The smallest part of a sample of oxygen gas tha t i s stil l recognizabl y the oxyge n that w e breathe i s the oxyge n molecule, which consists of two oxygen atoms linked together, and which i s therefore written as O2. If you split an oxygen molecule in half, you will get two oxygen atoms whose physical, chemical, and biological propertie s are utterly different from those of the oxygen molecule . Ozon e has th e chemica l formul a O 3. Each ozone molecule ha s three oxygen atoms joined together (Figure 1.1). It i s no t surprisin g that w e ca n cho p u p a sampl e o f water apparentl y almos t endlessly an d stil l hav e water . Molecule s tend t o b e ver y smal l entities . A teaspoonful o f wate r contain s abou t 200,000,000,000,000,000,000,00 0 wate r mole cules.1 Textbooks like to suggest hypothetical counting games as an aid to the visualization of very large numbers. In accordance with this tradition, I can tell you that if th e whol e populatio n o f Earth set ou t t o coun t th e molecule s i n a teaspoon of water, each person counting at the rate of one molecule per second , it would take over a million years. But let's get back to gases. The Invisible Sea

We live a t the botto m of an invisibl e sea . Nature, working through giganti c astrophysical, geological, and biological processes, has generated for us a molecular atmosphere o f ga s within whic h w e liv e an d withou t whic h w e canno t survive . Those fe w of us, suc h a s divers or astronauts, who leav e the gaseou s se a have t o take some of it with us, or we die. We need gases—and not just the air. Man use s gases to weld steel , to fil l lase r tubes an d neo n lights , to anesthetiz e patients, to give sparkle t o sof t drinks , beer, and champagne , to fl y airships, floa t 1

It's easie r to write this huge number as 2 x 1023, where 10 23 ("te n to the twenty-three") mean s 1 with 2 3 zeros after it , or 10 multiplied b y itself 23 times. A thousand is 10 3; a million i s 10 6.

Newton Gets It Completely Wrong |

wrecks, coo k hamburgers , inflat e tires , an d commi t genocide . Dee p unde r th e ground, the decompositio n o f primeval forest s b y heat an d pressur e ha s give n u s coal and inflammabl e natural gas , which i s an important, if minor, source of energy. In the meantime, we pollute the atmosphere with gases that at best erode buildings and chang e the colo r of oil paintings, an d a t worst poiso n lif e an d perilously disturb the delicat e heat balance o f this planet. Gases can be indispensable t o man or catastrophically destructive . As Willy Loman might have said, attention must be paid to such substances . If you walk into a chemical suppl y company, you can purchase sample s o f many different gases . Some are familiar enough: oxygen, nitrogen, carbon dioxide, carbon monoxide, helium, chlorine . Thes e are substances that appea r weekly in the dail y press. The chemical properties of these gases are so different a s to suggest that there is no important basic property shared by all gases. Consider two well-known gases. Helium exist s i n th e stars , i n a fe w underground cavities , an d i n ver y smal l quantities in the air . It was first discovere d in the Sun , by examining the nature of the Sun' s light—henc e its name, from th e Greek for Sun, Helios. Helium is a complete wim p o f a gas , almos t incapabl e o f interactin g wit h an y othe r substance , which i s why it avoided detection fo r so long. Chlorine, on the other hand, attacks almost everythin g an d i s reminiscen t o f the mythica l chemis t wh o discovere d a universal solven t but faile d t o find a bottle capabl e o f holding it. It kills painfully , as British and French soldiers found out in 1917. It is pale green, one of the few visible gases. In general, chemical experienc e suggests that each gas is unique, which i s true, and has very little, if anything, in common with most other gases, which i s not true. That which is common to all gases is the way in which their molecules move. That is the real subject of this chapter, and it has implications tha t reach far beyond the nature of gases. The Violent Crowd Look at Figure 1.2. It shows a n imaginary cubical box constructed i n the ai r of the room in which you are sitting. The way that the molecules in it behave has been the subject o f controversy for at least a century. Th e secre t o f time ma y reside i n this box. Note ho w smal l th e bo x is. Th e letter s nm stan d fo r nanometer, whic h i s one thousand millionth par t of a meter, which ca n be written 10" 9 meter. If everyone in China ha d on e of these boxes and , by order of the Party, lay the boxes en d t o end, touching each other, the total length of the line would be only about five meters . Descartes thought that the universe wa s continuous, like jelly, but he didn't d o

Figure 1.2. Molecule s an d empty space in the ai r around you.

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any experiments to back up his guess. Look at the box. The six objects represent six molecules draw n t o scale . Oxyge n an d nitroge n molecule s loo k ver y muc h th e same, so we don' t differentiat e betwee n them in ou r picture . It is clea r that air is mainly empty space. Th e averag e distance betwee n molecule s i n th e ai r aroun d you is about ten times their largest dimension. It is as though the averag e distance between canaries in a cage was about 1 meter. So that you don' t forge t th e kind o f numbers we are dealing with, bear in mind that a teaspoonful o f the air in your house contains somewha t more than 10 20 molecules (1 with twenty zeros after it) . This is about 2000 times less than the numbe r of water molecules i n a teaspoonful o f water. Water molecules in liqui d wate r are crowded together ; th e livin g condition s i n liquid s ar e slumlik e compare d wit h those in gases. Two vital facts are not revealed by the drawing : • Molecule s in a gas are in constant motion. • Th e average speed of a molecule in a gas increases with temperature. Be ver y clea r wha t thi s motio n i s an d i s not . W e are not talkin g about drafts , winds, hurricanes, o r convection currents. Even in a tightly closed room in the absence of breathing creatures, moving machinery, or sources of light or heat, the gas molecules ar e always moving. In the cylinde r o f oxygen standing i n th e hospita l storeroom, th e oxyge n molecules ar e endlessl y i n motion . An d the y ar e moving fast. Very fast. An Aside: Why Molecular Motion? There is no such thing as a motionless atom or molecule, and there is hardly an aspect of the nonliving or living physical world which can be completely understood without taking into account molecular motion. The concept of temperature and the nature of heat both have a deep connection with molecular motion, and molecular motion ha s a strange connection wit h the arro w of time and th e deat h o f the uni verse. Back to the Madding Crowd Professors have a weakness for analogies. So here's one: A gas, any gas, is similar to a crowd of flies. The analogy is dangerous, but we can learn from the dangers . First of all , flie s ca n see ; the y don' t normall y bum p int o eac h other . Molecule s ar e "blind"; in a gas they ar e continually blundering int o eac h other . Every collisio n changes the speed and direction of both molecules involved, so that a molecule in a gas resembles a flyin g dodge m car, continually gettin g jolted. Another differenc e between flies and molecules is that the molecules in our box are presumed to fly in straight lines unless they hit something. Flie s practice their aeronautical skills. An improved fly analogy is a crowd of straight-flying, blind, dea f flies, but thi s is still misleading. Flies get tired. They often relax , and in the end they die and lie on the floor with their legs up. Molecules don't do this; the molecules in an oxygen cylinder never stop moving—until the en d o f time, as they sa y at MGM. Again improving our analogy , we like n the molecule s i n a gas to a collection o f straight-flying, blind, deaf , radarless, tireless, immortal flies. We're getting there, but the problem, as we will soo n see, is that flies have a sense of smell an d molecule s don't . First, however, let's look at the speeds of molecules.

Newton Gets It Completely Wrong [

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How fast d o molecules move in a gas? That depends o n two things, the mass of the molecul e (les s correctly, its weight) an d th e temperatur e o f the gas . The question needs sharpening. Since any given molecule is continually changing direction and speed due to collisions, it is more informative to speak not of its "speed" but of its average speed. If you drive from home to office, your speed is hardly constant; it drops to zero a t red lights and rises a little above the spee d limit on the freeway . However, you can work out your average speed from only two observations: just divide the distance from home to office by the time for the complete journey. Average speeds for molecules in a gas can be both measured experimentally and calculate d theoretically. Her e ar e som e approximat e averag e speeds, i n mile s pe r hour , for molecules in some still gases at room temperature: Hydrogen in a steel cylinder 380 Helium in an airship 280 Oxygen, on a dreamy day in St. Tropez 103 Carbon dioxide in a soda-syphon refill 83

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The masse s o f these molecule s increas e alon g th e series : hydrogen, helium, oxygen, carbon dioxide. Here we see the mass dependence o f the average speed: at the same temperature a heavier molecule travels slowe r o n the average than a lighter molecule. The average speed of the molecules in a sample of gas is a constant quantity, the same today as it was 500 years ago, provided the temperature is the same. If the temperature goes up, th e averag e speed goes up. Th e average speed of an oxygen molecule rises by about 7% in going from 0° C (32°F) to 40°C (104°F). Not a stupendous increase, but i t has practical implications. We will see that it is becaus e particles get faster a s they get hotter that the Sun is able to radiate energy. You might car e to compare molecular speeds in gases to the speed s o f more familiar objects , again in miles per hour: Concorde in full fligh t 145 Lamborghini, cruising 18 Ben Johnson, 1988 Olympics (assisted) 22. Carl Lewis, 1988 Olympics (unassisted) 22.

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Now consider the followin g problem, which is based o n the fac t tha t althoug h solutions o f alcohol, like beer, are liquid, the smel l o f alcohol ca n be easily detected. This is because in all liquids, molecules escape into the surrounding air. If they didn't, liquid s would no t evaporate . At room temperature th e calculate d average speed of an alcohol molecule is about 800 mph. Here's the problem: A diligent , bu t worldly-wise , professo r o f physic s return s fro m a late-nigh t "seminar" and gingerly opens his front door . Why is it that his whisky-laden breath is not immediately detecte d by his loving, and equall y worldly-wise, wife, who i s waiting for him, 10 yards away, at the foo t o f the marble stairs? After all , molecules traveling at an average speed of 800 mph shoul d be able to cover 10 yards in about one-fortieth o f a second . I n fact , i f the ai r i n th e roo m wer e still , i t woul d tak e months for the smel l o f alcohol to be detectable at that distance . Why? Why is th e professor's secret safe until he plants a guilty kiss on his wife's skeptical cheek? The answer lies in the astronomical number of collisions that a molecule makes

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as it blunders abou t in a gas. If you coul d follo w th e pat h o f a single molecule of, say, oxygen in the air, you would find that in round numbers, it collided with other molecules about 6000 million times in one second. Molecules have a hectic social life, eve n by jet-set standards. An oxyge n molecule in ai r changes direction a t an incredible rate. It would tak e a very long time to figh t it s way across a room. The fact that you can quickly detect the smel l of cooking all over the kitchen is due to the help given to the molecules by drafts o r convection currents which move whole chunks o f air rapidly fro m plac e to place. Similarly, if you pu t a drop o f ink i n a bath o f motionless water, the colo r will sprea d ou t because o f molecular motion, but it will spread very slowly. Drop the ink in a river, and it will travel downstream at a rate determined by the bulk flow of the water. The difficult y tha t a molecule has i n fightin g it s way across the roo m is analogous (here we go again) to a passenger trying to get to his platform during rush hour at Grand Central Station and being jostled by other passengers going in different di rections. Agai n we ca n lear n fro m th e imperfec t analogy . The passenge r knows where h e wants t o g o and direct s his fee t i n tha t direction , when allowe d t o between pushes . I n contrast , molecules i n a stati c sampl e of gas have n o predeter mined destination : they are not heading anywhere, they just move. After ever y collision the y trave l i n a directio n determine d b y th e detail s o f the collision , lik e billiard balls , bu t i n thre e dimensions , no t two . Molecule s have n o wil l o f their own. That i s wh y th e fl y in ou r previou s analogy had t o hav e no sens e o f smell, since otherwise, even if blind an d deaf , i t might direct its flight towar d food . Th e essence of molecular motion in gases is that it is completely determine d by the last collision. We say that the motion is random.2 The flight o f the fly is not random. The professor' s wife know s tha t th e alcoho l molecule s leavin g he r husband' s lips, once they have slowed down fro m th e initial pus h given by his lungs , travel between tw o well-separated points a t less than a snail's pace . Calculation shows that i n si x months the average , point-to-point distance traveled between startin g point an d fina l destination , by a n alcohol molecul e i n stil l air, is about 1 0 yards. The total zigzag path length traveled is about 35 million miles! War would be farcical if projectiles traveled through the air in the way that molecules do. Billy the Kid would have looked even stupider than he was if his bullets had performe d a rando m danc e afte r leavin g hi s gun . However , a bullet weigh s about 10 23 times as much as an oxygen or nitrogen molecule and is far too heavy to be diverted by such puny objects. Linebackers aren't usually stopped in their tracks by gnats. They are, however, slowed down by air resistance, which is basically the cumulative effec t o f a myriad o f collisions between a moving macroscopic objec t and th e molecule s tha t i t encounters . Th e sam e effec t work s if you tr y sprintin g through a cornfield.

2

There is a medieval riddl e that illustrates the dangers of assuming that a process is genuinely random. The problem was published i n a book by Claude-Caspar Bachet de Meziriac (1581—1638). A boat, crewed by 15 Turks and 1 5 Christians, runs into a storm. The boat can be prevented fro m sinkin g only if half the crew are thrown into the sea. A Christian suggests tha t they form a circle and throw in every ninth man until there are 15 left. This is done, and, lo and behold, all the Turks are thrown in and all the Christians survive. The secret is that the organizer of the fiendish scheme knew his Renaissance puzzle books. He arranged the circle like this: CCCCTTTTTCCTCCCTCTTCCTTTCTTCCT and started counting from th e first Christian. Th e Turks had assumed that the process was random. In Turkey they tell it differently .

Newton Gets It Completely Wrong

A Pause for Doub t We have converted the ai r from a structureless, thin, invisibl e sou p into a horde of frenetic particles—molecules—foreve r o n th e move , batterin g int o eac h othe r a t tremendous speeds and incredible frequency. The average speed of the molecules in the sample remains constant as long as the temperature remains constant. What we have found is genuine perpetual motion. Stubborn, deluded inventors are still see n sitting confidently in the corridor s of patent offices, carryin g the plans of ingenious contraptions that onc e set in motion ar e supposed to run forever , i n the absence of any subsequent input of energy. They don't run and they won't run; only nature has taken out a patent on perpetual motion. At least that's the story that I've been telling. But is it true? I have give n you th e basi c assumption s tha t g o into th e scientist' s model of a gas. Could there be an entirely different an d more correct model? History shows that even the greatest minds ca n construct theories that work but that have one minor flaw—they are completely erroneous. Newton Gets It Wrong Thomas Willi s (1621-1675) , a professor o f natural philosoph y a t Oxford , discovered the crippling diseas e myasthenia gravis. 3 He was an iatrochemist, a physician who believed in the chemical basis of the body's workings, so it was natural for him to be aware of his famou s contemporary , the chemist Rober t Boyle. One of Willis's brighter students wa s Robert Hooke, and when Boyl e was looking for an assistant , Willis recommended Hooke. Thus i t was that i n 1655 , the twenty-year-ol d Hooke came to work with the twenty-eight-year-old Boyle. The conjunction o f Boyle and Hooke was heaven-sent. Hooke knew how to construct air pumps of the type that had been invented in 1650 by Otto von Guericke of Magdeburg. Hooke built a pump fo r Boyle, who, by creating a moderate vacuum in a glass vessel, showed tha t ai r was necessar y for life (mic e died), for combustio n (fires wen t out) , and fo r the passag e o f sound. (Vo n Guericke had alread y show n that light , bu t no t sound , travele d throug h a vacuum. ) In a famou s experiment , Boyle trapped a volume of air inside a glass tube and varied the pressure on it. You can do the same by putting your finger over the nozzle of a bicycle pump and push ing the handle in. As the handle enter s farther int o the barrel of the pump, the volume of the trapped air decreases and you must push harder to keep the pump han dle wher e i t is . I t i s a s thoug h yo u ar e strivin g t o compres s a spring . Boyle' s qualitative observation—tha t whe n th e pressur e o n the ai r sampl e increases , th e volume decreases—is not very surprising. Bu t Boyle did something that was still a rarity in the seventeenth century ; he made quantitative measurements . He recorded the pressur e an d th e volum e o f the ai r during the experiments . H e found that when h e double d th e pressur e o n a sampl e o f air, the volum e halved . Whe n th e pressure went up three times, the volume went dow n to a third o f the original volume. All his experiments wer e done at about the same temperature, that of his laboratory. H e conclude d tha t fo r a sampl e o f gas kept a t constan t temperature , th e pressure of the sample multiplied b y its volume was unchangeable. As one got bigger, the othe r got smaller. W e write thi s result as : pressure time s volume = a constant, and call it Boyle's law. 3 Willis was in charge of the dissection of the corpse of Anne Green, hung for infanticide in 1650. The "corpse" came back to life o n the operating table.

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Boyle's law , publishe d i n 1662 , is on e o f th e firs t example s o f a physical law . Any theory ahout the nature of gases has to lead to Boyle's law; if it doesn't, it must be wrong. (In fact Boyle' s law it is not a n exact law, but i t is not bad under norma l circumstances.)4 Boyle sought a n explanatio n fo r the "spring " o f the ai r an d propose d tha t ai r consisted of "many slender and flexible hairs," like a sheep's fleece, "each of which may indeed, like a little sprin g be easily bent or rolled up." The problem with this idea i s that a s a theory it is useless. I t qualitatively explain s Boyle' s observations, but you can't derive Boyle's law, or any other property of a gas, from Boyle's theory. The Curse of the Fa t Sumo What happene d nex t wa s a n excellen t exampl e o f a completel y incorrect theory agreeing perfectly with experimental results. This has happened mor e than once in the history o f science, and the present case contains a warning that applie s t o any kind of explanation, scientifi c or not. Thus the theory that sumo wrestling tends to makes you fat is beautifully confirmed by the fact that almost all sumo wrestlers are enormously bulky. In the absenc e of any other experimental data , the theor y looks good. The curse of the fat sumo fell on Newton. He succeeded in elegantly explaining Boyle's law. Incorrectly. Newton proposed that the particle s o f the air (we would cal l them molecules), were motionless i n space and were held apart by repulsive force s between them, so that any attempt to reduce the volume of a sample of gas was analogous to the compression of springs. He assumed tha t the repulsive forc e was inversely proportional to the distance between the particles: double the distance and the force is halved. He showed that, on the basis of this assumption, a collection of static particles in a box woul d behav e exactl y as Boyl e had found . His model led straight to Boyle's law. Probably the greates t scientist ever , Newton managed to get the righ t answe r from a model that was wrong in ever y possible way . Experiment shows that molecules in a gas are not motionless and, contrary to Newton's second assumption, that molecules almost always attract each other unless they are actually touching. Nevertheless, i f all tha t w e kne w abou t th e behavio r o f gases wa s Boyle' s law, ther e would be no grounds for challenging Newton's theory. It gives the right answer. Unfortunately, Newton' s mode l doe s no t predic t o r explai n an y othe r propert y of gases. He had been struck by the curse of the fat sumo. Beware. We believe that we have a better model than Newton's. It explains far more facts than his does, as we will see in Chapter 16, and the final test of a model is whether it explains the experimental facts . Nevertheless , we again ask: Why should we believe i t t o b e true ? Ar e molecule s reall y movin g continually , eve n i n a n undis turbed, closed container? Maybe there is a better theory waiting around the corner. Maybe we will also find that new fact s abou t gases will be completely inconsisten t with our present ideas . Science is not carve d o n tablets o f marble. Theorie s have arisen , hav e worked , have been challenged, and have been superseded. S o why should yo u believe any thing that I have writte n u p t o now? How skeptical should yo u be about th e pro nouncements o f scientists? 4 You can see one reason why i t can't possibly be true always, since if you compress a gas enough you will force the molecules to touch each other. A t this stage you can increase the pressure by a factor of two but the volume will be almost unchanged; it will not be halved, as the law claims.

2 I Believe Read my lips .. . —George H. W. Bush

The book that you are holding purports to give a description o f the physical world. Why do you believe what I tell you? Because I am a professor of physical chemistry and have canvased your vote? On an overcast autumn afternoo n in 1976, 1 wandered dow n a nondescript side street off Charing Cross Road in London and strayed into a dingy secondhand bookshop tha t coul d hav e bee n th e fil m se t fo r a whimsical tal e of a kindly ol d bookseller. There was no apparent order , either in the physical stackin g of the books or in their subjec t grouping . The poor lightin g and th e autumna l colors of old books combined to give a mistaken impressio n o f dirt. There was an affable-lookin g gray haired lad y shifting books from on e pile to another. Against one wall, surrounded by shelving, stood a glass-fronted mahogany cupboard containing four or five rows of leather-bound books. A half hour after I had com e in, I walked out into the dusk, clutching a parcel. I was carrying a block of gold. I had pai d 10 0 pounds for a 1688 edition o f Les Principes de la Philosophie by Rene Descartes. When I reached hom e I searche d throug h th e openin g page s like a schoolbo y looking for the dirty words in a dictionary. There it was on page 4: Je pense, done je suis. I think, therefore I am. Starting from th e most famous sentence in the histor y of philosophy, Descartes attempted to build an all-embracing account of the nature of man and the universe . The question that, above all others, worried Descartes was: Why should I believe anything—what can I know for a certainty? We still lack a final answer. It is a question tha t coul d be asked by HMS every time a scientist claim s that somethin g has been proved—like perpetual molecular motion in gases. We are going to look at three very different attempts , not t o find certaint y but a t least to avoid error in ou r ongoing attempt to understand th e universe . Befor e w e start, I would point out that this chapter is not a treatise on epistemology, and it is a very long way indeed fro m a summary of any individual philosopher's lifework. It is a signpost, as is much o f this book. Descartes (1596-1650) Part of what w e claim to know, we derive from th e evidenc e collected by our ears, eyes, nose, and sens e of touch, but b y far and awa y our majo r source s o f information ar e the written , visual , o r word-of-mouth account s o f what other s have seen, heard, smelled, or touched. Now, you can' t see, hear, or smell the molecule s in the ai r around you , so why should you believe it when I tell you that molecules in a gas are in constant motion, or even that molecules exist ? You have never directly experienced a molecule with

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your senses, nor are you likely to. As late as the beginning of the twentieth century, there was at least one prominent physicist who refused t o accept the known experimental fact s a s being evidence for the existenc e o f atoms. Today there ar e instruments tha t apparentl y produce picture s o f atoms. Bu t as k yourself a tough question: Ca n m y physica l sense s b e trusted ? I n th e end , howeve r comple x th e scientific equipmen t that we use, the final observe r i s the human brain. Can it be trusted? Descarte s wrote "Pourquo i o n peu t doute r d e l a verit e d e chose s sensi bles." Roughly and clumsily : "Why one can doubt the existenc e of things revealed by the senses." Descartes's questioning o f the sense s was not ou t of place in an er a in which i t had becom e quit e clear , despite th e contrar y evidenc e o f the eye , that th e Eart h went aroun d th e Sun . H e was no t th e firs t t o suspec t th e senses ; th e root s of his doubt went back to Plato. There are still many today who maintain tha t all we can know of the "external" worl d are the images that we carry in our minds and the relationships tha t our minds create between those images. There is no guarantee that what goe s on in our heads correspond s even roughly to what goe s on in the external world—if such a world exists . Although Descartes was not the first to doubt the validity of observation, he was one of the most ruthless in his conclusions. He wanted absolute certainty; he wanted, in a world of apparent illusion, to penetrate the sensory mists and reach the undeniable truth s behin d man' s perceptio n o f hi s world . H e use d th e metho d o f doubt: if something coul d be doubted on any grounds, then it must be mercilessly stripped awa y from th e body of accepted knowledge: "I was convince d tha t I must once and fo r all seriously undertake to rid mysel f of the opinion s whic h I had formerly accepted, and commenc e t o build anew from the foundation , i f I wanted to establish an y firm an d permanen t structure s in the sciences. " Notice the aim. It is science, no t philosophy , althoug h unlik e mos t present-da y scientists , Descarte s would have seen them as inseparable. Since the senses are suspect, we must reject them, at least initially, as a source of knowledge. This is, to put i t mildly, a drastic step. The senses are our source of information. Wha t ca n w e kno w withou t them ? Descarte s answered: "Cogit o erg o sum." This is usually translated a s "I think, therefore I am," but a philosophical acquaintance of mine prefers " I experience, therefore I exist." Take your pick.1 Three Latin words formed the one tiny rock to which Descarte s clung in the sea of his doubt . But it was hardly enough, this saf e littl e subjective island. H e wanted to fin d a way back to the worl d because his ultimat e ambitio n wa s to construc t a truthful accoun t of how the physical universe worked. The fact that "I exist" is important, especiall y t o me , bu t i t hardl y provide s a basi s fo r understandin g th e movements o f the planet s o r th e mysterie s o f magnetism. If Descartes was t o ex plain nature, he had to prove more than his own existence. To do so he cheated, not in his terms but unquestionably in ours: he "proved" the existence of God: From this on e idea , that the ide a o f God is found i n me , o r that I exist pos sessing this idea, I conclude s o clearly that God exists, and that my existence a Saint Augustine (354-430 ) ha d related thoughts, a s seen in the passage in Confessions (Boo k 11, Chapter 14) , which begins: "Everyon e who observes himself doubtin g observe s a truth, and about that which he observes he is certain; therefore he is certain abou t a truth."

I Believe 11

depends entirel y on Him in ever y moment, that I am sure that nothing coul d be known by the human mind more evidently or more certainly. And it seems to me that I now see before me a road which will lead from the contemplatio n of the true God (in whom all the treasures of science and wisdom are hidden) to the knowledge of other things. Notice Descartes's attempt at consistency; since he knows nothing but his own existence, it is to his thoughts that he turns to look for God, not to an as yet unproved outside source. This was a slap in the face for the Church and the Holy Scriptures— it never even occurred to Descartes to appeal to their authority. Having, in his own estimation, proved that both he and an all-knowing God existed, Descartes proceeded to the nex t stage : to establish wha t h e deeme d t o be a foolproof criteri a for determining i n which cases our senses could be trusted. This is di e keyston e o f his attac k on th e proble m o f knowledge. After all , the $64,000 question i n epistemolog y is Wha t ca n I be sur e of ? If Descartes had a n infallibl e truth detector, then he could begin to investigate the universe, accepting only those messages that were validated by his wonderful gadget. We ar e bombarde d b y a continuou s strea m o f sensor y impressions , bu t i n Descartes's view not all of these impressions have equal status—many of them may be suspect, perhaps eve n sent t o us by Satan. Nevertheless, there ar e certain fact s about the external world that Descartes labeled "clear and evident." Thus, it would be "clear and evident" that iron is harder than butter; one could hardly doubt that. Now Descarte s realized tha t bein g sur e o f a fac t wa s rio t proo f of its truth . S o h e cheated again. He appealed to the God that he had invented: God would not deceive us. If a fact appears to us to be "clear and evident," it does so because God, knowing the fact to be true, allows us also to see it as clearly and evidently true. This i s not a n argumen t that a modern scientist o r philosopher, o r even HMS, would accept . Notice that ther e i s absolutel y no questio n o f Descartes's invoking reason here. 2 The "proof" of God's existence and the subsequen t assumption o f his honesty are firmly within the fiefdo m o f faith, not th e realm of reason. Worse is to follow. I f God guarantees ou r unerrin g judgment, ensuring tha t we know what i s true, then how can we err at all? Descartes admitted that he could err , and he gave the proble m a lot o f attention. H e solved i t by invokin g fre e will , als o a gif t fro m God. A t this poin t th e reade r ma y well b e raisin g hi s eyebrows . For if I suppose something to be true, how d o I know that it is because God has made it "clear arid evident" to me, or because I am using my free will and have made a mistake? There are more problems with Descartes's philosophy, but they are not for us. In the end , Descartes's philosophy rests on God. He lived in a society bathed i n religious belief, and to most of his contemporarie s the existenc e and omnipotenc e of God was self-evident . Descartes's acceptance of God was hi s onl y major concession to the prevailin g framework of knowledge established by the Churc h arid th e Greeks. In a world in which these were the unassailable authoritie s in all matters, Descartes brushe d the m asid e an d proclaime d tha t al l yo u neede d t o reac h th e truth was your own (God-given) intuition. For Descartes, Almighty God guaranteed 2 As Suzanne says to her betrothed, Figaro, in Beaumarchais' The Marriage of Figaro, "Giving a reasion for being right amounts to admitting I could be wrong. Are you my humble servitor or aren't you?"

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the correctnes s o f his inner feelin g tha t somethin g wa s clearly and evidentl y true . But althoug h he gave the Almighty an indispensable plac e in his philosophy, it is limited t o th e role s o f Creator and guarantor ; he i s rarely appeale d t o otherwise . After h e made the universe, it developed according to the laws of nature. He is not the mover of the planets, only their builder. The universe proceed s on its way mechanically. This belief lies at the core of deism, a doctrine we will meet again in the eighteenth century and that stil l speaks to many scientists. 3 Descartes wa s inevitabl y accuse d o f fostering atheism , a strang e accusatio n i n the light of the essentia l role he gave to God as the guarantor of truth. Descartes actually denied to atheists the capacity to really know the truth about anything, as the following extract clearly and evidently shows : That an atheist can clearly know that the three angles of a triangle are equal to two right angles, I do not deny . I merely say that this knowledge o f his i s not true science, because no knowledge which ca n be rendered doubtful should, it seems, be called science. Since he is supposed to be an atheist, he cannot be certain that he is not deceived, even in those things that seem most evident to him... . He will never be safe fro m [doubt ] unless he first acknowledges God. Despite this, Descartes's works were put o n the banned list of the Catholic Church in 1663. He had not even given Rome's authority the courtesy of a challenge; he had just ignored it. God existed because Descartes said he did, not because of Holy Writ. The Church had alread y faced a similar sidestepping o f its authority when Marti n Luther had opene d up a personal path to God, a path that made the Papacy and its hierarchy irrelevant , just as Descartes's path to philosophical trut h asked no help from centurie s o f philosophy an d religiou s dogma. Descartes's younger contemporary Baruch Spinoza also believed that "trut h manifest s itself." He was excommunicated by the Amsterdam Jewish community in 1656. 4 Descartes is classifie d by history a s a philosopher, bu t th e bul k o f his writing s are on what we would call science. Most of his scientifi c writings, as distinct fro m his mathematical work, are almost meaningless. H e theorized about nature instea d of observin g it. H e rejected th e ide a o f atoms an d buil t a strang e physical worl d consisting of vortices in a continuous fluid . This hypothesis had no basis in experiment. Descartes's faulty syste m o f science wa s taught i n most European universities for about a century, until Newton and Galileo supplanted hi m in the eighteent h century. Descartes's reputation a s a scientist wa s short-lived. During the Enlightenment, his scienc e wa s savage d b y Newto n an d Newton' s followers , but hi s statur e a s a mathematicia n an d philosophe r i s no w unquestioned . Hi s Discourse on the Method heralde d th e ag e of the Enlightenmen t (se e Chapter 6) . In Europe , more than perhap s anyon e else , he lai d th e foundation s fo r modern philosophy b y un3

The universe wa s not purely mechanical . Descarte s believed tha t man had a soul, althoug h animals didn't , but for him the soul was not the causal differenc e between a dead and a live body. We don't di e because ou r souls leav e us. A dead body is a broken clock; the soul deserts i t because i t is dead. 4 Descartes was not the stuf f fro m which martyrs are made. On hearing o f Galileo's indictmen t by the Inquisition fo r his belief in a heliocentric solar system, Descartes chose not to publish his Treatise on the Universe, in which he too supports th e same system.

I Believe 11

derrnining ever y othe r syste m o f philosophy goin g back to Aristotle . I n hi s ow n terms, he was completely honest about the problem of knowledge. In the twentiet h century, Sartre singled out Cogito ergo sum as the point of departure for existentialism, as "a truth which i s simple, easily attained and within the reach of everybody; it consist s i n one' s immediat e sens e o f one' s self. " Voltaire , i n hi s Lettres Philosophiques, puts his finger on an essential point: "Descartes gave sight to blind men; they saw the errors of the ancients and his own. . .. He destroyed the absurd chimeras wit h whic h youn g mind s ha d bee n fille d fo r tw o thousan d years ; h e taught the me n o f his tim e t o reason. . . . He was estimabl e eve n i n his mistakes. " For scientists, Descartes's refusal t o be brainwashed b y precedent i s a lesson that they, hopefully, keep permanently in mind. Does he bolster your confidence in the hypothesis o f perpetual molecular motio n i n gases? In no way: he doe s no t prove that molecules in a gas do what I say they do. But he does do something more useful. He tells you that you don't have to accept what I say just because I am classified as an "expert. " To remind us tha t intellectua l idol s ca n be human, I quote fro m Joh n Aubrey's biographical sketc h o f Descartes: "He was to o wise a man t o encumbe r hirnself e with a Wife; bu t a s he wa s a man, h e ha d th e desire s and appetite s o f a man; he therefore kep t a good conditioned hansome woman that he liked and by whom h e had som e children (I thinke 2 or 3)." Francis Bacon (1561-1626)

In complete contrast to Descartes's skepticism, Baco n trusted the senses completely. Observatio n was everything, it revealed th e truth, and n o supernatural guarantees were needed. Nature, for Bacon, was "an open book" that could not possibly be misread by an unprejudiced mind. As Leonardo da Vinci had said a century before: "Experience neve r errs. " Baco n would hav e foun d absur d Descartes' s conclusio n that the knowledge acquired by the senses of an atheist was somehow les s reliable than that acquired by a believer. The suggestion that the Devil might deliberately be deceiving us ha s no plac e i n Bacon' s scheme o f things. He was a straightforward, no-nonsense thinker, although there are those who would rephrase this descriptio n to read "a naive, unsophisticated dilettante. " HMS in general believes what he sees, and scientists generall y put their fait h i n experiment. For this we have to thank Bacon, a few Greeks and Romans, and a succession o f European thinkers, mostl y livin g in th e sixtent h an d seventeent h cen turies, some of them in an intellectual atmospher e that modern man has recreated only in twentieth-century dictatorships . Th e dominanc e o f dogma in Bacon's day, and in the previous few hundred years, was almost absolute. Most scholars in fourteenth-century Oxford accepte d almost anything written by Aristotle or the father s of th e Church , whethe r o r no t i t wa s confirme d by thei r senses . A t th e tria l o f Galileo the defendant found that the evidence of his eyes, as aided by his telescope, was confronted not by conflicting observations but by centuries-old dogma . For his inquisitors, Holy Writ was the fina l arbiter . Galileo claimed t o have observed fou r previously undetecte d moon s o f Jupiter. Th e Churc h rule d tha t the y coul d no t exist. Francesco Sizi, an almost forgotten contemporar y of Galileo, explained why. There were onl y seve n heavenl y bodies (seve n has a strong place in mystic lore) , and each had an astrological significance. The proposed moons had no astrological

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significance, therefor e the y coul d no t influenc e man , therefor e the y coul d no t exist. Cesare Cremonini, an Aristotelia n colleagu e o f Galileo at Padua, refused t o look through Galileo' s telescope. Why would anyon e want t o see what no one but Galileo ha d seen ? "An d anyway , peerin g throug h thos e spectacle s give s m e a headache." Th e professo r o f mathematics a t the Collegi o Romano declared tha t if he wer e allowe d t o firs t buil d th e suppose d fou r satellite s o f Jupiter int o som e glasses, then h e too would se e what Galile o saw. Bacon would have aske d to look through th e telescope, and if what he saw clashed wit h the tenets o f the Church or the ancients, then too bad for them. His single-minded insistenc e o n the primacy of observation was no less a rejection of authority than Descartes's. He believed wha t he saw, not what he read. Bacon was not a practicing scientist, but he affirmed tha t knowledge could onl y be built on the observation of nature. In parallel with this "commonsense" view of nature, he saw the purpose of science as "the relief of man's estate," the betterment of ou r materia l environmen t an d health—antibiotic s rathe r tha n relativity . Thi s concept o f the role of science was to profoundly influence the seventeenth-centur y attitude towar d scienc e i n Englan d an d th e philosoph y o f the Enlightenmen t i n eighteenth-century France. The trouble with Baco n was that he distruste d theory . We agree with his belief that th e basis o f science i s observation, but fac t gatherin g is not enough . Withou t theory, science is merely picking up shells o n the beach. Science is not a Baconian flea market of unrelated data, but Bacon, with English down-to-earthness, was suspicious o f hypothesizing intellectuals: "The intellect, left t o itself, ought always to be suspected." And again: "For the wit and mind o f Man . .. if it work upon itself , as the spider worketh his web, then it is endless and brings forth indeed cobwebs of learning, admirabl e fo r the finenes s of thread an d work , but o f no substanc e an d profit." Lik e Descartes' s vortices. Bacon was particularl y contemptuou s o f Greek philosophy, which he considered to be "puerile, or rather talkative than generative . . . fruitful i n controversies, but barre n in effect." 5 Bacon' s allergy to contemporary theory is understandable; fo r an intelligent man with a skeptical mind, the largely theoretical framework o f learning built up by the Churc h and the disciple s o f Aristotle was too much to swallow. Unfortunately, his contempt for empty hypothesizing blinde d hi m t o th e wor k o f Copernicus and , possibl y becaus e o f his meage r knowledge o f mathematics, h e als o ignore d th e monumenta l advance s o f Kepler and Galileo. Despite hi s avoidanc e o f theory, Bacon' s works ar e no t devoi d o f the kin d o f questions that troubled other philosophers. Thu s he revolted against the concept of final cause s (th e belief that things wer e a s they were fo r a purpose) and champi oned the idea of efficient cause s (things were as they were because they were the effects o f a preceding cause). And he used a very significant phrase which qualifies , in a most importan t way, his laudin g o f observation. He says that th e min d ha s "a power of its own." He was aware that a mind that receives sense impressions with out interpretin g the m an d puttin g the m int o som e kind o f workable framework is incapable o f grasping reality. For Bacon, reality, or rather ou r knowledge of it, contained an input from th e mind. 5

He was less blunt tha n Hobbes in his ranking of the Aristotelian tradition : "Whe n men writ e whole volumes of such stuff, ar e they not mad, or intend to make others so?"

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Bacon grew up in the court circles of Queen Elizabeth I, and his ambitions were stupendous—politically a s well a s scientifically. The Lor d Chancellor o f England proclaimed famously, "I have taken all knowledge to be my province," by which he meant that he was going to define the directions and organize the categories of existent knowledge, an undertaking he thought he had completed in Instauratio Magna (1620). There wa s a marvelous self-confidence abou t the way Bacon wrote. Despite his avowal to avoid the arrogance of the Aristotelians in his approach to nature, his implied humilit y i n th e presenc e o f nature sometime s smell s o f a prosperous nine teenth-century Yorkshire mill owner avowing, "I'm a humble man. " He was put on trial fo r corruption in 1621 . Fo r the las t fiv e year s of his life , h e wa s barre d fro m holding public office an d banished from the cour t of Jarnes I. He died of a fever tha t developed from a chill following an excursion into the snow: "It came to my lord's thoughts, why fles h migh t not b e preserved in snow , as in salt . . . . They alighte d out of the coach, and went into a poore woman's bowse at the bottome of Highgate hill, an d bough t a hen, an d mad e th e woma n exenterat e it, and the n stuffe d th e bodie with snow, and my lord di d help do e it himselfe."6 Perhaps the only experiment he ever did killed him. He died in debt, having failed i n his attempt to create a system of philosophy t o replace that of Aristotle. Above all, Bacon lef t a legacy of belief in th e evidenc e o f the sense s an d i n experiment, and a vision of the role of science as the means of improving the material condition o f man. Bacon was not a scientist; neither ca n he be ranked among the great philosophers. Nevertheless, his sponsoring of inductive reasoning, arriving at general conclusion s fro m th e accumulatio n o f facts, wa s enormousl y influential . He expound s th e inductiv e metho d i n hi s Novum Organum (1620) , a titl e tha t could be translated a s the New Instrument, meanin g a new too l for arriving at the truth. Collect enough cases and you can generalize—that was his message. But first observe. It is natural tha t he admire d Machiavell i fo r describing me n a s they are, not as the moralists hoped they would be. Bacon's belief in the primacy, and reliability, of observation, and the magnificent prose that he used to convey his ideas indirectly affected th e whole subsequent history of science. Although, like Descartes, he contributed little directly to knowledge, he helped to shape the intellectual climat e of the Enlightenment and the following centuries. Th e Age of Reason, that great blossoming of free thought, acknowledged three prophets: Newton, Locke, and Bacon. Bacon's bold and prophetic vision o f a world enriched b y the practical consequence s o f science underlies nearl y all applied research. Ironically, that vision wa s not based at all on the inductive reasoning that h e so espoused, since scienc e had don e almost nothing i n his da y to improve the lot of man. When the Dutch scientist Christiaa n Huygens (1629—1695), wrote to the politi cian Colbert to explain the aim s o f the newl y establishe d Academi e des Sciences , in Paris , h e explained , "L a principale occupatio n d e cett e assemble e e t l a plu s utile, doit etre, a mon avis, de travailler a 1'histoire naturelle a peu pre s suivant l e

6

The account come s from Anthony Powell' s entertainin g editio n of John Aubrey's Brief Lives. Bacon's great contemporary, Descartes, also died a s a consequence of cold, in this case the raw Swedish winters .

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dessein de Verulamus."7 Bacon had been created Lord Verulam in 1618 . A century and a half after Bacon' s death, when Emmanuel Kant wrote his greatest work, The Critique of Pure Reason, he dedicate d i t to Bacon. In 1847 , William Whewell, the Oxford scientis t an d philosopher , wrote, "If we must select som e one philosophe r as the hero of the revolution in scientific method, beyond all doubt Francis Bacon must occupy the place of honour." The search for facts, the sacrosanct standing of observation, the implicit belief in reason—these were not the invention of one man. There is something to be said for the "time is ripe" school of history, the supposition that it is the total social, political, an d scientifi c environmen t tha t make s inevitabl e th e changin g directio n of man's thought . Nevertheless , every change has it s standard-bearers , those whos e flags ar e see n abov e the battle . Baco n was suc h a one . Video-cli p summaries o f world philosoph y ten d t o oppos e Bacon to Descartes , labeling on e a n empiricis t and the other a rationalist. The classification has its justifications, but in both cases it need s qualification , and i t i s sometime s forgotte n tha t the y both, despit e thei r different paths , sa w reason and scienc e as the hope of a better future fo r mankind. This belie f is firml y linke d t o Bacon' s name, but i t i s als o state d ver y clearl y i n Descartes's Discours de la methode. Does Bacon's observational approach at least help u s t o believe that molecule s exist? He asks us to observe and, by employing inductive reasoning , use our observations to come to conclusions . This doesn' t wor k too well with molecule s since they ar e not observable , except i n favorabl e case s i n highl y specialize d laboratories. Nevertheless, if you are prepared to believe in the collective honesty of the international scientifi c community, you can accept their observation s as standing in for yours. In fact , molecule s wer e part o f the scientist' s explanatio n o f nature lon g before we could observe them. Their existence was deduced fro m th e behavior o f matter. The basic, experimentall y determine d laws governing the behavior of gases were shown t o b e consisten t wit h th e simpl e nineteenth-centur y mode l o f a ga s de scribed i n th e previou s chapter . Th e mode l was based no t o n th e observatio n of molecules but o n the supposition o f molecules. Up to now there is no aspect of the behavior o f gases that i s not consisten t wit h th e model . Does this prove tha t th e model i s correct ? Asking a muc h weightie r question : Wha t doe s "proof " mean? Neither Bacon nor Descartes helps us here. One trusted his senses; the other trusted his God . Neither help s m e to dismis s th e suggestio n that ther e coul d b e anothe r model fo r gases that i s jus t a s successful , or eve n more so , than th e presen t one . How d o I prove that a given model is the correc t one? Where does certainty lie in this world? Karl Popper: The Certainty of Uncertainty In so far as a scientific statement speaks about reality, it must be falsifiable: and in so far as it i s not falsifiable, it does not spea k about reality. Karl Popper, The Logic of Scientific Discovery

7 "The principal occupation of this assembly, and the most useful, shoul d be, in my opinion, to work on natural history in a manner similar to that of Verulam."

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Despite the fact that knowledge is based on observation (at least that is the credo of HMS), the fac t i s that the Osca r winners i n th e histor y o f science have almost always been creators of theory: Newton and universal gravity, Darwin and evolution, Maxwell and electromagnetic fields, Einstein and relativity. It is theory that allows us to comprehend a multitude o f facts i n the ligh t of a handful of concepts. Theory is the outcome of man's apparently inherent drive to order the universe. Theory explains, theory predicts, theory suggests new directions for thought and experiment. It is , i n th e end , because of theory that w e ca n pla n th e path s o f spacecraft, con struct compact disc players, synthesize new pharmaceuticals, and reveal the structure and mode of action of the AIDS virus. There are some extremel y successful theories, but w e should not be misled b y their successes . Science is not a means of obtaining absolute truth. There i s a n enormous amount o f highly persuasiv e dat a supporting evolution; most scientists believe in the theory, but i t has no t been proved.6 Fact s may be regarded as indisputable; theories are not. What criteria, if any, are there fo r proving that a theory i s true? Is there a castiron metho d o f proving the trut h o f our mode l of a gas? Or of any othe r scientific theory? Most scientists will tell you that a theory is true as long as it works. Thus it was once "true" that the Earth was flat, in the sense that for early man the assumption of the Earth's flatness led to no incorrect conclusions. Ships disappearing over the horizon might be assumed t o be too far away to be seen properly. The flat-Eart h theory was demolishe d (excep t in th e eye s of a few eccentrics) by a flood o f facts that were consistent only with a roughly spherical Earth—and we can now photograph the glob e from space . At a higher level , Newton's system of mechanics wa s true for a couple of centuries. I n the twentieth centur y it was shown to be lacking, to be an approximatio n to a new "truth, " th e theor y of relativity. However, for almost al l practica l purposes, Newto n still suffices ; w e don' t nee d relativisti c me chanics to compute the path of a Scud missile. In this limited sense , Newton's theory is still true. Theories come and theorie s go, because science is, at the deepes t level , skeptical. Th e mott o o f the theoreticia n coul d b e "It' s righ t unti l on e fac t prove s it' s wrong." Is this a fatal weakness? My few antiscience acquaintances harp on the historically hig h deat h rat e fo r scientific theories—another on e bites the dust . They have a n all y i n th e philosophe r Pau l Feyerabend, , wh o sa w scienc e a s merel y a fashionable ideolog y and a very fault y wa y o f understanding th e world . And , he warned, ideologies , like fair y tales , contai n "wicke d lies. " Scientists, he accuses , are all too ready to abandon their beliefs: "We can change science and make it agree with ou r wishes. We can turn science fro m a stern and demandin g mistress into an attractive and yielding courtesan who tries to anticipate ever y wish of her lover. " I never realized that I was in such an erotic profession. Feyerabend exaggerated, and he knocked down large numbers of straw dolls . Not unnaturally, scientist s see the flexibility o f theory in a very different, an d totally unerotic, light. Scientists rarely claim infallibility; the ugly fact that destroys the beautiful theory i s just on e more challenge (althoug h if the defunc t theor y i s one' s own , it is 8

There are ongoing battles in the United States about whether high schools shoul d teach creationism. I n Israel, in 1992 , the ultra-orthodox communit y was deeply offende d b y an advertisement campaig n run by the Pepsi-Cola Company, which portrayed man's evolution firo m the apes—and his final enlightened realization that he should buy Pepsi-Cola.

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useful t o have a large glass of whisky handy). The strength of science is that it admits to its limitations, and its errors. Having said which, there are theories, like evolution, that appear to be unshakable. Surel y there must be a criterion for the correctness o f a theory? I do not believe there is, and i n this I am, as are probably the great majority of my scientific colleagues, a disciple of Sir Karl Popper (1902-1995) . Popper is a philosopher whose best-known work has been in the area that we are presently discussing—th e validit y o f scientifi c theory . Poppe r take s a s a basi c property o f any scientifi c theor y th e possibilit y o f it s bein g disproved. I n othe r words, that whic h canno t be disprove d i s not a theory. Take the statemen t tha t a newly minted coi n fallin g fro m a small heigh t ont o a hard, level , smooth surfac e can end up only as heads, tails, or on its edge. This is not a theory; it is a statement of fact. It certainly will never be disproved. On the other hand, the medieval belief that garli c destroys the powe r of magnets could b e terme d a hypothesis, a miniature theory. It can be disproved, and i t was disproved by the Italian Porta who, i n 1589, wrote: "Not only breathing and belching upon the lodestone after eatin g garlic, did no t sto p its Virtues, but when it was anoynted ove r the juice of Garlick, it did perfor m it s offic e a s well a s if it had neve r been touched wit h it." En d o f hypothesis. That , accordin g t o Popper , is th e natur e o f theories—they ca n b e dis proved. But Popper goes further: Theories can only b e disproved, they can never b e proved.

In other words, science is a lie detector. Newton provides a magnificent example. His mechanic s accounte d fo r a myriad o f observation s on thi s Eart h and i n th e heavens. Ove r th e years , ever y ne w consisten t fac t an d calculatio n hammere d home the absolute correctness of Newton's theories. They accounted for the motion of the moon, the trajector y o f artillery shells, the movements of molecules in a gas, the fligh t o f airplanes. I t took a brave man t o doub t a theory tha t neve r gav e th e wrong answer. There wer e a few who questione d Newton's assumption o f an absolute time and spac e "out there," independent o f man—but anyone doubting the validity of the laws of motion was not taken seriously by the scientific community. The Newtonian pudding had bee n proved by repeatedly eating it. And then, afte r two centuries, strange observations began to undermine the infallible laws, observations that seemed to deny the validity of our (Newtonian) understanding o f time and space . At the en d of the nineteenth century , all the armies of previously determined fact s could no t save the Newtonian universe because for a growing number of problems Newton gave catastrophically incorrect answers. Observatio n clashed with theory , and, as it always must, observatio n won. Humpty-Dumpty could not be put togethe r again . Bacon would have smiled. Popper understood: no on e ever proved Newton to be right, but i n the en d his theor y was disproved, or , more correctly, shown to be an approximation to a more general theory. This classic example of scientific fallibility can be taken as an illustration o f Popper's statement that the multiplicatio n o f positive case s doe s no t increas e the probabilit y o f a thesi s being correct. This proposition goes against our intuitions, and there are those who disagree with Popper on this point. It is interesting to compare Hume: "A wise man proportions his belief to the evidence." Popper has underlined what many scientists implicitly accept: science demands absolute open-mindedness, and those who claim infallibility for science are betraying it. We must always prepare to be wrong. No theory is final, and Popper believes

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this to be true in the socia l and political sphere s as well. In Locke's words, "broa d daylight" may be unattainable, but we may reach, in his beautiful phrase , "the twi light of probability." Even Popper's theory may be disproved ! On Having One's Feet on the Ground

There hav e bee n philosophers , lik e Hume , wh o woul d weaken , o r destroy , th e claim o f science to understand realit y by questioning the ver y existence o f cause and effect . Berkele y went further , denyin g the existenc e o f matter i n the common sense meaning of the word. Ludwig Wittgenstein stated that nothing that was unobserved could eve r be validly inferred from wha t we can observe, a belief which, if taken seriously , could sto p muc h o f theoretical scienc e dea d i n it s tracks . Wh y have we ignored these skeptical voices and single d ou t only three representatives of world philosophy t o presen t thei r cas e fo r scientific truth ? In fact , wh y bothe r with philosophy a t all? The attitude of the majority o f scientists to philosophy is : "Science is one thing, philosophy is another. Science has proved its basic validity, not only by rationalizing the workings of Nature but by predicting observations and entitie s which sub sequently materialized . I have n o nee d fo r epistemology. " A s Leibni z said , "Al though th e whol e o f this life wer e said to be nothing but a dream, and th e visible world nothin g but a phantasm, I should cal l this dream or phantasm rea l enough , if, usin g reaso n well , we wer e neve r deceive d by it. " Mos t of us woul d agree , so what place has philosophy anyway? Why is Leibniz not enough? One reason i s that twentieth-centur y finding s o n the behavio r o f the physica l world have plunged us into a universe where "using reason well" often completely fails t o provide a n explanatio n o f what w e observe . It is our goo d luck tha t thes e dilemmas, which forc e us to face complex and fascinating philosophical problems , are no t relevan t t o mos t field s o f science . Thu s a se t o f accepte d concept s ar e enough to account for such questions a s the stabilit y of bridges, the fligh t o f birds, and the chemical properties of matter. It is when we start to dig beneath the surfac e and as k what determines the behavior of the elementar y particles of matter, and. of light, tha t w e star t t o los e contac t wit h suc h primitiv e concept s a s matte r an d causality an d begi n t o suspec t tha t th e skeptica l philosopher s wil l hav e th e las t laugh, tha t w e wil l neve r fin d a rational explanatio n fo r our perceptions . Todaj f some scientists ar e asking questions tha t ech o the age-ol d concern o f the philoso phers with the nature of knowledge. This is the main concern of Descartes, Bacon, and Popper . The y wer e chose n partl y becaus e the y ar e what I would call , i n th e broadest meaning , commonsens e philosophers . The y all , i n th e end , accep t tha t our perceptions give us an image which is, if not a duplicate, then a good approximation to the externa l world , and that that world operate s according to laws that , even if they are man-made an d temporary, can be used to predict and systematize our perceptions. Thi s is what most of us, including scientists , believe . Scientists, and HMS , generally behave as though they sympathized with Bacon and Popper. Most of us behave as though we believe in the scientist's workin g concept o f cause an d effect , an d tha t ou r sense s tel l u s somethin g rea l abou t a rea l world, even though modern physics reveals a cosmos that is ultimately enigmatic, a "drea m an d a phantasm." For truth, as we shall se e throughout thi s book, plays very hard to get.

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Truth in Practice Truth, three sorts therof Natural, Mathematical and Moral. —Bishop Berkeley, notebook s

We have seen three classic approache s to scientific truth, none entirel y satisfying . Scientists shoul d have a vested interest in "truth," despit e Popper! In searching for that truth in the laboratory, the practicing scientist ofte n lean s toward Bacon, even though she probably does so unconsciously. Bacon used inductive reasoning, which roughl y means that if you have enoug h evidence it provides the basis for a safe conclusion. Thus if I drop fifty brandy glasses from 30,00 0 feet onto a concrete parade ground and they all break, Bacon would be amazed at my stupidity, but he would confidentl y state that the next glass that I drop will certainly break and that I can formulate a general law as to the breakability of brandy glasses dropped from 30,00 0 feet. Most of us would tak e this law, obtained by inductive reasoning, to be inviolable. Is inductive logi c our answer? Inductive reasoning is used b y all of us, every day, and i t is widely used in science. But it is defective because the next case may always be the one that doesn't fit in. This is the weakness of inductive reasoning, a weakness that Hume focused on . The method, said Hume, depends o n the axio m "Instances o f which w e have ha d no experience, must resemble those of which we have had experience, and that the course of nature continues alway s the same." But this cannot be proved logically. We must be aware that if we have used inductive reasoning to construct a theory, then the first case that doesn't fit could bring that theory to its knees. This is exactly the case that Popper focuses on. Popper sees science as advancing by a process of falsification. T o idealize hi s thesis : W e work within a n accepte d framework , sa y Newtonian mechanics , an d then , whe n somethin g doesn' t fi t in, w e realiz e tha t Newtonian mechanics i s wrong or incomplete and we look for a new framework. In the best of all possible worlds, this is how things should happen, but what usuall y happens i n the laboratory is altogether different . When I find a fact that doesn't fi t in with a well-established theory , I instinctively look for experimental error. This is certainly a judicious first move. In the meantime, I slander th e new fact, I say it is "puzzling," "a controversial finding," "anomalous," "unverified"—an d I ma y b e right . I f th e awkwar d observatio n doe s eventually turn out to be experimentally spotless, I have a choice: I can call the existing theory in doubt or I can document the "anomaly" and carry on as before. This happened wit h the "anomalous " movemen t of the planet Mercury , which was observed in the nineteenth centur y but did not overthrow the Newtonian mechanic s that faile d t o solv e the proble m o f its motion . I n th e twentiet h centur y Einstei n showed that it could be explained by the theory of relativity, a more general theory than Newton's. Thomas Kuhn, particularly in his Structure of Scientific Revolutions (1962) , has stressed wha t h e sees as the inordinate inerti a o f the scientifi c communit y an d it s exaggerated dependenc e o n paradigms—establishe d an d accepte d framework s o f thought. Kuh n claim s tha t paradigm s are not, as Popper suggests , given up whe n disproved, but only when they are replaced by a new theory. There is some truth in this, but it does nothing to invalidate Popper's central thesis. Induction, Bacon's method, gives us onl y a probabilistic definition of truth. A s

I Believ e | we saw , those who clai m that thi s probability is increase d a s the numbe r o f confirming cases grows, are challenged by Popper. Is Popper too pessimistic abou t the possibility of proof? Is there a better way than Bacon's to arrive at truth? Deduction: A Surer Path? We go back to Aristotle, who firs t clearl y define d inductiv e an d deductiv e logic, and try the latter approach. The idea in its classic form i s to start off with two irreproachable statements and then, by the rules of logic, to arrive at an irreproachable conclusion. This is the famous syllogism. For example: All elephant s have a long memory and a long trunk. Dumbo is an elephant. Therefore Dumbo has a long memory and a long trunk.

7f the first two statements are true, then the last statement must be true, because the logical ste p tha t too k me there i s valid. Th e syllogis m wa s a cornerstone of logic until the beginning of this century. It has come under criticism , partly because the final statement is already contained within the premises—you are not proving anything that you didn't really know. The essenc e o f a syllogis m is a compariso n o f its conclusio n agains t observed fact, s o that it is the fac t tha t can destroy the theory . Thus, startin g off with a basic assumption (theory) , one can work out its various consequences and wait until one of them is at variance with fact. At this point you have disproved the theory; unfortunately, in all the successful case s you have not proved the theory, you have merely given yourself growing confidence that the theory is correct. This method is sometimes called the hypothetico-deductive method: you have a hypothesis, you use deductive logic to examine its consequences, and you compare them with the observed facts. For example: All homosexuals are evil. (Hypothesis) Benjamin Britten was a homosexual. (True) Therefore Benjamin Britten was evil. (False)

From al l account s h e wasn't ; therefore , th e hypothesi s i s wrong . I t sound s ver y much lik e Popper: "there i s no mor e rational procedur e than th e metho d o f trial and error—o f conjecture an d refutation ; o f boldly proposing theories; of trying our best to show that these are erroneous; and of accepting them tentatively if our critical efforts ar e successful." The method i s clearl y related t o the inductiv e method : i n practice , afte r a few observations, on e attempt s t o se t u p a theor y an d the n t o deduc e consequence s from th e theory. The inductive method places little or no initial emphasi s o n a hypothesis, while the hypothetico-deductive method brings in a hypothesis a t a very early stage of the game . It is a fancy nam e fo r the approac h we have taken toward the credibilit y o f moving molecules . N o on e ha d observe d molecule s whe n th e model was firs t proposed , but a hypothesis wa s constructed and i t has weathere d the storm; it agrees with all the facts known at the time or revealed since. The test is always the observed facts. Where doe s "th e scientifi c method " fi t int o al l this ? Ther e isn' t a scientifi c method. There are many—and none of them is foolproof. A given scientist may use

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quite different approache s to different problems . Sh e might start one investigatio n by collecting large amounts o f data, hoping to detect a pattern; she might star t another by considering a well-known anomal y and come up with a hypothesis. An d there i s no guarantee that the root s of the hypothesis ca n be traced directl y to the data; they may originate in an association of ideas, an analogy drawn with another problem, a chance remark. One poin t i s incontestable: th e "truth " o f science must alway s remai n ope n to critical scrutin y and will sometimes hav e the status o f a beauty queen: looks good today, but nex t year she'll be dethroned. That is because the real test of a scientific theory is not whether it is "true." The real test is whether it works. The Fragility and Strength of Science

What does all this mea n for this book? Will the "truths " of present da y science b e here toda y an d chuckle d a t tomorrow ? Some o f them, yes . Th e curren t theorie s concerning th e origi n o f life can' t al l be right. An d wha t abou t th e questio n tha t prompted this chapter? Are we really sure that molecules move in the fashion that we have described? I would be t my life on it. The kinetic theor y o f gases is based primarily o n the assumptio n tha t a macroscopic sample of a gas is composed of a huge number o f molecules in continual mo tion, their averag e speed being constant a t constant temperature . Ou r faith i n this assumption, and in the theory as a whole, is based on the fact that the theory allows us to mathematically deriv e conclusions about the expected behavior o f a gas, and that thes e conclusion s hav e bee n verified experimentally tim e an d agai n fo r al l kinds of gases and all kinds of properties. In the spirit of Popper, we can say that we have constructe d a theory that could, in principle, be shattere d b y one set of data that didn' t fi t in. Until that happens , we accept the theory . I believe i n ou r model for a gas, and I am askin g you t o believe i n it , because n o on e ha s disprove d th e model. The analogy of the senseles s flie s i s not perfect; real molecules experienc e forces fro m eac h other, and i t is primarily because these forces ar e ofte n no t accurately know n tha t th e exac t calculatio n o f certain propertie s i s not possible . Th e nineteenth-century theory is too simple, but i t still, fo r many purposes, suffice s t o deal with the behavior of most gases, provided they are not at too high a pressure or too lo w a temperature. I will go out o n a very shor t an d sturd y lim b an d predic t that, in its general principles, th e kinetic theory of gases will never be shown t o be wrong. I would ris k betting my salar y o n 75 % o f this boo k being undisturbed fo r th e next decad e o r so . Bu t I might lose . I had a n uncl e wh o be t obsessivel y o n do g races. Man y years ago , there wa s a race a t the Whit e Cit y stadiu m i n Londo n i n which on e o f the si x greyhounds was the trac k recordholder for the distanc e an d another was the holder of the world record . It would hav e been madness to bet on any other dog. The starter's gun rang out, the traps opened, and the two superdogs, who wer e i n adjacen t traps , leape d forward , bumpe d int o eac h other , an d stag gered. My uncle, who claimed to have a "system," bet on another dog , which won . In racin g an d i n scienc e ther e ar e n o "sur e things, " onl y odds-o n favorites . M y uncle died bankrupt. In the en d we are forced to say of theories, and o f dogs, "I believe," rather than "I can prove. " Scienc e goe s t o th e courthous e backe d onl y b y circumstantia l evi -

I Believe |

dence. That' s th e bes t we ca n do . But , as Popper point s out , in Conjectures and Refutations (1962) , it's more than can be said for most human activities : "The history o f science , lik e th e histor y o f al l huma n ideas , i s a histor y o f irresponsibl e dreams, of obstinacy, and o f error. But science is one of the very few human activities—perhaps the onl y one—in which the error s are systematically criticized an d fairly often , i n time , corrected." This philosoph y fit s badl y wit h thos e wh o wan t eternal verities, an d th e faithfu l ofte n contras t the Roc k of Ages with the shiftin g seascape of science. Faith I believe in the Almighty , but I protest. --Isaac Bashevis Singer

Personally, I find tha t th e faith-versus-scienc e controversy ha s th e smel l o f past centuries. I am happy t o follow Baco n and agre e to a separation o f forces: "W e do not presume, by the contemplatio n o f nature t o attain t o the mysterie s of God. . . . only let men beware . . . that they do not unwisely mingle or confound these learnings together. " For Bacon, reaso n an d commo n sens e were irrelevan t t o religion : "The more absurd and incredible any divine mystery is, the greater honor we do to God in believing it; and s o much the more noble the victory of faith." Galileo likewise sidesteppe d th e question : "Both the Hol y Scriptures an d natur e originate i n the Divine Word. . . . [T]wo truths can never contradict one another." Later, the famous seventeenth-century chemist Robert Boyle was to declare that "there is no inconsistence between a man's being an industrious virtuoso (an amateur scientist), and a good Christian." Man y thinkers hav e explicitly state d tha t reaso n i s a tool that ca n only be applied to nature, that Go d and the spiritual worl d li e outside its range. But there is always a suspicion that , in societie s in which the religious authorities could make life hard fo r heretics, the statement that reason was irrelevan t to religio n wa s a rus e t o kee p thos e authoritie s ou t o f the natura l philosopher' s realm. It is very possible that this ploy was used by Bacon. It was certainly not used in this way by the Franciscan William of Ockliam (c. 1285—1349), who had s o little fear o f papal authority that he accepted excommunication rather than retract what were regarde d as heretica l statements . H e ver y firml y place d th e natura l worl d within th e realm of reason, and Go d outside it, although he was too much o f a believer to deny God the credit for the Creation or the right to interfere with the workings of the world, if he so wished. In this he was very similar to Newton. If the Creato r does not appear as a real player in this book, it is because I know nothing about hi m o r her. As Georg Lichtenberg (1742-1799 ) asked : "Afte r all , i s our idea of God anything more than personified incomprehensibility?" I n a letter to Voltaire, Diderot dismisses th e ide a o f God as not philosophicall y necessar y an d suggests tha t it had i n al l likelihood bee n though t up b y an enem y o f the human race, since it had cause d so much conflict. Voltair e saw things slightl y differently : "The worl d embarrasse s me, I cannot conceiv e o f so exquisit e a cloc k without a maker." Personally, I am tempted to believe that if God did onc e exist, she created the Universe but died in childbirth. One thing that nearl y al l o f us believe in i s the realit y o f an externa l world , In that suppose d rea l world ther e ar e two elements tha t al l scientists, an d mos t lay-

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men, have taken as fundamental: matter and motion. Thomas Hobbes (1588-1679), the grea t English proponen t o f materialism, believe d tha t ther e wa s nothin g but matter in motion. His books, and Descartes's, were read by the young Isaac Newton. And seve n year s afte r Hobbes' s deat h i t wa s Newton , the jealou s and sometime s dishonest genius , wh o wa s t o publish th e law s o f force tha t wer e t o explai n th e movement o f molecules an d th e path s o f the planets , finall y establishin g th e au thority of science in Western culture.


II

In which Reason nearly triumphs and is then maligned

Civilization has periodically renewed itself after lon g periods of stagnation. Athens in the sixth century B.C., the emergence of Islam in the sixth century A.D. , the twelfth-century renaissance i n Europe, and the "official" Renaissanc e were all wakenings to new dawns. Such a time was seventeenth-century Europe , when the blossoming o f science redirected world history and forever changed the way in which man saw himself and his universe. The scientific revolution had many heroes, but towering above them all were Galileo and Newton. It is their achievements that we look at in this section, but not only their scientific achievements; for Newton, albeit unknowingly and unwillingly, was to be the man whose reputation was to underpin the rationalism o f the comin g Age of Reason—the Enlightenment of the eighteenth century. In the next few chapters we will see what Newton did, and how a handful of simple physical laws united Earth and Heaven, liberated men's minds, and subtly eroded faith. But we will also see Newton's enemies massing on the horizon.

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Thomas Aquinas versus Neil Armstrong Projectilia perseverant in motibus .. . —Isaac Newton, Principia

On 4 October 1957 the firs t man-mad e satellite t o go into orbit was launche d fro m the Sovie t Unio n (R . I. P.) 1 Sputnik' s spee d an d trajector y wer e calculate d usin g laws publishe d 28 0 years previously. Si r Isaac Newton's law s o f motion ar e stil l generally sufficient , eve n i n th e ag e o f relativity an d chaos , t o accoun t fo r th e movement o f most bodie s i n th e everyda y world. Thei r nea r infallibilit y i n tha t world ha s prompte d m e t o curs e Si r Isaac o n thre e occasions : i n 194 4 (London, Hitler's V2) , in 197 3 (th e Gola n Heights , Assad' s artillery) , and 199 1 (Haifa , Sa daam's Scuds) . Waiting for the impacts , I spared a warm, thought for the sixteenth century Italian Tartaglia, who is said to have abandoned researc h on the dynamic s of moving bodies because he was fearful o f possible military applications . Chandrasekhar, a Nobe l laureate i n physics , put s Newto n among the greates t three intellect s wh o hav e eve r lived , in an y field . H e didn't stat e who th e other s were. Newton's work o n the motio n o f bodies wa s a turning poin t i n intellectual , not onl y scientific, history. Both he and Galile o realized the natur e of the connection betwee n movemen t an d force , a connection tha t wil l be ou r concer n i n thi s chapter. It was above all the law s o f motion tha t gav e validity to the concep t of an ordered universe, a cosmos understandable by human reason . Newton's marriag e o f force an d motio n di d no t a t al l confor m with th e Aris totelian concepts that had been basically unquestioned fo r two millennia, bu t eve n today Aristotle' s totall y incorrec t pictur e o f motion seem s mor e natura l t o mos t people. Common sense can be a dangerous guide. We start by looking at the nature o f force. Force

We are pushed int o the light by the force exerted on us by our mother's wombs, and for th e res t o f our live s w e generate , exploit, an d ar e subjecte d to force . Physica l force dominate s mankind' s earlies t memories : th e weigh t o f material objects , th e gentle pressure o f encircling arms, the battering force of the gale. If we could see forces instea d o f objects, we would be dazzled by an incredibl y 'On the same evening I was singing to my guitar at a rather wild party in Paris. After the first song there were cries of "Sputnik! Sputnik! " I am still unsure if this was the "highest" acclamatio n or a hint that it would be hetter for everyone if I were sent into orbit.

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dynamic infrastructure, a close-knit, shifting jungle, underlying the physical world: the strange forces holding together the atomic nucleus, the electric forces that stabilize atoms and shape molecules, the gravitational force that binds the planets to the Sun and holds the galaxies together. All of which leaves us without a definition of what force is. We need more tha n the tension in our biceps as a guide to the nature o f force. We are not helped over much by everyday language; common usage is a frequent enem y of understanding. Of course, science has no monopoly on any word, and no harm comes from talking of the forc e o f de Gaulle's personality. More harmful, for HMS's mental health, ar e those who debas e the language by purveying nonexistent ye t profitable commodities suc h a s cosmic force. And what i s one to make of Tolstoy, in War and Peace ? "Man's free will differs fro m every other force in that man is directly conscious o f it; but in the eyes of reason it in no way differs fro m an y other force." Oh yes it does. So what is the scientist's force ? What Is This Thing...? When it comes to understanding th e basi c component s o f nature, I seek solace i n that schoo l o f philosophy tha t define s thing s b y thei r behavio r an d regard s th e question o f what things ar e as meaningless. Many of us are tempted to concur wit h Noam Chomsky , who suspect s tha t th e brai n i s a n inadequat e instrumen t wit h which t o arrive at the complete truth about the universe. The Big Questions ma y be beyond the capabilities o f the human computer , just as dogs will never understan d jokes. We understand a very great deal about what forces d o but are far from finalizing the discussion abou t what forces are. Maybe we never will. Newton very specifically refused to commit himsel f a s to what gravitational forc e was , but h e nevertheless accounte d for the movement s o f Earth and Moo n and deduce d th e masse s of the Eart h and th e Su n by knowing only what gravit y does. We have discovere d forces tha t Newton never knew, but basicall y we still onl y defin e forc e by what i t does. So don't look down on dogs. What Forc e Does

We are going to se e what forc e does—an y force . Galile o and Newto n will b e ou r guides. Since we will often be using gravity as an example of a force, I will assum e that: • Yo u are aware of the attractive force of gravity exerted by the Earth (otherwise you'd fal l off) . - Yo u are prepared t o believe that all the heavenl y bodies exer t a pull on an y material body (otherwise Neil Armstrong "would have fallen off the Moon). We start with Newton's first la w of motion because of the very deep connectio n between forc e an d motion . Th e la w appeare d i n Lati n i n 168 7 i n Philosophiae Naturalis Principia Mathematica—arguably th e greates t scientifi c publication i n history. The First Law

Paradoxically, the first la w tells us what happens to the motion of a body in the absence offeree . I t says that nothing happens :

Thomas Aquinas versus Neil Armstrong | Every body continues in its state of rest, or of uniform motion in a straight line, unless it is acted upon by a force.

If th e firs t la w seem s les s tha n a showstopper , yo u shoul d recal l tha t Steve n Hawking (who, like Newton, holds the position o f Lucasian Professor of Mathematics at Cambridge) has referred to Newton as "a colossus withou t paralle l in the history o f science."2 A major componen t o f Newton's unparalleled achievemen t wa s his formulation and use of the laws of motion. Historians wil l tell you that Newton' s first la w owed muc h t o Galileo and tha t hoth ha d bee n peekin g a t Descartes an d hi s contemporar y Pierre Gassendi . The y have a point, but we are not here to portion out credit. We are here to show that the first law makes sense, even though Aristotle would have dismissed i t out of hand. It helps t o rephrase th e law , splitting i t into two statements tha t bot h stress th e resistance to change of a body, whether i t is moving or not: (i) A body at rest will remain at rest unless acted on by a force. This sounds like common sense; rocks rarely walk without encouragement. (ii) A body moving in a straight line will continue to do so at constant speed provided that no force acts on it.

This appear s to deny dail y experience. Aristotle and Spinoz a woul d hav e contradicted Newto n had the y bee n around . Descartes , over forty year s before Newton, had propose d tw o law s resemblin g (i ) an d (ii) , so h e wa s a believer , bu t Sain t Thomas Aquina s woul d definitel y hav e shake n hi s head . An d h e ha d commo n sense, popular opinion, the sages of antiquity—and God—on his side . Neil Armstrong, Thomas Aquinas, and the Hand of God Aquinas lived in a world where carts stuck in the mud arid ships became becalmed . It was obviou s that if you stopped pushin g (o r pulling) a cart, a log, or a galleon, it would quickly stop moving—the evidence of one's eyes could not be denied. Thus , in apparen t contradictio n t o Newton' s firs t law , i t wa s generall y believe d tha t a moving body will not continue movin g at constant spee d in the absence of a force. A modern Aquinas would smile patronizingly and point out that if your car continued movin g indefinitely afte r yo u switche d of f the engine , you woul d sav e a tidy sum in running expenses . But Aqiiinas had a problem: the Su n rose every day. He believed that i t circle d the Earth; it returned da y after day, just as the Moon returned night after night. How could th e heavenl y bodie s remai n i n constan t motio n withou t a forc e actin g o n them? Ship s didn't . O n leve l ground , cart s didn't , an d rock s certainl y didn't . I n Aquinas's world the only forces permitted wer e those that involved the direct contact of one body with another, a hand pushing a broom, the wind pressing on a sail. What hand was pushing the Sun? At the beginning of the Summa theologiae, the bulky summing up of the relation of God to man that Aquinas produced in the thirteenth century , he states that God's existence can be proved by reason. And he presented five proofs. So when Aquinas

2 He was, perhaps unknowingly, echoing a phrase in a letter of recommendation written for Newton by his teacher at Trinity College Cambridge: "unparalleled genius. "

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asked himsel f whose han d wa s pushing th e Su n and th e Moon, he kne w the an swer—the hand o f God. Neil Armstrong knew better. At about 5:00 P.M. (Houston time) on 1 7 July 1969, the Apollo 11 spacecraft wa s a little under 30,00 0 miles fro m th e Moo n on its return journey to Earth. At this point in space the gravitational tug of the Moon on the Apollo wa s roughly canceled out by the equa l and opposit e pull o f the Earth. The craft wa s thu s traveling through spac e effectivel y unacte d upo n b y an y force , it s rockets were turned off , an d i t was subjected to negligible net outside (gravitational) force. This was a golden opportunity to test Newton's first law. Here was a body moving in a straight line in th e absenc e of any significan t force . Newton, if asked, would hav e sai d tha t Apollo woul d trave l onwar d a t constan t speed . Aquina s would have said that it would stop, unless God was pushing it. The speed was almost constant: at 4:30 P.M. it was 2946. 8 mph; at 6:00 P.M. it was 2933.9 mph, a difference o f about 0.44%. From ground station data on subsequen t journeys int o fa r space , it i s ver y clea r tha t onc e spacecraf t ar e wel l awa y fro m heavenly bodies, and hav e switched of f their rockets, they maintain a n effectivel y constant speed—in the absence of any significant external force. The first law really works. The mistake of those who think like Aquinas is that they don't recognize that resistance is a force. Thi s is what they leave out when they describe the forces acting on a body. When I stop pushing a cart, it slows down because there is still a force acting on it, the combine d forces o f friction an d ai r resistance. If they were absent, the cart would go on rolling forever. The cart is not disobeyin g the first law. Initially it is difficult fo r most people to believe in the first law; they can't recall seeing a body moving steadily in the absenc e of a force actin g on it. There are always forces o f resistance that will slo w down a moving body that has no means of propulsion. But nevertheless if , as in th e cas e of our spacecraft , a body is moving and there is no net force acting on it, it just keeps on moving. Newton realized that all material bodies have this strange built-in property, which we call inertia, a stubborn resistance to changes in motion. If they are at rest they "like" to stay so; if they are moving at constant spee d they "prefer " t o continue doin g so . We don't kno w why. We believe it because Galileo suspected it, and Newton showed that he could correctly calculate the paths of the planets, only if he assumed it. It is a correct theory because i t works. The huge advantag e that Newto n has ove r Aquinas i s tha t Newton's laws allow the quantitative calculatio n of the paths of almost any moving body on Earth or in the heavens. If that word almost worries you, we'll clea r it up later. The firs t la w come s with Newton' s name attache d t o it , but Galile o really got there before him. End-of-twentieth-century man has a laboratory in space denied to Galileo an d Newton , but Galile o ha d physica l intuition—an d h e reasoned . H e watched spheres rolling on plane surfaces and noted that if they rolled down an inclined plan e the y accelerated ; if they rolle d up a plane , the y slowe d down . H e guessed that this was an effect o f gravity tugging at the spheres. A sphere set rolling on a horizontal plane was neither slowed dow n nor speeded up by gravity, and the smoother the plane, the further th e sphere rolled. Galileo realized that, even in the absence of a propelling hand, a sphere would roll on forever if there was no resistance. In real life , a t least dow n her e o n Earth, there alway s i s resistance , an d i t slows down the rolling sphere on the horizontal plane.3

Thomas Aquinas versus Neil Armstrong |

1 occasionally loo k through m y cop y o f Descartes's Principes de philosophic, partly for the sensor y pleasure tha t I get from th e feel , color , and smel l o f the yel lowed seventeenth-centur y pages. 4 The text contain s th e Frenc h equivalen t o f the phrase "stat e o f motion." Thi s appear s t o be the firs t tim e this phras e appear s i n print. It allows us to express the first law very concisely: A body maintains its state of motion unless acted upon by a force.

Gravity is not th e onl y force tha t scienc e recognizes. We will meet others , but th e laws of motion apply to all of them. By the way, if you look in the right places, you will find simpl e examples of the first law. Here are three. The Mass Turnpike and the Firs t Law To test th e firs t la w o n Eart h it woul d b e nic e t o hav e force-fre e conditions , bu t these are not obtainable o n Earth—there is always a source of resistance. It is, however, possible to chea t an d attai n a condition i n whic h tw o o r more force s cance l each othe r in suc h a way that there i s zero net forc e actin g in the direction of motion of a body moving in a straight line. According to Newton, such a body should just keep on moving at constant speed along that line. An example of such a body is Carl Lewis, during the las t 80 or so meters of a 100-meter sprint , during which his speed i s mor e o r les s constant . Th e firs t la w applies : Lewi s travel s a t constant speed, because his legs are exerting exactly the same force as the air and track resistance to his motion—the net force acting on him is zero. The same principle holds, in less excitin g circumstances , whe n yo u cruise steadil y alon g the Massachusett s Turnpike. And it applies t o a parachutist fallin g steadil y earthward, pulled dow n by gravity but resiste d b y the equa l an d opposit e forc e o f air resistance. Zer o net force implies constant speed , not zero speed. I am not suggestin g that th e precedin g example s prove the firs t law . In no case did we measure the forces and show that they add up to zero. But reflect on the firs t law the next time you watch the end o f a sprint race, or cruise along Route 66. And try to dismiss common sense! Aristotle Gets It Wrong Again It took man centuries to grasp the first law. The commonly accepted, and incorrect, reasoning u p t o the Renaissanc e was, of course, due t o Aristotle. He argued thus: motion i s possibl e onl y i f the force , F , acting o n a body i s greater than the resis tance, R. If the propellin g force i s equal t o the resistance , tha t is, F=R, ther e is no net forc e actin g on the body and so , according to Aristotle, it will no t move . This sounded lik e commo n sense , bu t i t wa s wrong , as a parachutist coul d hav e tol d him. It means that a parachutist, at the point a t which th e ai r resistance, actin g on him an d hi s parachute , becam e equa l t o th e pul l o f gravity, h e woul d sto p i n midair. Thi s spectacula r part y tric k seem s t o be a n extremel y rare phenomenon . Aristotle came to the wron g conclusion . Zer o force doe s not mea n zero speed; i n 3 Galileo believed that if the experiment was performed o n a grand scale, the ball would go on rolling around the center of the Earth forever if there were no resistance. 4 1688 was one year after Newton's Principia. Who first bought my copy? I doubt if it was Newton; he was alive but he must have read the Latin version some years before. I would like to think that it was John Locke, Newton's friend.

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fact, i t means zer o change of speed. His theory works in on e special case , when a body is at rest, because there is no force acting on it. Then zer o force really does go with zero speed. Weightlifters regularl y demonstrate the validity of the firs t law for bodies at rest. They exert exactly the sam e forc e upwar d o n the motionless ba r as the downwar d force due to the weight of the iron that they hold above their heads. Zero net force on the bar, zero change of motion. Principle, Book II

Newton graspe d tha t ther e wer e negligibl e frictiona l force s actin g o n the planet s and that this was the reason they kept moving—there was effectively zer o net forc e acting on them in the direction in which they were moving. God was not pushin g them, an d nothin g wa s hampering thei r progres s through th e heavens . The y ha d been given a push, long ago, when the solar system was formed, and since then th e force actin g on them , i n th e directio n o f their flight , wa s negligible . Zer o force — zero change of motion. Newton saw that if there was a resisting medium in space, say air, it would continually slo w dow n th e planets , jus t as your ca r slow s dow n whe n th e engin e is switched off . Th e car does not stop immediately; it exhibits the property of inertia, the tendency of a moving body to keep moving. If the engine is turned off , th e onl y force acting is the resisting force, and it is this that slows down the car. Newton was aware, fro m th e observation s o f astronomers, that th e planet s wer e no t slowin g down, at least not detectably. He reasoned that there was effectively n o interplane tary matter and that space was a vacuum. He was very nearly right; there is a tiny concentration of molecules in space, but no t enoug h to significantly affect th e motion of the planets, not in your lifetime. Newton's conclusio n tha t spac e wa s empt y clashe d wit h Descartes' s belie f i n a univers e fille d wit h matter . Bu t Descarte s wa s a philosopher ; Newto n wa s a scientist. On Earth, resistance to motion is a practical problem, and Newton attempted to deal with it in the least known o f the three parts of the Principia, the secon d book, which is largely devoted to motion in a resisting medium. Inertia The first law of motion has sometimes been called the principle o f inertia, the ter m inertia implyin g in genera l the unwillingnes s o f a body to chang e it s stat e o f motion. We accept inertia a s a property of mass because we ar e brainwashed b y th e everyday world into accepting certain fact s as "common sense." Heavy bodies, like railway wagons, seem to almost consciously resist our efforts t o get them moving if they are stationary, or to stop them if they are in motion (facts that should hel p you believe in the first law. ) But being used to something doesn't explain it , and it may come as a surprise to HMS that we have no explanation of inertia. In 1883 the German scientis t Mac h (th e speed-of-sound Mach], who was an original, iconoclasti c physicist, proposed that inertia, at least for bodies in this part of the universe, was a property caused by their interaction with all of the other bodies in the universe. Albert Einstei n calle d thi s a "bol d idea, " bu t neithe r Mac h no r Einstei n eve r ex plained ho w inertia aros e from interactio n wit h the heavenly bodies, and Einstei n

Thomas Aquinas versus Neil Armstrong |

eventually abandoned the trail. Kant was also puzzled by inertia, which he saw as a force resistin g changes of motion. Inertia remain s a n unsolve d problem , another exampl e o f a scientifi c concept that we have become used to, that ha s had extensiv e practica l use, but that defie s our understanding. Dog s an d joke s again? Perhaps, bu t inerti a canno t be avoided and it will pop up again when we come to Newton's second law. It is not only movement in a straight line that persists in the absenc e of force. A spinning top would keep on spinning foreve r if there were no air resistance and no friction between top and floor. Rotational motion also demonstrates inertia. In certain types of machine a flywheel is used to keep the machine turning over smoothly. The heavy metal wheel keeps things going even when the source of power is not acting; onc e i t i s spinnin g aroun d rapidl y i t "wants " to kee p going . There i s research on the possibility o f using massive flywheels as a source of motive power for vehicles tha t trave l shor t distance s i n limite d areas , suc h a s deliver y trucks . If Mach was right, they will be driven by the stars. The Straight and Narrow Path

Two of our protagonists , Aquinas an d Newton , were victim s o f the excesse s tha t often accompan y hero worship. Saint Thomas Aquinas was careless enough to die in a monastery. The "Angelic Doctor" was promptly decapitate d b y awestruck monks, his bod y boiled an d th e bones preserved as holy relics. Whe n the widely admired Saint Elizabeth of Hungary was lying in state in 1231 , fervent fan s took cuttings of her nails, her hair, and (tremble Madonna) her nipples. Newton was spared this kind of ghoulish attentio n (it wasn't don e i n Georg e II's England) , but h e coul d wel l hav e bee n i n dange r a couple o f centuries earlier . Dr . Samuel Johnso n wa s o f the opinio n tha t Newton would have been worshiped a s a God had h e live d i n antiquity. Thi s wa s acceptable flattery, but a stranger phenomenon arising from the adoration of Isaac was the attempt to appl y Newton's famously successful law s o f motion to politics , medicine, and human behavior. Thus, Nicholas Robinson published "A New Theory of Physick an d Diseases , founded on th e principle s o f the Newtonia n Philosophy. " And there was the painful poem of Newton's friend Desaguliers, entitled: "Newtonian Syste m o f th e World , the Bes t Mode l o f Government" (1728) . Tw o lines ar e enough to illustrate its quality: Newton the unparallel'd whose Name, No time will wear out the Book of Fame. Newton shoul d hav e sued , but h e wa s dead . A n intellec t o f an entirel y differen t caliber, David Hume, also cam e unde r th e spel l o f the law s o f motion an d trans ferred th e firs t la w to the working s o f the mind: "The imagination , when se t into any train of thinking, i s apt to continue, even when the object fails it, and like a galley put in motion by the oars, carries on its course without any new impulse." The best-know n effor t t o forc e Newton' s firs t la w int o a farcicall y unsuitabl e mold wa s tha t o f the mathematicall y minde d theologia n John Craig , wh o i n hi s Theologiae Christianas Principia Mathematica (1699 ) (flattery or plagiarism?) proposed his ow n first law , which coul d be called the principle o f the inertia o f plea-

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sure: "Every man attempts to prolong pleasure in his mind, to increase it, or to persevere i n a pleasurable state. " Fo r a devou t Christian thi s la w describe s a suspi ciously hedonistic trajectory through life; Craig speaks like an undercover agen t for Hugh Heffner. A more theologically correct version might read: "Every man continues in a state of spiritual res t or constant devotio n to the straigh t and narro w pat h unless acted upon by a force of evil." The Real World The first law of motion is not enough to deal with the complexity of the real world, the worl d of cars, stars, people, and othe r moving objects. The law says that noth ing happens to the motion of a body in the absence of a net force , but i t doesn't sa y quantitatively wha t happen s i n the presence o f a net force . T o proceed we need to go to the second law of motion.

4 The Second Law Good god what a fund of knowledg e there is in that book— [D]oes he eat & drink & sleep, is he like other men?" —The marquis de L'Hopital, on Newton's Prindpia.

The last thing Newton would hav e wished t o be known as was a revolutionary. He was not to know, nor could he have guessed, that his second law of motion woul d help to change the intellectual atmospher e o f Europe. The start of the Indianapoli s 500 , the circulatio n o f your hlood, the path s of the planets—anytime that a hody moving in a straight lin e changes its velocity or direction, the secon d la w is at work. Anytime that a body at rest starts moving, we need the law to predict its behavior. Anytime that a body in motion i s acted on by a force, th e second law tells us, quantitatively, how that motion changes. Unlike the first law , i t wa s almos t entirel y Newton' s ow n achievement ; h e owe d littl e t o Galileo. The Stubbornness of Matter Newton's secon d law of motion as it appears i n the Prindpia ca n be expressed i n English as follows: The acceleration of a body is proportional to the force acting on it and occurs in the direction of that force.1

Three o f the basic conceptual components o f the univers e are contained i n th e second law : mass, force , an d motion . The y ar e related b y th e equatio n a = F/zn, which w e can write in words as: Acceleration = Force divided by Mass

To seek out the meaning of this relationship, w e will nee d to define th e three concepts involved. Acceleration wil l not be a problem. In discussing force w e have already adopted a typically British empiricist approac h an d settle d for a description of what force doe s rather than what forc e is. The nature of mass is more problematic.2 Befor e yo u insis t o n knowing what mas s an d forc e are, listen to that talente d 1 If you want to make your own translation, the original Latin goes: Mutationem motus proportionalem esse ui motrici impresse, & fieri secundum lineam rectum qua vis ilia imprimitur. 2 Not only is the concept elusive; we are not even sure where the name comes from. Ther e are those who point to the Latin massa, which means a piece of dough or clay. This could be derived from th e Greek maza for barley cake, a word occurring in the Agamemnon o f Aeschylus. I favor the Hebrew matza, the unleavened bread eaten at Passover. Anyone who has eaten a few squares of this bland comestible has a good intuitive feeling for mass.

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Danish goa l keeper an d physicis t Niel s Bohr : "I t i s wrong t o thin k tha t th e tas k of physic s is to fin d out how natur e j's . Physics concern s wha t we can say about Nature." Bearing whic h i n mind , w e no w g o to th e secon d law , whic h describe s wha t happens t o a body when a forc e act s o n it . I am no t talkin g abou t a hammer de scending o n a Dresden shepherdess. W e will limi t ourselve s to bodies that d o not shatter o r permanently distort. Acceleration: The Fas t Lane Car companies like to boast about how fe w seconds it takes for their latest mach o model to go "from zer o to sixty." I f you ar e rash enoug h to keep your eye s on th e speedometer for the first six seconds of blastoff you might see the needle climb from 0 to 60 mph. This i s exactly what we mean by acceleration: an increase i n speed. (We can define negative acceleration as a decrease in speed.) There is no guarantee that the needle on the speedometer of an accelerating car will climb smoothly, such that every second that passes gives an increase of precisely 10 mph i n the speed . If this were to occur in our case, then afte r 1 second the speed would be 10 mph; afte r 2 seconds, 20 mph; after 3 seconds, 30 mph, and s o on. If the ca r were to behave in this way, we would say that it is accelerating uniformly a t 10 mph pe r second. Uniform motion, on the other hand, is what occur s when a body travels at a constant speed, thereby covering equal distances in equal increments o f time. Anyone who drives a car knows what constant spee d is and also knows how acceleration feels . Anyone who has sat in an airplane that is taking off knows that acceleration—"picking up speed"—i s connected with force . You can feel the back of your seat pressing against you. What the second law says is that if there is a net force acting on a body it will accelerate and the acceleratio n ca n be calculated from th e equation. If we knew the net force acting on a racing car (the sum of the force exerted by the engin e and the frictional forc e opposing its motion), we would only have to know the total mass of car and drive r to work out the acceleration . The equation say s that for a given mass, m, the acceleration, a, is proportional to the force , F. 3 The bigger the force, the faste r th e spee d increases. Neglecting air resistance, a Boeing 747 that takes off on all four engines will accelerate off the runway at twice the rate it would if it used tw o engines. If it reaches 20 0 mph i n a minute usin g fou r engines , it will only reach only 100 mph in a minute i f it uses two engines . Both Galile o an d Newto n realize d tha t whe n a ne t forc e act s o n a bod y i t changes the velocity of the body. Thus, if a football rests motionless on the ground and I kick it, its velocit y changes fro m zer o to som e finite value. As the bal l flie s through the air , it is opposed by another force, ai r resistance. Thi s is the onl y forc e now acting on the ball, and it must change the ball's velocity. It does: the ball slow s down. If another player kicks it, its motion will again be changed by the force exerted by the player's boot. It could be said that the very fact tha t the ball change s velocity by definition mean s that a force has acted on it. Notice that the firs t la w i s really superfluous; it is a special cas e o f the secon d law. The first law says that the motion of a body is undisturbed i n the absenc e o f a 3 The reason that a and F are written in bold type is that they are both vectors: they have both size and direction . The velocity of the wind, or of a car, is a vector. Mass is not a vector; it has a size but not a direction. Weight, which is a force, is a vector.

The Secon d Law [_3?

net force acting on it. But this is exactly what the second law says when you put F = 0. You find a = 0, which means that th e body neither speed s up no r slow s down , which in turn means that its state of motion is unchanged, whether it is stationary or moving. The second law tells us how to quantitatively relate the mass and acceleration of a body with the force acting on it. It reveals one of the deepes t secret s of the physical universe: The resistance to change s in motion (to acceleration ) increase s as the mas s increases.

That's why the Hell's Angel on his Harley Davidson motorbike has a good chance of leaving you and your Porsche standing when the lights change. You have far more mass and therefore far more inertia than he has. Apples Again It was probably Galileo who first measured the acceleration of bodies as they fell to Earth. They accelerate because there i s a force actin g on them, the forc e o f gravity. This acceleration due to gravity is commonl y calle d "g," and , althoug h i t varies slightly depending on the exact location at which it is measured, we can, for most purposes, take an average value of 9.8 meters per second , per second . This means that afte r fallin g freel y fo r 1 second a body will attain a velocity of 9.8 meters per second, that is about 22 mph, the speed of an Olympic sprinter. After 1 0 seconds its speed, in the absence of air resistance, will reach about 220 mph. On the Moon the forc e o f gravity is about one-sixth of that on Earth; that means that the force o n a given mass, m, is one-sixth of what it is on Earth. It follows fro m the secon d law that the acceleration of a falling body must be one-sixth of that o n Earth, that is , one-sixt h o f g, namely, 9.8/6 = 1.63 meters pe r second , pe r second . After fallin g moonwar d fo r one secon d a n astronau t would hav e a speed o f only 1.63 meters per second , or less than 4 mph. Remember how gently Armstrong and Aldrin floated downwar d afte r taking a hop? And how high they could jump without great effort ? Notice that i f we dro p two bodies, one with a mass of, say, five times the other, they will fall with the same acceleration—provided we do it in a vacuum to avoid air resistance. Thi s i s what Galile o claimed, an d i t i s consistent wit h th e secon d law. The forc e F acting on the tw o bodies is just their weight, W. The forc e o n th e more massive bod y (it s weight) is fiv e time s th e forc e o n the lighte r body, but it s mass i s also five time s bigger so that i f we write a = W/m fo r the lighte r body, we have to write a = 5W/5m for the heavier body, a is thus the same, for these two and any two falling bodies. The Units of Forc e The uni t o f length i s th e meter , an d o f mass th e kilogram . The scientifi c unit of force i s the newton. The symbol for the newton i s N. It is useful t o have a sense of the magnitud e o f the newton , an d sinc e weigh t i s a familiar force , fo r which w e have a feel, w e us e i t by wa y o f illustration. (I f you wan t t o convinc e a colleague that weight i s a force, stan d o n his stomach. ) As has been frequentl y pointe d out, the weight of a smallish appl e is, pleasingly, about 1 newton, o r 1 N. That i s the downward force that the apple exerts on your hand and the force that you exert upward on the apple if you want to hold it steady. Newton said that force equals mass

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times acceleration. My mass is 80 kilograms. If I fall fro m a roof, my acceleration is 9.8 meters per second, per second. This gives 784 newtons for the forc e that I exert on the Earth—my weight. Newton probably weighed about 700 newtons. An Understandably Giant Step Anyone who has watched the blurred shots of astronauts walking on the Moon can sense tha t i t took little effor t fo r the heavily loade d explorer s t o leap int o th e air less. This rubs in the fac t that mass and weight are very different animals . If we define the mass of a body as "the amount of substance" tha t it contains, then it is clear that Neil Armstrong's mass remained effectively constan t durin g his journey to the moon. Plus or minus smal l percentages, the number and type of atoms in his body were unchanged . I n othe r words , hi s mas s was no t change d significantl y by hi s journey, but his weight was. What changed in going to the Moon was the force wit h which h e was attracted to the ground that he was standing on. The force o f gravity on the surfac e of the moon is only about 16% of what it is on Earth. It is the forc e of gravity o n a body that w e cal l its weight, and tha t forc e varie s wit h the plane t o r other piece of matter that the body is close to. Weight is a force. In contrast, mass is an amount of material* Armstrong' s weigh t o n th e Moo n woul d b e abou t 3 0 pounds weight, or about 136 N—by which i s meant that the forc e pulling his body toward th e Moo n wa s equa l t o th e forc e exerte d b y th e Eart h o n a mas s o f 30 pounds. That' s wh y h e jumpe d abou t s o easily . H e probably weighe d abou t 180 pounds weight (abou t 81 8 N) in the Spac e Center at Houston. Don't confuse mas s and weight. See n fro m th e point of view of a space traveler, weight is a thoroughly local property, depending on where you are in the universe. Now consider Phobos, on e of the tw o potato-shaped moon s of Mars. Its dimensions ar e roughly 1 2 by 1 3 by 1 7 miles. Th e forc e o f gravity at its surfac e i s abou t one-thousandth o f what i t i s o n Earth . Nei l Armstrong would weig h les s tha n 3 ounces on Phobos, about the same as a Hershey bar on Earth. The weakness of gravity is apparent. The fact that galaxies are held together by the force of gravity is a reflection o f their immens e masses. It is only in cosmolog y that gravity reveals awesome power. The Third Law

If you div e off a cliff, yo u will accelerate as you fal l because there is a net forc e acting on you—your weight. When you reach the ground, the same forc e i s acting on you, yet you do not move. This is not a contradiction o f the second law. You are stationary becaus e ther e i s n o net forc e actin g o n you . Th e explanatio n i s tha t th e Earth is pressing upward on you, and that this force is exactly equal to your weight. This is an example of Newton's third law . Newton saw forces as acting between two bodies, not a s one body exerting a force o n the other . He spoke of action and reaction,, which he declared to be equal and opposite. In the cas e of someone standin g o n th e Earth , this equalit y i s obvious: what i s perhaps less obvious is that while you were falling off the clif f the pull of the Earth on you (whic h you ca n cal l the action ) is equa l an d opposit e t o the gravitationa l 4

I know that this is an unsatisfactory definition, but it is understandable and useful. Th e real truth is that we don't really know what mass is.

The Secon d Law |

pull that you exert on the Earth (the reaction). Actually it doesn't matter which you call what. Ther e ar e two equa l forces , a s though there were a spring stretche d between yo u an d th e Earth , pulling bot h o f you togethe r with th e sam e force . Bu t there's somethin g wron g here. I' m movin g because the Eart h pulls me ; why isn' t the Earth moving if I pull it? It is! The force between you and the Earth is given by your weight, say 600 newtons. Thi s i s also, according to Newton's third law, the forc e tha t you ar e exerting on the Earth . We can therefore fin d th e acceleration , a, of the Eart h by putting the right numbers into a = F/m, remembering that m is the mass of the Earth, that is 6 x 1024 kilograms. Putting F = 600 newtons w e fin d tha t a = 10" 22 meters per second, per second . If it took you 1 0 seconds to fall to Earth, the Earth's velocity at the en d of those 1 0 seconds, because of the pull that you are exerting, would be 10~ 21meters per second. In familiar units: 2.25 x10"21mph. To give you an idea of how slow this is, if you traveled at this speed, it would take you about a billion years to travel onethousandth of an inch. Little wonder that the Earth doesn't appear to move for you. The difficulty o f fighting inertia is very clear here; it takes a mighty push, or pull, to get the Earth to detectably change its motion. The Limits of Newton' s Laws . . . had Newton not bee n a mere beginner at gravity he might have asked how the apple got up there in the first place. And so might have discerned an ampler physics. —Les Murray

1. Before Newton , there was no way o f predicting or understanding th e wa y i n which bodies moved under th e actio n of forces. Fo r the worl d o f everyday objects and for the known heavenly bodies, Newton gave an answer, except in a tiny number of curiosities, such as the exac t path o f the plane t Mercury. However, although the path of an artificial planet revolving about the Sun will be described reasonably well by Newtonian mechanics, that mechanics can predict neither the existence of the new planet nor the path in which man puts it. Newton himself realized that the fact tha t nearly all the planet s revolv e about th e Su n in the sam e plane was not a consequence of his laws. There is no reason they couldn't all be moving in differen t planes. He assumed tha t the plane in which they move was chosen by God. There are other, more prosaic explanations. 2. In the twentieth century , Newtonian mechanics wa s shown t o be entirely in adequate t o dea l wit h th e behavio r o f atoms. Th e answer s tha t Newto n couldn't provide were supplied by quantum mechanics. 3. Cosmology, the very area where Newton had had his greatest triumphs, was to demonstrate, in one of the most spectacular experiment s ever performed, that there is a complete schis m betwee n th e wa y Newton sa w time an d spac e and th e way Einstein's theory of relativity described them . We come to these matters late r on. Meanwhile, don' t b e tempted to downgrade Newton. H e remains a giant, an d i t i s worth rememberin g tha t th e experimenta l facts tha t le d t o twentieth-century scienc e became available only long after Newton's death .

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5 Predicting Catastrophe In other words, I am buried in my work, like Newton (who incidentally died a virgin) in his famous discovery of the la w of gravity (I think that was it). —Eugene Delacroix, letter to Georg e Sand

Circular No. 5636 of the Internationa l Astronomical Union , published o n 15 October 1992, stated that the Swift-Tuttl e come t (named in 1862) might collide with the Earth on 14 August 2126. The comet is large enough to threaten the continuation of civilized life o n this planet. The second sighting of what coul d be the most important objec t i n huma n histor y wa s b y a n amateu r Japanes e astronomer . Th e an nouncement triggere d a rash o f measurements, and a more accurate prediction of the comet's path showed both that it is the comet that was seen in China in 69 B.C., and tha t w e wil l b e saf e i n 212 6 but ma y be i n dange r o n 2 6 August 3044 . More measurements will enabl e the accurat e predictio n o f the neares t approac h (hope fully no t zero ) t o th e Eart h in 3044 . We know tha t thi s ca n be don e becaus e as tronomers have accurately predicted the return of comets before. The Norman Conquest of England in 106 6 wa s commemorate d b y a wall hang ing that ca n stil l be see n in th e tow n o f Bayeux in Normandy . On e o f the panel s shows an objec t i n the sk y that can be identified as Halley's comet , so called afte r the English astronomer who observed its return in 1682. (The Englishman Thomas Harriot, an early visitor to America, observed the return o f 1607.) Halley predicted that the comet would return in 1758. His calculations were improved on by others, who gave the expected date as March 1759. The comet appeared i n April, not bad agreement for an age without computers. How is it that we can make accurate predictions of this kind? What is their basis? Newton's Revelation

At the ag e of fifty, Isaa c Newton, already renowned throughout Europe as the greatest natura l philosophe r sinc e antiquity , bega n a n intens e stud y o f the book s of Daniel an d Revelation . His purpose wa s t o predic t th e dat e o n whic h th e worl d would end . Now, although Newto n had n o doub t tha t ther e wa s a n all-powerfu l Creator wh o determine d th e overal l pat h o f history , h e didn' t believ e tha t th e Almighty spent hi s day s and night s chaperonin g the universe, a permanent back seat drive r for the materia l world. Onc e the heavenl y bodies ha d bee n se t in motion, that motion wa s controlled by laws. And the laws were universal. The y controlled the pat h o f the Moo n and th e pat h of an arrow, the trails of the comets an d the surge of the tides. Newton was too religious to deny God the right and ability to manifest his power by interfering with the workings of the world, but in general, although Go d might be responsible for every sparrow that fel l fro m th e tree , he di d

Predicting Catastrophe |

not usually decid e how th e sparro w fell ; tha t was determine d by the law s o f motion—and the law of universal gravitation. Gravity is on e o f the handfu l of forces tha t mol d th e universe . I t is almost certainly th e forc e tha t wil l overwhelmingl y determin e th e en d o f the presen t uni verse. Newton revealed just how ubiquitous i t is. I Shot an Arrow ... Until th e spac e age , all man-mad e missile s fel l bac k to Earth . The Greek s had only the most evasive explanation o f this fact. The general attitude was that thing s fell becaus e that was their nature . I n this vein , Aristotle declared that the natura l place for all heavy things was on the ground—it was obvious. The moon presented a difficulty : wha t kep t i t u p there ? Aristotl e decide d tha t i t wa s mad e o f ether, which solve d everything . However , arrows an d apple s fel l t o Eart h because th e Earth wa s thei r natura l home , an d the y move d faste r a s the y approache d th e ground becaus e o f their happines s i n returnin g home . Galileo, doubting whethe r jubilation wa s withi n th e rang e o f emotions normall y expresse d by th e averag e apple, contented himself with determining how bodies fell, no t why. He measured the positio n of falling bodies a s a function of time, rather than creatin g anthropomorphic reasons for their behavior. He accepted that the Earth attracted all material bodies, but he ventured no explanation of why this should be so, or indeed o f why the Moon did not fall . Newton, born i n th e yea r that Galile o died, contemplate d the second-mos t famous apple in history and realized, like Eve, that perhaps any two bodies could attract eac h other, not onl y Earth and apple . In a superb gesture, he reached for the stars and extende d Galileo' s earthboun d idea s to any two material bodies i n th e whole universe . Universal Gravity Newton said three fundamental things about gravity: 1. It is a universal force. Any two bodies attract each other. Gravity operates between you and th e coffeepot , betwee n you and th e farthes t galaxy . The pull o f the Earth on a falling object is just the most familiar example of a phenomenon that is a built-in property of all matter. 2. A simple mathematica l expressio n allow s the calculatio n o f the strengt h of the gravitationa l force o f attraction, F, between any two bodies. The expression is known as Newton's law of universal gravitation:

In this equation mt and mz represent the masses of the two mutually attracting bodies and R the distanc e betwee n them . Th e dependenc e o n 1/R 2, is the reaso n we refer to the equatio n as an "invers e square " law . Regardin g G: many of the equa tions that govern the behavior of the universe contain a small number of constants, numbers that Nature hands ou t to us with no explanation as to their magnitude. We can only determin e the values o f such constant s by experiment, and this has been done very accurately for the so-called gravitational constant G. 3. Newton refused t o explain what gravity was. "I have not been able to discover

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the causes of those properties . .. and I frame no hypothesis [nonfingo hypothesis]. ... [I]t is enough that gravity does really exist, and act according to the laws which we have explained." Don't judge Newton too quickly on this last issue. Scienc e is very good at using shadowy concepts to make astonishingly accurate predictions. It is a mark of Newton's sophisticatio n a s a scientist that , livin g whe n h e did , he realized the limita tions o f his postulat e o f universal gravitation : "T o tell u s tha t ever y Specie s o f Things i s endow' d wit h a n occul t specific k Qualit y [he meant like gravity] b y which it acts and produces manifest Effects , i s to tell nothing." Nevertheless, Newton expresse d the belief that the caus e of gravity is not "incapabl e o f being discovered and mad e manifest." It was his refusa l t o be dogmatic, his belief i n the ulti mate triump h o f observation an d reason , that wa s t o be on e o f Newton's greatest contributions to the Enlightenment. His scientific honesty comes like a glass of icecold beer after a route march i n the desert . It is a pity that h e was sometime s les s than honest in dealing with his scientific rivals. It is worth pausing to consider Newton's famou s rejection of hypothesis. O n the face o f it, he appears in this respect to be a disciple o f Bacon, but it is very obvious from his work that he did hypothesize. His statement non fingo hypothesis ca n perhaps be understood, not literally, but as a protest against the placing of hypothesis above empirical laws . In this context it is interesting that Alexandre Koyre has suggested tha t fingo actuall y means "feign. " Wha t was observed had t o be believed; what wa s hypothesized coul d b e foun d wanting . Thi s poin t wa s centra l t o Newton's philosophy, as stated very clearly in the Principia. The idea o f gravitational attraction between th e bodies i n the sola r syste m ha d also been suggeste d by the remarkably productive physicist Rober t Hooke but no t developed. Newton realized that gravity was the key to the motion o f the heavenly bodies. H e wrote dow n th e equation s b y whic h i t i s possibl e t o accoun t fo r th e paths an d speed s o f the planets . Bu t he ha d t o have fact s agains t which t o chec k that his calculations made sense . The Basi c Facts

For Newton's theories o f planetary motion to have any credibility, it was necessary that his calculations of the paths of the planets agree with their observed paths. The most accurate data on the positions o f the star s and th e movements o f the planet s were those o f Johannes Kepler (1571-1630). Kepler, a Lutheran born i n souther n Germany, was a meticulous dat a gatherer and a mystic. His great good fortune was to have inherited the notebooks of the Danish astronomer Tycho Brahe (1546—1601), "without whos e observation books everything that I have brought into the clearest light would have remained in darkness. " Brahe was the pleasure-loving, star-intoxicated eldest son of a Danish nobleman . In 1566, on a legendary occasion during his studen t day s at the Universit y of Rostock, he fought a duel over the question o f who was the better mathematician, he or his opponent. The bout took place in near darkness, and a slice of Tycho's nose was carved off. He replaced it with an artifact made of silver and gold. The king of Denmark gave Brahe the island of Hven on which to construct an observatory. In Uraniborg (the Heavenly Castle) Brahe spent twenty years gazing at the stars. All in all, over his lifetim e he catalogued the positions o f a thousand stars , thus supplanting the far less accurate table s o f the second-century Alexandria n

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Figure 5.1. I f the time for a planet to travel from a to b is equal to that from c to d then, according to Kepler , the (shaded) areas swept out by the line joining the planet to the Sun are equal.

astronomer Ptolemy. When Brahe lay on his deathbed and handed his records to Kepler, it was on the understanding tha t Kepler would use the data to prove that the Earth was at the center of the solar system, in contradiction to Copernicus. For som e quarte r o f a century , drive n b y hi s Pythagorea n belief tha t numbe r ruled the universe, Kepler pored obsessively over Brahe's data, and out of the huge mass of numbers he conjured three simple and strikin g laws (Figure 5.1): 1. Planets trave l in elliptica l path s abou t the Sun . Aristotl e and Copernicu s had said circles. 2. I n equa l interval s o f time, a line fro m th e plane t t o th e Su n sweep s ou t equa l areas. Thi s implie s tha t th e spee d o f the plane t i s no t constant , contradictin g Aristotle. 3. For any planet, the squar e of its time of revolution around th e Sun , divide d b y the cube of its mean distance fro m the sun , is the same as for any other planet.1 Kepler was ecstatic : " I yield freel y t o th e sacre d frenzy ; I dare frankl y t o confes s that I have stolen the golde n vessels o f the Egyptian s to build a tabernacle for my God far from the bounds of Egypt. If you pardo n me, I shall rejoice; if you reproach me, I shall endure. The die is cast, and I am writing the book, to be read either now or in posterity, it matters not. It can wait a century for a reader, as God himself ha s waited six thousand years for a witness." In any event, he had to wait seventy years before Newton showed that his laws had a rational explanation . Kepler did not know wh y the planets took the paths that they did; his laws were empirical laws, extracted from Brahe' s data by trial and error . Notice that his thir d law suggested that th e planets , in some sense, collectively formed a separate uni t from th e stars. The concept of the solar system, implicit in Copernicus's work, was finally crystallizing. With the power of genius, Newton devised the la w of universal gravitation and, combining it with the laws of motion, constructed a n all-embracing theory that accounted for Kepler's laws and for the fall of apples. It is not consistent with our present purpose to follow Newton's analysis of planetary motion, but the magnitude of Newton's breakthrough was clea r to his contemporaries , and. it should b e clear to us. It is one of the very greatest examples of the applicatio n of mathematics to fact s derived from observation of the natural world. This was the hypothetico-deductive method in all its glory. Starting with a hypothesis (th e laws of motion and gravitation) based o n meager facts , Newto n had deduce d th e consequences , an d show n that they were compatible with Kepler's laws, laws based on observation of Nature. By showin g tha t th e planet s followe d paths tha t were based o n the sam e laws of motion and gravitatio n that applie d to the movement o f bodies o n Earth, Newton a

The students of the Japanese astronomer Asada Goryu (1734-1799) claimed that he independently discovere d Kepler' s third law.

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demolished Aristotle' s belie f tha t celestia l an d terrestria l bodie s wer e subjec t to different laws . The cosmos had been united . When h e wrot e hi s masterpiece , Newto n name d i t wit h concis e accuracy : Philosophiae Natumlis Principia Mathematica {Mathematica l Principles o f Natural Philosophy). Th e title page of the firs t editio n i s inscribed "Juli i 5. 1686," but i t appeared in the following year. 2 In 1686, Robert Hooke spoke to the astronomer Edmund Halley, who was actively involve d i n preparin g Newton' s manuscrip t fo r publication, an d aske d fo r hi s contribution t o Newton's work to be mentioned. Newto n deeply resented Hooke' s claims to priority, dismissing him as a man of "strange unsociable temper " and impulsively threatening to withdraw Boo k 3 of the Principia rather than have Hooke's name appear. Fortunately, he relented, but this was not the only occasion when the two men clashed, an d it cannot be said that eithe r emerge d with great credit fro m their quarrels. Scientists ca n be fiercely competitive. In our day we have witnesse d an unedifyin g priorit y wrangl e over the questio n o f which laborator y first identi fied the AIDS virus. Newton's use o f the law s o f motion, together with the la w o f universal gravitation, t o explai n th e motion s o f the heavenl y bodie s i s legendary . Bu t he di d no t close a chapter of scientific history; he opened one. After 30 0 years, gravity still occupies the attention of theoretical physicists; gravity is very peculiar. The Strangeness of Gravity, Part I

Newton, as we have seen, did not lack intellectual enemies , and the strangeness of gravity gave them fuel. How could two bodies be pulled toward each other withou t being in contact in some way? Force-at-a-distance: no strings, no springs, how does it work? It smelled of necromancy. Leibniz affirmed tha t "gravity must be a scholastic occult quality, or the effec t o f a miracle." Perhaps he was getting in a dig at Newton's obsessio n wit h alchem y an d magic . Newton, Leibni z declared , "ha d a very odd opinion concerning the work of God." In one of his letters Leibniz complained, "In th e tim e o f Mr. Boyle an d othe r excellen t men , wh o flourishe d i n Englan d under Charle s I I (in the earl y par t o f the reign ) no body would hav e venture d t o publish such chimerical notions . . .. But it is men's misfortune to grow, at last, out of conceit with reason itself, and to be weary of light." The chemist Robert Boyle was puzzled by the idea that a body could, because of gravity, move according to certain laws. How, he asked, could matter "obey " laws, as though i t had a will of its own ? How does a piece o f inert matter know that i t should obey laws? Bishop Berkeley also had deep doubts about Newtonian physics : Force, gravity, attraction, and term s o f this sort are useful fo r reasonings an d reckonings about motion and bodies in motion, but not for understanding th e simple natur e o f motion itself . . . . A s for attraction, i t wa s certainl y intro duced by Newton, not as a true, physical quality, but onl y as a mathematica l hypothesis . . . to be of service to reckoning and mathematical demonstratio n is one thing, to set forth the nature of things is another. 2 The title page also carries the inscription: "Imprimatur. S. Pepys, Reg. Soc. Prases." The famous diarist was the president o f the Royal Society.

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Berkeley, who was often astonishingl y in tune with modern thinking on the natur e of science, also had doubt s about the deterministi c philosoph y of cause and effect , implicit i n the Principia. Things fel l to Earth all right, but why conjure up a hypothetical attractio n to explain it? All that was happening was that every time we release somethin g it falls . Therefore , al l we ca n sa y is that thes e tw o event s always appear together , which doesn' t mea n tha t on e ha s a causa l connectio n wit h th e other.3 This was not the last time that science met philosophy. The Strangeness of Gravity, Part II

Suppose tha t yo u got into a n elevato r on the hundredt h floo r an d ha d th e unset tling experience o f hearing all the cables snap. The elevator plunges to Earth. Free fall. I expect tha t yo u will spend you r last moments doin g experiments. Take out your ca r keys, hold the m i n fron t o f you an d releas e them . The y sta y where they are, hangin g in th e ai r opposit e you r belt buckle, because the y fal l togethe r wit h you. Galileo said so: all objects fall at the same speed, and since the air in the elevator is falling with you, there is no problem of air resistance. No w suppose that you bad been aslee p when th e elevator started to fal l an d had woke n u p i n midflight . 1'he elevator has no windows. You would not know that you were falling. In fact, as far a s you ar e concerned, th e elevato r is not moving . Yet your keys don' t fall . Dr. Moriarty has apparently finally thrown the antigravity switch; gravity doesn't exist anymore for you, and this remains tru e as long as the elevator falls freely , accelerating as it goes. There is no detectable gravitational force acting on you or the keys. Furthermore, there is no experiment that you can do, inside the elevator, that wil l tell you whether you are accelerating and the force o f gravity still really exists "out there," or whether yo u are stationary and the force of gravity has vanished. We conclude that , fo r an observe r i n a freel y fallin g elevator , acceleration appear s to b e able to cancel out the forc e o f gravity. But a force ca n be canceled only by anothe r exactly equivalent forc e actin g in the opposit e direction , as in the cas e of two balanced tug-of-war teams. It looks as if acceleration induced by gravity is completely equivalent to the force of gravity. That acceleration can mimic the effect o f force can be verified by any airline passenger. If, against safety regulations, you leave your table down and place a glass on it, the glass will sli p towar d you as the plane accelerates o n takeoff. Thi s doe s not happen i f the plan e i s cruising a t constant speed . During acceleration a force ap pears to be acting on the glass. Note that to an outside observer, looking through the window of your plane, the glas s appears to be displaying the property of inertia; it tries to stay motionless with respect to the runway, as it was just before takeoff. For the motionless external observer there is no force acting on the glass. For you there is. We have a first hint here that the observed behavior of a system can depend drastically on the motion of the observer. The strange equivalence of gravity and its associated acceleration could , in principle, have been notice d sinc e Galileo' s time, but i t took the geniu s o f Einstein to 3

As Thomas Reid (1710-1796), the Scottish originator of what came to be called the "commonsense school of philosophy," pointed out, day invariably followed night, but they were not linked by cause and effect ; day s do not cause nights.

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realize its importance . T o most of us the equivalenc e would appear to be a meaningless fact , a simple consequence of the way we have constructed ou r experiment. For Einstein it was the trigger that led him to construct the general theory of relativity, one of the keys to the large-scale structure of the cosmos. Black Holes and Dirty Harry

When we come to discuss cosmology , we will need the concep t of escape velocity. As you get farther fro m th e Earth, you feel its gravitational pull lessening. That is a fact and it is reflected in equation (1) ; the bigger R, the smaller F. Increase R a thousandfold, and the force drops by a factor of a million.4 The drop-off i n gravitational force wit h distance suggest s that i f a projectile, a bullet say , is fired verticall y up ward with enough initial spee d it will not eventually be conquered by gravity and fall back to Earth, but will escape, speeding outward s forever, perhaps to circle the Sun. Travel int o dee p spac e i s obviousl y possibl e onl y i f we ca n overcom e gravity. The "easy" way to do this i s to fire a n objec t int o the sk y at high velocity and als o provide it with its own rockets. In this way, if it is tempted to slow down too much and eventuall y sto p an d tur n around , i t ca n giv e itself a boost b y turnin g o n it s rockets. Alternatively, the initial blast can be prolonged so that i t is still operating high above the Earth where the pull of gravity is weak. The hard way to escape the Earth's gravity is to fir e a simple missile , having no propellin g sourc e o f its own , say an arrow or bullet, into the deep blue yonder. What would the initial velocity of such an arrow have to be to escape the Earth forever? Using equation (1) it can be shown (as they so annoyingly say in the textbooks ) that th e minimu m velocit y neede d fo r a bod y t o escap e permanentl y fro m an y planet i s given by:

In this expression G is the constan t i n equation (1) , Mis the mass, and R is the radius o f the (assumed ) spherical plane t from which th e projectil e i s hoping t o escape. The expression does not take into account the slowing effect o f air resistance, but fo r reasonably aerodynami c bodies—say, rockets—the expression give s a very good rough answer. The important point to notice is that nowhere in the expression does the mass of the escaping body appear. This mean s that th e escap e velocity is the sam e for all missiles, a shotgun pelle t or an artillery shell. We have the data needed to work out the escape velocity from the Earth: M, the mass o f the Eart h = 6 x 10 24 kg, R = 6.37 x 10 6 m, an d th e numerica l valu e o f G is 6.67 x 10" 11, from which w e find tha t V E = 11. 2 km/sec . In more friendly unit s thi s is a little ove r 25,000 mph, o r 7 miles per second . This, then, is the minimu m ve 4

The drop-off i n gravitational pull at greater heights means that the Earth is pulling on your fee t more than on your head. This effect i s too tiny to have any serious consequences, but if you were approaching a neutron star or a black hole (Chapter 34), both of which have stupendous gravitational fields, you would start stretching and eventually be pulled to pieces!

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locity with which an object would have to leave the ground to ensure that it would never return . Th e muzzl e velocit y o f Dirty Harry's (Clin t Eastwood's ) Smith an d Wesson 29, using 0.45 Magnum ammo, is only about 1600 mph. On the Moon , VE i s abou t 5400 mph. Thi s i s stil l to o larg e for Armstrong and Aldrin's lunar modul e to escape fro m th e Moon under thei r ow n power, which i s why they di d it in two stages, firs t joining the circling space module. On Phobos, one of Mars's two tiny moons, V" Eis about 90 mph. Ivanisevic's firs t servic e against Agassi i n th e 199 2 Wimbledon fina l wa s time d a t 11 6 mph. I f directed vertically upward fro m Phobo s i t would neve r return—though i t is unlikely that this moo n will ever be included i n the Grand Slam circuit. We will return to escape velocities when we consider black holes. Jumping on the Bandwagon, Part II

Just a s th e law s o f motion wer e invoke d t o explai n everythin g fro m politic s t o morality, so the law of universal gravitatio n was dragged into politics, biology, and chemistry. Th e Enlightenmen t scientis t Maupertuis , wh o i n 173 2 publishe d th e first French text to accurately explain Newton's theory of gravitation, hazarded that the la w o f gravity might hav e a paralle l i n th e functionin g of living organisms. 5 David Hum e spok e o f the associatio n o f idea s i n Newtonia n terms . Ther e wer e those who likened a king and his courtiers and advisers to the Sun and its planets, the latte r hel d t o the forme r b y a n attractiv e force. Thes e attempt s to incorporate major scientific breakthroughs int o other fields now appear ludicrous, but the same phenomenon was to recur with Darwin and Einstein.

5 It was typical o f the unpleasant sid e of Voltaire's character that he dismissed Maupertuis's role and falsely claimed that he was the first Frenchman t o explain Newton to his compatriots. And this after Maupertuis ha d helped Voltaire to write the chapters on Newton in the latter's Lettres philosophiques.

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6 From Newton to D e Sade: The Partial Triumph of Reaso n Reason must be our las t judge and guide in everything. —John Locke, An Essay Concerning Human Understanding Glory to God who created the worlds and Newton! —The abbe Jacques Delille

The Enlightenment Something encouragin g happened i n seventeenth-century Europe . It became more fashionable t o shout, "That's no t reasonable!" tha n to whisper, "That' s heretical! " Some call the period that culminated i n the 1760s the Age of Reason, some speak of the Enlightenment. The French, who were at the heart o f the Enlightenment, called it "l e siecle des lumieres." It was a time o f intense intellectua l excitement , a time when me n bega n t o fee l tha t the y ha d th e abilit y t o understan d an d contro l th e world and that the means by which to achieve those aims were not revelation an d dogma but intelligence , reason, and science . Not since the Greeks had reason an d science had such a good press. Newton's role was central. Reason, fo r th e philosopher s o f th e Enlightenment , wa s no t onl y a mean s o f reaching truth but also a principle to be defended. Consistently, the Enlightenment was a time whe n toleranc e wa s increasingl y advocated an d th e influenc e of the established Churches continue d t o decline. Belief grew in the rul e o f rational, not arbitrary, law , both within and betwee n nations. 1 The men an d wome n o f the Enlightenment emphasized that morals should not be divorced from politics an d economics. They believed passionately i n education. Above all they took as axiomatic the primac y of the individual , hi s religious an d politica l freedom, his right to believe o r disbelieve . The y o f course rejecte d the concep t o f origina l sin . Man y of them saw pre-Christian Europe, and the civilization o f Greece and Rome, as a legitimate sourc e o f morality. The Enlightenmen t wa s t o irrevocabl y alte r th e menta l mold o f Western man ; i t bega n t o see m possibl e tha t Baco n (quotin g a Roma n source), was right: man i s the architect of his fortune. 2 1 Michael Polyani has controversially suggested that the glorification of a rational secular society, associated with the Enlightenment, led to the totalitarianism and nihilism that in turn are the direct roots, he believes, of the Communist and Nazi movements that have so scarred our century. Others have held similar views, but the topic, though provocative, is not appropriate to this book. 2 To he politically correct you can write people wherever I have written man or men i n this paragraph.

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The roots of the Enlightenmen t wer e many and ra n deep . We focus o n a smal l number o f outstanding themes , which ar e o f particular significanc e here because they are inextricably intertwine d wit h the scientifi c revolution o f the seventeent h century. We will glance at skepticism, a t reason, and a t deism. Abov e all, we wil l consider the role of Newton. Newton and the Principia di d not create the Enlightenment, although he has his champions, as have Bacon and The Advancement of Knowledge, Descartes and th e Discourse on the Method, Locke and his Essay Concerning Human Understanding or Montaigne and hi s Essays. They al l played a part, as did others , but i f I had t o choose one hero I would choos e Newton . More specifically, I would focu s o n th e Principia and , if forced to absurdly an d perilousl y narrow my field o f fire, I would target the second law of motion. Newton was very definitely not an Enlightenment man, but th e Principia, that towerin g monument t o reason, was a perpetual presence hovering behind the Enlightenment. Whatever portion is finally allotted to Newton, there is no question that scienc e played a star role in th e Enlightenment . In hi s influentia l Origins of Modern Science (1949) , Herbert Butterfield writes o f the scientifi c revolution of the sixteent h and seventeenth centuries, that "it outshines everythin g since the rise of Christianity an d reduce s th e Renaissanc e an d Reformatio n t o th e ran k o f mere episodes , mere internal displacements , within the syste m of medieval Christendom. . . . [I]t changed the character of men's habitual menta l operations .. . and the very texture of human lif e itself." He was carried away, but understandably . The Roots: Skepticism "We know nothing, not eve n whether we know o r do not know , o r what it i s to know or not know, or whether anything exists or not." So said Metrodorus of Chios, in the fourt h century B.C. Skepticism in this extrem e form ca n question ou r ability to know anything. It can question the validity of reason itself. A doubter of the highest order was the third-century B.C . Greek thinker Pyrrho of Elis, whose negative reflections were collate d by his follower , Sextus Empiricus . Pyrrho was on e o f a long line of philosophers, goin g through Plato and Descartes, who emphasize d th e doubtfu l validit y o f the informatio n provided by our senses. When Ernpiricus' s Gree k text wa s translate d int o Lati n by Henry Estienne, it fel l into sixteenth-century Europe like rain on budding wheat. The seedlings of skepticism wer e there waiting , and non e was more thirsty tha n the essayist , Michel d e Montaigne (1533-1592 ) an d hi s distan t relativ e Francesc o Sanchez . The y bot h veered toward a path that Descartes was to follow later, a path that led to the thoroughly skeptical conclusion tha t the only sure knowledge was of oneself. Sanchez states clearl y that nothing ca n be known, all that ca n be done is careful empirica l research, with the hope that patterns will emerge which wil l help us know how to act. Montaigne' s Apology for Raymond Sebond (1575 ) (which , incidentally , say s very little about Sebond) says a great deal about man's inability to know. Montaigne makes himself absolutely clear: "I determine nothing; I do not comprehend things; I suspend judgment; I examine." His motto, "Que scayje?" (What can I know?) was Descartes's departure point in his search for knowledge. Skepticism had a powerful revival in sixteenth centur y Europe, eroding dogma, fertilizing th e groun d fo r th e seed s o f th e scientifi c revolution. I n th e Wester n world, that skeptical, questioning spirit was to become a permanent part of our cul-

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ture. It began to be accepted that people have a right to question all things withou t being burned aliv e o r broken on the whee l b y pious clerics . There were t o be n o more Galileos. Perhaps the most representative skeptic of the period proceeding the Enlightenment was the son of a Huguenot pastor and the writer of Historical and Critical Dictionary, a book that had a strong effec t o n many of the Enlightenment thinkers, including Voltaire , wh o sai d o f th e autho r tha t "h e taugh t doubt. " Pierr e Bayl e (1647-1706) attacke d superstition , prejudice , and dogma , and mad e quie t fu n of the improbabilities of the Bible. He held tha t comets are natural, no t supernatural, phenomena, and that the bones of a dog are as efficacious a s those of a saint if only the worshiper believes in them. He was a skeptic, but not a super-skeptic. The portly eighteenth-century philosopher Davi d Hume was. Hume challenged man's abilit y to ever explain the world. He set out to use Newton's scientifi c metho d to build a moral philosophy modele d o n Newton's natural philosophy. Earl y on he dismissed religion , but the skepti c in him took over completely, and eventually he was prepared to state: "I am ready to reject all belief and reasoning." H e eve n proceede d t o challeng e th e validit y o f the concep t o f cause and effect . Metrodoms and Hum e went a doubt to o far for the philosopher s an d scientist s of the Enlightenment, whose skepticism was more moderate, but still sharp enough to challenge the scientific and religious establishment. The y were empirical in outlook: the world existed , it ran in conformation to certain laws, these laws could be discovered, even if (and here their skepticism also revealed itself) there were limits on our understanding o f the true nature of the physical world. One thing was certain: all our knowledge o f the natural world comes, as Bacon knew, from ou r senses. Thi s is the attitude that we find, modified by the characte r of each, in Newton and in Locke. The Enlightenment atmosphere of skepticism and empiricism was highly congenial to the advanc e o f science, especiall y since , to this antimetaphysica l mixtur e was added an ancient and highly metaphysical component—the belief in the existence o f order i n th e cosmos . Th e Pythagorea n ideal o f natural order , a univers e governed by immutable laws that were immune eve n to supernatural interference, is one of the great pillars o f the Enlightenment mind. The ground cleared by skepticism in the sixteenth centur y was not immediately occupied by the armies of reason. The Roots: Reason

I speak of reason, not o f rationalism. The y are far from synonymous. For the pro fessional philosopher, "rationalism" i s a technical term, including not only the belief in the use of reason to arrive at truth but also the proposition that we can arrive at important truth s abou t the worl d by the us e o f reason in the absence of experience. Thi s philosophy , represente d i n differen t way s an d degree s by Descartes, Spinoza, an d Leibniz , is no t wha t I mean whe n I talk o f reason. Reason , for us , refers t o the us e o f logic, to that rationa l discours e whic h has , wit h frequen t an d woeful exceptions , been accepted in the West as the normal tool for settling intellectual differences . The Greeks, as usual, had laid the foundations. Plato said that we must "strive to reach ultimate realities without an y aid from the senses," which makes him a ratio-

From Newton to D e Sade |

nalist as well as an advocate of reason. Aristotle was less of a philosopher than his mentor, but almos t single-handedl y he create d the forma l theor y o f logic; for him man wa s " a rationa l animal. " Plato' s teacher , Socrates , die d fo r his belie f in th e right to logically examine and questio n all things. He was not the last. Zeno tested the power of reason by constructing brain-teasing paradoxes, and Euclid wrote the earliest o f logicall y buil t texts , hi s Elements, whic h wa s a serie s o f geometri c proofs, eac h carefull y constructe d o n th e precedin g proof , th e whol e structur e being supported by a set of axioms. The apparen t certitud e o f mathematics, i n a sea of doubt, struck dee p int o th e minds o f several seventeenth-century thinkers, notably Thomas Hobbes and Ren e Descartes. Is there a more beautiful story of the stepwis e seduction of one mind by another (across two thousand years) than that of Hobbes opening Euclid in the middle and, not convinced by the proof before him , going back to the precedin g proof on which it rested and continuin g t o work his way backward theorem by theorem to the openin g axioms? Hobbes saw Euclid's step-by-step construction o f a system from (presumably ) unassailabl e axiom s a s th e perfec t mode l fo r th e scientifi c method. There was no lack of reasoning men before the eighteenth century, so why do we single out th e Enlightenmen t a s the Ag e of Reason? Why di d Voltair e declare th e eighteenth centur y to be "that centur y when reason was perfected" ? Becaus e th e standing o f reason an d logi c in the millenniu m befor e th e Enlightenmen t was not comparable to that o f irrational faith . Logi c was a n establishe d subjec t i n the me dieval university, but chiefl y a s an accessory to law and theology , not as a tool for examining the workings of the natural world. In theology, reason was certainly riot a universally welcome guest. At the Council of Trent in 1551, the papal legates criticized thos e within the Churc h who us e the pat h o f reason instead o f confirming "their opinions with the holy Scripture, Traditions of the Apostles, sacred and approved Councils , an d b y th e Constitution s an d Authoritie s o f the hol y Fathers. " Anselm, the eleventh-century Archbishop o f Canterbury had put it more concisely: "I believe in order that I may know, I do not know in order to believe." It i s tru e tha t Aquina s applie d reaso n t o th e questio n o f God's existenc e bu t would neve r have said so if he had doubted what the result would be. The implicit view of the Catholic Church was that reason could be used to explain and reinforc e the Scripture s but no t to challenge eithe r the m o r the Church' s descriptio n o f the cosmos. The notoriety o f Galileo's clash wit h the ecclesiastica l authorities i s ofte n use d to suppor t th e thesi s tha t th e ris e o f science i n th e seventeent h centur y was op posed single-handedl y by the Catholic Church. This is quite untrue ; if anything it was the Protestant churches on the Continent that took the lead in questioning the fruits o f rational science . Luther may have questioned the workings of the Papacy, but h e regarde d "how? " an d "why? " a s "dangerou s and infectiou s questions." I t was the Lutherans who perhaps put up the first seriou s oppositio n to the Copernican suggestion o f a heliocentric universe , which they saw as a direct attac k on the literal trut h o f the Scriptures . Luther said o f Copernicus, "The foo l want s t o turn the whole art of astronomy upside down." In 1549, his frien d Melanchtho n said of the heliocentric hypothesis: "Now it is want of honesty and decenc y to assert such notions publicly, and the example is pernicious." The straightlaced Protestant John Calvin als o blaste d Copernicus , bu t reaso n wa s no t exactl y th e stron g sui t o f

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Calvin, whose Go d arbitrarily and irrevocabl y sorted ou t soul s fo r Heaven or hell, before birth . Ther e wa s a limited numbe r o f tickets to Heaven—an d th e stadiu m was not that big. The Catholic Church was not s o quick on the draw . It took the Vatican about 80 years to wake up to Copernicus and attempt to ban his teachings. Like Copernicus, Galileo learne d tha t usin g reaso n i n discussin g natur e wa s no t th e wa y t o wi n friends an d influence people. However, it would be a mistake to highlight the rational aspect o f the struggle between Galileo and the Church. The pope did not chal lenge the most rational of Galileo's works—his mechanics; he challenged his observations o n the sola r system and his conclusion tha t the Sun , not the Earth, was at its center.3 In the religio n o f Reformation an d Catholi c Europe, the bound s o f reason were firmly prescribe d b y faith, an d i n som e countries the torture r wa s there t o ensur e that this cardinal principle wa s not forgotten. Protestant England breathed slightly freer air . The seventeenth-centur y chemist Robert Boyle could risk saying of other creeds: "Why a man shoul d be hanged becaus e it has not ye t pleased Go d to give him hi s spirit , I confess I am yet to understand." I n the sixteent h an d earl y seventeenth century , England produced a number o f influential, reasoning, antiauthoritarians wit h scientifi c leanings. Thu s Bacon had trumpete d the virtues o f observation a s against accepte d wisdom , an d Thoma s Hobbe s had attempte d t o build a sound basis for knowledge by using the kind of mathematical reasoning that had so enthralled hi m i n Euclid. The scattered beginnings o f dogma-free scienc e could be detected. More and mor e thinkers were prepared to use their commo n sense, and their senses, rather than appeal to the so-called wisdom of the ages. Why, then, is sixteenth-century England not included in the Age of Reason? Primarily because reason had faile d t o show an y earth-shattering popula r successes . Science and scientists were not held in particularly high regard. Bacon's prediction of a science-based Utopi a had le d nowhere i n practice. Hobbes was (unjustifiably ) under suspicio n a s an atheist. 4 Th e popularly perceived achievement s o f Galileo were confined to the wonders revealed by his telescope, and this is reflected in the way that writers an d poets referred t o him. Hi s highly rational work in mechanic s was barely taught i n the universities. Physics was in its childhood, alchemy was a cookbook heavily laced with mysticism, and biology had hardly advanced from the inaccurate catalogue of birds and beast s lef t b y Aristotle. As John Donne cuttingly commented, We see in authors, too stiffe t o recant, A hundred controversie s o f an ant. He was, understandably, far from alon e in hi s lo w estimatio n of science. Observa tion was to o ofte n undirecte d an d weakl y linke d t o theory—if a t all. Reaso n had few triumphs to flaunt . Expanding our view to take in the spirit of the times in general, it is clear that the 3

It is a curiosity of intellectual history that, in the eighteenth century, when the freethinke r Rousseau, in his Discours, blaste d science, it was a Jesuit publication that came to its defense. Hobbes nowhere says that there is no God; he merely says that God is completely incomprehensible. O n the other hand, the term atheist tended to be used against anyone who strayed outside the conventional beliefs of the time. 4

From Newton to D e Sade |

first decade s o f the seventeent h centur y were a n er a o f profound uncertainty fo r thoughtful men . Skepticis m flourished , religion ha d splintere d int o man y cults , reason was weak. Donne, not knowing that a new daw n was near, spoke famously for the times when he lamented, "I was born in the last Age of the World." And then cam e Newton. He was not alone . As an unwitting heralde r o f the Enlightenment, h e wa s precede d b y Baco n an d followe d b y Locke . A s natura l philosophers, hi s Englis h contemporarie s Rober t Boyl e an d Rober t Hook e were princely figures , a s was the Dutchman Huygens. But, among those whom we associate with the scientific roots of the Enlightenment, Newton was king. The Roots: Newton, the Catalyst We are all hi s disciples now. —Voltaire

Newton was not only a genius, he was popularly and almost universally perceived as such , an d hi s achievement s colore d th e intellectua l lif e o f Europe. He moved reason into the limelight, he catalyzed, although certainly not single-handedly, the Enlightenment. One has only to list a smattering of the adulatory comments about him by his contemporarie s an d to skimpily trac e his effec t o n the though t o f later generations to realize that if one wanted to elect a champion of the Age of Reason, Newton wa s th e ma n o f the hour . Roussea u was on e o f the ver y few prominen t thinkers who took almost no interest in the scientist o r his work, but the comparatively undereducated Rousseau was the Age of Reason's odd man out. Newton's influence stretched fro m Russia to America. Jefferson kept a portrait of Newton o n the wall of his stud y and considere d that Newton, Bacon , and Locke were the greatest men in history. As late as 1851 Schopenhaue r wrote : "The almost idolatrous veneratio n i n which Newton i s held, especiall y in England, passes belief. Onl y a little whil e ag o The Times called him 'th e greatest of human beings, ' and in 1815 (accordin g to a report in the Examiner) one of Newton's teeth was sold for 75 0 pounds sterlin g to a Lord who had i t mounted on a ring." The early spread of Newton's influence in Europe was mainly du e to the French. It wa s Voltair e who wa s perhap s primaril y responsibl e fo r initiating th e Frenc h love affai r wit h English philosophy an d science . Voltair e visited England in 172 6 and became an Anglophile, as reflected in his Lettres surles Anglais (1734) . It was chiefly through his eyes that the French began to see England as more than a nation of uncouth louts . As he wrote, "I t is inadvertently affirmed i n the Christian countries of Europe that the English are Fools and Madmen." In 1738 Voltaire wrote an account of Newton's work: Siemens de la philosophic de Neuton (sic). Earlier , aided by the scientis t Maupertuis, he had give n a simpler outline in his Lettres philosophiques (1734) , where he lauded Newton's empirical investigations and his tolerance in matters of philosophy and religion: 5 "a man like M. Newton (we scarcely find on e like him i n ten centuries ) is truly the great man, and those politicians and conquerors (whom no century has been without) are generally nothing but celebrated villains." Voltaire saw the philosophical implication s o f his hero's work. He realized that 5

Voltaire was also tolerant. He wrote of the Jews: "In short we find them not only ignorant and barbarous people. . . . Still we ought not burn them. "

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Newton ha d shifte d reaso n ont o a ne w plan e an d tha t hi s rejectio n of dogma unsupported b y facts was a model fo r an attack on the Church , Voltaire's favorite enemy. An antiauthoritarian, pro-scientific, skeptical attitud e was to characteriz e much of the anticlerical writing s o f the Enlightenment. One of Voltaire's lovers shared hi s enthusiasm fo r Newton and the new science . Gabrielle-Emilie Le Tonnelier d e Breteuil, marquise d u Chatelet , was a n unusua l woman fo r her time . Voltair e used t o perfor m physic s experiment s i n he r salon . She admired Newton because she sensed the significance of his work, both mathematical and physical. The only French translation of the Principia i s that o f the redoubtable Madame du Chatelet. Possibly she got help with the math from the mathematician Alexis-Claude Clairaut, another Newton fan—and anothe r of her lovers. Her admiration stopped short of that of a compatriot of hers who suggeste d that th e calendar be restarted with Newton's birthdate as the firs t da y of the new era. In Germany, Lessing compared Newton to Homer. An Italian, Francesco Algarotti, published (1727) , the patronizingly titled, II Newtonianismo per le dame, whic h was translated b y Elizabeth Carter and appeare d in English, as Sir Isaac Newton's Philosophy Explain'd for the Use of Ladies (1739). B Back in England, David Hume proclaimed Newton to be the greatest and rarest genius tha t eve r arose. The astronomer Halley wrote, "Neare r the God s no morta l may approach," and Pope's endlessly quoted verse ran, "Nature, and Nature's laws lay hid i n night. The n Go d said, 'Le t Newton be!' and al l was light." Thi s may be doggerel, but i t was polished compare d with some of the verse about Newton that appeared in the early eighteenth century. Well before Newton died in 1727 , it was seemingly bad form not to mention hi m in a poem. Thus , on e Willia m Somerville , at the en d o f a poem devote d to "Th e Chase," dutifull y tacked o n som e line s o n Newton . For th e firs t hal f o f the eigh teenth century , bookshops were never lackin g in third-rat e philosophica l text s or excruciating book s o f verses lookin g t o Newto n an d scienc e fo r a n intellectua l crutch. To grasp the statur e o f Newton in the eye s o f the eighteent h century , it is suffi cient to examine the plan of the cenotaph designed , but never built fo r him, by the visionary French architect Boullee. Supported by a huge cyprus-covered socle was an immense hollow spher e pierced by holes that let in sunlight simulatin g the positions o f the star s an d planets . At the bottom of the spher e woul d b e the auster e tomb o f Newton . Visitors , enclose d b y th e upwardl y slopin g walls , woul d b e drawn, a s thoug h b y gravity , to th e immediat e surrounding s o f the tomb , wher e they would turn their eyes toward the limitless heavens . The source o f this extraordinar y near worship wa s without doub t the fabulou s success o f the law s o f motion combined with th e law o f universal gravitation . The Babylonians, th e Chinese , th e Maya , and th e Arab s ha d al l been meticulou s ob servers o f the heavens . Ptolemy , Brahe , Kepler , and Copernicu s had , i n differen t ways, documente d an d systematize d the movemen t o f the heavenl y bodies , an d Galileo had discovere d new moons. But no one, since the beginning o f history, ha d rationalized th e movement, and it was the law of universal gravitation and the secElizabeth Carter (1717-1806) was a 'bluestocking', one of those women who defied the prejudice of the age and engaged in pursuits considered more suitable to men. Apart from Italian, she translated from th e French and Greek and wrote poetry.

From Newton to D e Sade |

ond la w o f motion that were the keys . As Voltaire wrote in hi s notebook : "Before Kepler, all men wer e blind, Keple r had on e eye, and Newto n had tw o eyes. " By a huge strok e o f genius, Newton ha d welde d hi s an d Galileo' s idea s o n force s an d had written dow n mathematical equation s that describe d the paths of the planets. He had unified the heavens in one great scheme, extending the rule of physical law to the whole o f the sola r system, and by implication t o the whole universe. It was rightly seen as an intellectual triumph o f unequaled splendor. Man , using observation and reason, had stretched out to touch and understand th e cosmos. It was not Copernicus wh o destroye d th e Aristotelia n universe . Copernicu s wa s a n Aris totelian who accepte d most of the master's teachings. And Galileo was a great pioneer wh o struc k a t the basis o f medieval physics ; but Newton' s achievemen t wa s incomparable, and was acknowledged as such. Voltaire commente d tha t Newto n ha d ver y fe w readers , "becaus e i t require s great knowledg e an d sens e t o understan d him . Everybod y however talk s abou t him." It mattered little that few of those who praised or chatted about the Principia could hav e understoo d it s contents . H e was a cultural idol , rather lik e th e eve n more popularly obscure Einstein. In 1705 he became the first scientist to be knighted, and his status was confirmed in 1727 by his burial in Westminster Abbey alongside the kings of England, a ceremony that made a strong impression o n Voltaire. Newton and Newtonianism became part of European culture to an extent previously exceede d only i n th e cas e of Aristotle. It is true tha t Galileo' s astronomical observations had been widely lauded , but his telescope tended t o get more praise than he did. (Kepler compared it to a magic wand, a cupid's arrow, "more preciou s than an y scepter!" ) Bu t it wa s becaus e o f Newton that th e me n o f the Enlightenment believed in a rational explanation fo r the working s o f the cosmos , and the y extended tha t belie f to a convictio n tha t ma n himsel f wa s rationall y explicable , perhaps only in terms of matter, force, and motion, like the heavens. It wa s Newton' s spiri t that , togethe r wit h Descartes' s mechanica l doctrines , fueled th e extrem e materialism o f Julien Offro y d e L a Mettrie as expressed i n bi s L'Homme machine (1747) , wher e i t i s propose d that ma n himsel f i s nothing bu t matter and motion. The Marquis de Sade quoted de La Mettrie more often than any other writer, and he accepted completely La Mettrie's materialistic view of the universe, including man. One can sense de Sade in La Mettrie's incorporation of sexual ecstasy into philosophy, and in his (convenient) belief that he had to live a life of sensual pleasure in order to achieve his philosophical aims . The success of Newton lurked behind the theories of Rousseau's pet bugbear, the fanatically antireligious Paul, baron d'Holbach, whose Systems de la nature (1770), coauthored with Diderot, propounded th e view that matter in motion was all that existed. On a different plane , it was the apparent complete success of the mechanical description o f the univers e an d the implied invincibility of reason that were to partially underli e the flavo r o f much o f the politica l an d socia l though t o f the Enlightenment. The leaders of the Enlightenment bot h respected scienc e an d used it as a weapon against superstitio n an d religion . Many of them sa w in th e scientific method the only way to attain knowledge. Newton neither foresa w nor intended an y of this. He was not the John the Baptist of the Enlightenment, and he would not have been at home with its ideals. The heralder of the Ag e of Reason left ove r 2 million written words devoted to religion and alchemica l thinking. I t was not a s a propagandist fo r reason that h e was wor-

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shipped. I t wa s his immens e persona l standin g an d hi s scientifi c triumphs tha t elevated the prestige of reason and the empirical approach . And although Newton philosophized, h e built no system of philosophy. His friend John Locke did, and it was his and Newton's empiricism that infused th e Age of Reason. Locke's Essay Concerning Human Understanding (1690 ) i s a key documen t of the Enlightenment. I t has a claim to be the bible of empiricism, and as such is very relevant t o th e histor y o f science. Fo r Locke , experienc e wa s th e onl y sourc e of knowledge. Locke was, as a student a t Oxford, fascinate d by science, especiall y in its experimenta l aspects . Th e interes t remaine d wit h hi m mos t o f his life . I n th e Essay h e writes , obviousl y referrin g mainly t o Newton , "Th e commonwealt h of learning i s not a t this time withou t master-builder s whos e might y designs , i n advancing th e sciences , wil l leav e lastin g monument s t o th e admiratio n o f posterity."7 Locke saw the scientific method as a less than perfect path to true knowledge, but h e nevertheless stated , i n Some Thoughts Concerning Education (1693) , that Newton had show n "ho w fa r mathematicks, applied t o some parts of nature, may, upon principles tha t matter of fact justifie , carr y us i n the knowledg e of some . . . particular provinces of the incomprehensible universe. " Locke's empiricism, a typically Britis h "commonsense " philosophy, and hi s belie f that th e basis o f knowledge i s experienc e followe d by rationa l though t melde d effortlessl y wit h seven teenth-century science. Half a century afte r Locke' s great text appeared, Immanuel Kant, a young theological student, was spending a large part of his time studying Newton. In 1756, before h e wa s twenty , Kan t published Monadologia physica, contrastin g Newton' s methods of thought favorably with those of his rival, Leibniz, who was much more abstract i n hi s approac h t o knowledge. Th e young philosophe r believe d tha t th e only road to scientific knowledge was via the mechanistic approach of Newton. Locke, Bacon, and Newton had a deep, and acknowledged, influence on the central documen t o f the Enlightenmen t i n France , the hug e Encyclopedia, edite d b y Denis Diderot, which was a n attempt to summariz e huma n knowledge. 8 This an tireligious and empiricist tex t was the most typical printed expression o f the Age of Reason. Th e mathematicia n an d philosophe r Jea n d'Alember t wrot e a Discours preliminaire t o advertis e th e Encyclopedic. Hi s her o worshi p i s typifie d by hi s opinion that "Newton, whose way had been prepared by Huygens, appeared at last, and gave philosophy a form which apparently it is to keep." No less.

7

Newton's relationship with Lock e ran aground in 1693, when Newton was suffering fro m what appears to be a mental breakdown. A notorious letter which he wrote to Locke starts, [with modernized spelling): "Sir, Being of the opinion that you endeavored to embroil me with women and by other means, I was so much affected wit h it as, that when one told me you were sickly and would not live I answered t'were better if you were dead. I ask you to forgive me this uncharitableness." It was at this time that Newton broke off his connections with Samuel Pepys. 8 The three Englishmen were all Protestants. Bacon' s mother was fiercely Protestant, Newton was an anti-Trinitarian who grew up in Cromwell's England, and Locke's parents were Anglican with strong Puritan sympathies. Rober t Merton has attributed the blossoming of science in seventeenth-century England to the fact that the Puritan virtues of methodical persistent action, empirical utilitarianism, and antitraditionalism were all congenial to the same values in science. Incidentally, Boyle, the pioneer chemist , and William Harvey, the discoverer of the circulation of the blood, were both Anglicans. O n the Continent, Kepler was a Lutheran and Huygens and Leeuwenhoek both belonged to the Dutch Reformed Church.

From Newton to D e Sade 5

The Diminution of God Read Voltaire! Read D'Holbach! Read the Encyclopedia ! —Gustave Flaubert, Madame Bovary

It is understandable that the skepticism and reason that underlay the scientific revolution fed the Enlightenment, but how did religion come to give qualified support to the Age of Reason? The answer lies partially in the nature o f deism. Newton, echoing Descartes in this respect, had dispensed with the need for a celestial driver ; once the Creator had set the planets in motion, they moved according to his laws and not by his active intervention. Go d could intervene if it was necessary, but i n genera l it wasn't. Thi s semimechanisti c view o f the univers e struck a responsive chord with the deists . Deism was firs t clearl y defined in 162 4 in Lor d Herber t of Cherbury's De Veritate. Deism dispose d t o a lesse r o r greater degree , depending o n it s proponents , with the mystic elements of Christianity: miracles, the Virgin Birth, the Trinity—in fact, mos t of what i s called revelation. Deism suited thos e who gav e reason a very high priority but were not prepared to take the plunge into atheism. Herbert's writings became progressively more acceptable toward the end of the seventeenth cen tury. Newton himself subscribe d t o the Arian heresy that denie d the Trinity . (It is, after all , no t reasonable t o believe that th e So n i s also the Father. ) Many of Newton's contemporaries found their credulity strained by mysteries and miracles, and this doub t was expressed i n numerou s publications , especiall y i n England. Newton's triumphs eased the path for such texts . John Toland' s Christianity Not Mysterious (1696) , publishe d whe n th e autho r was twenty-six, argued the case for reason in religion, as against divine revelation: "A Man may give his verbal Assent to he knows not what, out of Fear, Superstition, Indifference, Interest, and the like feeble and unfair Motives." His book, which triggered a series of deistical texts, was condemned to be burned by the common hangman, bu t Tolan d presse d th e sam e lin e i n Tetradymus (1720) , where, i n th e ne w scientific spirit , he attempted t o give natural explanation s o f a number o f miracles in th e Ol d Testament. H e had allies , includin g Kar l Bahrdt (1741-1792), wh o explained tha t th e thunde r tha t wa s hear d whe n Mose s was o n Moun t Sina i wa s caused by the patriarch's experiments with explosives ! Deism probably reached it s peak in the writings of Matthew Tindal, who, at the age of seventy-three, published a bombshell entitled Christianity as Old as the Creation (1730) . This tex t savage s the Bibl e and claim s tha t th e tru e God is Newton's God, the creato r of the awe-inspirin g universe tha t moves in accordanc e with his eternal laws. All deist s believe d tha t ther e wa s a creator , but mos t o f them, especiall y th e French deists, denied that God took a part in the day-to-day running of the physical universe. Man y of the deist s als o believed tha t Go d made n o moral demand s o n man. H e was manifested in th e ordere d working of the universe , which operate d according t o his universa l laws . Thu s compatibilit y wa s forge d betwee n religion and th e Enlightenment , whose leader s generally wished t o believe both tha t God existed an d tha t hi s universe fel l completel y within the realm of reason.9 This di9

The shift away from th e traditional doctrine of God as ever-present puppet master had a n echo

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chotomy fits in beautifully with Newton's universe, created by God but running according to changeless physical laws. The Principia wa s seen to justify deism , an d many deist s sa w natura l philosoph y (science) , rathe r tha n th e writing s o f th e Church, as the sure way to religion. Deism was effectivel y confine d t o a handful of European countries. Where science was widely practiced and respected, deism flourished. In scientifically back ward Italy , i n th e Iberia n Peninsula , th e Hapsbur g empire , an d easter n Europe, deism wa s almos t nonexistent . Benjami n Franklin , wh o spen t muc h tim e i n France, declare d himself to be a deist, although deis m di d no t gri p the America n colonies. A notable deist, although he arrived a bit late for the Enlightenment, wa s the English freethinker Tom Paine (1737-1809) . Science , he said, proved the existence of God. It was he who wrote the book that gave its name to an era—The Age of Reason, a book he described as a "march through Christianity with an axe."10 Voltaire was a deist. His contempt for organized religion was made clear in statements, books, and letter s and i n his courageous defense of the victim s o f religious wrath, a s in the cas e of the youn g Chevalier d e La Barre, who insulte d a religious procession an d damage d a crucifix. His tongue was wrenched ou t and he was beheaded, in spit e o f Voltaire's protests. Voltaire' s deism reveale d itself particularl y in hi s response to human misfortune and natura l disaster . He was profoundly affected, and his deism strengthened, by the huge earthquake that left Lisbon in ruins on the mornin g of 1 November 1755 . The sheer intensit y o f the shock , the consequent fire, the huge tidal waves, and the great loss of innocent lif e made a deep impression o n Europe. Voltaire included th e inciden t i n his nove l Candide, but hi s first written response was to write a poem on the disaster, mocking Leibniz's clai m that this was the bes t o f all possible worlds, and questionin g God' s involvemen t with th e world . Suc h sentiment s sa t very happily wit h deism , whos e adherent s saw God in retreat from th e natural world.11 The deists never had a n official creed , but deis m was the unofficial religiou s affiliation o f most o f the leader s of the Frenc h Enlightenment , an d th e influenc e of Newton should not be underestimated in this connection. Newton's Legacy Physics and mathematics ar e now on the throne. —Edward Gibbon

The Newtonian breakthrough cast a long shadow. Th e hundred year s between th e death o f the chemis t Rober t Boyle i n 169 1 an d th e Frenc h Revolutio n saw a remarkable peak in the popularity o f science, coinciding with a discernible decreas e of interest in religion, particularly in France. The masterly chronicler o f the times , Tocqueville, noted the "universal discredit " int o which religio n had falle n towar d in the concept of natural law, of which the Dutch lawyer Hugo Grotius (1583-1645) was a great proponent. Natural law was a product of man's nature, not of Christianity or God's will, and Grotius regarded it as so fundamental that not even God could change it. 10 Although William Blake pointed out, "The Perversions of Christ's words & acts are attack'd by Paine & also the perversions of the Bible. Paine has not attacked Christianity." 11 But somewhat less happily with Pope, "And, spite of pride, in erring reason's spite, / One truth is clear, whatever is, is right."

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the end of the eighteenth century . When Napoleon asked Laplace why God did not appear in his great Traite de mecanique celeste, the author quotabl y replied, "Sire, I have no need of that hypothesis. " The scientist s o f th e seventeenth-centur y scientifi c revolutio n wer e o n th e whole no t Enlightenment men. They generally aligned themselves with moderate religious an d politica l views, eschewing th e growin g disrespect fo r tradition an d authority that were a feature of metropolitan society in their day. But when, in 1767 the Baron von Grimm wrote "Enlightenment is spreading on all sides," the image of science had never heen brighter. The Ascent of Science

The Enlightenmen t i s inseparabl e fro m th e ascen t o f science i n th e seventeent h century. Th e prophet s o f a ne w ag e nearl y al l sa w Newto n a s on e o f it s mai n builders, and science as one of its essential building blocks. By the middle of the eighteenth century, science had attracted a rapidly expanding audience. At the beginning of the centur y there were only four scientifi c journals, of which the heavyweights were those produced by the Royal Society in London an d th e Academi e Royal de s Science s o f Paris. B y 1800, excludin g medica l journals, about seventy-five journals were appearing regularly. Scientific societies sprang up all over provincial France and were imitated in England, most notably in the "Luna r Society" of Birmingham (which was attende d by James Watt of steam engine fame, Joseph Priestley the chemist, an d Charle s Darwin's grandfather Erasmus Darwin) . The Literary and Philosophica l Societ y of Manchester wa s founded in 1785 . In America the effort s o f the tireless Benjamin Frankli n led t o the forma tion o f the America n Philosophica l Societ y i n Philadelphi a i n 1744 , an d Joh n Adams had a strong hand in th e establishmen t o f the America n Academy of Arts and Science s in Bosto n in 1780 . But the influenc e of science went fa r beyond th e growth of a new clas s of scientific amateurs. During mos t o f the eighteent h century , du e i n grea t measure t o Newton , th e highest quality of man was seen as his ability to use his reason. Which is not to say that religion died, or that reason ruled, but the civilizing effect o f reason, its appeal to the moderat e side of man, to his tolerance , flowere d i n Europe . Literature was not unaffected . The writing of an age provides insight int o its spirit. It would be misleading to suggest that the Age of Reason bred reasonable writers, and yet many of the greatest English and French writers of the age were characterized by qualities that appealed as much, if not more , to the intellec t o f the reader as to his passions. 12 In general, the authors flourishin g during the earlie r years of the century displa y an intrinsic respect for order and reason, and although it cannot be said that many had serious scientific interests , o r that the y were comfortabl e with th e scientifi c outlook, it is certainly arguabl e that science , usuall y meanin g Newton' s science , affecte d th e way that men of letters wrote. In England , elegance largely displace d th e vigo r o f Restoration prose an d th e blood and sweat of Elizabethan writing. Burns and Blake were not enamored of sci12

Gibbon's Decline and Fall of the Roman Empire is a wonderful example of the Enlightenment' s balanced rationalism an d clear-sighted view of man's estate. And his style is finger-lickin' good.

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ence and reason (or elegance), but Pope, Johnson, Addison, Steele, and Defoe, with their wi t an d thei r urban e satire , spoke to th e thinkin g a s much a s to the feeling man, eve n i f the y ha d doubt s abou t th e benefit s tha t science , especiall y i n th e hands of the Royal Society, was supposed to bring to mankind. Alexander Pope, the outstanding writer of his age, was subtly shaped by the rise of science. His Essay on Man, very popular in Enlightenment Europe in translation, was typical i n this respect. In it Pope says that we will "Laug h where we may, be candid where we can, / But vindicate the ways of God to man." He then goes on to speak very much o f man an d ver y little of God. A deist would have felt reasonably comfortable with Pope. God was the Creator, and there his role ended. Voltaire was ecstatic: "the finest , mos t useful, sublimes t didacti c poe m ever written." Pope , although he was far from avers e to making fun of the new science, was a great admirer o f Newton' s genius . Pope' s thoughtfu l humanis m spok e t o th e Englis h an d French HM S of the time , with it s clarity , its balance o f optimistic reaso n and reasoning doubt. Today's blind antirationalists contras t crudely with Pope's belief that man's passions need not be the enemy of his reason but could coexist constructively with it. The much quoted lines : Know then thyself, presume not God to scan; The proper study of mankind i s Man. are followed by a very much unquoted line that reveals th e tenor o f the times an d Pope's underlying respect for science: Go Wond'rous creature, mount where Science guides. 13 Other Englis h writer s wer e similarl y supportive . A s earl y a s 1668 , wel l befor e Newton's reputation was made, the poet John Dryden had enthused , "I s it not evident in these last hundred year s (when the study o f philosophy ha s been the business o f all th e Virtuos i i n Christendom) , that almos t a ne w Natur e ha s bee n re vealed t o us," an d "mor e nobl e secret s i n optics , medicine, anatomy , astronomy, discovered than in all those credulous and dotin g ages from Aristotle to us?" Not everyone was so enthusiatic. Jonathan Swift's praise was selective. The king of Brobdingnag declared that scientists "d o more essential Service to Country, than the whole Race of Politicians pu t together," but Swif t ridiculed what he saw as useless science . In Gulliver's Travels (1726 ) he poke d fun a t the apparentl y pointles s experiments reported to the Royal Society. In the fictional Grand Academy of Lagado there were plans for extracting the sunshine i n cucumbers and building house s from th e roo f downward . Swif t prophesie d th e downfal l of Newton's cosmology, but i t is significant that science , and th e activities o f the Royal Society, had a high enough profile to warrant his attention. Wher e he and other early eighteenth-century Englis h writers , suc h a s Addison , wer e critica l o f scientific matters, thei r wi t was rarely directed at the major natura l philosophers , bu t rather a t the "virtuosi, " the dabblers in science. 13 As Pope lay dying, he was asked by a friend i f he wished to see a priest. Typically of the age , he replied, "I do not think it essential but it will be very right and I thank you for putting me in mind of it."

From Newton to D e Sade |

In eighteenth-centur y Franc e th e glorificatio n of reason exceede d i n intensit y anything i n th e res t o f Europe. Within a period o f a few years there were a t least sixty printings o f Pope's Essay on Man, as well as enormously influential translations of the books of John Locke. A plethora of hooks, essays, pamphlets, and meetings advocated deism o r atheism. Translations were made of all those works, fro m the Greeks to Hobbes, considered to he atheistic or anticlerical enoug h to serve the cause of rationalism, although much of the output was anti-Church rather than proreason. The power of the Catholi c Church in France was still such that French in tellectuals ofte n ha d t o choos e betwee n dangerou s defianc e o f the authoritie s o r humiliating compromise . Thus, i n 1749 , when th e grea t naturalis t Comt e Buffo n published th e firs t volume of his Histoire naturelle, a theological committee at the University of Paris made it clear that he would run int o difficulties unles s he modified th e text , especiall y wher e i t deal t wit h th e creatio n o f th e Earth . Buffo n backed down on all "that might be contrary to the narration of Moses." As to his description o f the birth of the planets , Buffo n explaine d tha t they were "pure philo sophical speculation. " H e got away with it , but on e can understand th e Church' s nervousness; Buffo n ha d presente d a picture o f the Earth , and it s life-forms , tha t reached fa r into the past , one that took into account the possibilit y o f the gradual emergence of new species. This hardly tied in with Genesis. The French took much from the English. Voltaire vigorously advertised the Principia, Locke's Essay Concerning Human Understanding, an d Bacon's ideas. Grimm declared, "Withou t the English, reason and philosophy would stil l be in the mos t despicable infancy in France." In France, the demand for religious toleration, the atmosphere of skepticism, th e esteem accorde d t o the non-Christia n classica l pas t an d t o science—i n short , the Enlightenment—found vigorou s expression in the writings o f the philosophes , a n informal grou p o f writers, thinkers , scientists , mathematicians , an d others . They had (than k God!) no manifesto. They saw both churc h an d stat e a s dogmatic, dishonest organization s an d searche d for eternal value s no t in religious, national, o r cultural roots but in reason and personal experience. Their faith in human reason, and specificall y in science , wa s almos t unlimited . Wit h reaso n al l coul d b e explained, without need for revelation or mysticism. The attitude o f the philosophe s to Newton was a major influence on the French Enlightenment. The philosophes wer e not in general knowledgeable enough to understand th e full meaning of Newton's work, although a few were mathematicians o r naturalists. In France the officially accepte d physics had been that of Descartes. Perhaps partly because o f chauvinism, th e vas t superiorit y o f Newtonian mechanic s too k som e time to be accepted, but once it was, it became all the rage in France. Newton's conques t o f France was overwhelming . I t was no t s o much th e me chanics in itself that fire d th e Frenc h but rather a conglomeration o f ideas that included the superiority of the scientific method and the concept of an overall order in the universe, an order that was in principle subject to inquiry and ultimately understandable. To the philosophes, the scientific method seemed to be applicable to almost any fiel d o f human interest . Abov e all, if the cosmos could be shown to he explicable by simple universal laws, then perhaps there really was an ordered universe, and perhaps the affairs of men could be ordered by reason. No comment. Voltaire was not alone in his hope that the scientific method could be applied to history, and Coiidilla c suggested that the whole o f philosophy be rebuilt using the

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sciences a s a model. D'Holbac h was convince d tha t scienc e wa s th e salvatio n of mankind. Baron d'Holbach, a German millionaire, ran a salon in Paris that was a notorious meeting place for scientists, atheists , deists, and antiestablishmen t type s in general. The English chemist Joseph Priestley reported that all the philosophical person s to whom he was introduced there were "unbelievers in Christianity, and even professed atheists. " D'Holbac h was on e o f the man y a t that tim e wh o believed , lik e Priestley, tha t scienc e woul d brin g abou t a bette r lif e fo r mankind, an d tha t th e Church was standing in the way, preventing the spread of scientific teaching: "I t is as a citizen that I attack religion, because it seems to me harmful to the happiness of the state, hostile t o the mind o f man, and contrary to sound morality." But caution was the rule: when h e published hi s Systems de la nature in 1770, he did so under the nam e o f a man wh o ha d bee n dea d fo r ten years . The book, which i s an enormously long and unorganized defense of materialism and atheism, denied the existence of the sou l and o f God, and single s out necessity as the drivin g force behind behavior. Predictably , i t wa s condemne d an d ordere d t o b e burne d b y th e Par lement of Paris. The author was to be identified, arrested, and punished . I t is sai d that the ten people who knew that d'Holbach was the author kept silent fo r twenty years, until he died. A taste of d'Holbach's viewpoint is contained in the following passage, which carries definite Newtonian undertones: Man is the work of Nature; he exists in Nature; he is submitted to her laws. He cannot delive r himsel f fro m them , no r ca n h e ste p beyon d them , eve n i n thought. Instead therefore, o f seeking Nature, let him learn her laws, contemplate her forces, observe the immutable rules by which she acts; let him apply these discoverie s to his ow n felicity, an d submi t i n silenc e to her mandates , which nothin g ca n alter; let him cheerfull y consen t to ignore causes hidde n from him by an impenetrable veil; let him without murmuring yield to the decrees o f universal necessit y whic h ca n never be brought withi n his compre hension, no r eve r emancipat e hi m fro m thos e law s tha t ar e impose d upo n him by his essence. Reading these lines , an d thos e o f scores o f other eighteenth-centur y writers , on e could be excused fo r hoping that the Age of Reason was indee d just over the hori zon. I t was a time i n whic h Condorce t believed i n th e "infinit e perfectibility" of man an d o f science, and coul d writ e o f a day, coming soon, when, "th e su n wil l shine onl y on fre e men. " Th e political Freedo m Train has been delayed , but Condorcet's optimism wa s a product o f the times , times i n which th e standin g o f science and scientists was higher than it had ever been. The Scientist as Man-about-Town Everybody has begun to pla y at being the geometer an d the physicist . —Voltaire, Correspondence, IV.

Science had become a matter of popular concern. Newton's fierce (and often under handed) campaign against the great German philosopher and mathematician Leib niz—fought ove r the righ t t o be considere d th e originato r o f the calculus—wa s a

From Newton to D e Sade |

talking point i n the cour t of Charles II, although very few of that licentious assem bly could have known what the calculus was about.14 The same TV talk-show level of discussion wa s to befall relativity i n the twentieth century . Fro m the middle of the eighteenth century , scientists wer e more than welcome in the fashionable society of Europe. In Paris, public lectures on science attracted enthusiastic audiences . Bewigged gentleme n an d fan-flutterin g ladie s exchange d chitcha t abou t physic s and chemistry. The English author Oliver Goldsmith wrote, "I have seen as bright a circle o f beauty a t th e chemica l lecture s o f Rouelle a s gracin g the cour t o f Ver sailles." Th e effect s o f stati c electricit y wer e a popula r part y piece ; men-about town linke d hand s an d jumpe d abou t a s a weak electri c curren t passe d throug h them. Because of Newton, the orrery , a moving model o f the sola r system, became popular in the eighteenth century . The prestige of science i s reflected i n th e larg e number of aristocrats, and eve n heads o f state, who too k enough interes t t o personall y carr y out experiments , or have them carried out. Science penetrated to the bedrooms o f kings. The next time you are in the Louvre , look at the paintin g of Madame de Pompadour by Maurice Quentin de La Tour. One of books on the table next to which she sits is entitled Encyclopedia. There is no doubt whatsoever that this is a volume of the enormous and notorious encyclopedi a edite d b y Deni s Diderot : Encyclopedic: ou dictionnaire raisonne des sciences, des arts et des metiers. Diderot was in many ways the most human characte r among the philosophes. 15 He appear s t o wave r betwee n atheis m an d deism , an d althoug h n o scientist , h e shared th e belief of many o f the philosophes tha t scientifi c knowledge is the onl y reliable knowledg e tha t w e have . Th e encyclopedia , th e firs t volum e o f whic h came ou t i n 1751 , specificall y declared it s deb t t o Bacon , Newton, and Locke . It contained numerou s article s o n scienc e an d hundred s o n technology—o f whic h d'Holbach contribute d ove r 400. Rousseau provided an article on music. A glance at the encyclopedia will disillusion anyon e who believes that technology was practically nonexistent befor e the Industrial Revolution. It was the unfulfilled drea m of the philosophes to unite science and technology, but science had little to offer technology at that time. The editor also failed in his wish to supersede religion with science, but the great text helped to change the intellectual flavo r of Europe, edging it toward reaso n an d scienc e an d awa y fro m unquestionin g faith . A s th e editor s wrote, "Everything must be brought to light boldly, with no exceptions and unsparingly." In a letter to Voltaire, Diderot, who was an atheist, wrote, "Science has done more for mankind tha n divin e o r sufficient grace. " And this came from a man wh o was practically scientifically illiterate and who distrusted mathematics . The encyclopedia was far too subversive for the religious authorities. The Jesuits 14

In the course of this prolonged argument, each implied that the other was a deist. The fact that Newton's mechanics ha d shown that the planets coul d revolve without th e help o f God was one of the standard example s that deists would pull out to prove their case . But although Newto n was a Dissenter, he was certainly not a deist, and he had state d that if necessary God could mak e minor adjustments to the paths of the planets i f they strayed. Leibniz declared tha t "Newton' s God is a clumsy watchmaker." God was a hetter workman than this and had no need whatsoeve r to interfere with the mechanism o f his universe. In this sense it was Leibniz's universe tha t should have been the model fo r the deists, but in fact it was Newton who was almost alway s invoked in this context. 15 His letters to his mistress, Sophie Volland, provide a fascinating insight int o his times.

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and th e Church wer e enraged . Diderot was interrogated by the civi l authorities. 16 When seven volumes had appeared, the Council of State banned the encyclopedia : "The advantages to be derived from a work of this kind, in respect to progress in the arts an d sciences , ca n neve r compensat e fo r the irreparabl e damag e tha t result s from it in regard to morality and religion." It was said that the subsequent volumes , 8 to 17, were finally published because of La Pompadour's influence o n King Louis. Perhaps that is why, in her portrait, she has volume 9 next to her. (I wonder if Louis was awar e o f the poe m i n whic h Didero t recommends stranglin g king s wit h th e bowels of priests?) It is of significance that it is the Encyclopedic, predominantl y a text on scienc e and technology, that is often take n to be the most representative publication o f the Enlightenment. Th e presence in th e encyclopedi a of a large number o f articles o n medicine i s understandabl e i n th e ligh t o f the Enlightenment' s obsessio n wit h health an d the concept o f science as the means fo r curing man's ills , both literall y and metaphorically . Th e greatest teacher of medicine a t the time , the famou s Hermann Boerhaave, professor at Leyden in the Netherlands, regarded himself as a disciple o f Newton, on whose work he lecture d an d whose method s h e attempte d to employ in his work. In 1715 he published Oratorio de comparando certo in physicis, in which th e Newtonian theory of gravitation is given the place of honor. Boer haave insists that we must always be guided by experiment and observation, aided by mathematics an d the power of reason. His influence was remarkable; he and his students an d colleagues helped to spread the Newtonian message throughout western Europe. The Leyden school o f medicine als o paid homage in thei r lecture s to the empirica l principles o f Bacon and Locke , the othe r two members of the British trio. One of Boerhaave's students was Julien de La Mettrie, the extreme materialis t whom we met earlier. As we noted, de Sade was a follower of de La Mettrie, and so we ca n trac e a direc t lin e o f thought fro m Newton' s mechanica l univers e t o d e Sade's hedonistic , materialisti c pictur e o f man. I t would b e har d t o imagin e tw o more dissimila r characters , an d ye t th e shado w o f Newto n hover s behin d th e Frenchman's mechanisti c philosophy . H e specifically mention s Newto n in par t 3 of Juliette, where he accuse s the physicis t o f sidestepping th e proble m of free wil l in a deterministic universe—a problem to which we will return. Another book on La Pompadour's table appears to me to be Montesquieu's masterpiece, De 1'Esprit des lois (1750). This rambling, highly controversial, and highly influential treatise on the origin s of law, now regarded as a seminal text in sociology, was reprinted twenty-two times in eighteen months. Ther e was no doub t as to Montesquieu's inclinations: "Reaso n is the most perfect, most noble, and mos t exquisite o f all ou r faculties." And again : "I have not draw n my principles fro m m y prejudices but from the nature of things." It could have been Newton speaking, and it is clear that Montesquieu felt himself to be part of the scientific tradition. He was hardly suitable bedside reading for the king's mistress. His book attracted the wrath of the Jesuits, who sa w through it s feebl e li p servic e to Christianity. But they ha d no hold over La Pompadour. "Madame Whore," as some called her, was a well-read woman who read what sh e liked and whose favorite acquaintances include d math ematicians, natural philosophers , and assorted rationalists . 16

Diderot fought an incredible uphil l battle to get the encyclopedia published . On top of official opposition, h e was unaware for some time that his publisher wa s censoring som e of the article s without hi s knowledge .

From Newton to D e Sade |

Science was fashionable, and not onl y among the aristocracy. The middle class had als o been infected . In France an increasing numbe r of schools abandoned th e almost total emphasis o n the humanities and religious studies that had typified education i n most European countries for so long. The atheist Swis s millionaire an d philosophe Claude-Adrien Helvetius, in his popular book De 1'esprit (1758) , advocated a complete overhau l o f the educationa l syste m i n France , and incidentall y hinted that a drastic change in education could only be made if there was a political revolution first. Theolog y and history were both branded as weapons of the establishment. Th e essentia l ste p wa s t o remove educatio n fro m th e contro l o f the Church. Education was to be provided to all, irrespective o f sex or age. Dead languages were to be removed fro m th e syllabu s an d replaced by the stud y of science arid technical subjects. Political an d religiou s dictatorship s burn books . De 1'esprit wa s burned—an d the sciences began to be widely taught. For the first time, many schools established teaching laboratories. When the Old Regime fell and when the young Republic had to face the threat of war, scientists willingly helped in setting up a war industry. At that time, Lavoisier and the great mathematicians Laplac e and Lagrange were among the members of a committee appointe d t o revise weights an d measures . The y produce d the metri c system, officially adopte d on 25 November 1792. As has happened afte r othe r revolutions, political control o f the French Revolution passe d ou t o f the hand s o f the moderat e leaders . Th e Reig n o f Terror wa s driven by ambitious fanatics who had little patience with intellectuals. The revolutionary (and would-be scientist ) Jean-Paul Marat led a mini revolt against mathematically based science, probably partly motivate d by his own academic limita tions. The epithet "elitist " (as applied t o the monumental mathematica l wor k of Laplace, Lagrange, Fourier, and others) and the banner: "science for the people" are unpleasantly reminiscent o f the populist invective used in more recent times by the scientific lackey s of dictatorial regimes. The Academy of Sciences was abolished . But i n 179 3 Mara t wa s murdere d i n hi s bat h b y Charlott e Corday , an d th e political movemen t that he had led—th e Jacobins—was destroyed. French scienc e survived a politically motivate d crisis, the Reign of Terror passed, but th e Age of Reason was over.

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7 From Rousseau to Blake : The Revolt against Reason I am the eye with which the Univers e Beholds itsel f and knows itsel f divine. —Percy Bysshe Shelley, "Hym n to Apollo "

When h e wa s at school a t Eton, Shelle y spen t much o f his leisur e i n the stud y of "the occul t sciences , natura l philosoph y an d chemistry, " an d hi s pocke t mone y was spent o n "books relative to these pursuits, o n chemical apparatu s an d materials." Shelley was fascinated by the voltaic pile of Volta and had dream s of a world transformed by electricity. At Oxford Universit y the contents of his room include d "crucibles,... an electric machine, an air pump, the galvanic trough, a solar microscope, and large glass jars and receivers." This was the door to nature chosen by the archetypal Romantic poet who was later to approach the natural world almost solely through the gates of his imagination: "Earth and Ocean seem, To sleep in one another's arms, and dream. " Shelley had, in his youth, fallen under the influence of one of the Lunar Society, Dr. James Lind , an d ha d rea d suc h antireligiou s writer s a s Lucretiu s an d Con dorcet. It was the publication o f his Necessity of Atheism that resulted i n his being expelled from Oxford in 1811. That year, this son of a moneyed baronet wrote to his friend Elizabeth Hitchener that " I am no aristocrat, nor 'crat' at all, but vehementl y long for the tim e when me n may dare to live in accordanc e with Nature and Reason—in consequence , with Virtue , to which I firmly believ e tha t Religio n and it s establishments, Polit y an d it s establishments , ar e the formidabl e though destruc tible barriers." Lik e all the Romantics , he had been shape d by the French Revolution—but also by science. In Shelley' s lon g poern Prometheus Unbound, Heave n is asked, "Heaven , has t thou secrets?" to which the author supplies the Newtonian reply, "Man unveils me; I have none." The young poet saw the natural world through scientifi c glasses. On his honeymoo n wit h hi s sixteen-yea r ol d bride , Shelley , himsel f onl y nineteen , began to translate the works of the French naturalist Buffon. Reading the quotation at the beginning of this section, it is therefore natural to assume that "the ey e with which the Universe beholds itself" is Science. A reading of the whole poem makes it completely clear that the ey e is definitely not science. It is poetry. Prometheus Unbound wa s writte n i n Ital y in 1819 ; th e me n o f the Enlighten ment had die d long ago, and times were changing. By the 1820 s the caus e of rationalism was in retreat. The Industrial Revolution was approaching, and the love affair between science, reason, and thinking men was cooling. In his introduction t o

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the poem, Shelley, the once youthful reformer , says that its aim is "simply to familiarize the highly refined imagination of the more select class of poetical reader with beautiful idealisms o f moral excellence." O h dear. Shelley was not the first intellectual to become disillusioned b y science and the spirit of the Enlightenment an d to move toward the views expressed by Rousseau as far back as 1749. Rousseau, in his Discourse on the Arts and Sciences, had seen a threat in the development o f science, technology, and European culture in general. For him they had all led man away from the naturally good state of the noble savage and brought about his moral corruption. The Enlightenment emphasis o n reason was a provocation to those who feare d that imagination would be smothered by mechanics. When the backlash came, history followe d it s predictable course : the heroes o f the Ol d Regime became the vil lains of the new, and those who revolted against what they saw as the rule of reason usually saw Newtonianism and science as their archenemies. Willia m Blake, who associated rationalism with the rise of the machine-based industry that he loathed, was deepl y offende d b y Bacon, Newton, and Locke . "Bacon' s Philosophy," wrot e Blake, "ha s Ruin' d England," and h e identified Locke' s philosophy an d Newton's mechanics with the hated machine : I turn my eyes to the School s & Universities o f Europe And there behold the Loom of Locke, whose Woof rages dire, Wash'd by the Water-wheels of Newton: black the cloth In heavy wreathes folds over every Nation: cruel Works Of many Wheels I view, wheel without wheel, with cogs tyrannic Moving by compulsion each other, not as those in Eden, which, Wheel within Wheel, in freedom revolve in harmony and peace. Newton as culprit appears again in the poet Cowper's remark to Blake: "You retain health an d ye t ar e a s ma d a s an y o f us all—ove r u s all—ma d a s a refuge e fro m unbelief—from Bacon , Newton, an d Locke. " (th e Trinit y again) . Later , th e poe t Coleridge was to write tha t "th e soul s o f five hundre d Si r Isaac Newtons go to th e making up of a Shakespeare or a Milton." Even in this century Newton still remains a target for those attacking rationalism an d the mechanical universe : Here we all are, Back in the moderate Aristotelian city Of darning, and the Eight-Fifteen, where Euclid's geometry And Newton's mechanics would accoun t for our experienc e W. H. Auden, "For the Time Being" When the tables were turned it was in Germany that the revolt against Newton find reason sprang up most virulently. Goethe versus Newton Anyone who attempts to determine the extent of the Kingdom of God with the yardstick of reason faces utter misguidance. —AI-Qazwini

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The Enlightenment took on different color s in different countries . It was above all a movement that grew up i n Britai n and France . Rationalism failed t o grow healthy roots in eighteenth-century Germany, where the antirationalists wer e busy as early as the 1770s . It has been remarked that Germany passed straigh t to Romantic irrationalism withou t stoppin g at rationalism. Rationalis m in Germany , in contras t to France and England, hardly touched the middle class, or indeed the rest of the population, making a limited mark among a handful o f writers an d intellectuals , suc h as Lessing. When the middl e clas s di d wak e up , i t was t o the musi c o f Romanticism. By a perverse twist of history, it was Newton who was partly to blame. An important turnin g poin t cam e when Goeth e read Newto n an d becam e intereste d i n the nature of color. Goethe considered himsel f to be primarily a natural scientist. H e viewed Newton's use o f a prism to split light into a spectrum of colors as being symbolic of an attempt t o "spli t th e unit y o f Nature." Newton had bee n "puttin g Natur e o n th e rack." Notice the vague use of evocative, imaginative, but meaningless generalities. Goethe magisterially proclaimed, " A great mathematician wa s possesse d wit h a n entirely false notion on the physical origin of colors; yet owing to his great authority as a geometer, the mistakes which h e committed as an experimentalist lon g became sanctioned in the eye s of a world ever fettered i n prejudices." Goethe set out to construct an alternative theory of color. It took Goethe nearly twenty years to produce hi s Theory of Colors, his longes t book, and the one that he thought the most of. It contains very little science. Colors, in sharp contrast to Newton's treatment, are regarded primarily as objects of sensory enjoyment. It appealed more to painters than scientists, and indeed i t was eventually annotated by the antiintellectual English painter Turner, one of whose paintings was verbosel y entitled Light and Colour (Goethe's Theory): the Morning after the Deluge, Moses Writing the Book of Genesis. Colors were just a beginning, Goethe had a greater venture: to topple the spiritu ally empty edifice o f Newtonianism. Why he turned agains t Newton is a matter for speculation. The Sturm und Dran g (Storm and Stress) movement, with which Goethe was associated, laste d less tha n a decad e an d wa s a middle-class, antirationalis t move ment, a reaction to the perceived materialism of the French philosophies. 1 This materialism wa s see n a s a n inevitabl e consequenc e o f the mechanical , Newtonia n universe. T o the Frenc h an d Englis h Enlightenment th e univers e wa s potentiall y explicable using reason and science ; to the Stur m und Dran g movement it was an enigma hidde n behin d a curtai n o f mystery, to be reache d a s muc h throug h th e imagination a s through reason, and , fro m man' s poin t o f view, basically meaningless. A new buzzword emerged: Naturphilosophie. Th e German intellectuals abandoned th e rationa l approac h t o knowledg e an d substitute d intuitio n an d meta physics of the obscur e variety. Naturphilosophie wa s a flag aroun d whic h man y German writers an d philoso phers rallied . Heinric h Heine' s commen t o n on e o f them (Schelling ) say s muc h about the whole movement: "he does not feel himself at home in the cold heights of 1 An exception t o the rejection of the philosophes was the welcome given to their writings, and those of Locke, by German Protestants. The Thirty Years' War had lef t them with a thirst for religious toleration.

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logic, he i s happy to slip ove r into the flower y valle y o f symbolism." Madame de Stael wa s wittie r an d bitchier , avowin g tha t Germa n Romanti c philosoph y "spreads ove r al l thing s th e darknes s whic h precede d Creatio n but no t th e ligh t which followed." Naturphilosophie ha s been used to cover a variety of philosophical stances. Its adherents empathize d with Rousseau's emphasis o n man's instinct s and sensibilities, an d his desire for a culture that would include the virtues that he saw i n ancien t civilization s an d i n primitiv e societies . Naturphilosophie share d Spinoza's doctrin e tha t Go d reveal s an d fulfil s himsel f i n th e materia l world . Goethe said, "The world is the living visible Garment of God." But that world could not b e understood by Newtonia n mechanics. A s Schille r pu t it , i n Maria Stuart, "reason finally leads men astray." Observation, the suprem e Baconian virtue an d th e foundatio n of science, was demoted. Artisti c genius was now th e crownin g human virtue : "Th e geniu s doe s not observe. He sees, he feels," said Johann Lavater the Swiss founder of the antirational religious and literary movement known as Physiognomies, The perio d o f the Stur m un d Dran g movement i n German y has bee n labele d "Romantic," but Goeth e himself was not a romantic. Lik e the philosophes, he was suspicious o f mysticism an d wa s not religious; unlike them, he was violently opposed to the mathematical basis that Newton had constructed beneath the physical universe. Likewise , his compatrio t Schelling , althoug h h e concede d tha t reaso n had it s place, rejected th e ide a of a rational universe. 2 The predominant powe r in the universe was evil, and man himself was driven as much by his irrational natural impulses a s by his reason. For Goeth e and hi s compatriots , man's greates t gift wa s tha t h e coul d sa y "I. " They may be right, but thi s doesn' t excus e their irrationa l anti-Newtonianism, of which Hege l was on e o f the saddes t examples . Hege l completely misunderstoo d the Principia, an d repeatedl y misrepresented i t i n his lecture s i n Berlin. 3 Bu t he was th e Her r doctor professor, an d no t on e o f his audienc e eve r ha d th e nerv e t o point ou t hi s errors . Th e ma n wh o wrot e tha t "Reaso n i s th e Sovereig n o f th e World" was prepared to sacrifice reason if it suited his prejudices. The antipathy to Newton in Germany was bolstered at the turn of the century by Schlegel's translatio n o f Shakespeare's plays , which se t of f a strong Romantic revival: Shakespeare was hardly a typical Enlightenment man. The German Romantics believed, or wanted t o believe, despite clear evidence to the contrar y in Newton's writings, that he had confused mathematics with reality, a reality that was not susceptible to scientific analysis. The Infection Spreads

Naturphilosophie wa s picke d u p enthusiasticall y o n a visi t t o German y b y Wordsworth's grea t friend , th e Germanophil e poe t Samue l Taylo r Coleridge. Coleridge was one of those who held that higher reason, which is basically intuition , 2 Antirationalism, often combined with mystic nationalism, has a distinguished history in Germany. Perhaps the greatest German writer of the twentieth century, Thomas Mann, also pokes quiet fun at the rationalist intellectual, as represented by Settembrini in The Magic Mountain . 3 Hegel claimed (incorrectly) that Newton had not proved Kepler's laws and that he had "floode d mechanics with a monstrous metaphysics." See Hegel's Philosophy of Nature, trans. A. V. Miller (Oxford: Oxford University Press, 1970).

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has the power to uncover truths that were beyond the reach of the senses and of the "lower" reason, which o f course included science. Naturphilosophie, an d its explicit anti-Newtonianism , appealed strongl y to a number of English authors. Thomas Carlyle enthusiastically embraced its assumption that science is an acceptable human activity but not adequate to explain reality. In his almost unreadable Sartor Resartus, he contrasts the superficiality of scientific reason (Verstand) t o the "higher" reason (Vernunft): "T o the idea of vulgar Logic what is man? An omnivorous Biped that wears Breeches. To the eye of Pure Reason what is he? A Soul, a Spirit, and divine Apparition.... Deep-hidden is he under that strange Garment." The garment, as for Goethe, was matter. It is clear that the "high er" reason was not really reason at all. But then reason was no longer fashionable. Naturphilosophie, a t first sigh t paradoxically, had a n important role in the sci entific motivatio n of some of the greates t scientists o f the nineteent h century . Coleridge was a friend o f the prominent Englis h chemist Humphry Davy, with whom he discusse d philosophy . Th e Danis h physicis t Han s Christia n Oerste d wa s a friend o f Schelling, and both he and Ampere in France were deeply affected by the spirit o f Naturphilosophie. I t was th e all-inclusivenes s o f its visio n o f the worl d and its emphasis on the existence o f universal underlyin g causes that appeale d to the scientific impulse to find such causes for the behavior of the physical world. To this day, the same impulse drives those who are attempting to find a theory that explains all the force s of nature. One can still find those who see Goethe's holistic view of nature as being an antidote to the divisivenes s tha t they claim t o see in modern science . Thi s clai m is not too intelligible i n the light o f the fact that modern universities ar e packed with interdisciplinary (holistic? ) research projects—and no t becaus e of Goethe but be cause scientists realize d long ago that nature is a single entity. It doesn't nee d th e higher reason to see that. The Individual Mind It is fair t o say that by 1820 the highest quality in man was considered to be no longer his reason but his ability to understand himsel f and his place in nature . Reading much o f the literatur e o f the time , one ca n detec t th e shif t i n th e balance betwee n thinkin g an d feeling . Th e individua l increasingl y becam e th e hero o f poems—not th e individua l o f Donne's poems, who coul d addres s God in time s o f trial, but a post-Enlightenment her o wh o ha d t o fac e lif e an d mor tality alone . English poetry became subjective . Th e secondar y title o f the cen tral poe m o f the Romanti c era, Wordsworth' s grea t Prelude, wa s Growth of a Poet's Mind. Wordsworth was not unusual for the times, in that his attitude toward science, like Shelley's, suffered se a changes. The young man who wrote, "Science wit h joy saw Superstition fly" later wrote, in the preface to the second edition o f his Lyrical Ballads, tha t if me n o f science eve r di d anythin g tha t reall y mattered, then poets would b e willing t o write abou t it . Perhaps under the influenc e of his frien d th e great Irish mathematician William Rowan Hamilton, Wordsworth condescended to write his lines honoring Newton: And fro m my pillow, looking forth by light Of moon or favouring stars, I could behold

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The antechapel where the statue stood Of Newton with his prism and silent face , The marble index of a mind for ever Voyaging through strange seas of Thought, alone. Wordsworth as a young man had had a brief love affair with a French girl, and with the French Revolution: "Bliss was it in that dawn to be alive." But the Reign of Terror brought disillusionment , an d h e turned inward . Th e introverted themes of Romantic poetry contrast sharpl y with the naive optimis m o f the philosophes. With Wordsworth, mortality is often just under the surface, as it was with Keats, another child of his time, who believed, because of the Enlightenment, that we are material beings in a material univers e and that we must accept that fate. W e are mortal, but with n o divin e shoulde r t o lea n on , an d w e wil l neve r understan d th e deepes t truths, which, contrary to all the protestations of the Enlightenment, neither reason nor scienc e ca n reach . Keat s had th e tragi c sens e o f life. H e is recognizably a Romantic; there was no Enlightenment Utopia waiting for him. Reason in the Shadow s What Reaso n weaves, by Passion is undone. --Alexander Pope

At the end of the eighteenth century, rationality (Verstand, th e "lower" reason) was being downgraded all over Europe. The Romantics ruled the intellectual roost . At a dinner give n in 1817 by the second-rate English painter Benjamin Haydon, and attended by Wordsworth, Keats, and other writers, it is said that the toast was "Newton's health, and confusion to mathematics." Was the Enlightenment dream of a Utopia ushered in by science killed by the Industrial Revolution , which wa s bor n betwee n 178 0 an d 1820 ? Is it simplisti c t o suppose that many saw the social ravages of industrialization an d fel t that science, mistakenly identifie d with technology, had delude d man int o a false belie f in th e Garden o f Eden ? On e wh o definitel y sa w thing s thi s wa y wa s Willia m Blake' s friend, the painter Samuel Palmer, who looked at the expanding and ugly urban industrial landscap e an d crie d out , "I f so-called scienc e bid s u s giv e up ou r faith , surely we have a right to ask for something better in return!" And the clai m of the French Revolution that it would put scientifi c principles int o practice rang hollow in the ghastly realit y of the guillotine . Th e culminatio n o f the Enlightenment , th e great intellectua l revol t o f rational secularism , ha d ende d i n th e slaughte r of the Reign of Terror. The status of science was visibly eroded during these years. Thomas Carlyle dismissed the scientist's claim to have revealed nature's secrets : "Scientists hav e been nowhere but where w e also are; have see n some handbreaths deepe r than we see, into th e Dee p that i s infinite, withou t botto m a s without shore. " Typicall y of the times, the poet s Shelley , Coleridge, and Keat s (wh o was a pharmacist by training) had al l been attracte d to science in their youth and dabbled with scientifi c experi ments. (Coleridg e attended th e lecture s o f the great chemist Si r Humphry Dav y in order, so he said, to improve his stoc k of metaphors.) But the nature that appeared in their matur e poetr y was much close r to the unspoiled natur e o f Rousseau than the matter-in-motion of the Royal Society.

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Was i t b y chanc e tha t th e great flowerin g o f Romantic poetry i n Englan d occurred in the years when the status of science declined? Wordsworth, in the year of the French Revolution, wrote, Enough of Science and o f Art; Close up these barren leaves; Come forth, and bring with you a heart That watches and receives. Those barren leaves doubtless included the pages of the Principia. Galileo an d Newton , Boyle an d Lavoisier , Hooke and Huygens , had begu n th e demystification o f the natura l world . But , as th e eighteent h centur y progressed , many thought that things preciou s had been lost in that great adventure, not leas t the mystery of existence. D e Quincey would have said that imagination ha d died ; Blake branded science the tree of death. The scientific revolution had ha d littl e patience with what wa s seen as unclear thinking. When Boyle wrote of atoms in The Sceptical Chymist, he cited the mystic Pythagoras, but in the end he stressed that it was the prosaic evidence of the senses and the cold operation of reason that were the final arbiters. The day of the balance and the ruler, of the microscope and the telescope, had arrived. In Voltaire's Europe there coul d b e n o retur n t o th e day s whe n th e sixteenth-centur y alchemis t an d physician Paracelsus saw God as an alchemist and the cosmos as a chemical distillation. After the seventeenth century, no self-respecting natural philosopher woul d dream of saying, as did Paracelsus, "Man is a Sun and a Moon and a Heaven fille d with stars." Nature had been kidnapped by the professors . The models to which th e Enlightenment had looke d had been cast i n the ster n mold of the Roman Republicans. Enthusiasm wa s a dirty word in the vocabulary of Locke and Voltaire: it smacked of religious excess. The Scottish philosopher Adam Smith wrote , i n hi s classi c book , An Inquiry into the Nature and Causes of the Wealth of Nations (1776): "Science is the great antidote to the poison of enthusiasm and superstition. " Bu t the imagination, and th e suppose d intuitiv e abilit y of man to understand th e universe, could not be ignored for long. There arose a new skepticis m that, in contrast to that o f the sixteenth- an d seventeenth-century Europe, was directed not at the fossilized teaching of the Churc h and th e ancient s bu t a t the claim s o f science an d reaso n an d thei r no w hollow sounding promises of progress and justice. If science appeared to many to literally have taken the magic out of life, i t had, by way of recompense, promised to rescue man from the daily round of work and disease and deliver a "glorious and paradisiacal" world , as prophesied by Joseph Priestley. By the tur n o f the centur y it wa s clear that it hadn't. The poet William Cowper saw practical science "building factorie s with blood," and th e Industria l Revolution' s imag e was immortalize d i n Blake' s condemning phrase: "those dark Satanic mills" although he was possibly referring symbolically to Newton' s mechanic s rathe r tha n t o rea l machinery . Scientist s wil l poin t out , rightly, that to discover iron i s not t o make swords. The discoverie s of science in the sixteenth an d seventeent h centurie s wer e i n th e mai n no t directl y connecte d with the technolog y that blackened the Midland s of England. The creation of machines fo r weaving was the work of inventive engineers, not scientists . Bu t few in

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the late eighteenth and early nineteenth centur y saw it that way. For them the natural philosophers ha d brought misery. When the demolition team came to remove reason from it s pedestal and replace it with imagination, poet s were in the forefront . Wordswort h had onc e hoped that the "impassione d countenanc e o f the sciences " would shin e o n th e sou l o f the poet, but in the end it seemed to him that the mechanical, rational cosmos of Newtori had substituted a "universe of death" for the true universe, "which moves with light and life instinct, actual divine, and true." He had pinpointed th e loneliness of the mechanical universe . The Enlightenment concluded that we are responsible fo r our own destinies, but few wer e prepare d t o be alon e i n th e godles s universe o f d'Holbach, that "dead " universe whic h was the apparentl y inescapabl e en d poin t o f the natural philosopher's probings . Few woul d accep t Diderot' s compensatio n fo r losin g th e after world: "Wha t posterity is for the philosopher , the othe r worl d is for the religiou s man." Fo r HMS this offers col d comfort, an d eve n in the Ag e of Reason, humanit y clung to things irrational, steering clear of the depressing conclusion that all is matter an d mechanics . Thus , in th e eighteent h centur y w e fin d apparen t devotee s of reason displayin g intens e interes t i n phrenolog y and i n suc h shad y character s as Mesmer (whence mesmerism), an admire r of Paracelsus and th e propose r of "animal magnetism."4 Although a committee, set up at the request of Louis XVI and in cluding Lavoisie r and Benjami n Franklin , returne d a negative report o n the medical benefit s o f Mesmer's "cures, " h e stil l attracte d attentio n an d patients . The y wanted t o believe i n him . Eve n more successfu l wa s Count Cagliostro (real name Guiseppe Balsamo) , who, at the heigh t of the prestig e of the philosophes , tol d fortunes by gazing into water and speaking to the dead. Communication with the dead has a more obviou s appeal than th e silenc e o f the galaxies . In the fac e o f the col d comfort offere d b y reason, the appea l o f immortality is irresistible. I n this respect the Enlightenment threw littl e light into the nineteenth century . In 1874, William Crookes, a notabl e Britis h physicist wh o dabble d in spiritualism , studied th e evi dence for the existenc e of Katie King, the spiri t attendant o n the medium Florenc e Cook. Crookes came to the conclusion tha t Katie was genuine. He was subsequently, but on e hopes not consequently, knighted and elected to the presidency o f both the Roya l Societ y and th e Britis h Association. As late as the earl y 1900s , another prominent Britis h physicist , Si r Olive r Lodge , wa s completel y take n i n b y th e tricks o f spiritualist mediums . Ha d h e approache d th e phenomen a wit h th e ey e and min d o f a scientist, h e would hav e detecte d the frauds , bu t h e wanted t o believe—so h e did . Th e sam e nee d provide s a good income fo r TV evangelists an d psychics. Although reason trembled a s the eighteent h centur y progressed, it did no t fall . But if it was far too late in man's intellectual history to bury reason, at least it could be rebuked for its arrogance and put i n its place, which i n a way is what Romanticism did. In fairness to the philosophes, they had given what they generally called "passion," o r "the passions, " a place of central, sometime s dominant, importance in their schem e o f things. Diderot wrote to his mistress Sophi e Volland, "I forgive everything that is inspired by passion," and it would be a mistake to interpret tha t 4 Mozart's operetta Bastien and Bastienne was dedicated to his fellow Austrian Mesmer, and at the end of Act 1 of Cosifan tutte the two heroes are mesmerized.

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as lover's language, as an inspection o f Diderot's writings will show. Indeed man y of the philosophes ' statements soun d as though they come from th e mouths of the Romantics. Th e philosophe s ha d a mor e balanced attitud e t o "imagination " an d science tha n the Romantics . They rarely denied th e plac e o f the arts , nor th e absolutely essential place of the imagination in the creative process. It is a mistake, made by Blake and the Romantics, to see the philosophes and the other heroes of the Enlightenment as extremists in a war between reason and imagination. Much of their attractiveness come s from thei r recognition that, in general, the excesses of both reason and passion are equally to be avoided. Romanticism and Naturphilosophie wer e themselves doome d after 1830 , ironi cally from th e very expansion o f industrial powe r that they so loathed. A prosperous upper middle class grew up in England and Germany, its wealth usually based on industry. Science was now seen, in the guise of technology, to be producing welcome results in the real world, while the philosophers, especially the German variety, merely turned ou t obscur e and impoten t tomes. Th e middle-class became increasingly materialisti c an d politicall y conscious , an d i n th e nineteent h centur y science would regain its prestige, sometimes for the wrong reasons. The Enlightenment: A Different Perspective In recognizing the long-rang e liberating role of the Enlightenment, we should realize its limitations. I t was not a mass movement. At its peak it involved onl y a few tens o f thousands o f people, mostly rich o r middle-class. Th e Enlightenmen t an d Newton meant littl e or nothing to the average man. As Kant said, he was living in an Age of Enlightenment, but th e ag e was unenlightened. Th e "radical " leader s of the Enlightenmen t believed i n universa l education , wher e "universal " almos t al ways meant th e professional and merchan t classes , not th e proletariat . Only Condorcet, o f th e Enlightenment' s Frenc h luminaries , believe d tha t wome n shoul d have equal status t o men, although Diderot blamed men's historica l dominanc e of women fo r their "inferiority." 5 D'Holbac h declare d tha t women' s weake r organs prevented them fro m attainin g genius. Rousseau, despite a nod towar d equal educational opportunities for women, still proclaimed that women ha d n o originality and recommended that they concentrate on pleasing men. The editors of the Encyclopedic ha d n o qualms about including illustrations o f factories employin g child labor. It would be difficul t t o prove the thesis tha t the Enlightenmen t seriously dam aged religion at the time . The philosophes an d a significant number o f English intellectuals may have been deist or atheist, but the general population knew little of these things . I n fact , man y o f the clerg y were amon g those wh o bough t th e Encyclopedie, and some of the philosophes saw reason as, in principle, compatible with theology. In Englan d in particular , the clerg y saw scienc e a s a legitimate interes t that offered n o threat to belief. The "radicals " o f the Enlightenmen t lef t a permanent mar k on Western culture and o n man's concep t o f his role , rights, an d potential , but the y were no t revolu5 Diderot's attitude toward women might repay study. He sympathized with Clarissa, the harddone-by heroine of Richardson's sentimental novel, and he had a distinct, and documented, weakness for the nuhile breasts of Greuze's insidiously erotic peasant girls.

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tionaries in the image of Lenin or Che Guevara. They were writers and talkers, not guerillas, although some of them, like Voltaire, Rousseau, and Condorcet , suffere d or risked exile or imprisonment fo r their views. Some of them might have preferre d a secula r state , but fe w were democrats , and ther e i s little evidenc e t o sho w tha t they foresaw or desired the bloody revolution that was to come. They never created a party or a popular movement. All the "bi g names" excep t Condorcet died by the 1780s, s o that th e movemen t die d sociall y before th e Revolution . Marie-Jean-Antoine Nicola s d e Caritat , marqui s d e Condorcet , perhap s th e wises t o f th e philosophies, died in 1794 in a prison cell, persecuted by those who had perverted the principles o f the Enlightenment. Perhaps, in his last days, he recalled Diderot's resigned Iciment, "The philosopher may have to wait. He may find that he can only speak forcefully fro m the dept h of his tomb. " Nevertheless... The Enlightenmen t ha d it s triumphs . W e no longer , in th e West , officiall y bur n heretics or rack and then strangle servant girls who bewitch children , as happened in Switzerland as late as 1782. We can still echo Condorcet's cry for "reason, toleration and humanity." Perhaps the best epitaph for the Ag e of Reason was written by Tom Paine whe n he claime d tha t h e wa s "contendin g fo r the right s o f the livin g an d agains t thei r being willed away , and controlled , and contracte d for, by the manuscript-assume d authority of the dead. " In retrospect, the Enlightenment' s near-tota l belie f in reaso n an d scienc e a s a universal an d almos t imminent panace a now appears as naive optimism . An d yet the seventeenth-centur y scientific revolution an d th e eighteenth-centur y Enlightenment liberated us, giving us the confidence to use our reason and the confidence to doubt it. The Enlightenment gave us the right to question and the right to doubt, even the existence of God. It gave us the courage to challenge the wisdom of the ancients, no matter how sonorous the prose in which i t was couched, nor how established th e hierarch y o f its priests . Kant , who sa w th e Enlightenmen t a s a revolt against superstition , suggeste d for i t a quot e fro m Horace , Sapere aude! Dare to know! We dare. There was, however, a price to pay. The Enlightenment gave man a lonely dignity, a home in a mechanistic cosmo s in which God had a doubtful status . For those who accept this fate, it may be, as the materialist Hobbes said, that "there is no such thing as perpetual tranquility of mind while we live here." Three centuries later he was echoe d by Camus , who, accepting the absurdit y o f the cosmos , advises us to pull back on our bowstrings and face the enemy: "There can be no contentment but in proceeding." As for Romanticism, thankfully it still speaks to us, a reminder of the individua l mind. In book 5 of the Prelude, Wordsworth tells of a dreamer who meet s an Arab fleeing fro m a tidal wave that will swallow up the world. The Arab carries a shell and a stone, and explain s tha t both ar e in reality books: the ston e is Euclid's Elements of Geometry. The shel l is "somethin g o f more worth": "An Ode, in passio n uttered."

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When we say that Newton's laws can explain the movements o f the planets, we don't ask of what the planets were made. That kind of knowledge doesn't appear in his equations. All that we need to know about the planets in order to use Newton's equations are their mass and the forces acting on them. This is a classic example of the scientis t looking at an immensely intricate system , the universe, and singling out a specific aspect, with the hope, fulfilled i n Newton's case, that an explanation can be found for that aspect. Newton used one of the classic variations of the scientific method—he made a model. We did the same thing in Chapter 1. The box of molecules i n Figure 1.2, does not contain real molecules. Real molecules are complex entities containin g subatomic particles called protons, neutrons, and electrons. We completely ignored the internal structur e of atoms and molecules, and constructed an extremely simple model. The reason was that we were concentratin g on a simple property and asking a simple question: How do they move? For that limited purpose, it was sufficient t o take structureless blobs of matter, knowing that they were not accurate representations of reality. The complexity of a model is not required to exceed the need s demanded o f it. Science very often employ s models. Sometimes it is because we can do no better, we just haven't got the information. If the model works, we feel that it is justified. Ofte n we know that the model will be insufficient t o form a basis for the explanatio n o f all the physical properties of a system. If we had attempte d to explain th e interaction of light with our molecules-in-a-box, the simple model that we used would have been useless. We would have to construct another model, one that would be much nearer to reality. Throw a stone into the sea. Newton's laws will tell you how it moves through the air. Switch o n a bedside lamp. Newton would be mystified. He would be incapable o f using his laws to explain what is happening. Nearly a century was to pass, after Newton's death in 1727, before a new force took its place in the description of the cosmos. Electromagnetism was the key to the nature of light, and the intimat e structure, and properties, of matter.

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8 Lodestone, Amber, and Lightning Lodestone, amber, and lightning wer e nature's hints that there were strang e force s in Heave n an d Earth . Lodestone, a naturally occurrin g magnetic oxide o f iron, attracted nail s and , i f suspended, aligne d itsel f roughl y alon g a north-south line . I f ruhbed with suitable material, a piece of amber attracted piece s o f thread o r paper. These weir d propertie s stil l intrigu e children—an d adults . Th e compas s needl e fascinated Einstein as a child. How did the needle know which wa y to point? Even as late as the seventeenth century , many believed tha t magnets had souls. The pull of a magne t wa s likene d t o th e lur e o f a sire n fo r a sailor. Katherin e Philip s (1631—1664), a minor English poet, saw the turning and trembling of a needle in response to a lodestone as a manifestation of a kind o f love. Over the centuries, out of simple experiment s and observations , tw o ill-define d concepts emerged: electricity an d magnetism. They appeared to be quite indepen dent phenomena; you didn't get a shock from a magnet, and an electrically charge d rod didn't behave lik e a compass needle . How Many More Forces Are There?

We don't know . N o one would hav e thought u p magnetis m ari d electricity if their effects ha d neve r bee n detected ; they ar e not a consequence o f Newton's laws. So it's wort h keepin g a n ope n min d regardin g th e existenc e o f as-yet-undiscovered forces. As fa r as we kno w a t present , onl y fou r force s shap e th e universe . Tw o of th e four, the so-calle d weak and strong forces, ar e of very short range and operat e only within the nucleu s o f atoms, the tin y cor e at the cente r o f each ato m (see Chapter 12). The other two, long-range, forces tha t control Creation are gravity and electromagnetic force . Why electromagnetic! Wh y combine tw o phenomen a tha t see m s o very differ ent? You can't run a laptop compute r o n a magnet. And try cutting a magnet in half to isolate the north pole and the south pole. It doesn't work, you just get two smaller magnets, each complete with its own north and sout h poles—no matter how far you carr y the process . I t is impossibl e t o obtai n a single, isolate d nort h o r sout h pole of a magnet.1 This is in contrast to the independen t existenc e o f two kinds of electricity: positive an d negative electric charge. Electricity and magnetism appea r to be very differen t fro m eac h other . We will shortly show tha t they ar e madly i n 1 In 1931 the outstanding theoretician Paul Dirac predicted that monopoles should exist. Other theoreticians have predicted that they should have been formed in great numbers around about the time of the Big Bang. It has been claimed that the results of one experiment show the effec t of a magnetic rnonopole passing through the apparatus. This has not been confirmed. I f you want a Nobel Prize the hard way, you know what to look for.

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love; one (almost ) cannot liv e without th e other , but i t took a long time to realize that they are two face s o f one coin. Immobile Charge

Static charge , the kin d tha t make s som e artificia l fabric s stic k t o you r skin , ha s been known for centuries. If you rub two pieces of amber, or plastic, with a piece of suitable material, they repe l eac h other . Since they ar e presumably charged wit h the same kind of electricity, you have shown that like charges repel each other. You can observe the sam e phenomenon i f you rub two glass rods on a cooperative cat. However, if you hold a rubbed glass rod next to a piece o f rubbed amber, they will attract each other. You have shown tha t there ar e two kinds o f electricity and tha t unlike charge s attract each other . The names positive and negative, given by Benjamin Franklin, are purely conventional ; there i s nothing eithe r positiv e o r negative in the algebrai c sense abou t electric charge . It is convenient , however, to use the conventiona l label s becaus e positiv e an d negativ e charge s appea r t o cance l each other, just as +3 cancels -3. If equal amounts o f negative and positiv e charge are combined, the resultant net macroscopically measurable charge is zero. Until the beginning of the nineteenth century , electric charge was usually generated with a variety of "electrical machines," al l based on the frictio n o f a material such as leather or silk on a rotating disk or cylinder, often mad e of glass, occasionally of sulfur. Thi s i s a mechanical versio n o f dragging a comb through your hair. The charged body carried a static electric charge, which i t could lose if connected directly or indirectly to the ground. The discharge of charged bodies took a fraction of a second during which a momentary flow o f electricity might be induced t o flo w along a wire or a thread, but that was that. No one knew how to produce a constant, long-lasting flow of charge, and thus experiments on electricity were almost entirely confined to systems having a static, not moving, charge. To do any kind of quantitative experiments on electricity it is advisable to have a unit of electric charge, just as there i s a unit for mass and fo r length. One familiar unit of electricity is the amp (the ampere). The amp is a unit of flow analogous to the unit cubic meters per second that we use for the flow of liquids. The unit of electric charge i s named afte r th e Frenchma n Coulomb . The coulom b is define d as th e amount of electric charge that flow s pas t a given point in a wire in 1 second if the current is 1 amp. Most household lighting is run o n a 5-amp current, which means that if you took a specific point on a lamp filament, then in 1 second 5 coulombs of electric charge would pas s by. A current of about 200 amps (200 coulomb per second) through the human body will kill. Actually households run on alternating current. The current flowing in the wiring changes its direction abou t 60 times a second, so you would have to measure the total charge passing by a certain point per second, irrespective of the directio n in which i t was flowing. Most heating appli ances use 15-am p current. A total of about 3000 to 5000 coulombs passes throug h the heating coil when you boil an electric kettleful o f water. Several attempts were made to find the law that holds for the force between electric charges. Most of those who searched for this law assumed (correctly ) that they would find an inverse square law, by analogy with Newton's law for gravity. As the mathematician an d physicis t Henr i Poincar e (1854-1912 ) onc e remarked , "I t i s

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often sai d tha t experiment s shoul d h e mad e withou t preconceive d ideas. Tha t is impossible." In the 1760 s both Daniel Bernoulli and Joseph Priestley looked, unsuccessfully, for an inverse square law. The man who first succeeded was Henry Cavendish, who experimentally demonstrate d th e law , sometim e i n th e 1760s . However , Cavendish's results onl y came to public notice in 187 9 when James Clerk Maxwell published them. Thus, for over a century, priority was accorded to the French military engineer Charles Augustine Coulomb, who published hi s work in 1785 and 1787. If you've forgotten what the gravitational law looks like here it is again: F = G[m 1 xm 2 j/R 2

Electrically charge d bodies obe y a similar law . The forc e betwee n two charge s is given by: F = fC[q lX q 2 ]/R 2

in whic h th e place s o f the tw o masses ar e taken by ql an d q 2 , the magnitude s in coulomb of the two charges, and R is the distanc e between the charges. Increasing the distanc e between two charged bodies by a factor o f 5, reduces the electrostatic force between them by a factor of 25, whether the force is repulsive or attractive. In contrast to the value of G, the value of .Kin the equation for the electrical force depends strongl y on the medium in which th e two charges are situated. For example, the forc e between two charges in water is only about one-eightieth of that between the same charges in air, at the same distance. The gravitational force between two bodies is effectively independen t o f the nature of the material between them. Although machines fo r producing static charge by friction wer e common in th e eighteenth century, there was, until the beginning of the nineteenth century , no reliable wa y o f artificially producing a reasonably strong magnet . Here i s Michae l Faraday's description of how to make a magnet: Taking a bar o f iron, place one end " . . . pointing about 24l/2 degree s west of north, and downwards , so as to make an angle of 72 1 /2 degrees with the horizon. When the bar i s held in thi s position , with on e end o n a large kitchen poker in the same position, and the other end struck three or four times with a heavy hammer, it will become a good magnet." Chemical Manipulation (1827 ) Before th e nineteent h century , the highes t field s attainabl e from magnet s were no more than a few times stronger than that of the earth. Today there are commercially available scientifi c instrument s tha t produc e magneti c field s wel l ove r 350,000 times as strong as that of the Earth. Mobile Charge The concept of current electricity was probably first grasped by Otto von Guericke (1602—1686), who showe d that if he connected a charged ball of sulfur t o a nearby body, b y a thread, th e bod y displaye d th e sam e electrica l propertie s a s the ball . Charge had moved along the thread.

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The next ingenious amateu r t o significantly advanc e the caus e o f current elec tricity was the charismatic Benjami n Franklin, friend o f the philosophes. He stated that charge could be neither create d nor destroyed. In other words, he formulated a conservation law : charge is conserved. Discharging a body does not mean that th e charge i s destroyed ; it jus t goes somewhere els e o r is apparentl y cancele d by a n equivalent influ x o f charge of the opposit e sign . Franklin guesse d tha t electricit y came i n discret e particles and tha t lightnin g consiste d o f moving electri c charge. The 175 2 experimen t i n whic h h e fle w a kit e i n a thunderstorm i n orde r t o de mythologize the thunderbolts o f the gods, has become part of the mythology of science. Electricity flowed along a wet thread, from kite to ground. The nineteenth-centur y chemis t Josep h Priestle y declare d tha t th e discover y that lightning is an electrical phenomenon was perhaps the greatest since the tim e of Sir Isaac Newton. Less well publicized is an earlie r experiment conceive d o f by Franklin i n 175 0 but no t carrie d ou t by him. H e suggested constructing a bizarre apparatus consisting o f a man-sized box, on th e floo r o f which wa s a n insulatin g pad, on which the rash experimenter stands, and through the door of which rises a long, pointe d rod , extendin g 2 0 to 3 0 fee t i n th e ai r an d terminatin g i n a point . When lightning strikes the rod, the suicidal experimenter can , using an insulatin g wax handle, hold a grounded wire near the rod and see sparks jump across the gap. Rather you than me. The experiment, designed to show that lightning was electricity, wa s firs t actuall y performe d b y Dalibard , i n Franc e i n 1752 . It shoul d hav e come with a government health warning . Georg Richter (1711-1753) a rash Estonian, constructed a variation of Franklin's box in St. Petersburg. He was electrocuted in his box during a storm. Someone commented that they envie d him his glorious death i n th e caus e o f science . (Someon e els e remarke d tha t i t wa s a shockin g tragedy.) In the same year, Franklin received a medal from the Royal Society. I wonder if he spared a thought at the ceremony for poor reckless Richter. A Note on Conservatio n

Franklin's suggestion that charge was conserved is the firs t exampl e of a conservation law. Such law s play a central role in science . Conservatio n laws ar e general; for example , in any process in nature the total charge of the universe remain s un changed. Charge cannot be created or destroyed by mortal man. We shall be meeting more conservation laws, each saying something very fundamental about the nature of nature. Things Start to Mov e

Lightning being a somewhat inconvenien t sourc e of electric current , it was fortu nate tha t Franklin' s friend , Coun t (t o be) Alessandr o Volt a (1745-1827 ) foun d a way o f producing stead y currents o f electricity i n th e laboratory . This discovery , which was the key to the practical use of electricity in the early nineteenth century, owed a lot to Volta's compatriot, Luigi Galvani. In 1791, Galvani had observed that a frog's legs jerked when he passed a momentary current through them. He got similar responses by passing short-lived currents through corpses. His findings galvanized Europe. Galvani's source of current was a charged body, but subsequently , and fatefully , h e found tha t he got the same effec t by simpl y touchin g th e leg s o f frog s wit h tw o connecte d rod s mad e o f differen t metals. Galvani's interpretatio n wa s that livin g matter contained , o r could gener -

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ate, "animal electricity." It can, but this had little to do with his experiments. Today electroencephalography (EEC ) an d electrocardiograph y (EGG ) ar e routin e tech niques based on the body's own electricity, and of course there are electric eels. But the respons e of the frog s wa s to an external, not internal , sourc e of electricity. Gral vani didn' t realiz e it, but i t was the pair of metals that were generating the current of electricity. Volta became interested in Galvani's twitching corpses. Alessandro Volta was a self-confident type . His frien d Geor g Christof Lichtenberg (1742-1799 ) sai d o f him tha t h e "understoo d a lo t abou t th e electricit y o f women."2 Volta sneered a t Galvani's suggestion o f animal electricity : "Physician s are ignorant o f the know n law s o f electricity." He had littl e reaso n to snipe. Volt a had onc e pu t a coin o n hi s tongue , a coi n o f a differen t meta l underneat h hi s tongue, an d connecte d the m wit h a wire. H e experienced a salty tast e which he , like Galvani, (wrongly) interpreted a s electricity generate d by living tissue . Whe n he hear d o f Galvani's work, Volta proceeded to experimen t with whole frog s an d rapidly came to the conclusion that a current flowed when two different, an d physically connected, metals wer e applie d t o any moist body . He constructed pile s of alternating disk s o f copper an d zin c separate d b y wet , absorben t pape r o r even damp wood. This was the first man-made battery. 3 Since a battery is just a means of puEtiping electric charge , placing batteries hea d t o tail i n a row (in the jargon, "i n series") means that their total pushing power is the sum of that of all the pumps. By using many pairs of copper and zinc plates, Volta obtained strong currents that lasted fo r a considerabl e time . Th e "voltai c pile " wa s th e firs t convenien t source of current electricity . Volta invented th e phrase s "electromotiv e force " an d "electric current," an d commenced to persecute the animal world . He showed tha t an electric curren t coul d induce movemen t i n a variety o f unfortunate animal s an d in sects: "It is very amusing to make a headless grasshoppe r sing." Volta, who ha d a great sense o f humor, conveyed his finding s t o the Royal Society in 1800 . Th e announcement of the construction o f a source of steady electric current create d a sensation. Napoleon contacted Volta, created him count, coined a medal in his honor, and provided him with financial assistance for many years. Volta's pil e ha d th e disadvantag e o f all chemica l batteries : th e chemical s ge t used up. Nevertheless , the pil e provided , for the firs t time , a controlled, continuous sourc e o f electric current , openin g the wa y t o a number o f almost immediat e practical applications such as the telegraph and electroplating, and also to a whole new rang e of experiments. The concept o f voltage was born. Voltage (from Volta, of course) is the electrica l equivalen t o f pressure, measuring th e forc e wit h whic h a generator or battery can push electrons. Typical voltages are 1 to 2 volts for simple batteries, 6-1 2 volt s fo r most ca r batteries, 120—24 0 volts for domestic electricity , and abou t 100 0 volts for the shoc k delivered by an electric eel . EGG involves voltages in the single-figur e millivolt range, compared with 20 to 30 millivolts fo r EEG. The voltaic pile remained th e sourc e of electricity fo r commercial use, such a s telegraphy, until well into the 1800s. No equivalent technical advanc e was made in magnetism until 1820.

2

Maybe Lichtenberg was just envious; he had a desperately unhapp y marriage. Electric eels have a similarly structure d electric organ , but not of course based on metal disks.

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Magnetic Personalities

Magnetism's uncanny manifestation s provoked a rich folklor e fro m th e tim e tha t the lodestone was discovered, possibly by the Chinese in the third millennium B.C . One of the earlies t rational references to magnetism in the West was in the Roman Lucretius's poem De rerum natura (se e Chapter 14) . It i s typical o f the down-to earth atomist that he refused to countenance mystical explanations o f magnetism. The earliest known treatise on experimental physics, Epistola Petti Peregrin! de Maricourt ad Sygerum de Foucaucourt Miletem de Magnete ( A letter o f Peter th e Pilgrim of Maricourt to Sygerus of Foucaucourt, Soldier; on the Magnet) , contains an account of the author's experiments with lodestones. Peter completed his manuscript "in the year of our Lord 1269, eighth day of August" while he was serving in the arm y of Charles I of Anjou, a t the sieg e of Lucera in Italy. 4 He was th e firs t t o record that magnets had tw o "poles, " one seeming to look for the north, the other the south . Lik e pole s repelled eac h other, bu t nort h attracte d south . Peter' s book was taken to heart by William Gilbert, physician to Queen Elizabeth I and James I, who, despite his conviction tha t magnets had souls, was an experimentalist i n the Baconian mold. It was Gilbert, in his book De magnete, who firs t suggeste d that the Eart h itself was a giant magnet, thus explaining the behavior of the compass needle. The magnetic north pole, where the magnet points vertically downward, was discovered in Canada i n 1831 . Gilber t used the phrase "magneti c coition" rather than magnetic attraction, "because magnetic movements do not result from attractio n of one body alone, but fro m comin g together of two bodie s harmoniousl y (no t the drawin g of one by the other). " He seems no t to have realized that there can be coition when only on e body attracts the other . Gilbert thought tha t the attractio n betwee n magnets could provide an explanation o f the Moon's path about the Earth, an idea that was accepted by Kepler. They were both wrong. In 177 8 a blacksmith's daughte r name d Am i Lyo n worke d a s a provocatively dressed hostess in the Temple of Health, an establishment in the Strand . Billed as "Vestina th e Ros y Goddes s o f Health, " sh e wa s bette r know n i n late r year s a s Emma, Lad y Hamilton, Lord Horatio Nelson's mistress. Th e activities o f the Temple of Health were centered on a large "Celestial" bed constructed by a Dr. Graham and equippe d wit h 150 0 pound s o f "artificial and compoun d magnets " that , th e mercenary doctor claimed, revivified slackening sexual vigor. The bedroom reeked of expensive Oriental perfumes, and it usually cost a couple twenty pounds a night to us e th e bed . Som e gentlemen were charge d fift y pound s a night , bu t i t i s no t recorded what extr a services were provided fo r this sum. Considering the ancien t belief that i f one put a piece of lodestone under the pillo w of an unfaithful wif e i t would mak e her confes s her sins , i t is a wonder tha t Englis h fashionable society flocked i n suc h larg e numbers t o Graham' s establishment . Graha m die d a poo r man. Th e age-ol d mystique surroundin g magnetis m coul d no t compensat e fo r a flaccid successio n of disappointed clients . Dr. Graham' s Frenc h equivalen t wa s Friedric h Anto n Mesme r (1734-1815) , a 4 Dame Kathleen Lonsdale, who lectured t o me in crystallography, wrote a scientific text while in prison, but to write a scientific text in the midst o f a military campaign appear s to be a feat unique to Peter and to the Greek physician Dioscorides, who served as a physician i n Nero's armies (see Chapter 20).

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doctor who took many of his ideas fro m th e Jesuit priest Maximilian Hell. Mesmer exposed his patients to magnets while they sat by the side of a large tub containin g a murky solution o f chemicals. Th e committee appointed t o examine his method s and claim s include d Benjami n Franklin . Thei r conclusion , that "th e imaginaytio n does everything , th e magnetis m nothing, " implicitl y acknowledge s th e powe r of hypnosis, which wa s almos t certainl y responsibl e fo r some o f Mesnier's genuin e successes. H e appear s t o hav e initiate d th e medica l us e o f hypnosis i n wester n Europe.5 Unification All physical experiences are due to on e force. —Immanuel Kant

On 21 July 1820, the Danish physicist Han s Christian Oerste d (he was a friend of H. C. Anderson) published fou r page s in Latin entitled: "Experiment a circa effectur n conflictus electri a in acu m magneticum" (Experiments on the effect s o f an electrical conflict on a magnetic needle). This paper made Oersted's name. He had show n that the passage of an electric current through a wire influenced the orientation o f a compass needle placed near the wire. It was known, of course, that a compass feels a forc e fro m a magnet, s o Oersted conclude d tha t th e electri c curren t mus t hav e been acting like a magnet. For the first time, magnetism and electricity were shown to be related, an d Oersted use d th e term electromagnetism in referring to the phenomenon h e ha d discovered . He had pointed the way to the unification of two of nature's basic forces. Oersted made his observatio n while lecturin g t o a class o f students, an d i t has often bee n state d tha t th e discover y was accidental , apropo s o f which tw o com ments are in order. As Pasteur remarked, "In the field o f observation, chance favor s the prepared," and second, Oersted had been looking for such a n effect fo r years.6 Oersted's pape r wa s rapidly translate d int o severa l Europea n languages , Latin no longer being readily understandable b y the whole scientifi c community. It had an almost immediate technologica l effect. Willia m Sturgeon, who as a professional soldier i n th e Britis h Roya l Artiller y performe d experiments o n electricity i n hi s spare time, wrapped some copper wire around an iron horseshoe and passed a current through the coils. He had mad e an electromagnet. Across the Atlantic, also in 1820, Joseph Henry did likewise but, being American, used more coils of wire. His electromagnet could raise a ton of iron.7 5

Dsspite the frauds perpetrate d by charismatic imposters, there is good evidence that magnetic fields can affect livin g organisms. It is well established that certain iron-containing bacteria are affected b y magnetic fields, which is not really surprising. It has been claimed that there is a. good correlation between magnetic storms and suicides, but this remains to be verified. 6 It is a curiosity that the scientist Johann Ritter, who dabbled in astrology, had previously written a letter to Oersted prophesying that the next great discovery in the field o f electricity would be in "18192/30rl820." 7 Henry, like Michael Faraday, came from a working-class background and was an apprentice—to a watchmaker at the age of thirteen. He also, like Faraday, is reputed to have had his interest in science sparked by a book, which he apparently found under some floorboards. He tore up his wife's petticoat to provide insulation fo r the copper wire that he wrapped around his magnets.

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Oersted's paper was presented in Paris by Dominique Arago. Among those in the audience wa s a professor of mathematics a t the Ecole Polytechnique: Andre-Marie Ampere. Ampere's personal life reads like a soap opera. He was born in 1775 to a father who was guillotined whe n Ampere was eighteen . Ampere's wife die d fou r years after the marriage, his second wife (an d her mother) made his life unbearable, and they divorced. Ampere's son fell under the spell of a woman of a certain age, the formidable, charming, but not over compliant hostess, Madame Julie Recamier. (You can judge his taste by looking at the portrai t that David painted o f her.) He spen t about 20 years doing nothing constructive , unless you include intermittently gazing at the lady's decollete. Ampere's daughter married a mentally unstable alcoholi c officer. Ampere said that he had only two happy years in his life. His tombstone reads, Tandem felix, Happ y at last.8 He took up science after finding, in his father's library, a eulogy of Descartes, which convince d him o f the nobilit y o f a life in science. Just another of those chance encounters that so often determin e ou r fates. 9 Within a week of hearing of Oersted's work, Ampere, announced tha t he had observed a n attractiv e forc e betwee n tw o paralle l wire s throug h whic h a curren t flowed in the same direction. Currents flowing in opposite directions produce d repulsion. The force depend s o n the strength of the current, and we still use the forc e between tw o current-carryin g wires a s the fundamenta l basi s fo r the definitio n of the unit of electric current—the ampere. Arago, recalling the school experimen t i n which iron filings on a piece of paper are formed into a pattern by a magnet beneath the paper, passed a current through a wire piercing a piece o f paper on which iron filings wer e sprinkled . Th e filing s line d u p t o giv e concentri c circle s abou t th e wire. A current indeed acte d like a magnet, and the force between two current-carrying wire s ca n b e interprete d a s a magneti c forc e tha t i s exerte d o n a moving charge in one wire by the current in the other—and vice versa.10 The current in a wire, or any magnetic influence, will not exert a force o n a static charge . Stati c charge s an d stati c magneti c field s ar e completel y blin d t o eac h other,11 which is one reason that the connection between magnetism and electricity took so long to be discovered. Since Oerste d ha d show n that current s ac t like magnets , Amper e decide d tha t he could explain Oersted's and his own results if "one admit s that a magnet is only a collection o f electric currents. " Hi s detailed explanatio n o f the origi n of the cur rents i n a magnet was wrong . Nevertheless , between them , Oerste d an d Amper e 8

Would he have been cheered up coul d he have foreseen the daily stream of customers asking for "a 15-amp plug, please"? Prominent scientists ru n the risk of being immortalized in this way. Among the physical units that we use are a volt, an ohm, a coulomb, a farad, and a Faraday, a maxwell, a newton, a dalton, a curie, a Kelvin, a becquerel, and an einstein. 9 Who can say what chains o f scientific influence were initiated by a certain priest in the Jesuit College of la Fleche, who on 6 June 1611 rea d out a poem composed to mark Galileo's discovery of Jupiter's moons? One of the listening pupils was the fifteen-yea r ol d Rene Descartes. 1G The effect o f a magnet on a moving electric charge is used in all television cathode tubes. A stream of electrons (negatively charged particles) pass between the poles of a small magnet, the strength of which can be varied. The force on the electrons, and therefore the deflectio n from their straight path, depends o n the strength of the magnet. This is the mechanism by which the electron beam is made to sweep out the 650 lines that cross the screen. n You might ask why an electric current running through a wire, which is , after all , a flow of electric charge, does not exert an electric force o n an external charge. The answer is that the wire is electrically neutral. The atoms of which i t is made have positively charged cores (nuclei), and their total charge equals the total negative charge on all the electrons in the wire.

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had show n that electricity an d magnetism were two faces o f the sam e animal. The next step was taken in England. Working-class Hero I love a smith's shop and anything related to smithery . My father was a smith. —Michael Faraday, journal, 2 August 1841

Michael Faraday is on e o f the fair y tale s o f science—the working-class apprentice who rose to he courted by royalty. Handicapped by his lac k of a formal education , he would neve r hav e been a theoretical physicist , sinc e his knowledg e of mathematics wa s poor. He couldn't follo w th e mat h i n Ampere's papers. What Farada y did hav e wa s a n intuitive feeling fo r the working s o f nature, which he translate d into visual rather than mathematical terms . And he had an extraordinary talent for choosing the right experiment. The blacksmith's son had marvelous hands, and the natural world coul d not resist him. He was a scientific Casanova. Faraday's life was science . He avoided honors, turning dow n the presidenc y of the Roya l Societ y and a knighthood. Th e portrait o f the ma n wh o neve r attende d university an d whos e schoo l educatio n wa s effectivel y limite d t o the "thre e Rs, " hung o n the wal l o f Einstein's study . At the ag e of thirteen, he went t o work for a French emigre bookbinder and printer, in Blandford Street , off Baker Street in London, beginning a s a paperboy. The turning poin t i n his lif e cam e when he was rebinding a volume of the Encyclopaedia Britannica that included a n article on electricity. Th e author' s suggestio n tha t electricit y ha d th e natur e o f a nonmateria l vibration caugh t hi s attention . Anothe r boo k tha t fel l int o hi s hands , an d whic h awakened his interest i n chemistry, was Jane Marcet's Conversations in Chemistry, an early example of popularization. At the age of nineteen, he began to make up for his educational shortcomings by attending public lectures, at first at the City Philosophical Institute, where there was a voltaic pile . In 1812 a customer at the bookbinders, a certain Mr. Dance, was s o taken by the curiosit y an d intelligenc e o f the young apprentic e tha t h e gav e him ticket s t o atten d fou r o f the serie s o f lectures being give n b y th e renowne d chemis t Humphr y Dav y a t th e Roya l Institution . Davy, lik e Faraday , neve r wen t t o university , an d probabl y neve r wrot e dow n a mathematical equatio n i n his life , which would have made it easier for Faraday to appreciate hi s lectures . Farada y bound hi s lectur e note s an d sen t the m t o Dav y with a request for a position. Th e notebook stil l exists . Davy , who ha d bee n temporarily blinded by an explosion, accepted him a s an amanuensis. Fate played its next card when a n assistant a t the institutio n wa s sacked for fighting and Faraday was given his position . Dav y had jus t been knighte d and i t had gon e to his head, but more so to his wife's, who treated Faraday as though he were her personal servant. Unde r thes e no t too promising conditions, one of the greates t experimentalists in the history of science began to experiment, with the talent that genius ofte n has fo r asking the essentia l question s an d findin g simpl e experiment s t o answe r them. Faraday wa s a giant wh o pointe d theoretica l physic s I n a new direction , an d whose experiments were to lead directly to technologies which were to change the face o f civilization. In 1800, Nicholson and Carlisle constructed the first voltaic pile in England, and

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the availability of steady current began to pay off immediately in terms of new dis coveries. The y foun d tha t a curren t decompose d water, a n observatio n probabl y made in the same year by the German Johann Ritter. This was the first electrochemical reaction. In the same year Humphry Davy began a series of experiments o n the effect o f electric curren t o n chemicals , which le d t o th e discovery , amon g othe r things, o f th e metal s sodium , potassium , an d calcium . I n th e 1830 s Farada y showed tha t whe n a n electri c curren t wa s passe d throug h a solutio n containin g salts and there was decomposition to give new chemical species, the amount of decomposition was directly proportional to the amount of current passing. If a certain quantity o f oxygen gas is released fro m wate r b y th e passag e o f a current fo r fiv e minutes then twice as much ga s will be produced in ten minutes. Th e implicatio n was that electric charge was an integral part of matter and somehow involve d with the wa y that atom s were boun d together . After consultin g o n nomenclature with William Whewell, a distinguished Oxfor d professor who coined the word scientist in 1834, Faraday adopted the words electrode, cathode, anode, ion, electrolyte, and electrolyze. Today Faraday's experiments o n electrolysis are taken to be direct evidenc e for the existenc e of a discrete "packet " o f electric charge, the electron . We can almos t see the current going in, electron by electron, each electron joining onto a molecule or ion in the solutio n an d changing its chemical form. Why didn't Faraday realize that electricity came in discrete packets? Why didn't he discover the electron? Because for him, passin g electricity into a solution wa s like pouring in a continuous fluid with no structure. It resembled th e passing of time: you could select as much or as little time a s you liked, but ther e was no question o f time coming in discret e packets. Consistently, Faraday did not believe in atoms. Faraday's electrochemical experiments were important, but it was three entirely different finding s o f his that were to turn the course of history: 1. He showed (Figur e 8.la), o n 2 1 October 1821 , tha t whe n a current wa s passe d through a rod that was free to move, and one end of the rod was in the vicinity of a magnetic pole, the rod circle d around th e magnet . Electrical energy could be continuously converte d into mechanical energy . This was the origin of the electric motor. 2. H e showe d (Figur e 8.1b) , o n 1 7 Octobe r 1831 , tha t whe n a magne t moved through a coil of wire it induced a n electric current in the wire, but onl y durin g the time that it was moving and the strength of the magnetic field nea r the wire was changing. The mechanical energ y of motion could be turned into electrica l energy. The dynamo wa s born, and Farada y subsequently buil t the firs t primi tive electric generator based on this principle. 3. I n th e sam e year , he showe d tha t a curren t coul d b e induce d i n a circui t b y changing the curren t i n an adjacent circuit . The transformer an d the induction coil were born. At about the same time Joseph Henry, in America, discovered the same effect . Notice that what Faraday had shown, among other things, was that: A changing magnetic field created an electric current (2), and a changing electric current created another electric current (3).

These tw o facts , an d Oersted' s discover y that a stead y curren t coul d produc e a

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Figure 8.1a. Faraday' s demonstration tha t a magnetic field produces a force on a moving electric charge. The copper ro d revolves when a current flows .

Figure 8.1b. A changing magnetic field exerts a force on an electric charge. When the magne t moves , a current of electron s flows.

magnetic field , wer e to for m th e experimenta l basis fo r the complet e meldin g of electricity and magnetism in one theory. Every powe r statio n an d ever y electri c moto r i n th e worl d use s th e technica l consequences of Faraday's discoveries. But they had mor e than technological consequences. Farada y invente d th e ide a o f electric and magnetic fields. I f he ha d done nothing else, he would have change d science. Tha t is the reason that he appeared on Einstein's wall. The Power of Space

Magnets an d charge d bodies ac t throug h spac e t o exer t force s a t a distance , o n other, appropriate bodies. Faraday pondered on the problem of action at a distance, and ther e grew in his mind the idea that, surrounding a magnet or a charged body, there was an invisible, immateria l "sea," an entity that exist s in space, rather like the waves that spread out from a stone thrown into a pond. If a piece of wood is placed in the ripples generated in water by a vibrating body, and we were unable to see the waves, we might say that the vibrating body acts at a distance on the piece of wood. Faraday would sa y that, despite appearances, there is a field o f waves which exist s ove r the whole surface o f the water, not just where the woo d bobs up an d down . Despit e the fac t tha t i t could neve r have com e into being without th e vibrating body, the fiel d o f waves is an entity in its own right; it will persist fo r some time even i f the body stops vibrating. It is capable of moving bodies siibmerged i n it , acting as an intermediat e i n transferrin g movement fro m the vibrating body. For water this is an easily acceptable idea because the waves are of cours e visible. Fo r magnets o r electrical charge s it was a completely ne w con cept. Faraday did not envisage a field of waves but rather a static field that could be mapped ou t in terms of lines of force. Thu s a charged body can be considered t o be

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Figure 8.2. Visualizin g an electric field. The arrows surrounding the charg e A indicate the direction of the force felt by a positive test charge, P, placed at several positions in the plane of the page . Imagin e a n infinite number of simila r arrows abov e and below the page . A pair of opposite charges produce the pattern shown on the right .

surrounded by an electri c field, which could b e mapped ou t by drawing, a t every point in space, a tiny arrow whose direction would b e in the direction o f the forc e exerted by the field on an electrically charged body put at that point (Figure 8.2). In the case of a magnet these lines could be visualized by examining the pattern made by iro n filing s sprinkle d o n a piece o f paper lyin g on a magnet. I n thei r entiret y these lines defin e a magnetic field . Farada y admitted that he did not know what a line o f force o r a field reall y was, any more than Newto n knew wha t gravit y was, but breakthroughs in science have often ridden into town on the backs of enigmatic new concepts . Th e simplest wa y to picture th e fields create d by magnets or stati c charges is to define the m by what the y do. Notice how, as in the cas e of force, w e have onc e again fallen bac k on a n operationa l definitio n o f a basic scientifi c concept. You are what you do. Faraday's concep t o f fields wa s the produc t o f a brain tha t worke d wit h visua l images. Faraday saw fields. Hi s intuition fille d the univers e wit h silent , ever-present seas. When he lectured o n the magnet, he would hol d on e up with on e hand, knock on it with th e other , and declare , "Not onl y is the forc e here , but i t is als o here, and here, and here," moving the other hand through the air around the magnet. Today the concep t of fields ha s a major rol e in theoretical physics, on e o f the reasons being tha t field s ar e very convenien t i n quantitatively , an d qualitatively , explaining countles s phenomen a i n the materia l world. Thi s i s possible onl y because mathematica l equation s hav e bee n constructe d whic h giv e th e for m an d point-by-point strength of fields. Farada y could not d o this, but he di d not have to wait lon g before someon e did . Befor e w e mak e that step , we retur n t o finding s 2 and 3 , and loo k at them from th e fiel d poin t of view. Finding 2 (Figure 8.1b) can be interpreted a s a changing magnetic field produc ing an electric field. I t is this electric field that drives the electrons around the wire coil in which the y sit . Likewise, finding 3 shows tha t the changin g curren t i n th e first coi l (th e so-called primary) creates a magnetic field which , a s it changes, creates—in accordanc e with findin g 2—a n electri c fiel d a t the secon d coi l (th e secondary), which drive s the current in that coil. These interpretation s ar e a t th e ver y root o f the unificatio n o f electricity an d magnetism. The y show tha t thes e two force s ar e merely the differen t face s show n by one force under different conditions : A change in a magnetic field produces an electric field. A change in an electric field produces a magnetic field.

Lodestone, Amber, and Lightning !_?!

Faraday's field s too k into accoun t the possibilit y o f curved lines o f force. Thu s the iron filings nea r a current-carrying wire were arranged in circles going around the wire, and a compass needle placed near such a wire would point at a tangent t o these circles . When Ampere found that two current-carrying wires repelle d o r attracted each other he assumed, in analogy to gravitational force, that the force was a simple "straigh t line " interaction between tw o currents. Faraday realized that th e force arose from the tangential magnetic field du e to the current in one wire, acting on the curren t i n th e othe r wire (Figur e 8.3). Ampere couldn' t brea k awa y from Newtonian pictures . Initially, most contemporary physicists sa w Faraday's fields as a convenient fiction rathe r than havin g an y reality. The notable exception wa s William Thomson, better known to history a s Lord Kelvin. Thomson attempted to formalize Faraday's ideas in mathematical terms and in doing so he became convinced that there might be a connectio n betwee n electromagnetis m an d light . H e suggeste d as muc h t o Faraday, knowin g tha t i t would b e wis e t o leav e an y experiment s t o th e master . Faraday did not disappoint . H e passed a beam of light through a piece of glass sitting in a magnetic field and found an effect o n the light, There was a connection between light and magnetism. Th e Faraday effect i s still used by scientists intereste d in the detaile d structur e o f certain types of molecule. Probably drive n by a sense o f the unit y o f nature, Faraday wrote prophetically that h e ha d "th e ver y stronges t conviction tha t Light , Magnetism an d Electricity must be connected." Bu t Kelvin failed t o progress with hi s attemp t to construct a formal theory of fields, a theory that would unite light with electricity and magnetism. And a s Faraday moved int o a n ol d ag e clouded b y illness, i t looked as if his dream of unification would not be realized in his time. Faraday's intensive workload led to a breakdown in his health and clear signs of mental strain. In 1840, at the age of forty-nine (the age at which Newton had a mental breakdown), Faraday wrote som e anxious an d revealin g notes : "thi s i s to de-

Figure 8.3. The current-carrying wires feel a force perpendicular to both the direction of the current in them and the direction of the magnetic field acting on the wire. Only the magnetic field due to one wire has been indicated.

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clare i n th e presen t instance , whe n I sa y I a m no t abl e t o bea r muc h talking , i t means really, and withou t mistake , or equivocation, or oblique meaning, o r implication, o r subterfuge, o r omission, that I am not able , being at present rathe r wea k in the head an d able to work no more." There was a three-year gap in which h e did nothing, not even reading science . I n his fina l years Faraday live d i n a house pro vided fo r him by Queen Victoria , his health probabl y affected b y mercury poisoning. Thi s wa s a the n unrealize d healt h hazar d tha t undoubtedl y affecte d man y nineteenth-century scientist s who worked in the laboratory, where spilled mercur y often accumulated between and beneath floorboards and generated a permanent atmosphere o f mercury vapor. Faraday carrie d o n experimentin g unti l h e wa s ove r 70 . He died i n 1867 , th e year tha t Da s Kapital wa s published, an d h e was buried i n Highgat e cemetery, in North London, where Mar x was to join him later . He lived lon g enough to see his prophecy of a unified field theory for electricity an d magnetism fulfilled, b y a theoretical genius. Dafty Sees the Light

It wa s lef t t o th e Scottis h mathematica l physicis t Jame s Cler k Maxwel l (1831 1879), who wa s know n a s "Dafty " a t school, to su m up , i n th e for m o f equations , everything tha t wa s know n abou t electrornagnetism—th e wa y i n whic h electri c and magnetic fields behaved. What Maxwell did was to express mathematically th e form o f electri c an d magneti c field s produce d b y charge s o r electri c currents , whether th e currents were stead y or fluctuating. Thus i f you wave a charged body about, the electric fiel d i t produces will also fluctuate at any given point i n space. But we have seen that a changing electric field creates a magnetic field, and this too will change strength and direction a s you wave the charged body, in its turn create a changin g electri c field , an d s o on . Maxwell' s equation s describ e quantitativel y the changing strengt h of these fields at all points i n space. His book Electricity and Magnetism appeare d i n 1873 , almos t 20 0 years afte r th e Principia an d 10 0 years after Lagrange' s Mecanique analytique. Maxwell' s equation s ar e a s basi c a s th e laws o f motion, an d togethe r they for m th e foundation s o f classical physics—th e framework withi n whic h th e physical univers e wa s explained unti l the end of the nineteenth century . I will not write dow n Maxwell' s equations , which add almos t n o new physical idea to what had been found before him. What they did do was put the ideas of Oersted, Ampere, and Faraday into mathematical form : The first la w gives the shape and strength of the electric field if we know the distribution i n space of the electric charges that are producing it. The second la w says , among othe r things , tha t al l magnet s hav e tw o pole s of equal strength; you can't have a tremendously stron g pole at one end an d a feeble one at the other. The third la w gives the strengt h an d directio n o f the electri c fiel d a t any give n point, cause d by a changing magnetic field. I t can be used, for example, to fin d the electri c force actin g on the electron s in a coil of wire when a magnet move s relative to the wire .

Lodestone, Amber, and Lightning [_95_

The fourth la w give s the for m o f a magnetic fiel d cause d b y th e movement of electric: charge or the change in an electric field . Sometimes when you have a set of equations and you sit down with a pencil and paper, you find that they contain mor e than you thought they did. When Maxwell started to play with the equations, his excitement mounted . I n 1862 he wrote tha t "we ca n scarcely avoid th e inferenc e that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena" (Maxwell's italics) . I n 186 5 h e wrot e t o hi s cousin , " I have als o a pape r afloat , which, till I am convinced to the contrary , I hold t o be great guns." We saw earlier that the movement o f an electric charge induces a changing magnetic field, whic h sets off a train of changing electric and magnetic fields, each causing the changes in the other . Whe n Maxwell analyze d th e for m an d tim e dependenc e o f the electri c and magnetic fields produce d by a fluctuating electric current, he realized that his equations showed that the changing current would resul t in the formation of electromagnetic waves traveling through space at a speed equal to the known speed of light, and with a frequency equa l to that at which th e current fluctuated. This was one of the major breakthroughs in science: the proof that light behaves like an electromagnetic wave, that wherever you are in a ray of light you can detect fluctuating electric and magnetic fields. 12 The significance of Maxwell's results was little appreciated at the time, but Einstein and Infeld, in a book published i n 1938, wrote that Maxwell's equations were "the mos t importan t even t i n physic s sinc e Newton' s time , no t onl y becaus e of their wealth o f content but als o because they form a pattern for a new type of law." This was a law that deal t only in fields, not in matter at all. Newton had expresse d Galileo's (an d hi s own ) concept s i n th e languag e o f mathematics; Maxwel l ha d done the same for Faraday. Maxwell's mathematic s pu t hi s paper s ou t o f the reac h o f many contemporary scientists, including o f course Faraday, who wrote to Maxwell and asked if, when a mathematician has arrived at his conclusions, "ma y they not be expressed in common languag e as fully , clearly , and definitel y as in mathematica l formulae ? I f so, would it not be a great boon to such as I to express them so?"13 But Maxwell had little choice. His laws involve d time an d three spatia l dimensions—an d the formal ism of differential calculu s to describe them. Meanwhile, back in Germany, Hermann von Helmholtz (1821-1894), the director of the Physikalische Technische Reichsanstalt, set out to verify Maxwell's equations experimentally . Th e studen t tha t h e chos e t o actuall y d o th e wor k wa s a bright lad calle d Heinrich Hertz . In Karlsruhe, in 1886 , Hert z showed experimen tally that an oscillating electri c current produced waves that spread through space. Their wavelength was typical of what w e would no w cal l radio waves. Moreover, he showe d tha t th e wave s travele d a t the spee d o f light. Th e scientifi c worl d acknowledged hi s achievemen t an d finall y full y realize d th e magnitud e o f wha t Maxwell had done . It was completely clear that light was an electromagnetic wave 12 In Chapter 28 we discuss why I write "behave s like " and not "is. " "Faraday had an ally in Goethe, who was also allergic to mathematicians. H e compared them to Frenchmen: "Tal k to them and they will translate i t into their own tongue where i t at once becomes something altogether different. "

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and tha t other such waves , of almost any frequency, coul d be produced, or maybe existed i n nature , a hope that wa s spectacularl y realized wit h th e discover y o f X-rays, microwaves, and y-rays, which too k their place beside the already known infared (IR ) and ultraviole t (UV) radiation. It was als o clear that Faraday' s ide a o f fields ha d t o be take n seriously , even if neither he nor Maxwell knew what fields were. The Microscopic Origins of Electromagnetism Later on we are going to find that: 1. Th e materia l cosmos i s built o f three kind s o f long-lived particles, all of which are permanently magnetic. 2. Tw o of these three particles are permanently electrically charged. If thes e fact s ar e true , why aren' t w e givin g off sparks i n al l directions , an d wh y aren't there magnets everywhere? Electricity Matter i s built u p fro m ver y small entitie s calle d atoms . There ar e many differen t kinds of atoms, but they all have the same basic structure. All atoms have a massive central core, the nucleus, which is positively charged . This charge originates in one of the two types of particle that compose the nucleus—the protons. The other type of particle in the nucleus , the neutron , is electrically neutral , or, if you prefer , ha s no electri c charge . Differen t type s o f atom hav e differen t number s o f protons i n their nuclei, but the total electrical charge on a normal atom is zero. This is because the nucleu s i s surrounde d b y a clou d o f negatively charge d particles—th e electrons. The electric charge on an electron is exactly equa l in magnitude to that o n a proton but is negative. In normal circumstances the great majority of atoms have in their immediate neighborhood as many electrons as they have protons in the nucleus, which i s why the net charg e on the ato m vanishes. It is the attraction between unlike charge s that holds the atom together, and it is also electrostatic force tha t is responsible fo r the stabilit y o f molecules, holding the constituen t atom s together. The oxyge n and nitroge n molecules-in-the-box ar e neutral: eac h molecul e ha s a s many electrons as it has protons. There is no electrical force between the molecules until the y come really close to each other, almost justifyin g th e assumption in our model that there were no forces acting on the molecules between collisions . Incidentally, when you rub amber on a cat, a tiny number o f electrons ar e transferred t o the amber ; when yo u rub glas s on your sleeve, a minute numbe r of electrons go from th e glas s to you r sleeve . We are not alway s ver y good at predicting whether electron s wil l leav e substance s whe n w e rub the m on othe r substances . Sometimes the simplest phenomena are really complex. If you could shrin k yoursel f to the siz e of an electron an d wande r abou t insid e an atom, you would feel electric forces on you from al l directions. But we are so big compared with atom s that all we normally detec t is the net result, well outside the atom, o f their collectio n o f oppositel y charge d particles , whic h i s usuall y zero . Some atoms and molecules have a net charge because their number o f electrons is either mor e o r less tha n thei r numbe r o f protons. I n othe r words , th e numbe r o f negative and positiv e charges i n the atom is unequal. Suc h ions ar e always found

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in nature in conjunction with effectively equa l numbers of oppositely charge ions. The classic example is common salt, sodium chloride, which consists of orderly arrays o f eqiua l numbers o f positively charge d sodiu m ion s an d negativel y charged chlorine ions. Once again, if we are well away from the surface of such a crystal, we cannot detec t a net electri c field, althoug h we have sophisticated instrumentatio n capable o f mapping the electri c charge on the surfac e o f macroscopically neutral matter. All electric charge in the everyda y universe originate s in protons and elec trons, and we have good reason to suppose that the total negative charge in the universe is equal to the total positive charge . The universe appears to contain equal or very nearly equal numbers of positive and negative charges. It is tempting to see the Creator separatin g th e voi d int o positiv e an d negativ e matte r in equa l quantities. This numerica l balanc e effectivel y hold s fo r all bodies o f macroscopic size and i s negligibly affected b y charging a body. This is because it takes only tiny amounts of charge to produce very strong electric fields. 14 Attempting to seriously disturb the equality of positive and negative charge in a macroscopic bod y i s no t easy . Trying to ad d mor e charg e to a n alread y charge d body is a process that meets with a rapidly growing resistance because the charges repel any incoming charge and als o repel each other. The tendency of like charges to ru n awa y fro m eac h othe r i s th e reaso n tha t yo u groun d a piec e o f electrical equipment. Thus an y static charge on a negatively charged body will prefer t o escape to the Earth, where the electrons can put more distance between themselves . The discovery of the electro n and proton at least allowed a visual image of electricity to be formed: electric current was not a fluid, it was the flow o f charged particles. I n principle, eithe r positivel y o r negatively charge d particles ca n flow , bu t electric currents through solid matter are almost always carrie d by electrons, the common exampl e bein g th e flo w o f curren t throug h metals . Ions , whic h ar e charged atoms or molecules, are normally too large to move rapidly through soli d matter. In liquids o r gases, both positive and negativ e ions ca n move easily under the influenc e of electric force . The basic questio n remains: Wha t i s charge ? Is it somethin g painted ont o elementary particles ? Is it a n intrinsi c propert y of certain kinds o f matter, or can w e scrape it off? For almost every practical purpose that you could encounter, the simple early-twentieth-centur y pictur e o f intrinsicall y charge d particle s suffices . Later, when we consider quantum mechanics, we will go deeper. Magnetism All the component s o f matter are magnetic: the proton , the neutron , an d th e electron are all tiny magnets. The electron is a far stronger magnet than either the proton o r the neutron , an d i t effectively account s for all the magnetis m normally encountered b y HM S fro m ba r magnets . Th e magneti c field s i n medica l imagin g instrumentation ar e produce d b y electri c currents flowin g throug h coils—Oer sted's experiment . The electron thus has tw o quit e differen t magneti c string s to its bow. It is magnetic in itself, but because it is also electrically charged it can also give rise to mag14 Take two sugar cubes, and from one of them take one in every billion electrons and transfe r them to the second lump. Hold the lumps one kilometer apart. The force of attraction between them is about 1000 newton, equivalent to roughly the fighting weight of Mohammed All.

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netism when i t moves. Electrons in some atoms can be regarded as moving aroun d the nucleus, thus creating the microscopic equivalent of an electric current, whic h produces a magnetic field, jus t as Oersted di d macroscopically. The electron has a property calle d spin, a s has th e proton , s o that on e visually attractiv e way o f explaining the intrinsic magnetis m o f both particles is to imagine the m to be charged spheres tha t ar e rotating abou t their ow n axesT , an d t o suppos e tha t th e rotatin g charge produces tiny electric currents, which i n turn give rise to magnetism. Thi s is a nice simple picture, but it is not very satisfactory. One problem is that the neutron, whic h ha s n o ne t charge , is als o a magnet. 15 Ther e ar e othe r mor e seriou s problems with the picture. We can understand how nature generally succeeds in hiding fro m man what is a colossal quantit y o f electric force. Mos t o f the materia l i n th e cosmo s contain s a mixture of equal amounts o f positive and negativ e charge. But how doe s it manage to hide all that magnetism, if every particle in the cosmos is a magnet? If you take two identical bar magnets and place them head to tail, with the north pole of each magnet next to the south pole of the other, you will find that their joint ability to attract paper clips at a distance has been reduced tremendously fro m tha t of a single magnet. This is the principle behind the explanation o f the nonmagneti c behavior of the majorit y o f matter. In most of the molecules i n the universe there is an eve n numbe r o f electrons—each on e no t onl y having a charge but als o actin g like a magnet. The quantum theor y show s tha t in th e vast majorit y o f such molecules the electronic magnets "pair up" two by two, pointing in opposite directions, north to south , thus cancelin g each othe r ou t completely as far as the outsid e observer is concerned. Some atoms have an odd number o f electrons, so that when al l the electroni c couple s ar e dancin g th e las t waltz , on e lonel y gu y is lef t over , his magnet uncanceled. Suc h atoms ar e automatically magnetic, but i t often happen s that they too fail to exhibit thi s magnetism because when they are present in solids, adjacent atoms arrange their magnets head to tail. Molecules that have an odd number o f electrons—free radicals, as they are called—ar e strongly suspected o f being implicated in the induction o f cancer. Tobacco smoke contains such fre e radicals . Nuclei are built up o f protons and neutrons, both types of particle being magnetic. It is not surprising that many, but not all, nuclei are magnetic. This magnetism is extremely wea k compare d wit h tha t o f electrons . Th e nucleu s whic h i s th e strongest magnet is that of hydrogen, which i s a single proton. It is about 700 times weaker as a magnet than an electron. Despite the feeble magnetism of nuclei, it has been used to great effect i n two applications. Nuclear magnetic resonance (NMR) is a technique that allows the internal structure of molecules to be examined i n great detail. I t relies o n th e fac t tha t ther e ar e magnetic field s insid e molecules, and, if not, then such fields ca n be induced. The interaction of magnetic nuclei with thes e fields ca n be detected, and sinc e the field s depen d o n the internal structur e o f the molecule, much abou t this structur e ca n be deduced from the behavior o f the nu clear magnets. Many atoms have magnetic nuclei, and chemists an d biochemists i n particular hav e studie d thousand s o f molecules b y thi s method . Th e technique s were first used in the 1950s with small molecules, but it is now possible to examine much large r molecules, in particular, small proteins an d othe r biologically signifi 15 We will see in Chapter 31 that the proton and the neutron have an internal structure, both being made of charged particles.

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cant entities. I n effect, th e magnetic nuclei act as informers, revealing the nature of their clos e environment within the molecule. The same principles ar e used i n one of the mos t important modern methods o f medical diagnosis , magnetic resonance imaging (MRI). This technique normall y makes use of the magnetism of the proton. The proton is the nucleus o f the hydrogen atom, so that al l the hydrogen atoms in your bod y lin e u p somethin g lik e (hu t not exactl y like ) littl e compas s needles , when you are placed in the magnet of the MR Imager. If an electromagnetic wave is now passed into you (radio waves don't harm you), the magnetic field o f the radiation ca n act on these magneti c needles , flickin g the m around . Thes e movements, which ar e influence d by th e chemica l surrounding s o f the proton , can be moni tored. It is possible to "see" differen t organ s and tissues, by detecting the differen t rates at which the protons flick round in different environments . The surviva l o f an anima l depend s o n it s abilit y t o collec t sens e impressions , process them, and react. For this purpose, evolution has provided a nervous system in which electri c impulse s rus h between the brain an d other parts of the body, including the sense organs. The origins of animal electricity are not mysterious; there are comparatively well-characterized chemical and physical processes within cell s and their membranes, which ar e capable of producing the kind o f voltages detected experimentally.18 The consequences o f commercial electricity have been monumental, as you can appreciate by looking around your house or waking up to find that your car battery has run down . Probably the most significant social consequence o f the availability of controllable electric current is in the fiel d o f communications; radio, television, telephones, Internet, and fax machines rely on electricity, although there is a rapidly growing use of fiber-optic links to carry messages as light signals which ar e converted to electrical impulse s a t the receiver . Many a Ph.D. in sociolog y has been, and will be, based on the communications revolution of the twentieth century. The transmission o f electricity either through power lines o r on a smaller scale usually make s use o f copper wires. Passage of an electri c curren t throug h suc h a wire alway s results i n the heating o f the wire. Sometime s this i s exactly what w e want, as in heating coils, but more often it is just a waste of energy. An important scientifi c discovery, made at the beginning of this century, has recently borne fruit i n technological advances, which ma y overcome the proble m of heat los s and thu s have enormou s economi c repercussions. It is a good example, not merely of the practica l use o f basic science but a s a double example of the primacy of observation ove r theory. Superconductivity

The passage of electrons through metal has some similarities t o the path of a molecule in a gas. When a wire is connected to a source of voltage, the electrons feel a n electric field tha t exerts a force o n them and, according to Newton, results in their 16 As with magnetism, th e con men have hyped electricit y as a cure for all manner o f ills. The following quotation fro m th e 191 3 volum e of Scientific American comes from a n article entitle d "Electrified Chickens": "Chicken s livin g in electrified flats reach, in five weeks, the norma l weight o f chickens three months old. . . . Chickens s o weak that they could not stand up, an d wh o in the ordinary course would infallibl y have died, have been put in the electrified flats and became healthy and strong."

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acceleration. A s they mov e throug h th e wire , the y collid e wit h th e stati c meta l ions an d experienc e a resisting force tha t grow s as the spee d o f the electron s in creases, just as air resistance grows with the speed of a moving body. When the resisting force and the force o n the electron due to the voltage are equal, the electron settles dow n t o a stead y spee d (remembe r your law s o f motion!]. Thi s happen s very quickly. The collisions of the moving electrons with the other components of the wire result in an increase in the vibrational energy of the atoms of the wire. In straight language, they wobble more violently. This is reflected in a rise in the measured temperature of the wire; recall the connection between temperature and motion in the case o f the ga s in Chapte r 1. That' s wh y th e filamen t of an electri c lightbul b o r a heating coil heats up and glows. The slowing down of electrons by collisions is the cause of what we technically call the resistance of the wire, and it is clear that this resistance, resulting a s it doe s in a heating o f the wire , is a source of energy loss, through loss of heat, in the transmission o f electrical energy. As i n th e cas e o f a gas (remembe r the alcoho l molecule s an d th e professo r in Chapter If), th e spee d of the electrons between collisions far exceeds their average speed along the wire. In the average household wire, which is about 1 millimeter i n diameter an d carrie s a curren t o f 5 amps, th e averag e net spee d o f the electro n along the wire is only about 2 meters in an hour. This sounds ridiculous in view of the fac t tha t electric telegraph message s cross the Atlanti c in a matter o f seconds. But think of it this way: the transatlantic cabl e is a tube of electrons that move forward as a whole if there is a voltage difference betwee n the ends of the wire. Variations i n th e voltag e a t on e en d caus e change s i n th e overal l voltage difference , which in turn cause almost immediate variations i n the speed a t which the whole collection o f electrons move forward; th e curren t varies . That's ho w message s are sent. Not e that th e curren t varie s almos t simultaneousl y a t al l point s alon g th e wire. It is not the electron that leaves London that carries the message to New York; it is the electron that is already in New York. Thanks to a discovery made in 191 1 b y the Dutch physicist Kamerling h Onnes, we can dispense with resistance. He found that as he cooled mercury the resistance of the meta l droppe d until suddenly , a t about -269° C, the resistanc e falls t o zero, where it remains, provided the temperature is not allowed to rise. This was totally unexpected an d certainl y totally unpredicted. An y scientist woul d hav e tol d you that it was impossible; electron s canno t mov e through material without bumpin g into things. Observation won ou t over common sense, not for the las t tim e in science, and a slowly growing number of substances, not all metals, were found to display zero resistance a t very low temperatures. It was not unti l 195 6 that Bardeen, Cooper, an d Schrieffe r foun d a Nobe l Prize winning explanation—know n a s th e BCS theory, for the phenomeno n o f superconductivity. Thi s theory relies on quantum mechanics. Zero resistance means that once an electron starts moving along a superconducting wire it should never stop—until it reaches the end of the wire. There is no loss of energy—because there is no resistance. It is possible to take a loop of superconducting wire , induce a current i n it , and leav e it. The current will flo w fo r years, provided, of course, that you keep the coil cooled. The energy-saving possibilities of superconductivity are staggering when on e takes into account the enormous energy loss involved in transmitting electricity along high-power lines.

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So why don' t we use superconducting transmissio n lines ? Because there i s one drawback to the miracle o f superconductivity: i t only sets in a t low temperatures; no know n substanc e i s superconductin g a t normal temperatures . I t is possible to cool a number of metals, and other substances, down to superconductivity by using liquid helium, a liquid tha t boils at 4.2 K, or in more familiar terms -269° C. Unfortunately, liqui d heliu m cost s about the sam e per liter a s whisky, whic h preclude s its use t o coo l thousands o f miles o f transmission lines . I t is, however, feasibl e t o use liquid heliu m fo r relatively smal l installations , an d its main use is in the production o f strong magnetic fields suc h a s those use d i n MRI , an d i n th e magnets used in particle accelerators (see Chapter 31). In these types of apparatus the magnetic fiel d i s produced by an electromagnet, the siz e of the fiel d dependin g on the strength of the electric current in the coils. The current in electromagnets was once limited by heating problems caused by resistance, but these have been enormously reduced by the introductio n o f superconducting coils , cooled with liqui d helium . This allows higher currents and higher magnetic fields . The possibility o f using superconductivity o n a large scale is dependent on finding materials that are superconducting at temperatures well above that of liquid helium. Th e searc h fo r suc h material s wa s regarde d b y man y theorist s a s being a waste o f time. Th e officia l theorie s o f superconductivity suggeste d that so-calle d high-temperature superconductivity was impossible. Observatio n won out again. In the 1980 s a series of materials wer e found tha t exhibi t superconductivit y at temperatures much higher than that of liquid helium , temperatures that are attainable by cooling with liqui d nitrogen , which boils a t -196° C. Liquid nitrogen costs only abou t the sam e as milk, whic h is certainl y an advantag e but stil l doe s rio t make long-distance superconducting transmission line s a realistic possibility. The discover y of high-temperature superconductor s stimulate d an explosio n of interest, primaril y becaus e o f the obviou s commercia l possibilitie s bu t als o be cause the findin g contradicted theory . In the meantime, the search goes on for new superconducting compound s i n th e hop e tha t a t leas t on e o f them wil l wor k a t room temperature. Anyone finding such material could become a multibillionaire. Electro-nnagneto-gravitational Force?

Einstein sai d tha t th e histor y o f physical scienc e contain s tw o couple s o f equa l magnitude: Galileo and Newton, and Faraday and Clerk Maxwell. The recognition of the nature of electromagnetic forc e was a turning point in the history o f science. As far as the coars e structure o f the univers e i s concerned, gravity and electromagnetism are the only forces that matter. Gravity dominates cosmology , and electromagnetism dominates the structure of atoms and molecules. Gravity is the weaker o f th e two . Th e enormou s quantitativ e differenc e betwee n th e force s i s illustrated b y the fact that , at a given distance, the gravitational attraction between a proton an d a n electro n is about 10 39 weaker than th e electromagneti c attraction between them . The amalgamation of electricity and magnetism, in spite of their apparently distinct nature , was in accor d with man y scientists ' intuitive , bu t rationall y unjusti fied, feeling that simplicity is right, and more specifically that all forces are aspects of a single force. Einstein was driven by the desire to amalgamate electromagnetism with gravity in a unified field theory, but he never succeeded, which doesn't mean

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that i t can't be done . O r that i t ca n be done . Th e discover y of another two , very short-range, forces that operat e within th e nucleus di d no t made life easie r for the unified fiel d fans , but i n the middle o f this century one of those forces wa s show n to be related t o electromagnetism. The total unification of nature's force s ha s no t yet bee n achieved , but man y physicist s hav e a n intuitiv e feelin g tha t i t wil l b e sooner o r later . Thi s i s a n exampl e o f unrationalized belie f drivin g rationa l re search. Is this how science works?

9 Belief and Action Those who carry out scientifi c researc h are the recipients of a culture developed b y previous generations. —Thomas S. Kuhn, The Structure of Scientific Revolutions

Do ou r belief s affec t ou r work ? To what exten t d o metaphysica l reflections, religious faith, or scientific dogma influence the science, as distinct fro m th e weekend thoughts, of scientists? It would be nice to think that nothing would influence a scientist's searc h bu t th e objectiv e facts. Realit y often say s otherwise . Scientist s ar e part of the society in which they live, and it is natural to look for the part their environment play s i n thei r professiona l lives, an d th e effec t i t has o n their motiva tions and the way in which they see nature. At one time that environment included philosophy. In Pythagoras, science and philosophy were intermingled. S o it was with the alchemists; they saw more than the eye beheld. Substances, besides their observable characteristics, had othe r properties tha t wer e onl y divinable wit h th e inne r eye. Gold was a metal but it was, in a very real way, the symbol of regenerate man, shining with purity of spirit, resisting every temptation, and immune to evil. The basest metal, lead, represented man the sinner , made ugly by his sinning , susceptibl e to temptation and prone to evil. Although science and philosophy drifte d apar t during the sixteenth and seventeenth centuries , they have never stopped interacting, and there have been several periods i n th e las t thre e centurie s whe n scienc e has deepl y affecte d socia l an d philosophical thinking. W e have already seen an outstandin g example of science, in the shape of Newton and determinism, infecting philosophy. The influenc e o f man's belief s on hi s scientifi c activities has bee n les s direct. The religiou s belief s o f Newto n an d Boyl e strongl y influence d th e wa y the y thought of man and the universe, but a s far as their science was concerned, philosophy an d mysticis m wer e confine d t o thei r alchemica l pursuits . Althoug h the y saw their science as the means to reveal God's creation, nevertheless, their physics is physics. What is true is that their motivation spran g partly, and perhaps predominantly, from irrational sources. What can be loosely termed irrationa l motivation is far more common than the nonscientist might suspect, and it is well documented that philosophical consideration s that bordered on mysticism were never very far from th e mind s o f several of the leadin g scientific figures of the earl y nineteent h century. Can we discern an overt influence on their scientific results'? Can you distinguish a n airplan e buil t b y a n atheis t fro m on e buil t b y a believer ? (Stronger wings?) Ho w can the result s of science, based a s they ar e on observation, depend on the convictions of the observer? The decline in religious faith over the centuries has not blunted the edge of this question, because in considering the effec t o f belief

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on the scientist, we have to include no t only conventional religious faith but also, and far more important in modern times, the belief in existing scientific dogma. For while there is perhaps a separation between the professional life o f most scientist s and thei r forma l religion , ther e ar e othe r kind s o f fait h beside s th e belie f i n a supreme being. Galileo initiall y refuse d t o accep t th e elliptical orbit s that Keple r proposed for the planets . Fo r the ancients , circle s wer e perfec t forms , an d Galileo , in thi s in stance, wa s trappe d insid e a medieval mind-set . Th e abstrac t mystical principl e overcame the concrete observable fact. The problem is general. We tend to see what we expec t t o see , and thos e expectation s can b e governe d by accepte d scientifi c theory, by philosophical convictions , or by religious beliefs. Preconditioning of the mind affect s scientist s n o less tha n othe r men, althoug h th e present-da y scientis t is, by the nature of things, more susceptible in his professional work to the compulsions that aris e fro m existin g scientifi c theor y than t o the prompting s o f philosophy o r religion. Part of the scientist' s syste m o f faith i s existing science . In practice I believe i n much o f existing science, even i f faith i n a theory occasionally turns ou t to be un justified. Th e medieval shoemaker knew that the Saint of Shoemakers was protecting him; a century ago, my scientific predecessors knew that Newton would neve r be proved wrong—faith in both cases, but that faith could affect action , in scientist s as well a s shoemakers. An undergraduat e student who , o n the basi s o f his class room lectures, has reason to believe tha t his laboratory results, when plotted , will give a straight line, is capable of drawing such a line through a series of experimental points that resemble a silhouette o f Mae West. Science is not carrie d on in a sociological or philosophical vacuum. If it is, then how do we account for the complete failure o f whole civilizations, such as the Chinese an d Islam , to contribute significantl y to rational scientific theory (as distinct from mathematics o r technology) until they were exposed to the West? The crudest fashio n in which ideology can affec t scienc e occur s i n politica l or theological dictatorships. Mar x generally made no appearance in Sovie t scientific papers, bu t hi s influenc e was fel t indirectl y i n th e officia l frow n arouse d a t on e time by quantum mechanics , an d th e quashin g o f Darwinian evolution i n the ol d Soviet Union. Chairman Mao makes appearances in Chinese scientific papers published i n the 1970s. Th e autho r o f on e chemica l paper , fo r example , explain s tha t followin g Mao's precept that "the strong will overcome the weak," he used concentrated, not dilute, acid . Th e absur d politica l kowtowin g wa s obviousl y tagge d on afte r per forming th e experiments . On e can fin d a quotation to go with anything—as I realized whe n I was trappe d fo r fiv e day s a t th e sam e ship' s tabl e a s a pai r o f Latin scholars. In the West, in our time, except in the midst o f sick episodes like McCarthyism, a scientist's proclaime d religious an d philosophical belief s are , one would lik e to think, genuinely his own. How do they affect his science ? In the twentieth centur y scientists are not, as a group, professionally influence d by religion and philosophy . Som e are prepared t o discus s th e wide r relevanc e of science, o r to pee p throug h th e chink s throug h whic h som e o f them se e Go d or oblivion. But few would admit that a single experiment o r theory bears the traces of her philosophica l o r religious convictions , whic h i s as it shoul d be. An ecologist

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may have entered his fiel d because of a mystic belief in the sanctit y o f life, but hi s professional paper s will usually rea d muc h th e sam e a s those o f a less idealisti c colleague. A believing experimental physicis t toda y keeps his religion or philosophy fo r one se t of journals and hi s experiment s o r theories fo r another. Theor y is another matter . Ther e ar e physicists an d biologist s whos e attitud e towar d evolu tion and cosmology is demonstrably affected by beliefs connected with the "meaning" of human life . If "faith" is defined broadly enoug h to include th e unquestioning acceptanc e of most o f scientific lore, it has been claime d tha t fait h doe s reach int o al l laboratories. The best-known proponent o f this thesis is Thomas Kuhn (1922-1996). Kuh n has postulate d that , at any given time in its history, each branch o f science build s for itsel f a commonly accepted collection of concepts and theories, an official way, as it were, of looking at the world. Scientists work within the borders of this "paradigm," this faith . Ther e ma y be mor e than on e paradigm i n th e sam e discipline . Thus i n the sixteent h centur y yo u could loo k at the mechanic s o f bodies through the eye s o f Aristotle o r the eye s o f Galileo. Whereas Galileo saw a body being at tracted t o the Eart h by a force, th e follower s o f Aristotle saw it "coming home" t o where i t belonged. They each started of f with a different preconceptio n o f how na ture works . Kuh n woul d sa y tha t the y ha d chose n differen t paradigms , bu t h e points out that both of them have used the same observed facts to support their paradigm. Science changes, according to Kuhn, not by the falsification metho d of Popper, not by attempting to disprove wha t i t believes. O n the contrary , science i s an activity that occur s primarily within the borders of the paradigm ; experiments are designed t o reveal fact s tha t support , rather tha n challenge, the paradigm . In fact , anything that doesn't fit in is regarded as anomalous and is either treated with suspicion o r ignore d fo r as lon g a s possible . Kuhn' s pictur e o f the scientis t i s eve n more unflattering than this; h e suggest s that i f a fact doesn' t fi t in wit h th e para digm i t i s simpl y ignore d o r not eve n "seen, " He gives the exampl e o f sunspots, which, befor e Copernicus , were not recorded by Western astronomers because the heavens, includin g th e Sun , wer e suppose d t o be unchanging, whil e sunspot s i n fact appear to move across the fac e o f the Sun. Almost immediately afte r the publication o f Copernicus's book , sunspot s bega n t o b e recorded . Kuh n note s tha t i n China, where ther e was no doctrin e o f immutability o f the heavens , sunspots ha d been observed for centuries. Kuhn further reject s Popper's claim that when a paradigm is falsified i t is abandoned. According to Kuhn, abandonment o f an old paradigm occurs only when a new one is available. In other words, Popper says that when the raft is uninhabitabl e we jump into the sea, while Kuhn says we jump only when another raft is available. Popper, in reply, concedes that much science is not carried out with the object of falsifying theories , and he sees such science as second-class. He insists that science as a whole jump s forwar d b y th e proces s o f falsification. Ther e i s somethin g i n what both Popper and Kuhn have to say, but working scientists would surely wish to modify both points o f view. Working within the paradigm is not necessarily second-class science . Th e discover y o f th e structur e an d rol e o f DN A falsifie d n o major theorie s an d smashe d n o paradigms. There were a number o f previous suggestions as to the structure, but they were hardly in the class of a paradigm, a complete system of thought, like Newtonian mechanics o r Darwinian evolution. Is Popper sayin g tha t Watso n an d Cric k wer e give n th e Nobe l Prix e fo r second-clas s

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science? As for Kuhn, I feel tha t he ha s been telling the stor y of science with very carefully chose n examples of "scientific blindness." For every story like that about the sunspot s on e can find anothe r in which a completely unexpected observation has not been ignored or downplayed. The fact tha t a strange observation i s treated with caution i s just as it should be, provided it is not rejected out of hand because of the existing paradigm: first skepticism, then experiment. In fact Kuhn himself, in attacking Popper's falsificatio n criterion , stresses the fac t that an "anomalous" observation may be mistaken and shoul d no t therefor e b e taken as the basis fo r the disproof of a theory. Although Kuhn's emphasis on paradigms has been criticized (including by himself i n hi s late r work ) he ca n strik e uncomfortably close. Ther e i s n o doub t tha t young scientists are conditioned by their education and the prestige of established theory (and established scientists) , so that they are likely to interpret what they see in terms of existing concepts and theories. They will usually try to rationalize th e unexpected in term s of the curren t paradigm. This may not alway s be such a bad thing to do. After all, if the anomalous path of one planet had cast such grave doubt on Newtonian mechanics tha t it collapsed soo n after th e Principia wa s published , there is no doubt whatsoever that the progress of science would have been seriously impeded. Th e tendenc y o f a theory to push forward regardless of troubling in consistencies i s stressed in particular b y Imre Lakatos (1922—1974) , as a model for the actual historical development of science. The history of science should dispel any idea that HMS has that science is an activity carrie d o n b y completel y unprejudiced searchers-after-knowledge, floating free o f established dogma. That is the Saturday Morning Post, white-toothed, smiling face of science. An equally mistaken view of science is typified by the antimas culine polemics o f Sarah Harding in her book The Science Question in Feminism. Here we read of oppressive masculine concept s that have, in her opinion, resulted in science being primarily concerne d with the exploitatio n of nature. Scienc e has to be emancipated, to be imbued with new values—feminist values. A scientist's belief s an d actions may be as strange as any other man's, but wha t drives a scientist i s almost irrelevan t to those of his discoverie s that stan d the tes t of time. Faraday's motives have nothing to do with the validity of his work. Nevertheless, HMS may be surprised b y the exten t to which man y of the greates t scientists have been driven by irrational forces. Newto n had alchemy and religion. Einstein clung to a stubborn belief that God would not build a universe in which cause and effec t seeme d t o vanish, as implied by the quantu m theory , a belief that was enough to prevent an astonishingly creative man from accepting quantum mechanics. In the present context it is not relevant whether o r not he was justified; what is significant is that a philosophical belief caused him to stand outside the community of physicists, for three decades. Oersted, Ampere, Faraday, and Maxwell all had dee p religious or philosophical convictions. For all of them, the concept of the unity of nature, derived immediately from Naturphilosophie an d ultimately fro m Pythagoras , had a direct or indirect influence. Oersted, Ampere, Faraday, and Maxwell

Oersted (1777-1851) was a propagator of Kant's philosophy from his studen t days .

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His doctorate thesis was based on a defense of a lesser-known book of Kant: Metaphysische Anfangsgrunde der Naturwissenschaft (Th e Metaphysical Foundation s of Knowledge ) (1786) . Kant had a seriou s interes t i n science , an d th e particula r point in his book that impressed itself on Oersted was the argument that we experience only force, an d tha t there are only two basic forces. Thi s belief, fo r it was n o more than that, in the unity of nature's forces, was to guide Oerste d fo r the rest of his scientific life. The revolt against the Enlightenment certainly affected Oersted . In particular, he was a friend o f and read the works of the philosopher Friedrich Schelling, a practitioner of Naturphilosophie. Schellin g wrote much o n the philosophica l aspect s of science. He was fascinated by the "animal electricity " of Galvani. Oersted attended lectures on Naturphilosophie an d was again particularly struck by the concept of a single unifyin g forc e accountin g fo r al l natura l phenomena . I f Oersted ha d fol lowed Schelling blindly, he would never have discovered anything. Schelling didn't believe in observation: "Coming after th e ruination o f philosophy i n the hand s of Bacon and of physics in the hands of Newton and Boyle , a higher perception of nature begins with Naturphilosophie; i t forms a new orga n of intuition fo r understanding nature. . . . [T]he concept of empirical science is a mongrel notion." Oersted di d believ e in experimentation ; h e sai d o f Schelling, "He wants t o give us a complete philosophica l syste m o f physics, but withou t an y knowledg e of nature except from textbooks." But on two things h e was firml y i n Schelling' s camp : his sympathy fo r th e genera l principles o f Naturphilosophie, an d Schelling' s belie f that a program should b e initiate d t o establis h th e natur e o f the singl e unifyin g force an d demonstrate it s ubiquity. Oersted took this task upon himself. About ten years befor e his historic discovery tha t an electric current produced magnetic effects, h e announce d hi s belie f tha t light , heat , chemica l affinity , electricity , ari d magnetism were all form s o f "one primordia l power. " An y doub t a s to the influ ence of Kant and Naturphilosophie o n Oersted's scientific impulses shoul d be removed by a n excerp t fro m Oersted' s ow n account , written i n th e thir d person , of his crucial experiment, published i n 1830, (italics mine): Electromagnetism itself was discovere d in th e yea r 1820, by Professor Han s Christian Oersted , of the Universit y of Copenhagen. Throughout his literary career, he adhered to the opinion, that the magnetical effects ar e produced by the same powers as the electrical. He was not so much led to this, by the reasons commonl y alleged fo r this opinion , a s by th e philosophica l principle , that all phenomena are produced by the same original power. This was not retrospective cosmetics , Oersted also made attempts to fit chemistry into the same philosophical scheme . Oersted accepte d a basic axio m of Naturphilosophie, whic h wa s that, because man had been created in the image of God, human reason was a reflection of divine reason. But God had also created nature so that human reason could, by itself, construe the laws of nature. This triple linkage between human and divine reason and the law s of nature was on e of Leibniz's beliefs. It also brings to mind th e more direct linkage sensed by the fifteenth centur y physician an d mystic Paracelsus, who held that man contained the whole Creation in himself and could therefore reach a far deepe r knowledge of nature than could be attained by reason, through the asso-

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elation between an object and its corresponding representation in man. Oersted attempted to weld philosophy to the natural world. One of his university colleagues wrote that "Oerste d was searchin g for this connection between two great forces of nature... . [T]he thought o f discovering this still mysterious connection constantly filled his mind." By linking magnetism and electricity, he showed that the concept of the unificatio n of natural force s wa s no t merel y a Pythagorean dream. He insti gated the experimenta l ques t afte r th e unit y o f forces, whic h carrie s o n until thi s day. His last, unfinished, paper was entitled "The Soul in Nature." Ampere was a devout Catholic who stumbled upon that bible of secular rationalism, the Encyclopedie, an d was tempted sorely . As a mathematician, he must have appreciated the logical , rational tone of many o f the articles , and th e grea t text remained an influence for much of his life , challenging his faith but basically leaving it untouched. He, too, was a n earl y disciple o f Kant in France . He adopted Kant's division of our knowledge of the world into two types: phenomena, which are our direct sensation s (wha t goes o n in you r head) and noumena (thei r objective causes). However, like most scientist s h e believed in the real existenc e o f the externa l world, a belief that he felt was challenged by Kant. Ampere convinced himself not only that matter was a reality but als o that God and th e sou l existed . Ampere believed that we can , by the rationa l operation of the mind, reveal the natur e o f the noumena. His reasoning was that the interactions between the phenomena, which occur in our minds, must be related to the interactions between the unobservables, the noumena. He agreed with Kan t that noumena coul d no t o f themselves reveal their true nature, and h e held tha t all hypotheses a s to that nature stan d o r fall o n their succes s i n leadin g t o true predictions—which is a very modern approac h to science, and reminiscent o f Popper. Naturphilosophie, an d Kant , reached England in part through the poet Samue l Taylor Coleridge (1772-1834). Coleridge's writings contain ideas that are almost indistinguishable fro m thos e o f Schelling. Coleridge was a close friend o f Faraday's first mentor , Humphr y Davy . Th e poe t ha d scientifi c interests , an d Dav y wrot e (rather awful) verse . Did the flo w o f ideas reach Faraday through Davy, and influ ence his attitude to nature? There are differences o f opinion on this point. Like Oersted and Ampere, Faraday was deeply concerned with the nature of forces, bu t h e lacked th e broa d educatio n o f his Continenta l colleague s and share d th e Britis h aversion to mystic philosophies. Farada y was a religious man, belonging to a small Protestant sec t originatin g in Scotland—th e Sandemanians , who were fundamentalists, but no t of the tight-lipped kind. They regarded the accumulation o f wealth as unscriptural an d believed in the power of love (sacred, not profane) and the separation o f churc h an d state . Ther e i s piquanc y i n th e poorl y educate d Farada y reaching the peak of the scientific establishment, i n view of the fac t that the Sandemanians electe d their bishops with no regard whatsoever to the candidate's education. Professor Joh n Tyndall, the materialis t scientist , said o f Faraday: "He drinks from a fount o n Sunda y which refreshes hi s sou l for a week."1 But although Faraday was not a man with formal philosophica l inclinations , h e would hav e sympathized with that trend in Naturphilosophie, borrowe d from Spinoza , which identi fied Go d wit h th e materia l world . Thi s woul d hav e bee n i n accor d wit h th e 'Marie-Antoinette read pornographic books during lon g services, but i t is not recorded if this refreshed he r for the week.

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Sandemanian belie f that Go d was continually involve d with his universe and that the proof of his existenc e lay in the contemplation o f nature. I t was his universe, a universe crossed by many forces, al l of which were the face s o f one force . In his scientifi c writings, Faraday , unlike hi s Continenta l colleagues , was reticent about the beliefs, religious or philosophical, tha t sustaine d him , but his continual effort s t o show the unity of natural forces are in complete accord wit h the ideas tha t Coleridg e brought back from German y in 1799 . Apart from hi s wor k in electromagnetism, he attempted to find a connection between gravity and magnetism, and his work on electrochemistry, in which h e sees a connection between the forces o f chemical affinity an d electricity, fits into the general scheme.2 Maxwell was also deeply religious, his belief in God so strong that he wrote, "If we had see n Him in the flesh we should not have known Hi m any better, perhaps not s o well." I t i s ver y doubtfu l tha t h e wa s directl y influence d b y th e Germa n school of philosophy, but ther e i s at least one influence that ca n be traced back to Na turphilosophie. Considering hi s intellec t an d hi s master y o f electromagnetism , th e questio n could be asked: Why didn't he believe in a unit o f electric charge? In other words, why didn't he foresee the electron ? It is obvious to us that electricity comes in dis crete particles, but we believe in atoms and molecules, arid the electron is "real" for us. In Faraday's case we have conjectured that Naturphilosophie wa s the root of the trouble. The Naturphilosophen rejecte d the ide a of particles in nature. It is almost certain that Coleridge's friendship with Humphry Davy accounts for the latter's disbelief in atoms, which h e passed o n to Faraday. Maxwell admired Faraday greatly, and it is interesting to speculate that he too inherited the antiparticulate view of nature. When he dealt with electrolysis in his treatise, he felt himself force d to refer to a "molecul e o f electricity," but mad e excuses, terming the phras e "gross " and implying that it is merely a convenience, useful fo r calculations but having no reality. Naturphilosophie i s not completely dead; once in a very long while Goethe is invoked i n criticizin g science—whic h i s a pity . Goethe' s Faus t i s on e o f the grea t metaphors fo r man' s condition . T o see k inspiratio n fro m hi s mystica l pseudo science is like taking spiritual sustenance from Shakespeare' s laundry list. Scientists ar e the product of their environment , but they are not unique i n this respect. There i s a generally applicable sermo n i n th e Englis h poet Te d Hughes's admonition: "Th e progres s o f any write r i s marke d b y thos e moment s whe n h e manages to outwit his own inner police system."3

2 This research may have been stimulated b y the German Ritter, who, influenced by Kant, and before there was any experimental evidence , attempte d t o unify th e two phenomena . 3 For an amusing comment o n Hughes's remark, see the poem " A Policeman's Lot " by Wendy Cope in "Making Coco a for Kingsley Amis," Faber &Faber , London, 1986 .

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iv The structure of atoms has been hinted a t in the previous section, where we saw that atoms consist of a massive, positively charged, central body—the nucleus, surrounded by small negatively charged particles, the electrons. We cannot se e these particles and, even unti l the early years of this century, there were those, including severa l notable scientists, who refused t o believe in the existence of atoms. In this section we will go deeper into the structure o f the atom and of the many forms o f matter that nature and man have made. The story really takes off at the very end of the nineteenth century . The basic principles o f atomic and molecular structur e were completed by the middle of the twentieth century. We will look at the way in which th e structure of the atom was revealed, but not at the explanation for that structure. This is a little like noting the paths of the planets without knowing about Newtonian mechanics. I n fact, tha t mechanics doe s not help us to understand th e way in which atoms are built or the manner in which they behave. Fo r that we need quantum mechanics, which we will tackle later. Newtonian mechanics ca n describe the paths of the gas molecules in our opening chapter, but it says nothing about the internal structur e of those molecules, or how they react chemically, and why they very often don' t react. In Chapter 12, we are going to make a tourist's bus ride around the material world—on your left, metals; on your right, halogens. The study of the behavior of even a small class of molecules can fil l a lifetime, but, as the man said , I haven't got that many changes of socks; so we are going to take a panoramic view of the basis of existence. Modern material science and chemistry are built on the achievements of those who too k matter out of the hands o f the alchemist and into the scientific laboratory. We start this part by acknowledging their pioneering contributions .

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10

The Demise of Alchem y ... afoul and pestilent congregation of vapours! —Hamlet

"I have Immortal longings in me." Cleopatra, waiting to take the as p from Ira s and preparing t o meet eternity , declare s tha t sh e i s "fir e an d air ; m y other element s I give to baser life." Most of the spectators in Shakespeare's audience knew what she was talking about. Since antiquit y th e fou r elements : earth , water , air , and fire—ha d bee n par t of the accepte d syste m o f beliefs of Western man. Eart h was lowest , and wate r covered the Earth. The fact that in some places the Earth rose above the waters was just another piec e o f evidence fo r the constan t wa r between th e elements . Abov e th e waters were air and fire in that order. These, like Cleopatra, were the Elements that strove to rise upward, leaving behind th e base elements earth and water, which remained below in their natural habitat . The workings of the natural world were an almost complete mystery to sixteenthcentury man, but the elements explained a lot. Th e four elements controlled th e nature of men and matter rather than serving as building blocks. It was the proportions that mattered. Marc Antony says of Brutus, "This was the noblest Roman of them all. .. . [T]he elements so mixed in him that nature might stand up and say to all the world 'This was a man.'" Medicine, from the second century, had taken its language from the same source. It was then that the great physician Gale n wrote the idea into his immensely influ ential texts. The four humors tha t governed man's health and sickness corresponded one-to-one to the fou r elements . Eart h and melancholy were both dr y and cold; water and phlegm, moist and cold ; air and blood were moist an d hot; and fir e an d choler, dry an d hot . Most people had a n exces s of one of the fou r humors . Brutus had, according to Antony, an ideal balance, but in most men the balance was never static. Tainberlaine, in Marlowe' s play, famously restate s the commonl y accepted notion o f perpetual struggl e between the elements : "Natur e that framed u s o f four elements, Warring within our breasts for regiment." The elements were , conveniently, s o vague in their properties as to allow an explanation o f almost anything. The y could even change into each other. Donne says so: "Ayre condensed becomes water, a more solid body. And Ayre rarified becomes fire, a bod y mor e disputabl e an d in-apparent. " I n explainin g huma n disease , if everything els e failed, one could always appeal t o the influence o f the stars o n th e elements, which account s fo r the fac t tha t a knowledge of astrology was still need ed to qualify i n medicine i n Paris as late as the second half of the seventeenth century. A Paris physician who, in 1607 , suggested that one way to fight the plague in Paris wa s t o kee p th e street s an d gutter s clean , wa s completel y ignored ; bu t i n

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1658, one of Louis XIV's surgeons advised that the king should be bled in the firs t and last quarters of the Moon, "because at this time the Humours have retired to the center of the body," It was int o this world tha t Robert Boyle was born in 1627 . Robert was the four teenth o f fifteen childre n o f Roger Boyle, earl of Cork. It was sai d o f Robert Boyle that, like Newton, he "hath neve r been hurt by Cupid." He remained a bachelor all his life, living with his sister, the remarkable Lady Ranelagh, a woman whose high , self-imposed level of education wa s a distinct rarity in a society that regarded education for women as an unquestionable waste of time. In her house he set up a wellequipped laborator y in which h e carried out scientific experiments, helpe d b y assistants. He died in 1691, exactl y one week after his sister. They are buried togethe r in St. Martin's-in-the-Field in London. Boyle, like Newton, was a deeply religious man. Between them they did perhaps more than anyone else to build the mechanistic basis of physics and chemistry that was to finally dispense with the mysticism that pervaded medieval physics and especially alchemy . Typicall y of the transitiona l natur e o f the age , neither o f the m lost their belief in alchemy. In Newton's case this belief included the occult aspects of alchemy, but Boyle was more interested i n the ancien t attemp t to create gold. In 1689 h e persuade d th e governmen t to repeal a law, dating fro m Henr y IV, forbidding the "multiplying of gold." Boyle's scientific impuls e develope d early, inspired particularl y by his readin g of Latin authors who "conjure d up tha t unsatisfied greed for knowledge that i s yet as greedy as when i t first wa s raised." H e was intrigued b y "the ne w paradoxe s of the great star-gazer Galileo," who died when Boyl e was in Florence, where "did h e sometimes scrupl e . . . t o visit th e famouses t bordellos . . . (but) retained a n un blemished chastity. " Whe n th e tim e cam e tha t h e wishe d t o star t researc h int o chemistry he decided to leave Ireland, "a barbarous country where chemical spirit s were so misunderstood and chemical instruments so unprocurable that it was hard to hav e an y Hermeti c thought s i n it. " Hermetic referre d t o Hermes Trismegistus , Hermes the thrice-great, the mythical creator of alchemy. Both Boyle and Newton lived at a time when science was felt by many to be not too compatible with religion. Boyle felt the need to refer to this specifically, as witnessed by The Excellency of Theology Compared with Natural Philosophy an d th e explicitly title d Some Considerations about the Reconcilableness of Reason and Religion. In 1690, the year before he died, Boyle published The Christian Virtuoso: Shewing That by Being Addicted to Experimental Philosophy a Man Is Rather Assisted Than Indisposed to Be a Good Christian. ( A "virtuoso" wa s a n amateu r scientist.) Newton and Boyl e interacted. Newto n studied Boyle' s work and offere d a n (incorrect) explanation o f Boyle's la w (se e Chapter 1) , and Boyle , aware o f Newton's work, declare d Go d to b e a watchmaker . H e frequently use d th e grea t cathedra l clock at Strasbourg as an analog y for the working s of nature. " I consider th e fram e of the world, already made, as a great and, if I may so speak, pregnant woman with twins in her womb. . .. Such an engine as comprises or consists o f several lesser engines." Three centuries before, Bishop Nicole d'Oresme had coined the phrase "th e clockwork universe" an d ha d o f course see n God as the suprem e clockmaker . For Boyle, a s for Newton, the mechanica l univers e strengthene d hi s belie f i n a Great Designer. Boyle spoke often o f God's "concurrence" wit h th e operatio n o f the uni -

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verse, but miracle s wer e no t rule d out . Both Newton an d Boyl e were affecte d b y Descartes—Newton perhaps mostly by Descartes's mathematics an d Boyle more by Descartes's attempt to build a mechanistic, logical theory for the material world. Sometime i n th e 1640 s a grou p o f scholars an d other s intereste d i n "natura l philosophy" bega n t o meet regularly i n Oxfor d t o discus s wha t wa s then know n as experimenta l philosophy , but whic h we would cal l science . Boyl e was one of the members o f this "Philosophical! Clubbe," also known a s the Invisible College , which wa s patronize d by his sister , Lad y Ranelagh. A t one time i t spli t into tw o groups, on e i n Londo n an d on e i n Oxford , th e latte r grou p meetin g i n Boyle' s rooms in the university. In 1662 the informal club was given a charter by Charles II and becam e the Roya l Societ y of London for Improving Natural Knowledge. Five years earlier the moneyed Henri-Louis Habert de Mantmor had initiated a series of meetings i n his home in Paris, where scientifi c subjects were discussed . Th e constitution o f the so-calle d Montmor Academy stated, in the spiri t o f Bacon, that it s aim "shall no t be the vain exercis e of the mind o n useless subtleties " bu t "th e improvement of the convenience s o f life." The origina l member s o f the Roya l Society , which me t o n Wednesdays , wer e more lovers of science than scientists. It is a sign of the growing standing of science that, in addition t o scientists suc h a s Robert Hooke, Boyle, and others , there wesre, among the members of the society , figures suc h a s the architec t Christopher Wren, the poet Dryden, the diarist John Evelyn, and fourteen peers of the realm, including the duke of Buckingham. The motto of the new society was Nullius in Verba, which can be roughly translated a s "Don't trust anythin g that anyon e says," another very Baconian sentiment. Around abou t 1626 , Sir Francis Bacon published New Atlantis, which, thoug h fictional, was a supplement to his scientific writings. In it he foresaw the establishment o f scientifi c societie s an d researc h institute s modele d o n hi s "Salomon' s House." It is not surprising that the Royal Society saw Bacon as its spiritual forefa ther, especially i n view of his utilitarian vie w of science. The new societ y quickl y provided a focus fo r the collectio n o f scientific and technologica l report s and th e encouragement o f research. It contributed i n an indispensable wa y to the interna tionalization o f science. Thu s scientist s i n Europ e were invite d t o publis h thei r works in The Philosophical Transactions of the Royal Society, and on e o f the firs t members to be electe d afte r th e societ y was establishe d wa s the prodigiousl y talented Dutch scientist Christiaa n Huygens, who corresponded with Descartes, Newton, an d Boyle . The pionee r Dutc h microscopist Antoni e van Leeuwenhoe k was also elected to the society, in 1680. Scientist s in England and the Netherlands were corresponding abou t ne w experiment s whil e thei r respectiv e navie s wer e bom barding each other. 1 Science, by the time o f Newton, had become a supranational secula r church . Latin, although it was not completely replaced by French as the secular lingua fraii ca until toward the end of the eighteenth century, was ceasing to be universally un derstood, and Huygens, for example, used si x languages in his correspondence. (The "unsociable" Hook e was rumored to have doubte d the veracity of any docu 1

This scientific crossin g of the trenches wa s echoed i n 1806 when the English chemist Humphr y Davy was awarded a prize of 3000 francs by L'Institut Francais althoug h England and France wer e at war. Both Davy and the institute came under criticism in their respective countries .

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ment written in French.) Today the international languag e of science is English, and the scientific community covers the entire globe. The Invisible Colleg e still lives. The activities o f the Roya l Society in it s early day s attracted a good measure of ridicule. Samue l Pepys' s diar y entr y fo r 1 February 166 4 reveal s tha t h e wa s a t Whitehall tha t da y and hear d th e kin g laughing a t the societ y "fo r spending tim e only in weighing ayre and doing nothing else since then." "Virtuosi" became an accepted target for wits abou t town. Samuel Butler wrote a mediocre play called The Elephant on the Moon (1676) , in whic h som e o f the virtuos i ar e characterized as men "who greedily pursue / Things wonderful, instead of true." Thomas Shadwell , a mino r playwright , satirize s th e virtuos i i n a play o f that name . Bu t these wer e early days. After Newton the attitude toward science changed. Among th e trun k o f books tha t Si r Walte r Raleigh took t o se a wit h hi m wa s Robert Boyle's book The Sceptical Chymist (1661) , which marke d the firs t stirring s of modern chemistry. Written in the for m o f dialogues, it was, in the author's esti mation, " a book written b y a Gentleman, an d wherei n onl y Gentleme n are introduced as speakers. " The Sceptical Chymist contain s th e firs t clea r statement s o f the concep t o f a chemical element (although not a modern definition) and o f the differenc e betwee n a mixtur e o f elements an d a chemica l compound . Boyl e realized tha t i n a compound suc h a s water, composed of oxygen and hydrogen, the atoms are more than mixed together; they cling to each other in small groups. Water is not the same as a mechanical mixtur e o f hydrogen an d oxyge n gas, as you ca n prov e by throwing a burning match into a sample of each. Boyle was the firs t to thoroughly discredit the idea o f the four elements , an d he dismissed th e three principles (salt , sulfur, an d mercury) of the famous sixteenth century physician and alchemist Paracelsus. Hi s concept of corpuscles is an atomic theory in that it assumes matter to be composed of small, indivisible particles , and it makes a significant advance on the theories of Democritus and Descartes by postulating that there were a large number o f different type s of particles, each type associated with a different elementar y substance. Thi s accords with modern theory. Boyle accepted that he lacked a systematic method t o identify elements : " I have not yet, either in Aristotle or any other writer, met any genuine and sufficien t diag nostic for the discriminatin g an d limiting of species." Boyle stands between alchemy and chemistry. His great contribution was to realize that matter is composed of a range of elements, eac h of which, i n its pure form , is a collectio n o f identical corpuscles o r atoms. The atom s o f each elemen t wer e different fro m th e atom s of any othe r element. It is a reminder o f the natur e o f the intellectual worl d o f the seventeent h centur y tha t Boyl e was worried tha t hi s revival of atomism would arouse suspicions o f atheistic tendencies because atomism was associate d no t onl y wit h Democritu s bu t als o with th e atheisti c materialist , Lucretius. Boyle buil t o n th e idea s o f others ; but h e dre w togethe r divers e an d unclea r ideas, added to them, and expressed them in a way that was to influence the course of chemistry . Sometime s dubbe d th e Fathe r o f Chemistry, he wa s responsibl e fo r placing th e emphasi s o n careful experimentatio n and th e abjuratio n of Scholastic or occult explanations . I n the manner of a modern scientist , he chronicled th e details of his experiments, eve n the unsuccessful ones. He brought the concept of the chemical elemen t int o th e limelight . H e was amon g those who , fo r good o r bad,

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began the proces s o f separating philosophy fro m science . Bu t he coul d not mak e that brea k completely, any more than Newto n could , because h e was too much a child o f his time. He was not a great chemist, but he opened the door to chemistry. The Father of Chemistry?

If you ask a French scientis t t o name the father of chemistry, he will chauvinistically, but justifiably , answe r "Lavoisier. " If you were to ask an end-of-the-eighteenth century Frenc h merchan t wh o Lavoisie r was, h e woul d probabl y spit . Lavoisie r picked a n unfortunate profession for someone livin g a t the tim e o f the guillotine ; he wa s a tax collector , and h e became a millionaire becaus e o f it. It did no t hel p him, in the eyes of the Revolution, that he was also born into wealth and that his fa ther had bought him an aristocratic title in 1772, when Lavoisier was twenty-nine. Louis XV I funneled hug e amount s o f money int o th e state' s coffer s b y taxin g salt. Everyone was oblige d by la w to buy a minimum designate d quantit y o f salt and wa s taxed o n the basis o f that quantity . Ta x collectors like Lavoisier did well, but salt smuggling was common, so Lavoisier suggested that a wall be built around Paris in order to control the passage of carts into and ou t of the city . The wall was literally to be the deat h of him. Designed by the famous architect Ledoux , it was 10 feet tall , 1 8 miles i n circumference , and punctuate d b y 5 4 custom posts. It cost a vast amount o f money and was vastly unpopular. Th e due de Nivernois suggested that Lavoisier should be hanged. Forty of the gates were sacked in the Revolution. In 1780 . Jean-Paul Marat, the anti-Newtonia n revolutionary-to-be, publishe d a letter claiming that he had succeede d in making visible the "secret component " of fire. Lavoisie r scoffed, bu t Mara t was to have his da y when th e Revolutio n came. The fiery , self-proclaime d "Friend o f the People" accused Lavoisier of imprisoning the city and restricting its air supply: "Would to heaven that he had been strung up on a lamp-post." Lavoisier, who had supported the Revolution when it started, was arrested. H e was tried o n 8 May 1794 and execute d o n the sam e day , in th e grea t square now known a s the Place de la Concorde. His body was thrown int o an unmarked grave. Lavoisier's contribution to the understanding of matter arose from his insistenc e that i t wa s no t sufficien t t o repor t th e qualitativ e result s o f chemical reactions ; quantitative measurements ha d to be made. This sounds trivial today, but it does so primarily because o f Lavoisier. He was a quantitative experimentalist , whic h wa s just what chemistry needed so badly. The alchemists ofte n use d ill-defined materials, and there is no evidence that they attached any fundamental importance to the weights o f the materials the y used in their experiments . I t was rather the nature of the products that was their mai n concern. I t was not surprising that it had proved impossible to bring any kind of order into chemistrjr. Boyle's concept of elementary corpuscles, what we would cal l the atoms of the elements, broke through the mist, but real progress was impossible without quantitativ e studies . In Lavoisier's time , chemistry was dominate d b y the phlogisto n theory , which stated tha t whe n somethin g wa s burned i t gave of f an invisibl e substanc e calle d phlogiston. If this were true, it implied tha t burning a substance would resul t i n a decrease in its weight. The fact that burning ofte n resulted i n an increase in weight worried som e of the proponents o f the theory, but the y solved the parado x by giving phlogiston a negative weight, so that when i t escaped from a body that body did

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indeed increas e i n weight . On e can regard this "explanation " eithe r a s a demon stration o f creative thinking—the ability to break away from preconceived ideas — or as a disgraceful subterfuge . I have a weakness for the forme r view. Strange ideas can be true. After all, how many people believed in antimatter before it was found? And didn' t Kepler propose the "strange " but correc t idea that the attraction o f the Moon caused the tides , only to be dismissed b y Galileo for lending "hi s ea r to occult properties and such-lik e fancies"? Phlogiston prove d to be a myth, and i t was Lavoisier who killed it. By way o f illustration o f his wa y o f thinking, consider Lavoisier' s investigatio n of the burning o f tin. He weighed a piece of tin, placed it in a large vessel containing air, sealed the vessel, weighed it, and heated it. There was an obvious change in the appearance of the tin, which turned t o a powder. An eighteenth-century scien tist would have said that combustion had occurred . We would sa y that it had been oxidized, tha t i t had combine d with th e oxyge n in the air. Afte r th e seale d vesse l had bee n allowe d t o coo l down , h e weighe d i t again . There was no change in weight. Matte r ha d bee n conserve d i n a chemica l reaction . Th e conservatio n of matter (i n chemical reactions ) becam e a fundamental principl e i n science . Whe n Lavoisier opened the flask, there was an inrush of air. He reasoned that, contrary to the suppositio n tha t the tin ha d give n off something when it burned, i t had take n something fro m th e air . Consistently, the burned ti n was heavier than th e origina l metal. At about this time h e was visited b y the Englishman Joseph Priestley, who had also performed experiments involving combustion but had interpreted the m in terms o f the phlogisto n theory . Lavoisier sa w the tru e meanin g of his an d Priest ley's work : the y ha d bot h discovere d th e ga s oxyge n (th e nam e give n t o i t b y Lavoisier), and burnin g wa s merel y th e combinatio n o f a substance wit h oxygen, not th e los s o f a hypothetical substanc e wit h negativ e weight. Phlogisto n wa s a n unnecessary concept , holdin g u p th e progres s o f chemical science . Priestle y wa s not convinced, but Lavoisier had set modern chemistry on its path. Another Conservation Law The conservation of mass is a reflection o f the fac t that in ordinary life we can neither create mass nor destroy it, just as charge is inviolable. In the twentieth centur y Einstein showed that mass an d energ y were in fac t interconvertible , but thi s is almost irrelevant to everyday life, excep t in the conversio n o f mass to energy in nu clear reactors and nuclear weapons. Chemistry Takes Of f Lavoisier proceeded to examine a large number of substances, using his balance and his logic. He burned two small diamonds and showed that they were converted into carbon dioxide, the sam e gas produced by the complet e combustion o f charcoal. This demonstrate d that diamond i s a form o f carbon. He burned alcohol, showin g that the reaction produce d water and carbon dioxide , and deduce d fro m hi s measurements tha t alcoho l contained carbon , hydrogen, and oxygen . This kind o f experiment opened the door to the elucidation of the atomic composition o f complex substances. He , like Priestley, showed tha t oxygen was essential t o animal respiration: "One fifth onl y of the volume of atmospheric air is respirable." He realized that combustion of a number of organic materials, such as sugar, produced the sam e gas as respiration, namely, carbon dioxide. The analogy that he saw between combus-

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tiori and respiration was of seminal importance in the development of physiology. Lavoisier graspe d th e importanc e o f Boyle' s concep t o f elements . Whe n h e found a material tha t coul d no t b e decompose d hy an y mean s available , he as sumed that i t was an element. Inevitably, considering the state o f chemistry in hi s day, he made mistakes. He mistakenly though t that silic a (silico n dioxide) was an element because he found no method to break it up. Lavoisier listed thirty-two elements, some of which we now know to be compounds, and two of which, light and heat, are not material. Strangely, he did not accept the idea of the atom. There was no direct evidence for the existence of atoms in his day, and as late as the beginning of the twentiet h centur y the eminen t physica l chemist Wilhel m Ostwald fel t tha t the atom was an unnecessary concept. Lavoisier lai d ou t the principle s o f chemistry, a s he sa w them, i n the tex t that should be regarded as the tru e beginning of modern chemistry: Traite elementaire de chimie. Ther e h e state d explicitl y th e principl e tha t matte r i s conserve d ir i chemical reactions. The book was published i n 1789 . On 14 July of the sam e year the Bastille fell. On 1 4 July 1791 a group of incautious, radical-minded Englishmen gathered in the Royal Hotel in Birmingham to celebrate the second anniversary of the fall of the Bastille. A hostile mo b stone d th e hote l an d the n marche d t o Josep h Priestley's house. The scientist wa s not onl y a supporter o f the America n Revolution against the king of England, and the French Revolution against king and God, but moreover was hardly an orthodox Christian. He had published a book entitled History of the Corruptions of Christianity (1782), in which he had rejecte d miracles, original sin, and the Trinity, and, although a Dissenting minister, had declare d that everythin g was matter, including the soul. The standard early-nineteenth-century mob in England was anti many things: Bonaparte, the French, the pope, and Dissenters. They burned dow n Priestley' s home , containin g hi s laborator y and library . Wha t hurt him most was the loss of his scientific writings, "manuscripts whic h have been the result o f the laboriou s study of many years, and whic h I shall never be abl e to recompose; an d thi s ha s bee n don e t o on e wh o neve r did , o r imagined , yo u an y harm." The riots persisted for three day s as the eternal , mindless mo b howled for the blood of "philosophers." Man y fearful citizen s pu t u p notice s o n their houses proclaiming "N o philosophers here. " Priestle y emigrate d to Americ a three year s later and settled in Pennsylvania, where his lectures o n Christianity led to the formation of a Unitarian Society. He died in 1804, firm in his belief in phlogiston. The burning of Priestley's house i s symbolic of the dwindlin g o f the Enlightenment dream of endless progress through the operation of reason and man's humanity to man. Priestley lived with this dream : "Nature . . . will be more at our com mand; me n wil l mak e thei r situatio n i n thi s worl d abundantl y mor e eas y an d comfortable . . . and will daily grow more happy. .. . Thus, whatever was the beginning of this world, the end will be glorious and paradisiacal beyond what our imaginations can now conceive." Or will the crowd decide that there will be no philosophers here? Another Father of Chemistry

The man who finally unambiguously established th e idea of the chemical element in mode m scienc e wa s John Dalton (1766-1844), the so n o f a Quaker weaver. He

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was put i n charge of the village school at Kendall, in the Lak e District, at the age of twelve. The appointment wa s not an outstanding success . Dalton was perhap s th e firs t full-tim e professional scientist. Fa r fro m enjoyin g the inherite d wealt h o f a Lavoisier or a Boyle, he earne d mone y by teaching an d lecturing. Dalton was no t avers e to speculation, but observatio n cam e first . B y a series of simple experiments, he set out to show that certain substances coul d not be broken up to give simpler components, an d he began the accurate determination of the relative weights o f the atoms of different elements . It is still impossible to directly weigh a single atom, but there are ways of getting the relative weights of different atoms , if certain assumptions ar e made. Thus, suppose you tell me that you have an unknown numbe r o f place settings consisting of only a knife an d for k for each person . I f you now separat e all the knives fro m th e forks and give me the two piles, then by weighing them I can tell you the relative weights of a single fork to a single knife—without knowing how many knives an d forks I have, or what their absolute weights are. The only assumption I have made is that the two piles contain equal numbers. In 1803 Dalton published a memoir that contains th e following sentences: "An enquiry into the relative weights o f the ulti mate particles in bodies is a subject, as far as I know, entirely new; I have lately been prosecuting this enquiry with remarkable success. The principle canno t be entered upon in this paper; but I shall just subjoin the results, as far as they appear to be ascertained by my experiments." Using simple assumptions and arguments, Dalton arrived at the first-ever list of relative atomic weights, which he gave at the end of his paper. No one took much notice at first, but gradually it dawned o n the scientific community that Dalton's data opened the door to the experimental determination of the compositio n of molecules, in terms of atoms. The first ste p in determining the nature of any molecule is to find out which types of atoms it contains an d how many there are of each type. Without relative atomic weights this was impossible . Lavoisier had not believed in atoms; Dalton did. After Dalton, it was accepted by almost al l scientists tha t atom s existed, that they had fixe d weights , and that the y were indivisible . Dalton's lif e illustrate s th e growin g respectability o f science an d it s continuin g international flavor . In 1816, on e year after th e defea t o f Napoleon at Waterloo, the French Academi e de s Science s electe d Dalto n to be a corresponding member . I n 1833, after lobbyin g by a group including Charle s Babbage, the pioneer of the computer, the British government awarded Dalton an annual pension o f £150. When he was buried i n 1844 , about 40,000 people filed pas t his coffin . Afte r hi s death , on e of his eyes was dissected, in accordance with his wishes. Dalton was color-blind, a defect which he supposed to be caused by a blue coloration of the fluid in his eyes. The result of the dissection di d not support his hypothesis . A succession o f Italian an d Frenc h scientists—Avogadro , Cannizzaro, Gay-Lussac, and others—built on Dalton's ideas and corrected his errors, but the real breakthrough was Dalton's, whom many refer to as the fathe r of modern chemistry . After Boyle an d Lavoisier , h e i s th e thir d t o be s o dubbed , but ther e i s littl e poin t i n championing one or the other: chemistry evolved, it had its heroes, but it never had a Newton. The work of Faraday, Lavoisier, and Dalton underlay the science-based transfor mation of everyday life that blossomed in the nineteenth century .

II The Nineteenth Century The Origin of Species, published in 1859, inaugurated an intellectual revolution suc h as the world had not know n since Luther nailed his theses t o the door of All Saints Church at Wittenberg. —E. R. Pease, secretary of th e Fabia n Society

Science Brings Home the Bacon

In 1834, during a discussion in the Chambre des Deputes, the distinguished Frenc h physicist Arag o was asked to justify hi s request for government support of the sci ences. His colleagues demanded to know what practical benefits had accrued from the discoverie s of science? Arag o could onl y think of one example: the lightnin g conductor. By 1900 , HMS coul d hav e provided a far more impressive catalogue . By then, the practical applications o f basic science were everywhere to be seen, and the Baconian conviction that man could determine his own destiny through science was renewed. But not everyone joined in the applause. It wa s inevitabl e tha t theory , i n th e shap e o f Darwinism, an d practice , in th e form o f science-based technology, were seen as threats to belief. At its best, science ignored faith; at its worst, it challenged Holy Writ. The materialism engendered by technology ha d als o tainte d the socia l sciences , wher e economics an d the law of supply and demand were replacing more philosophical notions, such as the social contract, that had occupied the thinkers o f previous generations. Blind Admiration One of the books that I, as a ten-year old, found in my father's wildly heterogeneous library was Winwoo d Reade's Martyrdom of Man, from whic h I copied ou t som e frequently quote d lines: When we have ascertained, by means of science, the methods of Nature's operation, w e shal l b e abl e t o tak e he r plac e t o perfor m the m fo r our selves . . . men will master the force s o f Nature; they will become themselves architects o f systems, manufacturers of worlds. Man will the n be perfect; h e will be a creator; he will therefore be what the vulgar worship as God. That prediction o f a scientific Utopia was penne d i n 1872 . The socialis t Beatrice Webb summe d up , i n 1926 , her understandin g o f the prevalenc e o f suc h senti ments: It i s har d t o understan d th e naiv e belie f o f the mos t origina l an d vigorous minds o f the 'seventie s an d 'eightie s that i t was by science , an d by science alone, that al l human miser y woul d b e ultimately swep t away . This almos t

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fanatical fait h wa s perhap s partl y du e t o hero-worship . Fo r who wil l den y that the men of science were the leading British intellectuals o f that period? Naive or not, The Martyrdom of Man went through many editions, and it s exaggerated view s o f the potentia l o f science an d th e evil s o f religion ha d a wide appeal . Reade's success owed a great deal to Darwin, but just as much to the aura bestowed on science by the successe s o f the scientist s o f the nineteent h century . Few o f his admiring reader s full y understoo d th e meanin g o f th e grea t scientifi c break throughs, but those who did , or thought the y did, forme d a n influential and voluble minority. His audience wa s by no means universall y sympathetic to his athe ism, but it was very aware of why he thought that science had superseded the blood of th e Lamb . Never had s o many been both spirituall y influence d an d materiall y benefited b y science. Paradoxically , the impetus behind many people's respec t for science wa s the Industria l Revolution , a revolution tha t had ver y little t o do with science. The Iron God The nineteenth centur y opened as the Industrial Revolution was gathering momentum, an d b y the en d o f the centur y th e wester n Europea n nations dominate d th e world. That dominatio n depende d heavily—militarily , commercially, and psychologically—on the technological gap between Europe and the rest of the world. This gap was initially opened up by what ca n be termed the first Industria l Revolution, initiated i n late eighteenth-century England. The first Industria l Revolution , which was based on the powe r o f steam-driven machines, owed almost nothing to science. It was created not in laboratories but by practical men, men who had learned their engineerin g in factories an d mines. The counsel fo r Richard Arkwright, th e invento r o f the spinnin g frame , sai d i t al l i n court: It i s wel l know n tha t th e mos t usefu l discoverie s tha t hav e bee n mad e i n every branc h o f art an d manufacture s hav e no t bee n mad e b y speculativ e philosophers i n their closets , but by ingenious mechanics, conversan t i n the practises i n us e i n thei r time , an d practicall y acquainte d wit h th e subject matter of their discoveries . So much for those, Romantic poets included, who had lai d the blame for the social disasters o f the Industria l Revolutio n at the doorste p o f science. Establishe d sci ence was not a social force. Th e Royal Society had straye d far from th e day s when Hooke and Boyl e and their lik e had create d it , having become a social club for scientific nonentitie s and agin g aristocrats. As Richard Steele wrote in th e Tatler, as early as 1709, "When I meet a young fellow that is a humble admirer of science, but more dull than the rest of the company, I conclude him to be a FRS." British engineering impressed "th e natives" on four continents. Hal f the world's ships were built in the dockyards of Tyneside. One of the factors that raised the level of engineering was Charles Babbage's attempt to build a mechanical computer. 1 In 'The remarkable Ada Lovelace, Byron's only legitimate child, translated and annotated lecture notes taken in Italian during Babbage's visit to Italy, where his work had aroused great interest. A computer language called ADA has been developed, named in her honor.

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1822 the British government granted him £1500 toward the costs o f construction. The degree of accuracy needed i n the machining o f the parts pushed machin e tool technology to new heights. Th e era's monument was the Great Exhibition o f 1851, in which Great Britain was presented as what it had come to be called: the workshop of the world. 2 That workshop was not the child o f the Principia, but the turn of science would come, and it would be Galvani, Volta, and above all Faraday, Lavoisier, and Dalton who were to lay the foundation for what could be termed science-base d civilization, a phrase that I use to describe the specifically material infrastructure of life. The Magic Fluid

In the 1880 s a second industria l revolutio n too k place. This tim e i t was heavily based on science: it was the practical fruit of Volta's and Faraday' s experiments on electricity, and the realization of Dr. Samuel Johnson's dream, a century before, that "electricity, the great discovery of the present age," be made to serve man. Initially, th e productio n o f current electricit y wa s dependen t o n cumbersom e batteries and was largely limited to scientific laboratories. Napoleon backed the assemblage o f a massive galvanic pil e fo r the Ecol e Polytechnique i n 1813 . Despit e the inconvenience o f huge array s of batteries tha t ha d t o be regularly tended an d topped up with chemicals, it was such arrays that provided the source of electricity for th e newl y invente d telegrap h system . In 183 7 th e firs t electri c telegrap h lin e was set up, between Euston and Camden in London. It depended on Ampere's 1820 discovery (se e Chapter 8 ) that a magnetic needl e suspende d nea r a wire wa s de flected b y th e passin g o f a current . Amper e ha d i n fac t suggeste d the us e o f this phenomenon a s a basis for sending messages. The opening of the first line created a sensation; poster s declared, "The Electric Fluid travels at the rate of 280,000 Miles per Second. " The few miles o f cable that were laid were the forerunne r of the firs t cable laid across the Atlantic , in the 1860s . I n 1845, afte r severa l failures, Samue l Morse opened a line between Washington and Baltimore using his code, which was to become accepted throughout Europe in 1846. I n Germany in 1847, Siemens and Halske founded a company that constructed a telegraph network in Russia and subsequently ran a telegraph cable from London, through Berli n to Calcutta. The telephone had a harder birth, as evident from these sentences, taken from the report of the committe e se t up b y th e Telegraph Company t o examin e Alexande r Graham Bell's proposal: Technically, we do not see that this device will ever be capable of sending recognizable speech ove r a distance o f several miles. Messrs . Hubbard an d Bell want t o install on e of their "Telephone " device s i n virtually every home and business establishmen t i n the city . This ide a i s idiotic o n the fac e o f it. Furthermore, why would an y person want t o use this ungainl y an d impractica l device when he can send a messenger to the local telegraph office . 2

Not everyone was impressed by the goods that the workshop produced. At the Great Exhibition, William Morris "stood aghast at the appalling ugliness of the objects exhibited, the heaviness, tastelessness, and rococo banality of the entire display." But confident English capitalism had little time for aesthetes.

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Indeed. In the 1840s the increased availabilit y of electric current facilitated the establishment o f an electroplating industry . Up to the 1880s , the main sourc e of electric current for this industry, an d i n general, was the Daniell cell, a glass containe r containing two solutions separated by a porcelain partition. A n alternative battery, the lead-acid accumulator , invented in 1881, ca n still be found i n cars today but is obviously no t a convenient sourc e o f electricity fo r long-term, maintenance-free, commercial o r domestic use. It is not surprising that gas remained th e main sourc e of domesti c lightin g int o th e earl y twentiethth century . Bu t a totally ne w wa y of generating electric curren t wa s to almost completel y replace chemica l cells . Basic science was again poised to initiate a torrent of technical innovation . Albert, Victoria' s princ e consort , appear s t o hav e sough t ou t an d enjoye d th e company o f scientists an d writers . H e visited Michae l Faraday' s laboratory , in th e days whe n th e scientist' s experiment s wit h electricit y looke d lik e hig h schoo l demonstrations. Farada y wen t throug h hi s part y pieces—rubbin g rod s o n cloth , charging meta l spheres . Alber t asked , "Bu t o f what us e i s it , Mr . Faraday?" Th e reply was, "Of what use is a baby, sire?" 3 One of Faraday's simple experiment s ha d show n tha t electricity could be generated by the relative motion of a coil of wire and a magnet. This particular baby was to burgeon int o a giant. In 188 2 th e Ediso n Electric Illuminating Compan y began operating th e world's firs t electricity-generatin g plant based o n dynamos. Electri c current could be continuously and conveniently manufactured and sent anywhere. Faraday's research had borne practical frui t i n the dynam o and the electri c motor. In the 1880s , Alber t Einstein's fathe r ha d a modest factor y i n Munich, making dynamos an d othe r electrica l equipment . Hi s son was to be fascinate d by Faraday' s theoretical concept o f a field, rather than by the field's practical uses . Electricity sprea d everywhere : in industry , th e home , an d th e electrificatio n of transport.4 In 1860, Si r Joseph Swan passed a current through a carbon filament inside a n evacuate d tube . H e had create d a 25-wat t lightbulb . I t was no t long-live d enough to be commercially viable, but 2 0 years later electrical lightin g began to illuminate Europ e and America . The practical benefits o f basic research i n physic s had neve r been more evident. Technology, for the first time in history, was becoming dependent o n basic science . The Wireless

Maxwell's purel y theoretica l breakthrough , the discover y an d characterizatio n of the electromagnetic field, opene d the way to Hertz's radio waves and to the discov ery and utilization o f a spectacular range of electromagnetic waves. X-rays, discovered i n 189 5 b y Roentgen , evoked lyrica l panegyric s suc h a s tha t o f Silvanus P. Thompsons's: "November the eighth 1895, will be ever memorable in the history of Science. On that day a light which, s o far as human observation goes, never was on land or on sea, was firs t observed. " In 1901 Roentge n was awarde d th e firs t Nobel 3

Benjamin Franklin is said to have made a similar remark when he was asked about the significance of the first balloon ascent, which he witnessed in 1783. 4 Electricity provided a fruitful fishin g ground for frauds such as the "Electric Infant," reported in the English Mechanic (1869): "This interesting but inconvenient infant was, it is stated, so endowed with electricity that nobody could enter the room where it was without receiving constant electric shock."

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Prize in physics. Th e new rays excited prurient fancies; th e popular press was replete with cartoons of solid bourgeois gentlemen peering at young ladies throug h what were supposed to be X-ray glasses. But people were also well aware that medicine had acquired a powerful diagnostic tool. Sadly, the pioneers were unaware of the dark side of radiation, and many of them eventually died of overexposure to the new rays. In the next century, ultraviolet, infrared, microwave , and y-radiation were to become familiar and to reveal their uses and their dangers. The huge technological conseqiiences of Faraday's experiments, and Maxwell's mathematics, remai n th e archetypa l exampl e o f the growt h o f useful technolog y from basic science. Politicians who have to make decisions on the funding of basic research should learn a simple lesson from history: basic research very often pay s off. Another convincing example arises from man's efforts to understand the nature of matter. The Manipulation of Matter The advance of chemical theory, sparked primarily by Lavoisier and Dalton, had by midcentury brought chemistry to the stage where the synthesis o f novel molecules, and th e identificatio n and characterizatio n o f naturally occurring molecules, ha d become standar d laborator y practice. Chemistr y was no longe r cookery. The firs t half of the nineteenth centur y saw the growth of chemistry from a largely empirical activity, carried on primarily in small private laboratories, to a major scientific discipline that was to change the materials, colors, foods, an d pharmaceuticals of the world. In 1826, Justus von Liebig founded a chemical laboratory in Giessen, Germany, and from 1842 onward he used it as a training ground for young chemists, most of whom wen t int o industry . Germa n chemistry advance d rapidly and , before long , industrial companies began to establish thei r own research laboratories. New materials were developed. The availabilit y o f electricity allowe d the commercial developmen t o f a n electrolyti c proces s fo r producin g aluminu m fro m its ore . In 1884 , Comt e Louis-Marie-Hilair e d e Chardonne t obtaine d a patent for rayon. The Paris police opened a chemical laboratory not only for forensic purposes but als o to check o n the contaminatio n o f food b y chemicals. Th e synthesis , at the ag e o f seventeen , o f th e anilin e dy e Tyria n purpl e b y th e Englis h chemist William Perkin, who patente d hi s work in 1856 , opene d the wa y for brighter fabrics. Perkin als o achieved th e firs t laborator y synthesis o f an aminoaci d (glycine ) and the first synthesis of a perfume (coumarin) . Such feats would have been utterly beyond th e capabilit y of chemists workin g half a century before. The y were no w possible a s a consequence o f the developin g understanding o f the wa y i n whic h atoms were linked together to form molecules. The commercia l use o f aniline dye s wa s develope d primaril y b y th e German chemical industry, just as most of the commercia l applications o f electricity were pioneered i n German y and America . Thes e wer e fa r from being th e las t case s of British scientifi c breakthroughs being brought to th e marketplac e by othe r countries. Maybe it can be put dow n to what Lord Cherwell saw as the intellectual snobbery concerning technology, which took a long time to die out in England. In Germany thing s wer e different . Ma x Maria von Weber , the so n o f the compose r Carl

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Maria vo n Weber , became a n internationall y influentia l exper t o n railwa y con struction. A contemporary biographer sai d tha t thi s choic e o f technology as a career was "typical of a phenomenon decisiv e in our culture: th e transition from th e sphere o f fancy an d though t t o that o f applied activity , realistic creativity. " When war broke out between the two countries, the khaki dye used for British army uniforms in 1914 cam e from a factory in Stuttgart . The march o f physics an d chemistr y was joined by biology. It was in the nine teenth century that the intrusion o f the scientific method into biology initiated th e construction of a rational base for medicine. The Science of Life

In the fiel d o f biology the three most significant advances in the nineteenth centu ry, apart from the great Darwinian watershed, were the development of the cell theory of life, th e discover y o f the electrica l nature o f nervous activity , and th e germ theory o f disease. O f these, the ger m theory was undoubtedl y th e on e having th e major immediat e consequence s fo r HMS. In France , Pasteur wa s a national hero . The image of the child cured of rabies impressed itself deeply on the public. 5 Perkin's aniline dye s led to a major advanc e in biological science when the German scientis t Paul Ehrlic h realize d that i f the dye s could colo r the anima l fiber s wool and silk, they might be able to stain the components of the living cell. He presented hi s thesi s "Contribution s t o the Theor y and Practic e of Histological Stain ing," t o Leipzi g Universit y i n 1878 . I t was b y th e us e o f dyes tha t chromosome s were first see n under th e microscope. They were named by Erhlich: "colored bodies," (i.e . chromosomes). In 187 6 th e Germa n scientist Rober t Koch , fo r the firs t time , identifie d a germ connected with a specific disease, anthrax. Medicine was becoming both more scientific and more effective than it had ever been. The fact is, as Lewis Thomas pointed ou t i n 1977 , that befor e th e adven t of science, medicine wa s "a n unrelievedl y deplorable story . . .. It is astounding that the profession survived s o long, and got away with so much with so little outcry." "Scientific Tests Have Shown That..."

From the tim e o f Newton until well afte r th e middl e o f the nineteent h century , a growing number o f humanists sa w natural scienc e a s a subject warrantin g seriou s attention. This was partly because scienc e was considered to be a part of philosophy and also because most science was readily intelligible to an averagely educated man . I n the seventeent h centur y Lock e was s o interested i n th e Principia tha t Newton too k the troubl e t o explai n t o hi m personall y th e elliptica l path s o f the planets abou t th e Sun , and , a s we hav e seen , thi s interes t i n scienc e blossome d among intellectuals durin g th e Enlightenment . In the nineteent h centur y Shelley , Coleridge, Keats, Tennyson, and other s dabble d i n science , o r read an d discusse d it. Hege l considere d tha t th e centra l positio n o f the art s i n civilizatio n wa s n o 5

In the late 1950s I worked in the Institut Pasteur in Paris. There was a small collection of memorabilia and o f Pasteur's scientific instruments in a building across the road from th e laboratory in which I worked. Whenever I was there I felt as though I was visiting a shrine.

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longer justified and that they should be replaced by science, which for him embodied th e spiri t o f reason, "the Sovereig n o f the World, " "the substanc e o f the uni verse"—provided, o f course, that Newton was kep t ou t o f things. Emil e Zola was quite explici t abou t th e influenc e o f science: "M y aim ha s bee n a scientifi c aim, above all," and, "We have experimental chemistry and physics. . . . We shall have the experimenta l novel. " Th e Goncourt s proclaime d eve n mor e strongly : "Th e Novel has taken up th e studie s an d dutie s o f science." Scientific terms crept int o the vocabulary of writers and o f HMS. August Strindberg's wife, Frida, avowed that the nerve s of the sombe r dramatist were so sensitive to "electricity" i n the atmosphere that storms communicated themselves to them as though they were "wires. " As earl y as 1816 , Mar y Wollstonecraf t Godwin, Shelley' s secon d wife-to-be, had been influence d b y Galvan i an d Volta . A t eighteen , impressed b y newspape r accounts o f the effec t o f electricity o n corpses , she wrote Frankenstein. I t was elec tricity that brought the monster to life. Byron was doubtless more interested i n the supposed beneficial effect o f "galvanism" o n virility, a myth that was commercially exploited by enterprising quacks. The acknowledgment of science as an intellectual force of wide significance was not new , but i n th e nineteent h century , fo r the firs t tim e i n history , science wa s reaching out into practical, everyday life, building th e prestig e of the scientis t a s a benefactor an d an authority to whom to turn for advice. The Cadbury company in England was one of the first to use the newly acquired popular prestig e of the scientis t to promote its products. It produced a n advertisement showing a bearded, bald-domed, authoritative figur e i n a lab coat holding a tube of liquid. A distilling flask , a microscope, and other apparatus are also depicted. On one of the notebooks open on his table one can read the words "Absolutely pure Cocoa. No chemicals." All that is missing is the comparison with "other leading brands." Th e standing of science had been restored following its decline at the turn of the century. But James Clerk Maxwell laid his finger on the danger of uncritical kowtowin g to the new god : "Such . . . is the respect pai d t o science that th e most absur d opinion s ma y become current , provide d the y ar e expresse d i n lan guage, the sound of which recalls some well-known scientific phrase." His warning still reads well. A popular audienc e fo r science, and fo r technology, blossomed i n Europ e and America. Botanical and zoologica l gardens became popular. In England the princ e consort, Albert, gave his active backing to the building of a large complex of scientific an d natura l histor y museum s i n th e Knightsbridg e are a o f London. Crowds carne to see the skeletons of the dinosaurs. In 1851 Foucault suspended a long pendulum beneath the dom e of the Pantheon in Paris. Thousand s flocked to watch as the plane in which it swung apparently rotated as the Earth turned. In the 1890s the children o f the bourgeoisi e began to receive educational scienc e kit s a s presents, and thei r parent s meddle d wit h simpl e chemical s an d magnets . Scienc e was becoming par t o f popular culture , althoug h thi s was predominantl y a middle-class phenomenon. Science Comes Out of the Lab

Looking back fro m 1900 , w e se e a centur y i n whic h scienc e and technolog y increasingly established themselve s a s major force s i n the shapin g o f nations. In th e

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seventeenth centur y Newton had given science a previously unequaled status , but science ha d don e ver y littl e t o affec t th e lif e o f HMS. Newton's mechanic s an d Boyle's chemistry ha d no conspicuous practical consequences . Harvey' s discovery of the circulatio n o f the bloo d di d no t significantl y change medical practice , an d Gilbert's sixteenth-century investigations into magnetism had no technological follow-up. Technology up until about the middle o f the eighteenth centur y was rarely the outcom e of scientific advances . The art o f the watchmaker an d th e skil l o f the machine-tool manufacture r needed t o support tha t art, did infinitel y more t o improve industrial technology than the laws of motion. It was only around the middle of the nineteenth century that science began to feed technology, a process that gathered momentum as the century drew to a close. It was the seemingly endless benefits inherent i n science that produced the profound shift , durin g the nineteenth century , in the public attitud e toward scientific education and science as a profession. The Birth of the Professional Scientist

In early seventeenth-century Britain, nearly 60% of scientists had been educated at a well-known public school, and two-thirds of them had graduated fro m eithe r Oxford o r Cambridge. By the en d of the eighteenth century, only about 20% had com e from public schools or were graduates of Oxbridge, and fewer than 20% came fro m the upper classes . Scienc e was no longer the pastim e o f gentlemen; it had shifte d primarily int o th e hand s o f the middl e class . Th e chemist s Dalto n and Priestley , and many others like them, taught not in universities bu t in Dissenters academies where scienc e was given a respected place in the syllabus. Th e roll call of Quaker, Unitarian, an d generall y dissenting scientist s i s impressive . Science , fo r the Dis senters, was a route to the understanding of the workings of God. In th e nineteent h centur y th e numbe r o f people, especiall y fro m th e middl e class, who had had some scientific education grew rapidly. Even the working class was hearing the distant rumble of scientific drums. The great Michael Faraday was the scientifi c working-class her o o f the nineteent h century . Th e so-calle d lowe r class was breakin g out o f the cas t o f ignorance an d subservience . I t is significan t that o f the approximatel y 400 0 member s o f the Nationa l Secula r Societ y i n th e 1880s, nearly all were working men. The academic world o f England failed t o realize what was happening. Unti l the second hal f o f the century , neither Oxfor d no r Cambridg e offere d degree s in sci ence.6 Th e attitude o f the ancien t universitie s change d a s the nineteent h centur y unfolded an d a s scienc e becam e a sociall y acceptabl e profession . Respectability was bestowed o n science by such event s as the 185 4 serie s of scientific lectures at the Roya l Institution o f Great Britain, given in fron t o f the princ e consort . Among the lecturer s wa s Michael Faraday , wh o wa s a brilliant popularizer , an d Willia m Whewell, master of Trinity College Cambridge. All strongly advocated that science 6

Neither did they admit women, Dissenters, Jews, or Roman Catholics. In England the firs t -undergraduate laboratories in physics and chemistry were opened at University College London, a university founded in 1828 that was also the first to admit both men and women, regardless of creed, race, or class. As regards women, they were preceded by 2500 years by Pythagoras, who though he barred women from membership of the cult, allowed them to attend lectures.

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be given a central place in the educational system . Support came from unexpecte d circles. A certain Reverend F. W. Farrar wrote an essay demanding the "immediat e and tota l abandonment o f Greek arid Latin verse-writing as a necessary or general element in liberal education." Science was to be the main replacement. In the 1860 s i t became apparent tha t Oxbridge was ou t of step with th e times. Oxford took the lead in accepting physics as a subject for research at the university, and Manchester built university laboratories . In Cambridge the Cavendish physics laboratories wer e dedicate d i n 1874 , an d Cler k Maxwell became th e firs t Caven dish Professor of Experimental Physics. Across the English Channel, France had alread y introduced widesprea d scien tific educatio n i n th e eighteent h century . A s early as 1828, the Ecol e Centrals des Arts e t Manufacture s had bee n established . Technica l institutions , teachin g bot h pure an d applie d science, wer e well establishe d i n eighteenth-centur y Germany, and afte r th e tur n o f the centur y severa l of them attaine d university status . In th e older Germa n universities, i n th e firs t par t o f the nineteent h century , there wer e usually fou r faculties : philosophy, theology , medicine, an d law . In the 1860s , sci ence faculties began to appear , usually a s an spin-of f fro m th e facult y o f philosophy. Academic science would neve r look back, and i n universities, technical colleges, schools , amateu r scientifi c clubs , an d popula r lectures , scienc e wa s propagated through the middle, and eventually the working, class. America remained a scientific backwater during most of the nineteenth century . In the colonia l perio d most American men o f science saw England as the countr y with which they had contact , in the form of letters, visits, arid articles sent for publication. Predictably , i t wa s Franc e tha t supersede d Englan d after th e America n Revolution. Benjamin Franklin, who had close connections with the French scientific world , was a familiar figure o n the street s o f Paris from 177 6 to 1785 . France maintained it s attraction durin g the firs t hal f of the nineteenth century , but th e in fluence o f Germany grew rapidly in the latte r half of the century. As in Europe, the change fro m amateu r dabbler s t o professiona l scientist s wa s primaril y a nine teenth-century phenomenon , bu t Americ a initially lagge d behind Europ e in th e area of research facilities. A major mileston e wa s th e creatio n o f the Smithsonia n Institution, founde d in 1846 . By the end o f the century, American science was taking off. Ther e were a number of industrial research laboratories staffed b y university graduates, and severa l scientists ha d attaine d worl d stature . J. W. Gibbs at Yale revolutionized chemica l thermodynamics , and th e experiment s o f Albert Michelson at the Universit y of Chicago, on the spee d of light, perturbed the world of classical physics. In 183 2 there was not a single observatory in the Unite d States; fifty year s later there were nearly 150 , and by 1900 American astronomy had attaine d world-clas s stature. National prestige should not be underestimated as a motivation here. It was certainly a major facto r i n the constructio n of the, for those days, huge Pulkovo observatory near St . Petersburg in 1839 , b y orde r of the "Iro n Czar," Nicholas I, the creator of the Russian secret police. All ove r th e Wester n world , scienc e blossomed . Bu t no t everyon e was fille d with joy.

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The Backlash . . . the hideous new religion of Science . .. —Edmund Gosse, Father and Son

The predictable backlas h agains t the scientifi c bulldozer cam e most markedl y i n the 1870 s an d 1880s , whic h sa w a reviva l o f fundamentalist Christianity . Ther e was a revolt among many educated laymen against the, to some, menacingly spectacular growt h o f scienc e an d it s apparen t encroachmen t o n al l aspect s o f life . Queen Victoria led from th e top: "Science is greatly to be admired and encouraged, but i f it is to take the plac e of our Creator, and i f philosophers an d student s tr y to explain everythin g and t o disbeliev e whateve r the y canno t prove , I call it a great evil instead of a great blessing." The formidable William Gladstone (he was reputed to chew each mouthful o f food eight y times), then prime minister of England, also spoke for many when, in 1881, h e said: "Let the scientific men stick to their science and leave philosophy an d religion to poets, philosophers and theologians." It was not onl y Darwinis m that was perceived to threaten th e mildl y religiou s Victorian world. The upsurg e of geology, especially the wor k of Charles Lyell, fostered antibiblical notions, such as the immense age and gradual development o f the Earth. Investigations of life processes , inexorably cuttin g away the shrou d o f mystery that had single d out Life as something outside Newton's mechanistic universe , were deeply troubling—and still are, to some people. Not only the religious establishment, but also many laymen were worried by the rise i n atheis m an d th e prospec t o f humanitarianism a s a substitute fo r religious faith. I t was commo n to blame the declin e o f religion on science, although among the clerg y themselves there wa s jus t a s much, i f not more , concer n abou t th e so called new criticis m of the Bible , which tended to seek for rational explanations of the mor e unlikel y episode s i n the Scriptures . However , although ther e wa s a decrease in churchgoing during the century, it was not precipitous, and atheis m was not a widespread social phenomenon, its image being well out of proportion to the number of its adherents. 7 Notable voices were raised against what was seen as the arrogance of scientists. John Ruskin, the great (and neurotic) art critic, spoke out against the constructio n of the new physics laboratories, the Clarendon Laboratories, at Oxford. Specifically attacking Darwin, he declared that science should no t be pursued fo r its own sake, and not even for its practical benefits, but as an activity subordinate to ethics. What this would mean in practice to men like Maxwell was not clear, but Ruskin's words were repeate d frequentl y b y antivivisectionist s an d thos e opposin g vaccination . Ruskin's concern with ethica l problems remains valid to this day, especially in the life sciences and medicine. The distaste for science and th e accompanying objection to vivisection reache d greater heights on the Continent than in England, feelings typified by books such as Ernst von Weber' s Die Folterkammern der Wissenschaft (Th e Torture Chamber of 7

A high-profile atheist was Charles Bradlaugh, propagandist for scientific materialism, editor of the radical Reformer, an d president of the National Secular Society. Bradlaugh gave popular antireligious lectures under the name "Iconoclast." For five years he unsuccessfully attempte d to take his place in the House of Commons. He refused t o take the religious oath. In the end he sold out, taking the oath and his seat.

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Science) (1879) and the following passage from the novel Gemma oder Tugend and Laster (Gemma or Virtue and Vice) , by Elpis Melena (1887): "What can you expec t of a man who tramples on the most sacred laws of Nature, a man whose every last grand and noble feeling has died i n him, who cannot even appreciate the wonderful spiritua l qualitie s o f a daughter worthy o f worship, a man wh o seek s his pleasures in the lowest debaucherie s an d gory orgies, whose conscience an d hands are forever smeare d with blood. . .. In short what ca n you expect of a vivisector?" Not much, apparently. Darwinism was more readily accepted by the Church in England than i t was by the rigid Protestant sect s o f the Ne w World, a pattern that is maintained b y the almost complete absence of present-day controvers y over evolution in Great Britain, in contrast to the continuing clashes between fundamentalist s and secular authority i n th e Unite d States. 8 Nevertheless , socia l Darwinis m wa s mor e warml y embraced in the United State s than in Europe. Herbert Spencer's banner "th e surviva l of the fittest" proved a rallying point for moneyed laymen, tenured academics , and worldly clerics. Sai d John D. Rockefeller, "Th e growt h of large business i s merely the survival o f the fittest," and his conviction was confirmed by Graham Sumner, a professor o f political scienc e a t Yale, who diplomaticall y saw millionaires a s "th e naturally selecte d agent s o f society" (yo u never kno w wh o th e university' s nex t benefactor will be). The blessing of the Church was bestowed on mammon by Bishop William Lawrence of Massachusetts, who incredibly expressed the opinion tha t "godliness is in league with riches.. .. The race is to the strong." We could be generous and interpret that as a cry of woe, but it was not. The distinctly un-Christia n Bishop might have applauded Spencer' s opinion , borrowed from Malthu s an d expressed in Spencer's Man versus the State (1884), that it was not the business o f the state to help the poor , whom he implicitly categorize d as "unfit." Many concurred with Spencer's pseudo-Darwinian conclusio n tha t the traditional role of women in society was the resul t o f a process o f natural selection: selectio n fo r reproduction. This bi t of wishful thinking o n the par t o f male societ y was rarely challenge d by men, a n honorabl e exceptio n bein g th e prominen t musi c criti c Ernes t Newman, who, in an article on "Women and Music" (1895 ) wrote that men have started out with the theory of the natural inferiorit y of women, have assumed—like Rousseau , becaus e i t suite d the m t o d o so—tha t he r "true " sphere was the home and her "true" function maternity , and then persuade d themselves that they had biological reasons for keeping her out of the universities an d for denying her a vote. Which did not prevent the sexologist Havelock Ellis, a supporter of women's rights, from declarin g that "Nature has made women more like children in order that they may better understan d an d car e for children." Socia l Darwinism was profoundl y reactionary. Darwin is , i n th e twentiet h century , stil l a casus belli in th e Unite d States . I n 1965 a courageous teacher i n Littl e Rock filed a suit agains t the Stat e of Arkansas 8

In 1994(1), the broadcasting o f a program in the United State s on the significanc e of "Lucy," the 3.5-million-year-old "missing link" found in Africa by Donald Johanson, was, due to pressure, followed by a two-hour slot given to creationists t o "balance" accounts . This is unthinkable i n England.

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on the grounds that her right to free speec h ha d been violated by the local antievolution law . Sh e wo n he r case , bu t th e verdic t wa s reverse d b y th e Arkansa s Supreme Cour t in 1967 . Th e cas e finally cam e befor e th e Unite d State s Suprem e Court, which i n turn decide d fo r the teacher . Befor e i t came to its decision , ther e was an unprecedented approac h t o the Court by a group that included seventy-tw o Nobel laureates , who prepare d a documen t definin g the scop e an d natur e o f science. The kind of opposition the y were up against can be judged from the following quotation fro m a letter t o one of them, th e physicis t Murra y Gell-Mann: "Ask th e Lord Jesus to save you now! The second la w o f thermodynamics prove s evolutio n is impossible." It doesn't. Among America n intellectuals , response s t o evolutio n wer e perhap s condi tioned b y a strong streak of pragmatism. Unlik e their European counterparts, the y in general avoided appealin g t o vital force s o r cosmic will. Rather, attempts wer e made t o appl y evolutionar y idea s t o down-to-eart h problem s i n law , education , and socia l ethics. Everythin g was simply explaine d by the prosaic theme o f man's continual adaptation to his environment, both biological and cultural—which was a healthy approach after the tiresome, and sometimes batty, European invocation of will. The Achievements

All i n all , ther e wer e fou r majo r practical result s o f nineteenth-centur y basi c science: 1. Th e advent o f electricity as man's mos t versatile sourc e of energy and th e mai n basis of the coming twentieth-century technological explosion . 2. Th e practical consequences o f Maxwell's discover y of electromagnetic waves. 3. Th e advances in medicine consequen t on the germ theory. 4. Th e development of the chemica l industry . The major breakthrough, in terms of its intellectual influence, was undoubtedl y Darwinian evolution, which lef t it s mark on social and politica l though t an d infil trated philosophy an d literature . The achievements o f Maxwell and Farada y were immense but cannot be said to have had a widespread direct effect o n the way that people thought because, in contrast to evolution, most people sa w only the practical implications o f electromagnetism.9 The theoretica l aspects wer e not fel t t o be relevant t o man' s plac e o n Earth , althoug h th e concep t o f field s an d Maxwell' s equations were to have a deep effect o n twentieth-century physics . There is a similarity wit h th e grea t twentieth-centur y breakthrough s i n physics—quantu m me chanics, particle physics, and relativity—which were to have little effect o n the intellectual lif e o f HMS. There i s o f course a differenc e i n th e perceive d degre e of incomprehensibility between nineteenth- an d twentieth-century physic s that puts this century's physics wel l ou t o f the range of interests o f most people. This i s not to say that the advances of Einstein, Planck, and company had no practical or political consequences; the atomic bomb is not a trivial matter. But how many people' s way of thinking has been affected b y modern theoretical physics? 9

The pointillist artist Georges Seurat was intrigued by Maxwell's electromagnetic waves, but I doubt if this affected hi s art.

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There i s on e majo r achievemen t o f nineteenth-century science—namely , ther modynamics—that neither had significan t practical applications o f which the public were aware nor penetrated the imaginatio n o f HMS. To HMS the subjec t seems abstruse, an d irrelevan t t o dail y life . Moreover , it lack s visua l appeal . On e ca n imagine genes and galaxies, and one can handle electronic equipment. Th e second law of thermodynamics has as much visual appea l as a hymn, and the only mark it has made outside scienc e i s the usually totally inaccurate use of the word entropy whenever the speaker wishes to lend universality an d depth to an otherwise prosaic statement . Th e famou s predictio n o f the eventua l thermodynami c deat h o f the universe raised some interest a t the time but i s not now a topic of conversation i n pubs. Even in the Deep South, I doubt whether th e second law of thermodynamics will raise enough ire to be repealed by a state senate. Humanitarianism

It is natural in a book of this kind to present the nineteenth century as an era of scientific an d technological advance. The wide sweep of history has not been given a hearing, but an unprejudiced eye must surely record that the other great triumph of the century, at least in the West, was the flowering of humanitarianism, typified by Wilberforce's figh t agains t slaver y and Salisbury' s crusad e agains t child labor . In 1844, Engels published The Condition of the Working Class, and whateve r one ca n say abou t its eventual political fruit s i n eastern Europe, it was a plea for the downtrodden of the earth, those who were described in words by Dickens and Zola, and in images by Gustave Dore's drawings of the London poor. It would be gratifying to a scientist t o link the progress of science with the progress of humanitarianism, and a look at the nineteenth-century glob e reveals that very often th e map o f social injustice superimposes well o n the map o f scientific backwardness. But the correlation is a little too easy, and I make no attempt to encroach on the territory of the historian or the sociologist. The nineteenth century sa w the rise of Great Britain as a world power , and th e British were well aware of their industrial an d militar y strengt h and o f their massive contribution t o the advance of science. To give a taste of this national self-con fidence, I quote part of a chauvinistic articl e that appeared in 1897 , in the Illustrated London News. The underlyin g ton e of the articl e reflects th e materialisti c an d realistic fram e o f mind tha t typifie d much o f European society, and tha t owe d so much t o the technologica l fruit s o f science. Th e quotation sum s up, a t first hand , the prestig e o f science, th e associate d belie f in progress , and th e Britis h sense of world leadershi p a t the en d o f the nineteent h century . Notice that only on e nonBritish scientist—Siemens—is mentioned by name. Pasteur is apparently relegated to the status of a "Continental descendant o f the great Jenner." The su m and substanc e o f all the effort s o f Victorian science has been to pu t the bod y an d min d o f ma n mor e a t ease . Thank s t o th e Stevensons , th e Brunels, and their Disciples, to Faraday, Siemens, Kelvin, Rowland Hill, and their followers , space has been almost annihilated, an d the end s of the earth brought together . Simpson , Lister , the Continenta l descendant s o f the great Jenner, Parks and the pioneer band o f English sanitarians hav e alleviated th e sting of disease, and put ou r bodies more at ease. More than an y nationality,

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Englishmen have been busy to put our minds at rest by teaching us the nature of the world we live in, and making us less the creature s of chance. Th e seas have been charted , th e depth s o f space fathomed , the heaven s mapped , th e earth and its plants an d animals examined . Darwin, Lyell, Spencer an d Huxley have replaced empirical theorie s by a history written i n rocks, bones and living tissue. It must surely have been that God spoke English. What the writer of the article di d not know was that, as he wrote, yet another Englishman, working in the Cavendish Laboratories in Cambridge, was breaking into the unbreakable atom.

12 The Material Trinity: The Atom Colors, sweetness, bitterness, these exist by convention; i n truth there are atoms and the void . —Democritus When I was a young man, I also gave in to th e notio n of a vacuum and atoms; but reason brought m e into the right way. —Leibniz, letter to Caroline , princess of Wales , 12 May 1716

In 1863, Ernest Solvay, a Belgian industrial chemist , announce d a new process for making washing soda. It made him a fortune, which allowed him to engage in philanthropy and to express offbeat opinions , such as his belief in the evil of inherited wealth an d th e undesirabilit y o f money i n general . Among the project s to whic h his own undesirable money went was a series of international meetings , the Solvay Conferences. Einstei n attende d th e firs t Solva y Conferenc e o n Physics , hel d i n Brussels in 1911, an d was given the honor of being the final speaker. Madame Curie was also there, but the most significant talks were given by two other participants: Ernest Rutherford, who announce d th e discover y o f the atomi c nucleus, an d Jean Perrin, who gave the most convincing evidence until tha t time that atoms actually exist. For twenty-five centuries, the experimenta l evidenc e for the existenc e o f atoms was not strong enough to convince everyone of their reality. It was only in the early years o f the tweniet h centur y that th e distinguishe d Frenc h mathematicia n Poin care, after hearin g Perrin, could say, "Atoms are no longer a useful fiction . . . . The atom of the chemis t is now a reality." In recounting the story of the particles that make up the atom, we will gloss over two and a half millennia of the ide a of atomism. All the meaningful advances were made in the nineteenth an d twentieth centuries . Nevertheless, we will go back to the beginning and give the Greeks their due. The Greek Guess It is said that when, around about 1000 B.C., the Ionian Greeks came to Miletus, on the coas t o f present-day Turkey , they carn e without women , ensurin g their futur e by slaughterin g th e loca l me n an d marryin g th e widows . Th e innovativ e recip e worked; the communit y flourished . U p to about 500 B.C., Miletus was the wealthi est Greek settlement i n the East, and home to an impressive array of philosophers, including Anaximander , Anaximenes , an d Thales , whic h say s muc h fo r mixe d

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marriages. Leucippus, the firs t person that we know of to speak of atoms, was a citizen of Miletus but late r settled i n the Thracia n tow n o f Abdera, renowned fo r the stupidity of its citizens. Ther e he took as a student Democritus, of whom Aristotle said, "He thought about everything." One o f the thing s tha t Democritu s though t abou t wa s th e possibilit y tha t th e world wa s compose d of tiny, discrete, indivisibl e particles— atomos. My guess i s that he had been talking to Leucippus, but Democritus was a fragmenter by nature, believing that not only matter but both time and space were divided into discontin uous portions . H e also , correctly , guessed tha t th e seemingl y continuou s Milk y Way was in fac t a discontinuous collection o f thousands o f stars. Democritus i s usuall y given credit fo r being the fathe r o f the atomi c theor y of matter, but he did no experiments and had only the flimsiest evidence for postulating the existenc e of atoms. Democritus's theory was kept alive by the Roma n poet Lucretius (se e Chapter 14) in hi s masterpiece , De rerum natura, only on e cop y of which survived the Dark Ages, to be discovered in 1417. The idea of atoms was inevitable because it is natural to ask how finel y one can go on cutting up matter. Speculation along these lines le d to some strange conclusions. Buridan , th e fourteenth-centur y French philosopher , though t that : "On e could have such a small quantity of a substance that it does not continue to exist for a noticeabl e time . Thi s smal l quantit y wil l continuall y ten d toward s it s ow n destruction." This is taking an inferiority complex to absurd limits. Averroes, th e twelfth-centur y Muslim philosophe r an d physician , wa s muc h nearer the mark : "A line a s a line can be divided infinitely . But such a division i s impossible if the line is taken as made of earth." He was expressing the feeling that , although endles s subdivisio n i s an acceptable concept i n mathematics, we cannot go on subdividing matte r forever: sooner or later, surely there are irreducible parti cles. But since no one had see n them, the best tha t could be done was to venture, with Francis Bacon, that the atom "is a true being, having matter, form, dimension , place, resistance, appetite, motion an d emanations : which likewise, ami d th e destruction of all natural bodies, remains unshaken an d eternal. " The Smallness of Atoms A woman is about 2 million times "taller" than the average Escherichia coli bacterium i n he r hamburger . B y way o f comparison, Everest is only about 500 0 times a s tall a s the averag e man. A man i s abou t 1 0 billion time s "taller " tha n a n oxyge n atom. If the ato m were scaled u p t o the siz e of a golf ball, then o n the sam e scale a man would stretch from here to the Moon. Even with the best optical microscope available, no one has the slightest chanc e of seeing atoms, and a conventional electro n microscope would no t help us . Even in this century there were scientists who , despite a great deal of circumstantial evi dence, questione d th e existenc e o f distinc t microscopi c particle s i n matter . Fo r these skeptics, atoms were just a convenient hypothesis; matter was a kind o f infinitely divisibl e jelly. The Atom Revealed Why d o we believe in atoms? Look at Figure 12.1. I t is a schematic representatio n of a n imag e produce d b y a n instrumen t know n a s a scannin g tunnelin g micro scope, ST M for short . I t i s produce d b y th e surfac e o f a piec e o f commo n salt ,

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Figure 12.1. A very schematic representation of the surface of a sodium chloride (common salt) crystal as revealed by a scanning tunneling microscope.

sodium chloride , magnified about 3 3 million times. It has a definite structure, appearing to be a very regularly stacked collection of objects. These objects are atoms. Believe me. The first photograph of a single atom was made by A. V. Crewe in 1970, using the STM technique. Orderly stacking of atoms (or ions) is typical of metals and o f all crystals . Wh o does the stacking? You will get rather differen t answer s from a physicist and a Buddhist priest . Since microscope s infor m us wha t magnificatio n they ar e working at , we ca n use image s like that i n Figur e 12. 1 to estimate the siz e of atoms. They turn ou t to have diameters ranging between abou t a tenth to a half of a nanometer. What more can we sa y about atoms? Don't expect to turn the pag e and fin d a n image of the atom' s interior, taken throug h a super-STM or some othe r expensiv e toy. If current theory is to be believed, there is no possibility o f our directly observing the interio r o f an atom , even with a n as-yet-to-be-buil t supermicroscope. Nature doesn't let us get too close. Nevertheless, we know a very great deal about the structure of atoms. The tale o f the unravelin g o f the structur e o f atoms should b e awarded the Detective Book of the Century award. The real breakthroughs all came in the late nineteenth an d earl y twentieth centuries . W e will g o straight t o that excitin g period , one of the golden ages of science. The Electron Revealed

When you switch o n a light, an electric current flows through the filament or neon tube. Thi s curren t i s a flo w o f electrons, tin y negativel y charged particles , an d about 3 x 1019 (30 million million million) electrons flo w through the fixtur e every second. Wha t ar e electrons ? The smalles t stabl e component s o f ordinary matter . They ar e essentia l component s o f all atom s an d wer e discovere d i n 189 7 by J . J . Thomson, i n th e Cavendis h Laboratories of Cambridge University. Thomson was, by all accounts, not a particularly skille d experimentalist, but he was good enough to get a Nobel Prize. It ha d bee n know n fro m th e beginnin g o f the eighteent h centur y tha t i f electrodes were attached to a glass vessel containing air at low pressure, the air glowed. An interesting turn occurred in the investigations of this glow when technical advances made it possible to go to much higher vacuums. A key experiment was done in 185 8 by Julius Pliicker at the Universit y of Bonn. Figure 12.2 shows th e kin d of

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Figure 12.2. Cathod e ray s (electrons) leave the negativ e plate and strike the wal l of th e glas s vessel. The position of the resultin g glow can be altered by applying an external electric field.

apparatus he used. At moderate vacuums the gas in the bulb glowed, but as pumping continue d an d th e pressur e i n th e vesse l dropped , th e glo w disappeared. Instead, Pliicke r observe d tha t th e glas s next t o th e cathod e gav e of f a green light . There were some puzzling features of this eerie glow. The position of the site on the glass fro m whic h i t came coul d be altere d by putting a magnet near th e vessel . I t looked as though something wa s coming out of the cathod e and making its way to the glass . What were these "cathod e rays"? Some said they were tiny bits o f metal from the cathode. Heinrich Hertz (of kilohertz fame) thought they were radiation of some sort . Thomso n solve d th e puzzle , hi s crucia l experiment s bein g thos e i n which h e examine d th e wa y i n whic h electri c an d magneti c field s disturbe d th e path of the rays. The path o f the cathod e rays was deflecte d b y an electric field , whic h immedi ately suggested that the rays carried an electric charge. Furthermore, the deflectio n was awa y fro m th e negativel y charge d plat e insid e th e cathode-ra y tube (Figur e 12.2). This implied tha t the rays themselves were negatively charged. Thomson assumed that anythin g carryin g a charge must be material, and he se t out to find th e mass an d charg e of the particle s which h e believed t o constitute th e rays. He di d this b y measurin g th e deflectio n o f th e ray s i n electri c an d magneti c field s o f known strength . H e realized tha t al l h e coul d fin d fro m hi s particula r measure ments was the ratio, e/m, between the charge and mass of the particles in the cathode rays . Thi s h e did , an d althoug h h e hadn' t determine d separatel y eithe r th e mass or the charge of his particles, he ventured to propose that they were far smaller than atoms an d wer e a universal componen t o f all atoms. He was right. H e had discovered the electron . "The Saddest Words Are: 'It Might Hav e Been'" Hertz though t that cathod e rays were radiatio n and no t particulate because whe n he, like Thomson, had tried to deflect them with an electric field, he had failed. He used too weak a field, and in consequence may have missed ou t on a Nobel Prize. A sadder case is that of Walter Kaufmann i n Berlin, who, working at the sam e time as Thomson but usin g a different method , also measured th e charge-to-mas s ratio of cathode rays . Hi s results wer e actuall y nearer th e presentl y accepte d valu e tha n Thomson's. Kaufman n reporte d his experiment s but mad e absolutel y no speculation abou t the existenc e of a subatomic particle. Francis Bacon remarked that peo-

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pie often rejec t new ideas just because they are new, but i n Kaufmann's cas e there may b e anothe r reason : th e influenc e exerte d b y th e physicis t an d philosophe r Ernst Mach . I n th e yea r that Thomso n discovere d the electron , Mach state d tha t atoms wer e a "mathematica l mode l fo r facilitatin g th e menta l reproductio n o f facts"—in othe r words , a convenien t fiction . Mac h wa s a logical positivist (se e Chapter 37), although this school of philosophy only flourished some twenty years after hi s deat h i n 1916 . Th e logica l positivists were extremely suspicious o f hypotheses an d o f concepts, such as atoms an d electrons , that coul d no t b e experienced directly through th e senses . Kaufmann's respect for Mach's philosophy cos t him dearly. Absolute Values Thomson attempted to measure the charge of the electron but not very successfully . The man who di d succeed , and als o earned a Nobel Pri2:e, was Robert A. Millikan, at the time at the University of Chicago. Taking his value for e and Thomson's value for elm, the mass of the electro n turned out to be about 183 6 times less than that of the smalles t known atom , that o f hydrogen. Millikan publishe d hi s work in 1911 , the same year as Rutherford found the nucleus . The Nucleus Revealed Ernest Rutherford , Firs t Baron Rutherford o f Nelson arid Cambridge , was a bluff , rugby-playing New Zealander, the kind of man on e would expec t to be suspiciou s of complex theories and who indeed expresse d his wariness o f theory publicly and bluntly. He was an experimental genius . The boy from Sout h Islan d was awarded the Nobel Prize in 1908, knighted in 1914, elected president of the Royal Society in 1925, and made a baron in 1931 . A t the height of his succes s he declared his work to be of no practical value. In this, at least, he proved to be wrong. Our understanding of the nucleu s an d the ato m are the foundatio n on which stan d modern chemistry and much o f physics. Rutherford discovere d the nucleus , an d th e emptines s o f the atom . His experiment wa s not onl y on e o f the crucia l experiment s i n ou r understanding o f matter but als o a classic example of simple, logical scientific thinking. Rutherford's Experiment Suppose yo u fire d a revolver at a wooden fence , on e o f thos e continuous fence s made o f a laye r o f adjacent slat s o f wood. Yo u would expec t th e bullet s t o pas s straight throug h th e fence , a fe w perhap s deviatin g ver y slightl y fro m a straigh t path because of knots i n th e wood . Now imagine a set o f iron railings, lik e thos e around Buckingham Palace, and suppose that a thin sheet of plastic has been fixe d to them, to keep the win d of f the queen' s guards . Again fire you r pistol. The great majority o f your bullets wil l pass throug h the plastic , travelin g in a straight line . However, a small proportio n o f bullets wil l hit on e o f the railings an d wil l be deflected. Depending on exactly where the bullet strike s a railing, it will be deflected by a smal l o r larg e angle . I f you ar e reall y unlucky , a bullet migh t hi t a railing straight on and bounce back to you. The difference betwee n the two fences i s that in th e woode n fence , th e materia l o f the fenc e i s more o r less evenl y sprea d out, while i n the iron railings-plus-plastic-sheet th e mass is very unevenly distributed .

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A large proportion of the mass is in the narrow confines of the iron railings. A bullet hitting the plastic is hardly perturbed by the small amount of mass that it meets. A bullet hitting a railing encounters a massive object that can easily deflect it . This was the conceptual basis of Rutherford's experiments, carried out at the University of Manchester from 190 9 to 1911 . In 1896 the Frenchman Becquere l discovered that uranium salt s gave off invisible rays . Marie and Pierr e Curi e called this phenomeno n radioactivity. Th e thre e French scientist s share d th e Nobe l Prize in 1903 . During a stay at the Cavendis h Laboratory fro m 189 5 t o 1898 , Ernes t Rutherford discovered tha t certai n radioac tive substance s violentl y ejecte d positivel y charged , relativel y heav y particles , which he named alpha particles. It occurred to him that he could learn something about thes e particles, an d abou t matter i n general , if he use d the m a s projectiles , examining what happene d t o them an d thei r targets. In 189 8 he moved to McGill University in Canada, and among the research projects that he started was a study of th e pat h o f a-particle s (bullets ) after the y struc k a piec e o f gold foi l ( a fence ) about 0.0000 4 cm thick, so thin a s to be semitransparent. Whe n h e cam e to Manchester i n 1907 , Rutherfor d aske d on e o f hi s students , Han s Geige r (o f Geiger counter fame), to continue this work. Geiger found that most of the a-particles that originated in a sample of radium went straight through the foil , but that a few were slightly deflected. Rutherfor d asked another student , Ernest Marsden, to find out if any particles were scattered through larg e angles. Marsden succeeded: abou t 1 in every 20,00 0 particles was deflecte d by 90° or more from th e foil . Thi s was totall y unexpected becaus e the gol d foil wa s assume d to be a wooden fence, no t a set of iron railings. Th e model of the ato m currently in favor , whic h ha d bee n proposed by J. J. Thomson in 1908 , was what coul d be called the Christma s pudding model. If, reasoned Thomson , electrons were components o f all atoms, then, since matter is electrically neutral, there must be positively charged matter in all atoms. He supposed this positively charged matter to be evenly distributed in a ball, and the negatively charged particles, the electrons, were presumed to be scattered throughout this ball like raisins (Figure 12.3a). Rutherford chewe d ove r Marsden' s result s an d conclude d that , contrar y t o Thomson's model, the atoms in the gold foil had an extremely uneven distributio n of mass (Figure 12.3b). The foi l resembled a set of iron railings, not a fence. Nearly all the mass o f each ato m must be concentrated i n a very small volum e while th e rest was spread out in a diffuse cloud . That is why the averag e a-particle "bullet" met little resistance on its way through the atom. The puny electrons were brushed aside by the massive a-particles, which weighed well over 700 0 times as much as they did. Only those a-particles whos e paths took them close to, or directly toward,

Figure 12.3a. JJ . Thomson's raisins-in-a-pudding model of th e atom. The raisins are negatively, and the pudding positively charged.

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Figure 123b. Ernes t Rutherford's model of the nuclear atom. The positively charged nucleus sits in a negatively charged swarm of electrons. In the figure the siz e of th e nucleus is grossly exaggerated.

the tin y bu t massiv e centra l particles—th e nuclei—wer e strongl y deflected . The cause of the deflection was the enormous electrostati c repulsion between the positively charged a-particle and the positively charged nucleus whe n the y were very close to each other. In a historic paper entitled "The Scattering of Alpha and Beta Particles by Matter and th e Structur e of the Atom, " Rutherford briefly described hi s experiment s at a meeting o f the Mancheste r Literar y and Philosophica l Societ y in 1911 , an d a few months late r he addressed the Solva y Conference. He had discovere d th e nucleus . There have been few more fateful finding s in science . The discovery of the nucleus of the atom was announced a t the same conference at whic h th e Frenc h physicis t Jea n Perrin presente d th e stronges t circumstantia l evidence, until then, fo r the reality of atoms. You can find what Perrin did i n most freshman physics textbooks. Atoms Are Overwhelmingly Composed of Empt y Space Rutherford allow s us to make this statement. Consider an atom of tungsten. Almost all of the mass of the ato m is concentrated in a tiny central piece of matter, the nu cleus. Around the nucleus buzz seventy-four bits of matter, all identical. These are electrons. Yo u can thin k o f the electron s a s effectivel y formin g a spherica l clou d around the nucleus. Th e diameter of the atomi c sphere is about 100,000 times the diameter of the central nucleus. Imagine a sphere with a diameter of 5 miles, representing an atom. The nucleus o n the sam e scale would be the siz e of a tennis ball . The electron s don' t d o muc h t o fil l u p th e lonel y spaces ; the y ar e individuall y smaller tha n th e nucleus , an d the y ar e also ver y much lighter . Yo u can se e why Rutherford's a-particle s s o rarely hit a nucleus an d generally went straight through the gold foil. The nucleus o f a tungsten atom weighs over a third of a million times as much a s a single electron. Thus nearly 99.8 % of the mas s of a tungsten ato m is located in the tiny nucleus. This figure is typical of atoms in general. The shee r concentratio n o f mass i n atomi c nucle i i s awesome . A teaspoon of closely packed nucle i would weigh about 500 million tons, which i s more than the weight of the whole populatio n of the world . It i s extremel y har d t o compres s a lump o f iron. Befor e Rutherford , w e woul d have said that in such a lump the atoms are touching each other, like a pile of solid cannon balls, and that's why it is extremely difficult t o squeeze a piece of any solid into a smaller space. And yet Rutherford showed that atoms are almost ghostlike. The conclusio n i s that th e pitifull y thin clou d o f electrons tha t surround s a n atom effectively "fills " the seemingly empty space around the nucleus, as far as the intrusion of other atoms is concerned, a littl e lik e th e ai r force s o f neighborin g

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countries effectively fillin g thei r nationa l ai r spaces . Recal l Hamlet: "O ! tha t thi s too too solid fles h woul d melt. " It isn't al l that solid; your flesh is well ove r 99% empty space. And s o is every other object you look at. What Are Nuclei Made Of? Matter is almost always electrically neutral, but if electrons are negatively charged, then, as Thomson stated, atoms must have some other components carryin g a positive charg e equa l i n magnitud e t o tha t carrie d b y th e electrons . Rutherfor d ha d shown tha t these components are in, or constitute, the nucleus. The smallest atom known in the earl y 1900s, and today , is the hydrogen atom. A century of chemical research indicate d tha t almos t al l other atom s ha d weight s tha t wer e very nearly whole-number multiple s of the weigh t o f the hydroge n atom . In 181 5 th e English chemist Prou t suggeste d that al l atom s wer e constructe d fro m hydroge n atoms . Thus the sodium atom, which weighs about twenty-three times as much a s the hydrogen atom, was supposed to be built from twenty-thre e hydrogen atoms. In those days there was no way to test this hypothesis. Th e next step in the story belongs to two young men, one of whom only had tim e to make a single critical contributio n to science. In 191 3 th e Danis h theoris t Niel s Bohr, age d twenty-eight, publishe d a theory that, among other things, deal t with th e frequencies of the light that could be produced by atoms. He predicted that these frequencie s woul d depen d o n the magnitude of the positive charge on the nucleus of Rutherford's atom, so that experimental measurements of these frequencies could lead to a determination o f the positiv e charge on any nucleus. The young English physicist Henry Moseley chose to examine the frequencie s o f the X-rays that ar e given of f by any elemen t when it is bombarded by a suitable beam of electrons. Bohr's theoretical relationship exactl y fitted Moseley's results, and Moseley was thus able , in 1913 , t o give a list o f the electri c charge on the nucleus of the ten metals that he had examined . He noted two striking facts : 1. Al l the nuclear charges were very close to being whole number multiples o f the charge on the electron . Thus, in units of the charge on the electron , the nuclea r charge on the calcium nucleus was 20.00; on vanadium, 22.96, and so on. This is explicable if we accept that atoms are electrically neutral. If an atom has a whole number o f electrons, the total charge on the nucleus must be a whole number of electron charges. 2. Th e orde r of increasing nuclear charge was, with on e exception, identical with the orde r of increasing atomic weight. Start with th e lightes t atom , hydrogen, and giv e its nucleus a charge of one, in units o f the electronic charge. The next heaviest element is helium. Its nucleus ha s a charge of two units. After heliu m comes lithium; i t has a nuclear charge of three units. An d s o on. Mosele y had foun d a way t o answe r th e questio n typifie d by : "How d o yo u kno w ther e isn' t a n a s ye t undiscovere d elemen t wit h a n atomi c weight between those of hydrogen and helium?" There can't be because its nucleus would have to have a charge between one and two. We can count the elements. Today there is a known chemical element for all the nuclear charges going from 1 to 110 (see Figure 13.1). There can be no other elements in this range, because an

The Material Trinity 114

atom must have a whole number of nuclear charges . Any newly discovered, or produced, elements must have a nuclear charge of 111 upward. As Frederic Soddy put it, Moseley has enabled us to call "the roll of the elements." The numerical value of the nuclear charge is called the atomic number, sinc e it is the ordinal numbe r that we give to an element whe n all the element s are lined up on parade, arrange d according to increasing nuclea r charge. In 191 5 a British, Australian, an d Ne w Zealan d expeditionar y force , wit h th e strong approva l o f Winston Churchill , lande d o n th e Turkis h coast , no t fa r fro m Constantinople, i n an attempt t o unbalance th e Germa n high command . Gallipol i became a synonym for bloody military failure, Among the more than 8 million who fell in World War I, well ove r 200,00 0 fell at Gallipoli, among them signal s office r Henry Moseley, aged twenty-seven. Prout had proposed building up all atoms from amalgamations o f different num bers of hydrogen atoms. Since the hydrogen atom had a single electron , it was natural t o suppose that it s nucleus, whic h ha d on e positive charge , was also a single particle. This particle late r became known as the proton. Now, following Prout, we might construc t th e heliu m nucleu s ou t o f fou r hydroge n atoms . Wh y four ? Because the helium ato m weighs close to four times what th e hydrogen atom weighs. But thi s present s a nast y problem . Fou r hydroge n atom s woul d hav e th e righ t weight, bu t the y woul d hav e a total o f four protons , whic h mean s four positiv e charges in the nucleus. Thi s doesn' t agre e with experiment, whic h give s the heli um nucleu s two positive charges , that is, an atomi c number o f two. To get around this difficulty , yo u could suppose that there wer e also two electrons in the heliu m nucleus. Thi s would hardl y affect th e weight, and the two negative charges would reduce the total positive charge to two, the right number (Figure 12.4). That is how the atom was seen for about twenty years: as a tiny, massive nucleu s containing protons and electrons, surrounded by other electrons. As often happen s in science, the theory had a flaw. The Material Trinity Is Completed The dazzlin g complexity o f the material world can, for almost al l purposes, be reduced to a simple trinity: the proton, the electron, and the neutron.1 The neutron, a component of the nucleus of every atom except that of hydrogen, was the last of the trinity t o be discovered , in 1932 . Had they al l been a little younger , the scientist s who uncovered the neutron might have met on the battlefields of World War II. In 1930 the German scientist Walte r Bothe bombarded th e metal beryllium wit h a-particles. He detected what he thought to be an as yet unidentified form o f radiation emerging from th e metal, which sums up hi s part in the overall story. During

Figure 12.4. Tw o different model s of the nucleus of the helium atom. Historically the first (and wrong) model was that o n the right. 1 Descartes, entirely without experimental or theoretical justification suggested that there were three "elements," basic forms of matter that differed i n their size and motion.

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World War II, Bothe worked on the Nazi's nuclear energy project. At the same time, in Paris, another participant in our story was doing work for the French Resistance. In 1925 , a t the ag e of twenty-five, Frederi c Joliot began work as an assistan t t o Marie Curi e a t th e Radiu m Institut e i n Paris . H e wa s initiall y instructe d b y Madame Curie's daughter, Irene Curie. Frederic detected in her an "extraordinarily sensitive an d poeti c creature, " an d the y wer e marrie d i n 1926 . From 192 8 they signed themselves Irene and Frederic Joliot-Curie. They were both eventually to be Nobel laureates, like Irene's parents, Pierre and Marie Curie. The Joliot-Curies read of Bothe' s experiments an d wer e curiou s abou t th e natur e o f the nove l radiatio n that he reported. They repeated his experiments and allowed the "radiation" fro m the bombarded beryllium to fall on materials having a high proportion of hydrogen atoms, fo r example, paraffin wax , in whic h ove r 50 % o f the atom s ar e hydrogen. They found that protons (hydrogen nuclei) were ejected from the target, but at such high speeds it was difficult t o understand how they could have been given such velocities by radiation fallin g o n them . The y published thei r results o n 1 8 January 1932. Back i n England , James Chadwick, a studen t o f Rutherford's, rea d th e JoliotCuries' paper and tried out the effect o f the mysterious radiation o n a variety of targets. In contrast to those who came before him, he assumed that the so-called radiation wa s i n fac t a stream of particles and tha t th e velocitie s o f the atom s ejecte d from th e targets could be explained by using Newton's laws of motion for two colliding bodies. Using the known masses and the measured velocities of the ejecte d nuclei, he deduced the mass of the enigmatic bombarding particles. He concluded that the new particle had about the same mass as the proton. Furthermore, it was known that the "rays" were far more penetrating than beams of either electrons or protons, and it was therefore almos t certain that the new particle was electrically neutral. When either protons or electrons are fired a t matter, their paths ca n b e affecte d b y th e electri c charge s o n th e nucle i an d electron s o f th e atoms through which they attempt to pass. The uncharged neutron is blind to these charges and therefore penetrates matter relatively easily, even passing very close to nuclei without being disturbed. Chadwick had identifie d the neutron. H e published his results o n 27 February 1932, a little more than a month after th e Joliot-Curies' paper had com e out. Again the discovery was made in the Cavendish Laboratories, and Rutherford and Thomson were still on the staff . Chadwic k held that the neutron was nothing more than an electron and a proton going around together, but the neutron was slowly accepted as an independent particle in its own right during the 1930s . The basic components of the atom, and indeed its very existence, were thus established, afte r twen ty-five centuries, in the thirty-five years between 1897 and 1932. The neutron allowe d a simple picture o f the nucleus . Ther e was no longer any need fo r electrons in th e nucleus. Th e helium nucleu s was not compose d of four protons and tw o electron s but o f two protons and tw o neutrons (se e Figure 12.4). The mas s come s ou t right , as doe s the charge . The ato m had bee n completed . A decade later, James Chadwick headed th e Britis h group participating i n the Manhattan Project at Los Alamos. In 1942, Irene Joliot-Curie fled to Switzerland with her children. Frederic JoliotCurie joined the Frenc h Communis t Party and organize d the production of explosives for the Resistance. After th e war he was awarded the croix de guerre. In 1939

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the Joliot-Curies, worried by the rise of Nazism, had deposite d a sealed lette r with the Academie de Sciences. It contained the principle of the nuclear reactor and was not opened until 1949. We can now summarize what could be called the British picture of the atom: Atoms ar e all compose d o f three kinds of particles. Except fo r the hydroge n atom. The nucleus contain s two kinds o f particles: protons and neutrons, except for the nucleu s of hydrogen, which consist s o f a single proton. The proton and the neutron have nearly the sam e mass, but the proto n is positively charged, while th e neutro n i s electrically neutral . The mass o f the proto n is 1.67265 x 10" 27 kg; of the neutron , 1.67495 x 10~ 27 kg. 2 Aroun d the nucleu s buzz th e thir d kin d o f particle , th e electrons . Th e electro n ha s a mas s of 8.5473 x 10" 31 kg and carrie s a negative charge of 1.60219 x 10" 19 coulombs, exactly balancing the positiv e charg e of the proton . The number o f electrons in an atom is equal to the number of protons, so that the atom has no net electrical charge . The diameter of an atom is about 100,00 0 times the diamete r of its nucleus. The nucleus account s for over 99% of the total mass of the atom . Figure 12.5 depicts the nuclei of a few elements. The nucleu s an d th e electro n ar e hel d togethe r b y electrostati c forces . T o get some idea o f their enormou s power, imagine that yo u hav e taken a tablespoon of sugar and separated out the electrons from the nuclei. Now keep the nuclei in a box on Earth and tak e the electron s to the Sun , 93 million mile s away. If the electrons are held in the Sun by Superman, then about 1 million people would have to stand on the box o f nuclei o n Earth to prevent i t fro m movin g toward th e Sun . You can now understand wh y most macroscopic lumps o f matter in the universe ar e effec tively electricall y neutral . An y attemp t t o remove a significan t proportio n of the charge fro m a neutra l piec e o f matter i s me t b y a stupendou s forc e o f attractio n pulling the charge back. The power of electrostatic forces poses a problem concerning the stability of the nucleus. W e have said that any nucleus i s made of protons and neutrons. Now th e neutrons have no charge , but th e proton s ar e positively charged . How does a collection o f protons kee p together ? Surely they woul d repe l eac h othe r wit h suc h force tha t th e onl y stabl e nucleus woul d be tha t o f hydrogen, which consist s o f a single proton . Ther e i s a hint her e tha t ther e ar e force s othe r tha n thos e tha t w e have dealt with. There are, and we will meet them later on.

12.5. The composition o f th e nuclei of som e elements. Protons arid neutrons are indicated by the letters p and n.

2 If you want t o get some idea of the smallness o f these numbers, multiply them by 10 27 (a billion billion billion) and you see that a billion billion billion protons, for example, have a mass of only 1.67265 kilograms.

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Unstable Nuclei A larg e number o f nuclei ar e unstable. This i s true o f all th e nucle i abov e atomic number 83 (bismuth), but it is also true of some lighter nuclei. Of the approximate ly 35 0 naturally occurrin g isotopes, about 5 0 are radioactive. Instability i s manifested b y the breakup of the nucleu s an d th e violen t ejectio n o f particles or radiation. Th e particle s ar e eithe r th e a-particle , whic h i s simpl y a heliu m nucleus , consisting of two protons and tw o neutrons, or the (3-ray , which is an electron. The radiation i s y-rays. The typ e of particles o r rays ejected depend s o n the particula r nucleus. Radioactiv e breakup gives a new nucleus , whic h in som e cases i s stable but in others may itself be radioactive. The same applies when this daughter nucle us breaks up, s o that ther e ar e well-known case s of chains o f radioactive breakup, until finall y a stable nucleus i s formed. The moment of breakup of a specific atom cannot be predicted, but fo r a very large collection o f atoms we can sa y that half of them will disintegrat e in a certain time. This half-life ca n be anything from a tiny fraction o f a second t o thousands o f years, depending o n th e nucleus . W e can d o nothing t o alte r half-lives, whic h ar e immune t o change s in temperatur e or pressure or to chemical reactions. a-Particles, a s befits suc h massive , charge d particles , cause considerable dam age when they strike matter, but they are also stopped afte r a short distance because they interact s o violently with thei r surroundings, p-particles (flying electrons) are far mor e penetrating , being , for example , abl e t o penetrat e dee p int o th e huma n body, y-rays can easily pass through your body, and they can knock electrons out of atoms tha t stan d i n thei r way . Thi s i s the origi n o f their harmfu l medica l effects , and the rationale behind their use in destroying tumors. The classic destructiv e us e o f radioactivity is the atomi c bomb, which i s based on the finding , b y Otto Hahn (1879-1968) and Frit z Strassman n (1902-1980 ) tha t when neutrons penetrate a heavy nucleus, the resulting nucleus can disintegrate to give more than on e neutron , a process that Frisc h termed fission (Figur e 12.6) . If this happens i n a sample o f suitable material, sa y uranium 235 , each nucleus tha t disintegrates can be responsible for the disintegration of two (or more) other nuclei, which can result in the disintegration of four nuclei, which ca n end in a mushroom cloud. This i s because the process of fission releases very large amounts o f energy. It is a curiosity tha t the mos t destructiv e reaction i n histor y migh t no t have bee n discovered when it was, but for two women. Ida Noddack heard about some experiments i n whic h Enric o Fermi ha d bombarde d uraniu m wit h neutron s an d ha d concluded tha t he had produce d heavier nuclei. Noddac k thought otherwise , correctly hypothesizing tha t the uraniu m nucleu s had spli t i n two. No one took any notice. Whe n Hah n an d Strassman n performe d thei r experiments , i t wa s th e

Figure 12.6. Th e neutron is absorbed by the uraniu m nucleus, and fission follows. Sometimes U-236 returns to U-23 5 and a neutron.

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physicist Lis e Meitner (1878-1968) , a refugee fro m Hitler , and he r nephe w Ott o Frisch, who realized exactly what the implications were . Notice that, without being explicit abou t it we have been talking about the realization o f the centuries-lon g drea m o f the alchemists—t o transmute on e elemen t into another. Each chemical elemen t is defined by the number of protons in the nucleus o f its atoms , the atomi c number. Thi s numbe r ca n chang e a s a result o f radioactivite decay , as Rutherford and Sodd y were the firs t to state. Later on we will see that man can synthesize nuclei with higher atomi c numbers than any found in nature, thus building previousl y unknown elements . A Question of Priorities I guess I'm just an old ma d scientist at bottom. Give me an underground laboratory, half a dozen atom smashers, and a beautiful gir l in a diaphanous veil waiting to b e changed into a chimpanzee, and I care not who writes the nation's laws. —S.J. Perelman

There wil l be readers wh o will protest that ther e ar e more than thre e elementary particles. Wha t abou t th e scienc e sectio n o f the New York Times, which almos t monthly report s successfu l or unsuccessfu l experiment s costin g million s o f dollars, and revealing or attempting to reveal a new particle to be added to a long list of exotic elementar y particles—quarks , leptons , muons , baryons , omeg a particles , neutrinos, positrons , gluons , an d s o forth ? Thos e o f thes e particle s tha t ca n b e made to appear in the laboratory are usually induced to do so by bombarding either nuclei o r simpl e particle s wit h a variety o f projectiles, includin g protons . The y generally "live " fo r less tha n a millionth o f a second before bein g annihilated b y collision wit h matter or by disintegration. A physicist will tell you that the motley crew o f subnuclear particle s partiall y liste d her e hol d th e deepes t secret s o f the universe. Thi s may be true, but to understand th e workings of the everyday world these particles are irrelevant. 3 To build a house, to understand th e working of the liver, to design a new pharmaceutical o n a computer, to launch a spacecraft, t o design a fiber-optic informatio n network or an artificial heart valve, to investigate the mode of action of a virus, you need know nothing about the nuclear physicist's particles. Ther e i s hardly an y human activity , except writing articles-on-particles , for which on e needs t o know abou t the existenc e o f any othe r particle s bu t protons , electrons, and neutrons . If w e ha d neve r discovere d th e nuclea r physicist' s exoti c particles , lif e a s w e know it on this planet would be essentially the same as it is today. Most of the particles resemble ecstatic happiness: they are very short-lived and have nothing to do with everyday life. Somewhat unfairly, it could be suggested that the motto of those who wor k on these particle s b e the smu g statement o f the Englis h mathematicia n G. H. Hardy: "I have never don e anything 'useful. ' N o discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least differenc e t o the amenity of the world." 3

Except for positron emission tomography (PET), a method of scanning the cells of the body using positrons.

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Research in particle physic s i s expensive. I t costs hundreds o f millions of dollars or more to construct the installations necessar y to produce a new particle having a lifetim e measure d i n millionth s o f a secon d o r less . I quote th e New York Times: "Big Science Squeezes Small-Scale Researchers" (29 Dec. 1992). The articl e below the headline discusse s the plight of small-scale research projects that have to battle fo r government fund s agains t th e demand s o f particle-seekers. I n th e New York Times of 5 January 1993, a headline referred to a report published b y a group of 315(1} physicist s workin g wit h equipmen t costin g abou t a quarte r o f a billio n dollars: "315 Physicists Report Failure in Search for Supersymmetry." This kind of thing i s red mea t for anti-intellectuals, bu t i t is no wonder that in som e informed circles, both scientific and nonscientific, there is questioning of the justification for the high cost of searching for new particles in a world in which the budgets for research int o ecological , medical, an d othe r "relevant " problems ar e ofte n insuffi cient. In order to accelerate protons to huge velocities, so that they can smash into each othe r an d (hopefully! ) produc e wha t som e believe i s the fina l undiscovere d particle, a vas t installation , th e Superconductin g Supercollide r (SCSC ) wa s planned t o be built in Texas . Cost? About $11 billion. The particle, known a s the Higgs boson, will almos t certainl y hav e n o practica l applications . Th e U.S . Con gress decide d t o stop fundin g th e SCS C project. On e congressman said , "It's good science, it's simply not affordable science. " HMS may suspect that among the motives for these gigantic ventures are national pride and scientifi c empire-building. He should als o realize that ther e is a real fascination about particle physics, a fascination that I hope I can convey in Chapter 31. "You've Come a Long Way, Baby"

Both Marie Curie and her daughte r Iren e were Nobel Prize winners. Marie' s wor k on radioactivity was a central part of the story of the atom. Irene and her husband , Frederic, discovered artificial radioactivity, the production o f radioactive element s that do not appear in nature. Neither Marie nor Irene was a member of the Frenc h Academic d e Science , despit e thei r Nobe l Prizes . The y wer e women . Iren e ap peared twice before the Academie in an effort t o convince i t that women should be permitted as members. She failed. Th e British Royal Society has an equally prou d record; it only legally allowed women members in 1923.

13 The Stuff of Existence Human senses cannot penetrat e t o th e insensible particles of bodies , and by observing their Figure, Size, Connexion, and Motion, tell why rhubarb purged, hemlock killed , and opium made man sleep. —John Locke

We may not kno w exactl y why rhubar b purges, but durin g the twentiet h centur y we have opened up the internal worl d of atoms and molecules. We can build molecules that nature never dreamed of, molecules tailor-made to meet our needs. The evolution of alchemy into science accelerated dramatically following the discovery of th e basi c structur e o f the ato m an d th e incursio n o f quantum mechanic s int o chemistry, a process initiate d primaril y i n the 1920 s and 1930 s by the American scientists Gilbert Newton Lewis and Linus Pauling. In this chapter we will briefly outline th e natur e o f the everyda y material universe: the chemica l elements an d the molecules that can be built from them. Man's prehistoric fascinatio n with naturally occurrin g materials, an d their un expected transformations, gav e birth t o alchemy, a 2000-yea r search fo r artificia l gold an d fo r the panace a that would cur e all ills, the philosopher' s stone . We can understand why the alchemist s spok e of materials i n the language of the occult . It must hav e seeme d magica l to earl y man tha t on e coul d take a heap o f rocks arid conjure a shining, toug h materia l fro m them , a materia l fro m whic h on e coul d make sharp , durable tools and weapons . Completely inexplicable change s o f this sort gave credence to the belie f that substance s could be transmuted; if rocks gave iron and ice gave water, why (and this was the great dream), why couldn't lead give gold? Alchemy, from th e beginning, had both a practical and a mystical side, and the straightforwar d descriptiv e entrie s i n th e notebook s o f the alchemist s wer e mingled with a running commentar y devoted to the sign s o f the zodiac and othe r astrological or magical matters. The psychologist Jung saw alchemy as a sublimated search for spiritual wholeness, but though some of the alchemists wer e mystics, many were involved as much in a material, as a spiritual, gold rush. To the alchemist, nature seemed to exist in endless variety, but, as we have seen, the instinctive searc h for simplicity le d to early attempts to construct theories that would account for the behavior of matter in terms of a small number of so-called elements. Th e best know n o f these effort s i s the ancien t Gree k belief that earth , air, fire, and water were the basic building blocks of the universe, but the Chinese had a very simila r traditio n o f five element s o r "powers" : earth , wood, metal, fire , an d water. Even while th e sterile doctrine of the fou r Elements was being taught in European universities , th e alchemist s wer e buildin g u p a bod y o f experimenta l knowledge concerning the way that differen t substance s reacte d to each other , to heat, an d t o corrosiv e solutions . Ou t o f this cumulativ e an d disjointe d body of

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practical experience grew a trail that led through Boyle and Lavoisier to Dalton and Rutherford and the modern concept of elements. It was this concept that allowed a rational explanation of the material world. In th e nineteent h centur y chemist s finall y acquire d sufficien t know-ho w t o begin to confidently analyze material into its elementary components, and to start building molecules unknown in nature. This expertise was the basis for one of the first realization s o f Bacon's dream o f the applicatio n o f science t o th e benefi t o f man. It was the nineteenth centur y chemical industr y that gave the poor man colored fabrics. During the nineteent h an d twentieth centuries , i t became clear that al l matter, in it s splendi d variety , i s constructe d fro m eighty-thre e differen t chemica l elements—nature's building blocks . To these naturally occurring elements, man has, up to the time of writing, added another twenty-seven new elements created in the laboratory.1 The Chemical Elements: Roll Call

All norma l matte r i s made o f protons, neutrons, an d electrons , but th e commo n currency of research, the basi c units o f matter consists o f the elements , a t least as far as the chemist, biochemist, geologist, metallurgist, physiologist, molecular biologist, medical man, and so on are concerned. The first element s with which ma n playe d were carbon, from burne d material , and a handful o f metals, such a s gold, which are loath to combine with oxyge n of the ai r an d produc e powder y oxides—whic h i s exactl y what iro n doe s whe n i t rusts. The economy of the Athenian polls, the birthplace of democracy, depende d on slaves and o n a shiny metallic elemen t extracted from th e mines nea r th e city; silver wa s on e o f the earlies t element s isolate d b y man. A more usefu l element , known to prehistoric man, was copper, which was employed in the manufacture of weapons and tools, especially whe n alloye d with tin—hence the Bronze Age. The Iron Age seems to have been largely based on iron that came from meteorites, sinc e analysis o f objects fro m tha t er a shows th e presenc e of relatively high percentages of nickel, typical of meteoritic iron. Many iron ores are just dirty rust, which is basically iron in combination with oxygen. At some time in prehistory someone must have heated an iron ore in a wood fire. Luckily , at high temperatures, carbon has a greater affinity fo r oxygen than does iron, and in the heat of a fire it takes oxygen to its bosom, turns int o carbo n monoxide and dioxide , and leave s metallic iro n behind. Thi s simpl e chemica l reactio n was to turn Englan d into th e leadin g worl d power in the nineteenth century. A dozen elements were known long before Christ was born (althoug h the modern concep t of an elemen t wa s unknown): carbon, sulfur, copper , silver, zinc, tin, lead, gold, mercury, arsenic, antimony, and iron. All these species are elements because the y ar e singl e substances , eac h compose d o f on e singl e typ e o f atom . For nearly 300 0 years, from abou t 1000 B.C. to A.D . 1735 , only three more elements were isolated: phosphorus, platinum, an d bismuth. I n the eighteent h centur y an other sixtee n wer e discovered , i n th e nineteent h centur y anothe r fifty , o f which 1 The new elements are invariably radioactive and very short-lived. Their nuclei break up to give those of atoms of already known.

The Stuff of Existenc e

Humphry Davy found six important elements: boron, sodium, potassium, calcium, barium, and cadmium. Thus at the dawn of the twentieth century, all but two of the naturally occurrin g element s ha d bee n discovered . Al l th e man-mad e element s were made in the twentieth century, most of them at the University of California, at Berkeley, by teams o f scientists le d b y Segr e an d Ghiorso . There are n o elements that have been detected in the stars that do not exist on Earth. Order Emerges

The 110 elements known at the time of writing are shown in Figure 13.1, i n the periodic table of the elements. The table contains the name of each element, the conventional symbols used to denote the element, and the atomic number (the number of protons in the nucleus), conventionally symbolized by the letter Z. At the time of writing, some of the man-made elements have not yet been named. The number of protons in the nucleus, Z, determines the chemical identity of the atom. Z gives the number of positive charges that there are on the nucleus. For an electrically neutra l ato m this must equa l th e numbe r o f negative charges, whic h can onl y be supplie d b y the electrons . In neutral atom s the numbe r o f protons i n the nucleus thus determines the numbe r of electrons. When atoms meet each other there is a collision of electronic clouds. Sometimes the collision results in no change in the atoms. In such cases, if the collision is in a gas, the atoms just go their separate ways. This is what happens in a cylinder of helium gas, for example. In some cases, however, atomic or molecular encounters result in a drastic rearrangement of the electrons of the colliding species, and then we speak of chemical change. Whether a reaction occurs or not is almost entirely in the hands o f the electrons ; the nature s of the nuclei , those tiny speck s that ar e s o far

Figure 13.1. Th e periodic table of the chemical elements. The number in each square gives the atomic numbe r of the element—the number of protons in the nucleus. The name and conventional symbol of each element i s given. The elements marked with an asterisk have been discovered but not officially named. For the significance of th e sexual classification see the text.

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away fro m th e border s o f the atom , are no t to o relevan t t o th e rearrangemen t of electronic clouds . The chemical behavior of atoms is completely dominated by their electrons. So true is this that the nucleus can be altered an d the atom retains its chemica l characteristics , provide d the numbe r o f electrons remain s th e same . An example will illustrate the principle. The hydrogen atom's nucleus consists of a single particle, one proton; the hydrogen atom has one electron. Some hydrogen atoms found in nature have nuclei consisting of two particles: one proton and on e neutron. These atoms are given a special name , deuterium, popularl y know n a s heav y hydrogen . Wh y "hydrogen" ? Because th e deuteriu m ato m stil l need s onl y on e electro n to electrically balanc e the singl e proton , an d therefor e both "normal " hydroge n atom s an d deuteriu m atoms both have one electron. It is this electron that determines almost completely the chemical behavior of the two types of atom. So similar is this behavior that we are entitled t o call them both hydrogen.2 All known elements exist in two or more nuclear variations, all having the same number of protons and therefore the same number of electrons and the same chemical properties. These variations on a basic atomic theme are termed isotopes. They differ onl y in the number of neutrons in the nucleus. Thu s hydrogen has three isotopes (Figure 12.5), namely, hydrogen (nucleus: one proton), deuteriu m (nucleus : one proton plus one neutron), and tritium (nucleus : one proton plus two neutrons). About 0.015% of the atoms in a sample of hydrogen obtained from natural sources are deuterium atoms. Tritium, which was first detecte d in 1950, also illustrates the fact that while the chemical properties of different isotope s are (almost) identical,3 their nuclear properties can differ entirely : tritium is weakly radioactive, giving off (3-rays (electrons). About one in 10 18 hydrogen atoms is a tritium atom; at least that was the number before thermonuclear weapon testing began in March 1954. It then went up about a hundredfold but is now dropping back to its previous value. A historically significant isotope is uranium 235, which account s for about 0.72% of the naturally occurring uranium atoms (uranium 238 accounts for most of the rest) and has been the basis of nuclear reactions producing huge amounts of energy. The fact tha t the chemistr y of an element depends o n the numbe r o f protons in its nucleus suggests the possibility of transforming one element to another by pushing more protons into its nucleus, or knocking some out. This alchemy was first observed by chance by Rutherford in 1919 whe n he found that he could knock a proton ou t o f the nitroge n nucleu s b y bombarding nitrogen wit h th e nucleu s o f the helium ato m (the a-particle). The first deliberat e transformation was performed by Cockcroft an d Walto n in 1932 , a t the Cavendis h Laboratory. A beam o f speeding protons smashed into a lithium (thre e protons in the nucleus) target and knocked out protons, producing helium atoms , which have two protons in the nucleus. Reactions resulting in nuclear change occur in nuclear weapons and in the stars.

2

The behavior of hydrogen and deuteriu m can be very different , if their nuclei are involved. An important practical example of this is the use of heavy water in some nuclear reactors, base d on the fact that deuterium nuclei absorb neutrons far better than the protons in normal water. 3 The chemical properties d o in fact vary slightly between different isotopes of the same element, a difference mainl y manifested b y tiny differences i n the strength of the bonds to other atoms. Thus deuterium is a little more strongly bonded to other atoms than is normal hydrogen.

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The Periodic Table The periodic table of the elements (Figure 13.1) is constructed by arranging the elements i n orde r o f increasing atomi c number , which mean s increasin g numbe r of protons in the nucleus, and therefore an increasing number of electrons in the electrically neutral atom. It is clear that the atom s o f different element s have differen t weights. Similarity i n th e propertie s o f certain element s make s a periodic arrangement convenient, an d was the spur for the first attempts to arrange the elements in some kind o f order. Thus th e element s helium, neon , argon , and s o on, in th e fa r righ t hand column, labeled VIII , are all gases occurring in nature as single atoms, which hardly reac t wit h othe r substances . Thi s i s wh y the y ar e sometime s calle d th e noble gases. All the element s i n th e colum n labele d I are soft , silver y metals tha t react vigorously with water and combine rapidly with the oxygen in the air. A numbe r o f chemists, th e firs t apparentl y bein g d e Morvea u i n 1772 , played around with the arrangement of the elements , but the present for m o f the periodi c table i s primaril y th e resul t o f the wor k o f the Russia n Dimitr i Mendeleev. Mendeleev felt himself to be a disciple o f Newton. He wrote, in his Principles of Chemistry (1869) that it was necessary to harmonize chemical theories "with the immortal principle s o f Newtonian natural philosophy , an d s o hasten th e adven t o f true chemical mechanics. " I n hi s 188 9 lectur e a t th e Roya l Institutio n i n Londo n he tried, unconvincingly , t o appl y Newton' s third la w o f motion to th e behavio r of atoms in molecules. Mendeleev arranged the elements i n the order of their relative atomic weights , bu t thi s i s prett y muc h th e sam e orde r a s that base d o n atomi c numbers, the number of protons in the nucleus. Mendeleev saw that i f the element s tha t were known a t his time were arranged in order of increasing atomic weight, then certain properties recurred at regular intervals: "Element s placed accordin g to the value of their atomi c weights present a clear periodicity of properties." Thus , in terms of atomic numbers, atoms 9,17, 35, and 5 3 were al l corrosiv e gase s tha t interacte d violentl y wit h metal s an d mos t other substances. He therefore arranged them beneath eac h other—see the colum n labeled VII. These element s are known as the halogens . (Elemen t 85, astatine, is a man-made element , firs t produce d i n 1940. ) H e di d likewis e fo r al l th e othe r known elements. At the end he found that there were spaces in his table, which i s not surprisin g sinc e som e o f the element s ha d no t ye t bee n discovered. I t wa s rather like laying out an incomplete pac k of cards into four suits; you would kno w exactly wher e t o leav e holes . Mos t chemists wer e very skeptica l about hi s table, which is difficult fo r us to understand because it looks so convincing. Once again, a new ide a met sticky brains.4 What eventually wo n everybody over was that whe n three o f the missin g element s (gallium , germanium , an d scandium ) wer e found , they had properties corresponding almost exactly to those predicted by Mendeleev, including their atomic weights. What Mendeleev had done was to look at the properties o f th e know n element s abov e an d below , an d t o lef t an d t o righ t o f th e "holes," and predict the unknown properties by taking a rough average of the properties of the hole's neighbors. 4

Mendeleev himself was wary of new discoveries ; he refused t o believe in J. }. Thomson's discovery of the electron.

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When Mendelee v was buried i n St . Petersburg i n 1907 , his student s carrie d a chart showin g th e periodi c tabl e in the funera l procession . Two decades afte r hi s death, quantum mechanics provided a very satisfying theory of atomic structure, in which th e way the electron s ar e arranged about the nucleu s inevitabl y lead s t o a periodicity in chemical properties. Atoms must have a definite number of protons, and we know all the atoms from atomic number 1 to atomic number 110 . Th e heaviest ar e all extremely unstable , and it is becoming harder and harder to create new nuclei. The largest nuclei are so unstable tha t they fall t o pieces almost befor e w e can look at them. Th e genesis of the element s wil l be discusse d later , but ther e hav e been som e funn y theorie s i n this field. 5 The heaviest element s that we know, those above uranium (atomi c number 93), have all been made by man. The method is basically t o bombard know n element s with a variety of nuclear projectile s and hop e tha t al l or part of the projectil e will stick to the target nuclei long enough for us to separate, identify, an d characterize a new element. A typically brutal synthesis was the bombardment of curium (Z = 96) with a massive projectile, the carbo n nucleus ( Z = 6), to give the ne w elemen t no belium (Z = 102). Of the known chemical elements, about 80% are metals, but i f you take a spoonful o f earth you'll find that, on the average, it contains about 46% by weight of oxygen and abou t 28 % of silicon. The dominanc e of silicon an d oxyge n is accounted for by the fact that earth, clay, and rocks contain very high proportions of these two elements. Aluminum, a very common constituent o f clays, is the third most common element, at about 8%. Carbon (0.02%) and hydrogen (0.14%) are comparatively rare. By comparison with th e dea d world o f rocks, a woman contain s abou t 62 % by weight o f oxygen atoms, 23% carbon , 10 % hydrogen , 2.5 % nitrogen, 1.4% calci um, 1.1 % phosphorus , and smaller percentages of potassium, sulfur, sodium , iron, and cobalt. Very small amounts o f other elements, such as copper, zinc, manganese, magnesium, and selenium , ar e necessary fo r the health y functionin g of the body. You can buy all these elements fairly cheapl y from a chemical company. A human being costs about a couple of hundred dollars , retail. By far the most abundant element in the universe is hydrogen, the main component of the stars. Molecules The element s ar e characterize d b y a n extraordinar y rang e o f qualities, an d tha t range become s seemingl y infinit e onc e atom s combin e wit h eac h other . Atom s combine, either naturally or at man's inducement, to form literally millions of combinations. When these combinations are reasonably stable, we call them molecules. Thus th e nitroge n molecul e consist s o f two nitroge n atom s tha t g o around wit h each other in a stable pair, if no one interferes with them. Likewise, the sugar molecule i s a combination o f twelve carbo n atoms , eleve n oxyge n atoms, an d twenty 5 Sir William Crookes, whose belief in the spirit world we have encountered previously, believed that the elements all evolved by a process of Darwinian evolution from a primary material, which he called "protyle."

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one hydrogen atoms and, a s you know , if it is lef t i n a dry container i t appears to last forever . Molecule s vary greatly in their stabilit y under norma l conditions , bu t the vas t majorit y o f them, sa y benzene, water , o r th e plasti c polyviny l chlorid e (PVC), can be kept in bottles for years without any, or almost any, detectable sign of change. Molecule s hav e propertie s that , unles s yo u hav e som e chemica l knowl edge, are usually completel y unpredictable o n th e basi s o f the propertie s of their constituent atoms. With a modicum of chemical knowledge you can make a reasonable gues s a t th e chemica l an d physica l propertie s o f most molecules , althoug h their biological effects ma y be totally unexpected. Well over 90% of all known molecules have been made by man. The potential of atoms to produce new an d varied properties in combination i s illustrated b y the fac t tha t th e followin g commonly occurring molecules, som e of which are shown i n Figur e 13.2, are made only of combinations o f one or more of the atoms hydrogen, carbon, and oxygen: polyethylene, water, cellulose, ozone, butane, glucose, benzene, carbo n dioxide, acetone , alcohol (th e kind i n drinks: ethyl alcohol o r ethanol) , ether , cholesterol , formaldehyde , testosterone, progesterone, cortisol, pheno l (carboli c acid) , an d antifreez e (ethylen e glycol) . Thousand s o f other molecule s ar e constructe d onl y fro m combination s o f varying number s of these three atoms. Add nitrogen atoms to the building blocks and you can construct most amino acids, TNT, urea, nitroglycerine, the cyanide ion, lysergic acid diethylamine (LSD), epinephrine (adrenaline) , nicotine, morphine, and thousands more. Now throw in sulfur an d phosphorus and you can build most proteins, DNA, penicillin, an d s o on . I f yo u stil l doub t th e extraordinar y flexibilit y o f atoms , yo u should reflect o n the fac t tha t about 99% o f the livin g parts o f any member o f the animal o r plant worl d ar e made solely from fou r kind s o f atom: carbon, hydrogen, nitrogen, and oxygen.

Figure 13.2. A tiny selection of importan t molecules that can be built from carbon, hydrogen, oxygen, arid nitrogen atoms.

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The preceding selection of molecules should convinc e you that atoms in combination usually have properties entirely unrelated to those of the isolated elements. A heap o f carbon, when shaken wit h a mixture of hydrogen and oxyge n gas, gives nothing but a heap o f carbon i n a mixture o f gases; it doesn' t behav e lik e choles terol or cellulose. The atoms have to interact much more seriously than forming a simple mechanica l mixture . Chemica l combinatio n involve s a rearrangemen t of the electrons of the species combining . A further poin t that come s out o f an examination o f Figure 13.2 is that i t is not only the type s and number s o f atoms i n a molecule that determine it s properties . Look at dimethyl ethe r and ethanol , both o f which hav e two carbon atoms, six hydrogen atoms, and one oxygen atom—C2H6O. They certainly have differen t chemi cal and physica l properties . T o start with, ethano l is a liquid an d th e componen t that makes whisky drinkin g worthwhile, bu t dimethy l ether is a gas. It is precisely this sensitivity of molecular properties to molecular structure that accounts for the incredible variet y o f matter. Perhap s th e best-know n exampl e o f propertie s de pending o n structur e i s th e carbo n atom , which occur s i n natur e i n tw o forms : graphite and diamond. In graphite, which is a soft material, the atoms are arranged in planar sheets that can slide over each other; each carbon atom is joined to three others. In diamond eac h carbon atom is joined to four others , arrange d at the corners o f a regular tetrahedron, t o produc e a singl e immensel y rigid , three-dimensional skeleton , similar t o a syste m o f girders an d accountin g fo r the diamond' s hardness. Recently it has been found possible to synthesize a new form of carbon, a network of sixty atoms forming a ball-like structure (a "bucky ball") that has bee n christened buckminsterfullerene, afte r th e architec t Buckminste r Fuller , th e de signer of the geodesic dome. The Behavior of Atoms

Galvani an d Volt a foun d tha t the y coul d obtai n electri c current s b y a suitabl e arrangement of two metals and a damp solid. Unknowingly , they had provide d an explanation for many of the chemical properties of matter. The title of the next section is a tribute to the connoisseur of the "electricity o f women." Atomic Sexuality

Divide th e periodi c tabl e int o thre e classes : male , female , an d bisexua l (Figur e 13.1) Th e male elements ar e the metals; they are hard an d flashy , an d thei r atom s tend t o give up electron s to the soft , subtler , female elements , the nonmetals. The bisexual atom s ar e the semimetals, which ar e prepared t o accep t o r donat e elec trons. I n th e tabl e the y ar e locate d betwee n th e mal e an d femal e elements . Thi s classification i s an oversimplification, but almost all classifications are. Now consider potassium iodide. Potassium i s a group I metal which is so reactive that, if held i n the hand, it would soon eat through the skin. Iodine is a violet, iridescent, crystallin e soli d that , a t room temperature, gives off a corrosive, choking violet vapor. When potassiu m and iodin e react , they d o s o violently, giving a harmless white crystallin e solid, potassium iodide , which, fa r from bein g dangerous, is a component o f the "se a salt " sol d i n you r supermarket. What happens i s that potassium atoms (male) in contact with iodine (female ) giv e up a n electron to their partner . Th e initiall y neutra l atom s are now bot h electricall y charged . The

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potassium atom, having lost a single negative charge, now carries one net positive charge, which represents the fact that there are nineteen protons in the nucleus but only eighteen electrons in the atom. Conversely, the iodine atom now has one more electron tha n i t has proton s in th e nucleus , s o it carrie s on e net negativ e charge. Charged atoms or molecules ar e called ions. Thousands of materials consist of assemblies of oppositely charged ions. Potassium iodide is a white solid which, when examine d by X-ray crystallography, is revealed as a very orderly array of ions, each ion of one kind having six close neighbors o f the othe r kind (Figur e 13.3a). It is the attractio n between opposit e charges that gives the crystal its stability, and we say that the crystal is held together by ionic bonds. Most substances that are of combinations of metals and nonrnetals are called salts and consist of ions, held together by ionic bonds. The word salt the common name for one specific salt—sodium chloride—comes from the Latin sal6 Notice that the additio n o f an electro n to the iodin e ato m an d th e los s o f one from th e potassiu m ato m chang e bot h o f them fro m viciou s beast s int o sleep y pussycats. This is an illustration o f the fac t tha t although it is the nucleus that determines a n element' s name, it i s th e electroni c clou d tha t determine s ho w th e atom behaves. Mos t metals hav e a stron g tendency to giv e up electron s t o non metals. When they have don e so, they cal m dow n an d ar e much more stable. The nonrnetals have a strong tendency to accept electrons, and they too usually change from highly active, corrosive substances into harmless, negatively charged ions. Many salt s brea k up (dissolve ) in water , a process that liberate s th e ion s fro m their neighbors . Th e free-floatin g ion s ca n mov e in a n electri c fiel d s o that solu tions o f salts conduc t electricity , just lik e electron s i n a wire. That' s wh y James Bond threw an electrical appliance into the bath in which the villain had fallen. He knew that the bathwater, which contained salts, would conduct electricity very efficiently. Pure water is a very poor conductor. Back to Volta. The tendency fo r a metal atom to give up a n electron varies from metal t o metal . Pu t a coppe r ato m i n contac t wit h a zin c atom . Th e zin c ato m "pushes harder," and the result is that electrons try to pass from zin c to copper. It is this inequalit y i n th e "pushin g power " o f different metal s that i s the basi s of the voltaic pile and of similar chemical batteries. When identical metal atoms get together in a piece of metal, for a stag party, they have no one to whom to give their electrons, but they release one or more electrons anyway. Thus a piece o f metal i s a collection o f positive ion s floatin g i n a sea of electrons (Figur e 13.3b). Sodiu m meta l is a n ordere d arra y of positively charged sodium ions , eac h o f whic h ha s contribute d on e electro n t o th e negativ e sea .

Figure 13.3a. Th e arrangement of ion s in a crystal of potassium iodide.

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The Roman army was partially paid in salt, each soldier receiving his salarium, or salary, presumably in accord with Pliny's sentiments: "Heaven knows a civilized life is impossible without salt."

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13.3b. A thin slice through a metal. The regularly arranged positive ions are held together by an electron sea.

Copper atom s giv e up tw o electron s each . Without these electrons , the positivel y charged meta l ion s woul d repe l eac h other ; i t i s the negativel y charge d electron s that are the mobile glue, sometimes calle d the electron gas, that holds them together by electrostatic attraction. We say that the atoms in a metal are held together by a metallic bond. In 1900, only three years after J. J. Thomson's discover y of the electron , the German physicis t Pau l Drude suggested that some of the electron s i n metals were fre e to migrate. The mobility o f the electron s explain s electrica l conduction . I f you pu t a metal wire between th e terminals o f a battery, electrons flow int o on e end o f the wire and out of the other; the electron gas is moving.7 If we take a walk inside a metal, we find that the ions are arranged in regular arrays (Figur e 13.3b). The arrangemen t o f atoms i n metals an d crystal s i s in fac t in variably orderly . Robert Hooke, in 1665 , suggested, with sharp physica l intuition , that th e beautifu l macroscopi c shape s o f crystal s wer e a resul t o f th e orderl y arrangement of their atoms . He stacked musket balls i n differen t way s to help hi s speculations, bu t sinc e nothin g o f importance wa s know n abou t atoms , h e coul d not progress. Strong Bond s

Most substance s ar e neithe r metalli c no r saltlike ; the y ar e molecules o f the kin d shown i n Figur e 13.2 . Take, for example, that medi a personality , th e ozon e molecule. It is built solel y of three oxygen atoms. No ions here. The atoms in ozone are held togethe r b y sharing electrons. Mos t o f the electron s i n th e ozon e molecul e spend thei r time wandering about in the space between the three nuclei, formin g a cloud of negative electricity, which pull s the nuclei towar d it (Figure 13.4a). Most of th e molecule s i n you r body ar e held togethe r by suc h covalent bonds. Yo u are most likely to find covalent bonds when you have atoms that have pretty much the same tendency to push (or pull) electrons. Thus , for example, the "pullin g power " of th e nitroge n an d oxyge n atoms is quit e similar , an d whe n they ar e brought to gether neithe r i s th e outrigh t winner , s o the y shar e electrons , creat e a covalen t bond, and form the nitric oxide molecule, NO.

13.4a. The formation of a covalent molecul e from three atoms. The electron clouds of the atoms merg e to give one molecular cloud. 7 When an electric current passes through a piece of wire, the electrical balance between positive ions and electrons is left unchanged. All that happens is that electrons leave one end of the wire but are replaced by electrons coming in at the other end. A wire carrying a current does not carry a net charge, which is why, as stated in Chapter 8, you can't feel an electric field outsid e such a wire. If you touch it, electrons will flow into you, but they are still being replaced at the end of the wire. A body with static electricity on it has got a net inbalance of charge, and the excess will flow into you if you touch the body.

The Stuff of Existence

Carbon atoms, when foun d i n the natural world, are almost always either in the form o f the covalentl y bound molecul e carbo n dioxid e o r in molecule s i n which two o r mor e carbon s for m covalen t bonds betwee n themselves , givin g chains o r rings of carbon (Figure 13.2). Gentle Bonds: Molecular Velcro Ionic, metallic, and covalen t bonds vary in their strength according to the particular atoms involved . A different an d muc h weaker bond foun d i n natur e i s named after a Dutch chemist. Van der Waals force exist s between all molecules. It is a very weak attractiv e force tha t has it s origin in the attraction of the positivel y charged nuclei o f each molecule for the electron s of the othe r molecule (Figur e 13.4b). The van de r Waals' forc e i s generally larger between large r molecules, which explain s why i t is important in th e interactio n betwee n biologica l molecules suc h a s proteins. The last type of chemical bond that occurs in nature is also weak, but it controls all our destinies—the hydrogen bond (no t bomb). Recall that a hydrogen atom is a proton with a single electron running aroun d it. If a hydrogen atom sits on an oxygen atom, say, one which is part of a molecule, the powerful pul l of the oxyge n nucleus (i t has eigh t protons) will partiall y shif t th e hydrogen' s lon e electro n i n th e direction of the oxygen's electron cloud (Figure 13.4c). This partly bares the hydrogen's nucleus, the proton , which is of course positively charged. The net result is the creation of a spot of positive charge at the edge of the oxyge n atom. This charge can attract the negative electron cloud of another molecule, thus gluing two molecules together. Usually hydrogen bonds form when the hydrogen atom is sitting between two oxygen atoms or two nitrogen atoms, or one of each. The glue is not very strong, but it is ideal if you need to have two molecules joined to each other in such a way that the connection is normally stable but can be broken nonviolently if need

Figure B.4b. Va n der Waals force between two hydroge n atoms, The attractive forces outweigh the repulsive.

B.4c. The hydrogen bond between two molecule s of water. Each oxygen atom carries two "balloons " o f negative charge and two hydroge n atoms.

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be. We will se e that this is exactly the requiremen t o f the DN A molecule if it is to fulfil it s role. Both the van der Waals force and the hydrogen bond are easily formed and easily broken. You can classify the m as molecular Velcro. The Semimetals A majo r characteristi c o f metals i s their abilit y t o conduct electricity , some much better than others . The nonmetals d o not have this ability ; they have no "electro n sea." Their tendency i s to accept electrons, not give them up . Th e semimetals are neither her e nor there. Take silicon, the symbo l of the electroni c age. Silicon crystals have a structure lik e diamond; eac h silicon ato m form s fou r stron g (covalent) bonds t o neighboring atoms. This structure , lik e diamond , ha s n o loos e electrons left over , as there are in a metal. But silicon is a bigger atom than carbon and i t has more electrons. It doesn't tak e too much t o get a few electrons to break away an d wander through th e crystal . These electron s allow silicon t o conduct electricity — not ver y well, bu t bette r by fa r than nonmetals . No w when a n electro n leave s an atom o f silicon, i t leave s a "hole " behind wher e i t ha s been . Thi s hol e ca n als o move. Well, it isn't reall y the hole that moves , it's a n electro n from a neighboring atom falling into the hole and leavin g a new hole o n the neighboring atom (Figure 13.5a). Since a silicon atom with an electron missing is positively charged, when a hole moves, so does a positive charge. But moving charge is what we call an electric current. Thus silicon has two ways to conduct electricity: the few free electron s can move, and the positive charge can move. Now we can start to play clever tricks. If you look at the periodic table, you can see that the next element after silico n is phosphorus. Phosphorus has an atomic number of 15 compared with 14 for silicon, which mean s tha t i t has on e more electron . Suppos e w e pu t a phosphorus ato m into a silicon crystal. It uses some of its electrons to join on to four neighboring silicon atoms , just as silicon does , but i t has on e electron extra, with nothing t o do. This electron can wander around, and it increases the electrical conductivity of the crystal. In fact, if the crystal is "doped" with very small amounts of phosphorus, its conductivity depends almost entirely on the phosphorus atom's contribution to the "free" electro n population. Suc h a crystal is called a n n-typ e semiconductor , "n" for negativ e charge carrier, "semi" because it doesn't conduc t anywher e a s near as well as a metal.

Figure B.5a. Insid e a silicon crystal. The two electron s involved in a bond between neighboring atoms are symbolized by two dots . An electron deserting a bond between two silico n atoms leaves behind a positively charged hole. Another electron can fall into this hole, with the result that the hole moves.

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Figure 13.5b. A n aluminum atom has invaded a silicon crystal but does not hav e enough electrons to for m four bonds to neighborin g silicon atoms. There is thus a built-in positive hole in the crystal into which an electron can fall.

Now look at silicon's othe r neighbor on the same row of the periodic table. Aluminum has a n atomic number o f 13 and therefore has one fewer electro n than sili con. Pu t a n aluminu m ato m in a silicon crystal , ctn d i t doe s it s bes t t o for m fou r bonds to its neighbors, but it has one electron too few (Figure 13.5b). You can think of on e o f the bond s a s being incomplete , lacking a n electron . This missin g (nega tive) electron creates a positive hole, and the number of these holes, and the electrical conductivity of the dope d silicon, depend s o n the amoun t of aluminum i n th e crystal. This i s a way o f producing a p-type semiconductor , where "p " stands for positive. Semiconductors forme d the basis of the electronics revolution. The transistor is based o n successiv e layer s o f p- and n-typ e silicon-base d semiconductors , for example, npn and pnp. Subsequent technology ha s been marked by dramatic minia turization o f such devices and also the developmen t of new semiconductors based on other semimetals, in particular gallium and arsenic. The whole field depends on the chemist's ability to produce very pure substances, because even minor amounts of impurities can result in differen t batches of semiconductors having widely varying and unpredictable conductivities . In recent years, semiconductor device s have been built that, in response to electrical impulses, produce very pure light, effectively o f one frequency. Thes e "semiconductor lasers" ar e revolutionizing communications technology . Ther e are now telephones that conver t your voic e to electrical impulses (that' s no t new) , whic h are then converte d t o ligh t b y a minute semiconducto r laser . Th e light , travelin g along glass fibers, carrie s the message that, at the othe r telephone receiver , is converted back to electrical impulses an d then to sound. We are in the age of optoelectronics, but only because we know how to handle the necessary materials. The Creation of Materials Man is now routinely making new molecules, unknown i n nature, a capability that has altere d th e visual , tactile , an d medica l environmen t o f muc h o f mankind . There is no possibility, within th e confines of this book, to survey in depth the nature o f materials and ou r ability to conjure with them , but w e will very sketchily summarize the main types of synthetic materials to be found in our world.

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Ceramics A rough definition of a ceramic is a tough, durable substance, resistant t o environmental attack and compose d of a blend o f metallic or semimetallic elements and a nonmetallic element, which is usually oxygen. A well-known ceramic is Carborundum, the common name for silicon carbide . Here the semimeta l i s silicon an d th e nonmetal i s carbon . Anothe r exampl e withou t oxyge n i s silico n nitride , a n extremely hard-wearing material that is used for turbine blades. Almost all ceramics up t o modern times were based on silicon an d oxygen , because these two elements for m the basis for clay and sand . There is an atomic pattern that recurs in many different type s of ceramics (Figure 13.6). The arrangement of the atoms is based on tetrahedra consisting of a silicon ato m surrounded by fou r oxygen atoms. The radius of the silicon atom is about three and a half times as large as that o f the oxygen . We thus have a collection o f footballs and tenni s balls, an d what happens in large three-dimensional structures is that the football s for m tetrahedra and the tennis balls creep into the central cavities. If you look at Figure 13.6, you will be able to appreciate that in such large structures every oxygen belongs to two tetrahedra , s o that ther e i s a continuou s chai n o f links runnin g throug h th e material. In general the strengt h o f ceramics comes from thei r interlinke d arra y of atoms, rather like a pylon or a bridge, in which one can continuously walk along strong interconnections. Compar e this with, say , oxygen gas, where th e onl y stron g bonds are between discret e pairs o f oxygen atoms, and th e forc e holdin g individua l oxygen molecules to each other is very weak. Similarly, a crystal of sugar is a collection of discrete molecules that falls to pieces in water, each molecule floating around on its own. Disordered Solids If you heat a crystal, the atoms , or ions, vibrate more and mor e energetically until , if the temperatur e i s high enough , they shak e the ordere d structure t o pieces an d

Figure 13.6. (a ) The building bloc k of man y important silicates, (b ) Two linke d blocks, (c ) A linear chain o f blocks, (d ) Another common pattern.

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the individual atom s start wandering where they will. You have made a liquid; the orderly arrangemen t of the soli d ha s disappeared . Now , suddenly lowe r the tem perature. Th e melt solidifies and, before th e atom s can find thei r wa y to the positions that the y had i n the ordere d structure , they are trapped, wherever the y are. The resulting soli d ha s no t go t a regular structure, Th e soli d i s amorphous, fro m the Greek for "without form. " Almost all types of glass are amorphous . As w e sa w earlier , glass has foun d a n importan t new us e wit h th e comin g of fiber-optic communication . Thes e fiber s obviousl y mus t hav e a hig h degre e of transparency, otherwis e th e ligh t signal s would di e ou t to o quickly . All glass absorbs light to a certain extent, but it is a measure of the state of glass technology that a pane o f standard windo w glas s absorbs as much visibl e ligh t a s a 10-mile-thic k block of the glass used in optical fibers . The Infinite Variety of Carbon In 184 6 the Germa n chemist Johann Gmelin first use d the ter m organic chemistry for th e stud y of carbon compounds. Most university chemistry department s hav e professorships i n organi c chemistry . Wh y no t a professo r o f sodiu m chemistry? The reaso n i s twofold : the enormou s importanc e o f organic compounds an d th e tremendous number of carbon compounds. The carbon atom has the ability to easily form a strong covalent bond to other carbon atoms so that molecules with chains or rings of carbon atoms are found everywhere. Some simple examples were shown in Figur e 13.2, in which all the large r molecules show n have a number o f carbonhydrogen bonds . The vas t majority o f carbon compound s contai n suc h bonds . Of the 1 5 million or so known molecules , some 12 million are organic. And the num ber is growing. Many chemists spen d th e whole o f their professiona l lives making new organic molecules. Molecular Monsters One particular class of carbon compounds plays a starring role in the living world and in the material environment of much of mankind, namely, polymers. A polymer is a chain, produced by linking together small molecules, known in this context as monomers. The monomers in a chain may be identical, as in a simple necklace, or similar. Monomer s are usually smal l carbon-containing (i.e. , organic] molecules. Polymer chains ca n reach enormous lengths, containing thousands o f atoms, The synthesis and industria l productio n of man-made polymers are of major economic significance, but by far the most important polymers occur naturally. The most abundant organi c polymer on earth is almost certainl y cellulose (Figure 13.2) , a polymer of the sugar (3-glucose, which is the tough substance that forms the oute r cove r o f the plan t cell . Cotto n is almos t pur e cellulose ; woo d i s abou t 50% cellulose. We make about 200 million tons of paper a year from cellulose. Glucose is also the basi s o f starch. In animals, glucose is stored in anothe r polymeri c form, a s glycogen , which i s a heavil y branche d molecul e containin g anywher e from about 2000 to 600,000 glucose units. A macroscopic sample of any polymer is invariably a mixture of chains of different lengths . The normal functions and structure of the cell are almost entirely in the hands of a group of polymers: the proteins. Proteins consis t of chains o f amino acids. Twenty amino acids ar e used by the cell s o f the human body, and i n an y given protei n

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the sam e amin o acid may appear many times. Differen t protein s contai n differen t numbers and differentl y ordere d combinations o f amino acids. The number o f possible protein s i s vast. Th e number o f different protein s i n th e huma n cel l i s wel l over a thousand. The protein s hav e a n astonishingl y varie d rang e of tasks. Som e o f them ac t a s structural components , holdin g th e cel l i n shape . Othe r protein s ar e antibodies that protect, or should protect, the body. Fibrinogen is a protein that is essential in blood clotting. Muscles depend for their contractile action on two proteins, myosin and actin . There are proteins whose job is to carry materials fro m on e place to another, like the hemoglobin molecule that ferries oxygen from the lungs to the rest of the body and depends for its action on the presence of four iron atoms. All enzymes are proteins. Enzyme s catalyze (speed up), the reactions which , a t the mos t basi c level, are life. From man's point of view, the most important polymer on earth is the DNA molecule, the molecule that carries genetic information from one generation to the next. The Importance of Shap e When a small molecule, such as a drug or a hormone, acts on a living cell, it initial ly binds to one or more very specific sites on the cell surface or within the cell. This binding i s usually by van de r Waals (Velcro) forces, which, because they are weak, allow the smal l molecule to break away relatively easily a t a later time . A crucial factor in successful binding is a good match between the shape of the absorbing site and the shap e of the absorbe d molecule. For example, the actio n of all enzymes in the livin g cell depends o n their cornin g into contact with othe r molecules an d interacting with them. This interaction does not occur anywhere o n the enzyme molecule but a t specific sites , usually termed active sites. Like a lock on a door, active sites are shaped so as to accept only one specific molecule (key) or only molecules containing a small group of atoms arranged in the righ t shape. Thi s ensure s tha t a given enzyme speeds up onl y a certain type of reaction and does not act as a general accelerator o f cellular reactions . Complementarity of shapes i s a device exten sively used by nature to ensure the smooth functioning of living matter. Shape has life-or-deat h implication s whe n i t come s to the desig n of new phar maceuticals. Th e nineteenth-century Germa n scientist Pau l Ehrlic h describe d th e action of drugs as being a "lock and key" phenomenon, in which onl y the correctly shaped key would fi t the lock. His idea has been extremely fruitful i n studying th e reaction between large molecules such as proteins an d smaller , biologically active molecules such as drugs and hormones. In studyin g the shape s an d interaction s o f proteins an d othe r larg e molecules, increasing use i s being made of visual representations o f the molecule s o n a computer screen. The evolution of very fast computers with large memories has revolutionized thi s field. It is possible to "put a protein o n the screen, " rotate it, focus i n on certain parts of it, and thus examin e the detaile d shape o f the protein and o f its active site, and us e the informatio n as a guide to how the protei n functions. Thi s kind of approach is being used more and more to examine th e interactio n o f drugs and small , biologically significan t molecules with proteins . Th e drug need no t be synthesized i n th e initia l stage s o f the research—i t ca n be built o n the compute r screen an d the n manipulate d o n the scree n to se e how wel l i t fit s int o the activ e site of the protein.

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Man-made Polymers The firs t man-mad e polyme r wa s produce d b y Le o Baekland i n 1905 . H e too k formaldehyde—the materia l used fo r preserving medical specimens—an d phenol , commonly calle d carboli c acid, and heated them together. He got a hard black material which he called Bakelite. He filed a patent application in 1907 a day before a certain Jame s Swinburn e arrive d a t hi s loca l paten t offic e t o appl y fo r the sam e patent. Bakelit e was a common plastic i n the 1930 s an d 1940s , but th e limeligh t was take n by nylon i n 1934 . Nylo n made it s popular debu t i n 193 8 i n Dr . West's Miracle Tuft Toot h Brush. Our daily surroundings, i f we are city dwellers, are no w replete with polymers, from polyethylene to polyvinyl chloride. In the day s of Bakelite the creatio n of polymers was not fa r removed from cook ery—a bit o f this, a bit o f that, heat , an d stir . Polymer chemistr y and physic s ar e very sophisticated discipline s today , and we have reached th e stage at which ne w polymers are being tailor-made for specific purposes. Liquid Crystals If you have a digital watch, the displa y is almost certainly made of liquid crystals , a class of compound that was discovered in 1888. Liqui d crystals can flow like liquids, but thei r molecule s ar e normally arranged with a high degre e of order, like solid crystals . The simples t possibl e kin d o f liquid crysta l consist s o f long, thin molecules, that above a certain temperature behave like a normal liquid, the molecules bein g completely fre e t o move a s they wish . Whe n cooled , the liqui d sud denly changes into a form that , although stil l fluid , ha s it s molecules al l roughly lined u p i n th e sam e direction , lik e par t o f a logja m floatin g downriver . It' s as though a plate of cooked spaghetti changed fro m th e usual chaotic mess to a plate of approximately aligned strands o f spaghetti—aligned but stil l sloppy enough to pour of f a slanted plate , thus behaving like a liquid. When all the molecules in a sample of material ar e roughly parallel, the sample will exhibit different physica l properties fro m th e sam e sample i n th e liqui d state , in whic h th e molecule s ar e tumbling around freely. On e of these properties is the way that the sample reflects and scatter s light, and i t is this property that has been used i n liquid crysta l displays. In your watch th e number s chang e as a result o f the actio n o f tiny electri c fields tha t ar e capabl e o f changing th e orientatio n o f liquid crysta l molecule s so that they line up wit h the directio n o f the field . Suc h crystal s ar e man-made, but there are natural substances that are liquid crystals. A very important type are the ph osph olipids. Phospholipids are the mai n constituents o f the membranes of living cells. They are long floppy, molecules that naturally tend to align themselves with each other. In fact, man y phospholipids, whe n shaken with water, have the tendency to spontaneously for m closed , hollow spherica l aggregates , termed vesicles or liposomes. Such sphere s hav e fascinatin g physical properties , but yo u migh t car e t o reflec t that mere shaking can induce the formation o f a structure that resembles large portions of the membranes of living cells. No "vital force" was needed to construct this highly organize d entity. Real cell membranes consis t of double layers of phospholipids o f this kind, with a variety of other molecules embedded in them.

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Theory Pays Off

Chemistry handles th e visible cloth fro m whic h the universe is made. Only in the investigation of the fundamenta l particles o f matter has chemistr y nothin g to say. But it is chemistry that has shown us what the Earth is made from, what living material is , an d (i n the guis e o f biochemistry an d molecula r biology ) how th e cel l works. Its methods hav e enabled us to analyze and purif y th e materials that have made possible the communications revolution: microchips, semiconductor lasers , fluorescent screens for monitors, and so on. Modern medicine depends on a multitude o f substances, fro m anesthetic s t o antibiotic s an d hormones , tha t ar e eithe r synthesized o r purified by the skill s of the chemist. Chemistr y enables us to build materials that nature could not, on her own, produce; materials that have colored our buildings and our clothes, have alleviated our ills, and eased the daily grind. Chemistry has been called the central science, and no other discipline ha s contributed s o muc h t o th e understandin g an d bettermen t o f ou r condition , eve n though the products of man's ingenuit y have sometimes turned around and bitten him. In the pas t two chapters we have seen how man' s curiosit y abou t the nature of the materia l universe , and hi s powe r o f reasoning, have le d from alchemy to th e nuclear atom and onwar d to science-based technology. Before we get carried away by modern man's ingenuity, it is fitting that we now pause, turn off the TV, and look back over the centuries at two of our scientific ancestors .

de int erIu

Honor Thy Father and Thy Mother

Science and the search fo r order in the universe have their roots in the ancient world. In the following pages we look back at two of our intellectual ancestors , one a mystic, the other a materialist; one a charismatic leader and the other a tough-minded poet . They represent two essential ingredient s o f the human ques t for knowledge.

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14 Scipio's Dream He sat on a rubbish heap for fault y geometrical figures, Nearly straight lines, kinky circles, bent rectangles, 3.7-sided triangles Their skinny, useless shapes clinked and sagged under his weight Like a heap of ten thousand metal coat-hangers. —Adrian Mitchell, Pythagoras on Elba

Those who ar e not permanentl y hunting fo r food o r money have tim e to hunt for meaning. Philosophers , introspectiv e adolescents , Frenc h fil m directors , poets , and HM S all seek an underlying o r overbearing order. The search for natural order in the physical world, the drive to detect pattern, may in the end be a consequence of the computer architecture (the way our brains are wired) or of the computer soft ware (the way our brains are programmed). Undeniably, our attempt to understan d the cosmo s has been drive n b y far more than the wish to improve our standard of living. The searc h fo r orde r i n th e wide r sense , th e "What-does-it-all-mean? " syn drome, is at least partially motivated by the awareness of suffering an d th e smell of mortality. Th e tw o quests , fo r natura l orde r a s exemplifie d by science , an d fo r metaphysical orde r exemplified by religion , have ofte n overlapped . Orde r i n th e natural worl d hint s a t an overal l desig n and b y inference an overal l Designer , so that belief in a deity is bolstered by the symmetry of the Tyger. The intertwining, or even identity, of the two quests was rarely questioned before th e seventeenth cen tury. Newton took the ordered motion o f the planets as evidence of the existence of the Creator . He agreed with th e psalmist : "Th e heaven s declar e the glor y of God, and the firmament sheweth his handiwork." The yearning for the scientist' s Gran d Design and the mystic's Ultimat e Reality is unlikely to fade. Scientists , ofte n drive n by irrational rather than rational belief in the unity of nature, have strive n to unite arid simplify. Thi s is not a recent phenomenon, associate d onl y with Oerste d an d Faraday , Maxwell and Einstein . The simplifications, an d unifications , of myth an d religio n hav e been associated wit h every stage of human history, from th e caveman's wall paintings onward . Simplification was raised to the statu s of a principle by the fourteenth-century Franciscan philosopher Willia m o f Ockham: "Wha t ca n b e explaine d b y th e assumptio n o f fewer thing s i s vainl y explaine d b y th e assumptio n o f more things. " Ockham' s razor still guides those seeking to account for natural phenomena. The traceable roots of both Western science and philosophy li e in Greece and i n the Gree k settlement s o f Asia Minor . Th e Frenc h philosophe r Rena n calle d th e marvelous flowering o f Greek thought "th e onl y miracle in history." There, in th e Greek world, the firs t know n Western philosophers appear: Thales, Anaximander, and Anaximenes. There, reason separated itself from myth and mysticism, but that

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separation wa s rarely complete, and the mingling of the mystic and the mathematical is nowhere more intimate tha n i n the shadowy , enigmatic figur e o f Pythagoras of Samos. He has a right to be seen as the father of the Western search for order. His spirit is still with us. The Godfather

Pythagoras was born about 580 B.C., about the tim e that Nebuchadnezzar II sacked Jerusalem. The first definit e sighting of him that we have is in Samos, a lush islan d just off the coast of present-day Turkey, with a tradition of wine making initiated by the god Bacchus in person. Pythagoras's whereabouts befor e Samo s are unknown; the grapevine has it that he was born in either Tyr e or Sidon and spent many years in Egypt and Babylon delving into the occul t and mathematics . H e seems to have made a reputation a s a thinker i n Samos, but he next appears in Croton (now Crotone) on the sole of the Italian peninsula, where he joined an existing Greek colony and quickl y set up a tightly knit , secretive cul t characterized b y asceticism, vege tarianism, a belief in the transmigration of souls, and a ban o n bean eating . "To eat beans," sai d th e Pythagoreans , "is to eat one's parents ' heads. " Th e rationale was that lif e wa s breath an d sinc e bean s induc e flatulence , t o break wind afte r eatin g was proo f o f having eate n a livin g soul . Shelle y wrot e a piec e i n prais e o f th e "Pythagorean diet. " The similaritie s betwee n th e Pythagoreans ' lifestyl e an d tha t o f the Buddhis t priesthood o f India i s striking. There is an ancient rumo r that Pythagoras traveled as far as India. He was fifty whe n Buddha was about thirty. There wer e Mafia-lik e aspect s t o th e Pythagoreans . Their leade r wa s a charis matic, well-traveled, snapp y dresser : white robe and trouser s an d a gold coronet . He is said to have sacrificed an ox (not a horse) every time he proved a new mathe matical theorem . On e Hippasu s o f Tarentum wa s reputedl y drowne d a t se a fo r blabbing ou t the secre t rules b y which th e cul t wa s governed . Afte r Pythagoras' s death, his followers infiltrated local (southern Italian!) politics and apparently controlled dozen s of city-states for about half a century. Popular history has not been kind to Pythagoras. Today almost the only response that his name invokes is "the square on the hypotenuse." He would have been gratified t o find that there is a pleasant, white-walle d red-roofe d por t in Samos name d after him: Pithagorio. But his legacy is far larger than that. His statue, alongside that of Aristotle, Euclid, Ptolemy, Christ, and a n assortment o f saints, stands abov e the massive wes t door of Chartres cathedral. His spirit pervade s scienc e an d philoso phy. Newton revered Pythagoras. Let us begin to see why. The Legacy of Pythagoras : The Numbers Gam e

Pythagoras said "All is number" an d "Numbe r i s the ruler o f forms an d ideas , an d the cause of gods and demons. " Divide th e infinitel y lon g numbe r 1111111 1 . . . b y 9 . Th e answe r i s 1234567901234567890123. . . . O r divid e 101010101 0 . . . b y 9 an d yo u get 112233445566778900112233. . .. So what? Triviall y amusing ? It would no t hav e been to Pythagoras—nothing to do with numbers was trivial; they were a bridge to the deepest, hidden secret s of the universe, a path to what Plato was later to see as the reality behind the shadow.

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The Pythagorean s were obsesse d wit h numbers . Wit h you r sixth-centur y B.C . eyes, look at what the Pythagoreans saw when they looked at the first fou r integers, 1,2, 3, and 4:

A straigh t line ca n be draw n betwee n an y two points, a plane throug h any three. The simplest solid with plane sides must have a minimum of four corners . One can build a temple to the God s with lines, planes , and solids . I s it so strange that th e Pythagoreans regarded the numbers 1 through 4 as being special? Take their sum, 1 + 2 + 3+4 = 10. Arrange ten points in a triangle:

The central dot together with four dot s along any side makes 5, which, i f you are a Pythagorean, represents earth , water, fire, air , and the soul. The three points at the corners o f the triangl e enclose a hexagon, an d 6 , the su m o f 1 + 2 + 3, represents life, althoug h I don't kno w why. Together with th e centra l do t the hexago n gives seven, a number of mystic significance to many civilizations an d representin g intelligence and light , the prerogative s of Athene. (Th e Japanese had seve n gods responsible for happiness.) The infinit e series o f numbers 1 , 3 (=1 + 2), 6 (= 1 + 2 + 3), 10 (= 1 + 2 + 3 + 4), 1 5 (=1 + 2 + 3 +4 + 5), and s o on, were dubbed perfect numbers, o f which 1 0 was re garded a s by fa r and awa y the mos t significant . It was give n a specia l name , th e tetraktis, TetpaKTU^, and was sacred. Pythagoras swore by it. The supposed occul t significance of numbers ha s occupie d man fro m prehisto ry. The Chaldeans held 4 and 7 in specia l regard. The Chinese constructe d magi c squares, a game overlooked by the Greeks . Relax in your favorite chai r an d impro vise: On e is one , the only , the Godhead , the cosmo s . . . me, numero uno. Tw o is ying and yang, heaven and hell, man and woman. Three is the Trinity, the triangle, the male genitals . .. and so forth. All of which is harmless rubbish and which, for a Pythagorean, misses the point. Take the Trinity. If there was for Christianity a purely religious significance attached to 3, it has long been lost. It is the personae of the Trinity—Father, Son , an d Hol y Ghost—that ar e the object s o f veneration, no t th e number 3 in itself. With the Pythagoreans it was the numbers tha t were in danger of canonization. The Game Turns Serious Inevitably th e religiousl y inspire d manipulatio n o f number s le d som e o f th e Pythagorean cul t i n th e directio n o f mathematics. A s an example , go back to th e perfect numbers 1, 3, 6,10. . .. The next three in the series are 15, 21, and 28. Now note tha t th e su m o f any tw o successiv e perfec t number s i s a perfect square . For example:

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U 3 = 4 = 22 3 + 6 = 9 = 32 6 + 10 = 16 = 42 10 +15 = 25 = 52 etc .

Those with high school algebra might try proving this result, which is for us a mild curiosity but for the Pythagoreans was a hint of cosmic order. And it was really cosmic order that obsessed them, and that in different ways has obsessed man ever since. Take the perfec t numbe r 28 . Its factors (th e numbers by which it can be exactly divided) are 1,2,4, 7, and 14 . Add them together. You get back 28! By the tetraktis! This mus t b e another type o f perfect number, on e tha t i s th e su m o f its factors . If you get your kicks from solving puzzles, you could try looking for other suc h perfect numbers. 1 An easy one is 6, which, a s we have seen, is a perfect number in th e sense that it is the sum of 1,2, and 3, but is also perfect in the new sense since 1,2 , and 3 are also its factors. Another two are 496 (the sum of all integers from 1 to 31) and 8128 (the sum of all integers from 1 to 127). Thus 8128 is the sum of its factors: 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032 , and 4064. 1 warn you tha t up t o 19 February 1992 , onl y thirty-tw o perfec t number s o f th e "factor " kin d ha d bee n found. Th e larges t has 455,66 3 digits, an d yo u wil l no t therefor e be surprise d t o learn that five of the known numbers were unearthed by the use of Cray supercomputers. The Pythagorean concept o f means, which remains a part of elementary mathe matics to this day , will have special significance for us shortly. Among other types of mean th e Pythagorean s define d the arithmetic mean (o r average) of two num bers, which i s given by (x + y)/2; and the harmonic mean, which i s given by 2xy/(x + y). The arithmetic mean of 6 and 1 2 is (6 + 12)/2 = 9; the harmoni c mean is (2x6 x 12)7(6 +12) = 8. The later Pythagoreans were interested i n mathematics, a s distinct fro m mysti c numerology, but the y remained essentiall y a religious cul t wit h belief s that ofte n echo older religions. We remember their math because we use it; we tend to forge t the, for us, wasted time they spent trying to find a number or group of numbers t o associate with materia l object s and abstrac t concepts . T o us these associations ar e meaningless. The number 1 represents intelligence ; 2 is opinion, becaus e you can jump from each of its component "Is " to the othe r (1 + 1). Even numbers were de clared t o be feminine, and od d wer e masculine. I n a male-dominated societ y thi s inevitably led to the doctrine that even numbers were evil and odd were good. Certain number s wer e considere d t o hav e aphrodisia c propertie s an d wer e writte n down and swallowed—with unrecorded effects . Multiplication ? The Pythagoreans appear to be the firs t t o have state d that mathematics wa s an activity that could be divorced fro m the practical world. Mathematics undoubtedl y arose from practical need s such a s commerce and th e constructio n o f buildings. It was the Pythagoreans who saw that there was an abstract entity behind the socially 'For the foolhardy, here is a helpful hint: if 2P-1 is a prime number, then (2 P-1) x (2 P-1) is a perfect number. Thus fo r P = 5, 2P-1 = 31, which i s a prime, leading to 496, a perfect number. Prime numbers of the form 2 P-1 are known a s Mersenne primes after the remarkable Marin Mersenne , mathematician, theologian , estimato r o f the speed of sound, an d frien d of Rene Descartes.

Scipios Dream

useful instrument . Thi s was one of the critica l turns, i f not the critical turn, in th e history o f mathematics, an d i t had a deep influence on later Greek thinkers, Plat o and Euclid in particular. It is here that we see the beginning of what is today called basic science , the stud y o f nature, an d knowledge , for its ow n sake . Plato, a fir m Pythagorean, specifically stated tha t arithmeti c shoul d be studied fo r its intrinsi c value, not for the purposes of commerce. A majo r discover y of the Pythagorean s was tha t A/2 , th e squar e root of 2, could not be written dow n a s a/b, wher e a an d b are whole numbers . V 2 i s the numbe r which whe n multiplie d b y itsel f gives 2. It can b e proved that ther e is no wa y of writing this as the ratio of two whole numbers, in the way that we can write 1.5 as 3/2, The Pythagoreans called V 2 and simila r numbers irrational, as we still do, and the existence of such numbers disturbe d them since they saw the cosmos as based only on rational numbers, which coul d be written as alb. Despite the mathematics , th e real influence o f Pythagoras over the centurie s is rooted i n th e mystic , som e woul d sa y metaphysical, conten t o f his thought : hi s search for cosmic harmony. The Music of the Spheres Take a guitar—there must be an acoustic guitar left over from the sixties , or a hightech electronic brain blaster belonging to you or your son. Pluck the thickest string. If you r hous e i s i n order , you shoul d hea r th e not e E . Measure th e lengt h o f the string, which shoul d be about 25.8 inches. Now place an index finge r between the fourth an d fift h frets , th e strip s o f metal crossin g th e fingerboar d (Figur e 14.la). Press down firmly o n the string and with a finger o f the othe r hand pluc k it again. You should be listening t o the note A. Measure the length of string that vibrated— the length between the fift h fre t an d the bridge of the guitar. It's about 19.3 inches. The ratio of the two length s that you have measured is 4 to 3 . The two note s that you have played, E and A, define a musical interval of a fourth, becaus e you hav e played the first and fourth notes of a major scale.

You are repeating an experiment performed by Pythagoras. You may not be amazed by the fact that a pleasant musical interval is related directly to a simple numerica l ratio. He was apparently thunderstruck. Follow him further: play the "open" string again, th e E . Now pu t you r finger betwee n th e sixt h an d sevent h frets . Pla y an d measure. The second note that you have heard is a B, and you have played an interval of a fifth. Th e ratio of string lengths is 3 to 2. Transport yourself back again to the sixt h century B.C. , to a time long before th e

Figure 14.1a. Pythagora s discovers cosmic harmony .

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frequencies o f notes could be measured, before psychological or physiological explanations could be generated to account for the scales that please our ears. For the Greeks, the striking link between music and numbers wa s astounding, beautiful in its simplicity an d a reflection at the deepes t level of the harmony o f nature. It was without doub t a major sourc e of Pythagoras's belief in cosmic order and its numerical basis. Let us go a little deeper. Earlier in this chapter w e talked about means. Pick up the guitar again . Let the length of the open E string be 12 units (Figure 14.Ib). If you play a length of 6 units, you ge t an interva l o f an octave—yo u ar e playing the nex t highes t E . Now notice that, as we found earlier, the arithmetic mean o f 6 and 1 2 is 9, and th e harmonic mean of 6 and 1 2 is 8 . Play lengths corresponding to 9 units an d 8 units. You are again playing the A and th e B. The arithmetic an d harmoni c means evok e harmonious sounds . To Pythagoras this was an exampl e of a far deeper order , an orde r that encompassed Heaven and Earth. It is to Pythagoras that we trace the first use of the word cosmos both to label the universe an d t o impl y beautifu l and harmoniou s order . I t was h e wh o propose d that ever y plane t emitte d it s ow n musica l tone , th e combine d soun d bein g th e "Music of the Spheres, " which, accordin g to his disciples , onl y Pythagoras amon g mortals coul d hear . Ther e is a n ech o her e o f the ancien t Hind u belie f that, apart from audibl e sound , there was an "unstruck sound," inaudible t o man. Pythagoras, more than anyon e else , has th e righ t to be considered the fathe r of the Western way of seeking order in the universe. Hi s influence stretches fro m an cient Greece to the modern world. 2 Pythagoras and the Ancient World Pythagoras's fingerprint s ca n b e detecte d al l ove r th e Gree k and Roma n world . Plato was influenced by the Pythagorean doctrine of the transmigration of souls. In

Figure 14.1b. Th e mathematics of music. 2

Pythagoras said, "A friend is another self." Like most denizens of Soho coffeehouses i n the 1950s, I played the guitar. On 1 June 1957, The Vipers, the group of which I was a foundermember, reached number eight on the British Hit Parade. The Vipers were later helped by George Martin, who went on to greater things as the Beatles' arranger. Late one night in the Two Is, in Old Compton Street, the Royal Shakespeare Company actor Mike Pratt pointed out to me that th e fourth and fift h chord s that were part of my limited musical vocabulary had been the origin of Pythagoras's dream of cosmic harmony. Mike died, cruelly early, long ago. I record my gratitud e to him for initiating my interest in Pythagoras, thus allowing me to sense, if not hear, the music of the spheres.

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his Phaedo, where h e tells the unforgettable story of Socrates' las t day, he invent s (for h e was not present ) a discussion o n immortality i n whic h Socrates ' companions are nearly al l Pythagoreans. A t the en d o f the Republic Plat o introduce s th e music o f the spheres . Late r in his lif e Plato fell for numerology and the nonmathe matical significance of numbers. Perhaps Pythagoras was indirectly responsible fo r the motto reputed to have been chiseled abov e the door of Plato's Academy: "Let no one ignorant of mathematics ente r my door." Almost certainly it was the Pythagorean doctrine that the sphere was the perfect solid body that induced Plat o to declare the Earth to be spherical . Euclid wa s a mathematical fa n o f Pythagoras in th e thir d centur y B.C . Ovid , in his Metamorphoses, portray s Pythagora s expoundin g transmigratio n t o th e leg endary kin g o f Rome, Num a Pompilius , wh o predate d Pythagora s b y a century ! Cicero's Republic contain s a section entitled Somnium Scipionis (Scipio' s Dream), in which th e elde r Scipi o Africanu s appear s i n a dream t o his grandso n and presents a panoram a o f the universe , heavil y dependen t o n th e philosoph y o f th e Pythagoreans. Transmigration , immortality, an d the music o f the sphere s al l make their appearances. And then came the Barbarians. Pythagoras Survives the Dar k Ages

Thrown out of southern Russia by Attila's Huns, the Ostrogoths fled westward an d in A.D . 452 invaded th e Italian peninsula. Th e Roman Empire in the West had ru n its course. From A.D . 493 Theodoric the Got h ruled th e kingdo m of Italy. The Dar k Ages were to last for several hundred years . These particular Barbarians were not all that barbaric. Like the Romans that they had conquered , the y wer e Christian , albei t adhering , lik e Isaa c Newton , t o th e Arian heresy. They sensed tha t th e Roman s had somethin g t o teach the m and , i n view o f the fac t tha t Theodori c had bee n educate d i n Constantinople , i t is understandable tha t h e employe d Roma n advisers . On e suc h wa s Aniciu s Manliu s Torquatus Severimus Boethius, who wa s dubbe d "th e last of the Ancients." I t was he who would carr y the Pythagorean torch, almost alone, through the millenniu m that led to the Renaissance. Boethius's (unrealized) ambition was to translate all the works of Plato and Aristotle into Latin. Pythagoras lef t n o writings; much o f what we know o f him i s contained i n Plato' s writings , particularl y Timaeus. Throug h Plato , Boethiu s me t Pythagoras. The translations o f Boethius ha d a n enormou s influenc e on medieval learning . With th e birt h o f the universitie s i n twelfth-centur y Europe, it was his text s tha t were used, almost exclusively , to teach arithmeti c an d music . He himself wrote a five-book treatise , De institutions musica, which was the standar d Europea n tex t on music for a thousand years, fro m th e fift h centur y onward. Boethius's treatise was firmly based on the scal e that Pythagoras ha d constructed , buil t o n simple ratios of string lengths . The curricul a o f th e medieva l universitie s typicall y include d seve n subject s classified int o th e quadrivium (arithmetic , geometry , astronomy, an d music ) an d the trivium (rhetoric , grammar, and dialectic) . Note that music was classified with the sciences, another legacy of Pythagoras. We see the Pythagorean connection very clearly whe n th e musi c syllabu s i s examine d i n detail . Instrumenta l an d voca l

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music were regarded as the least prestigious branch of music. Of higher importance were the study of the "harmony " of the body and spirit of man, and here we detect the ancien t belie f in fou r humors, which onl y when they were perfectl y (harmo niously) balanced allowed man to be perfect. Music reached its highest peak in the music of the world, musica mundi, which subject included the study of the four elements (earth , water, fire, an d air) , the movement of the heavenly bodies, and th e dance of the four seasons—subject s not on the curriculum at Juilliard. Music, math, and nature mingled—this is pure Pythagoras. It was largely through Boethius's text that th e messag e of Pythagoras wa s preserve d fo r some 50 0 years until, fro m th e eleventh centur y onward, origina l Greek texts reached Europ e via the translation s of Arab and Jewish scholars. Boethius was unlucky in his choice of patron. Theodoric was an unpredictable, violent man. Fo r obscure reasons, he had Boethiu s imprisoned in Pavia, and afte r nine month s o f uncertainty ha d hi m horrifyingl y torture d an d the n clubbe d t o death. Yet the spirit triumphed. During his incarceration, Boethius penned De consolatione philosophiae, in which th e personifie d figure o f Philosophy solaces th e author in his misery. This monument to man's dignity in the fac e o f the slings and arrows was probabl y number tw o o n the best-selle r lis t i n Europ e for a thousan d years, and was translated by both Alfred th e Great and Queen Elizabeth I. Pythagoras Corrected To be proved wrong 2000 years after you r death i s a fate tha t ha s befallen some of the best people. Pythagoras did not escape. He, or at least his school, was responsible fo r generating a series o f relationships betwee n th e musica l not e emitted b y a plucked string , the length of the string, and the weight hanging on it. These results were certainly not the outcome of experiments, but i n the great medieval Scholastic tradition they went unquestioned an d untested until, afte r two millennia, a musician actually hung weights on strings, plucked the strings, and listened. He didn't hear th e note s tha t h e wa s suppose d to , an d hi s ow n experiment s sparke d of f a reinvestigation (o r investigation) of the physic s o f vibrating strings . The musicia n was Vincenz o Galilei , a virtuos o lutenist , an d i t wa s Boethius' s boo k tha t ha d aroused his curiosity. I would like to think that it was his experiments that fostere d an interes t i n scienc e i n hi s son , Galile o Galilei. Thus woul d th e lin k b e made , through Boethius , between the Pythagorea n origins of order and th e seventeenth century scientific revolution. Newton and the Ancients Newton firml y believe d that his wor k was merely a resurrection o f knowledge already bestowed o n the sage s of old by the Almighty . While Si r Isaac was loathe to give credit to his contemporaries when they propounded view s similar to his own, he wa s wildly generou s to the ancien t Greeks , th e ancien t Hebrews , the ancien t anybody who b y some stretch of the imaginatio n ha d mad e a pronouncement resembling something that he had said. By a deviousl y twistin g argument , worth y o f a Jesuit , Newto n attribute d t o Pythagoras a statement of the law of universal gravitation. In bestowing on the Su n the power to hold the planets o n their courses, Newton was doubtless awar e of the second-century B.C . Pythagorean belief that identifie d the Su n with Apollo Musa-

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getes, the "conductor " o f the Muses who san g the music of the spheres. And whe n he famously spli t th e light of the Su n into a spectrum, Newton counted seve n colors, because there were seven notes in the Pythagorean scale. It is ironic that the mystic sid e of Newton, which was probably of more importance to him than anything else, has been widely ignored, and yet if one looks underneath his scientific writings one finds that they are permeated by the belief in a harmonious, ordere d cosmos that was the visible representation of an underlying profound mysti c order . The belief in a n all-embracing scheme, o f which moder n unified fiel d theorie s ar e typical , ha s bee n th e commo n groun d o f scientifi c thought fo r centuries. Th e spiri t o f Pythagoras infused the live s o f Galileo, Newtori, Kepler, and a host o f their successors. As the late Paul Feyerabend remarked, when Copernicus set out to order the heavens he did not consult his scientific predecessors bu t wen t bac k t o a "craz y Pythagorean"—Philolaus . Th e searc h fo r a mathematical framewor k on which to hang the visible worl d i s in no smal l measure the legacy of Pythagoras, the man whom the philosopher Whitehead regarded as the founder o f European philosophy and European mathematics. The Poets Abandon Pythagoras

Pythagoras spoke to scientists an d poet s alike. Aeschylus, at least according to Cicero, was a follower of Pythagoras. Chaucer knew of Scipio's Dream, as did the au thor o f the medieva l Roman de la Rose. The music o f the sphere s wa s a common literary devic e up t o the Enlightenment . Lorenzo , in The Merchant of Venice, declares: "There's not the smallest orb which tho u behold'st, / But in his motion like an angel sings." And the Elizabethan Sir John Davies, in Orchestra, puts into Antinous's mout h th e sentimen t that: "al l th e world' s grea t fortune s and affair s / Forward and backward rapt and whirled are, / According to the music of the spheres. " It is difficult t o know when idea s such as the music of the spheres changed fro m being objects of belief to being literary conceits. When Wordsworth speaks of "harmony from Heaven's remotest spheres," we know that he does not believe in literal harmony, as did the Elizabethans. The Romantics' vision of the universe was anti-Newtonian. The Pythagorean vision of mathematically based cosmic order was abandoned by the Romantic poets. Wordsworth retreated int o subjectivity— a retrea t that stil l shape s Western poetry. The poets have staged an almost wholesale withdrawal t o the inner world, despairing by default of a universal framewor k an d leavin g the searc h for cosmic order in the outside world to the scientists. No contemporary poet would undertake to emulate Lucretius' s delineatio n o f the universe , an d fe w poet s toda y woul d wis h o r dare to write of the harmonious cosmos. But here is one of the few exceptions: (The next total eclipse of the Sun, visible from London, will be in the year 2142.) I shall not see it, nor the last child born, nor even yet his son. Still it will happen. This is a calculation you can count on; not

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like the railway timetable that can be disrupted, cancelled, or run late . It does not need us, and we cannot interfere. If, by that time, there should be no one left aliv e down here to witness, even so it will take place. And knowing this we are at once diminished, ye t at the same time strangely reassured-—stirred by the synchromes h of cosmic gears, as if believing what has order must have purpose,—as if we sense d the music o f the spheres . Tony Lucas, Total Eclipse The Atomist's Reply Thou great Lucretius! Thou profound Oracle of Wit an d Sence! —Thomas Shadwell, The Virtuoso

Since none of Pythagoras's writings have survived, we only know of him at secondhand. Bu t we do have the text o f a poem about the universe, penned b y a Roman 600 year s afte r Pythagora s lived . I t wa s writte n b y a very differen t ma n fro m Pythagoras, a man for whom the mysticism of the Pythagoreans was symbolic of all the superstition that, usually in the guise of religion, was deluding man . Lucretius was an atomist and a materialist, no less awed by nature than Pythagoras but seeing it with cooler, dare one say braver, eyes. Because his poem was written i n ancien t Rome , it is not read much thes e days , but i t deserves to survive . It represents a tradition i n science that i s no less central than the Pythagorean belief in order. Lucretius is the voice of all those who are prepared to challenge authority and fac e the cosmos as it is, even if that means a cosmos without faith . Lend Me Your Ear s

The realit y of previous generation s i s problematic for many o f us, rathe r lik e th e difficulty tha t teenagers have in believing that their parents have a sex life. The average schoolboy sees the ancients a s a bunch o f remote bores, dressed in bedsheet s and talking Elizabethan English—but they ofte n spea k to us as directly as our contemporaries. Here a short, bitter poem from Italy:

Scipio's Dream

[\79__

I hate and I love, And i f you ask why, I have no answers, but I discern, Can feel, my senses rooted in eternal torture. Translator: Horace Gregory The pain transcend s th e centuries . Th e poem behind th e translation wa s writte n about 2000 years ago in Latin, by Catullus, a poet's poet, passionate, jealous, sarcastic, and hopelessly in love and hate with Clodia , the flight y wife o f the stodg y governor o f Cisalpine Gaul . Like the majorit y o f present-day poets, h e ha d difficult y making a living from poetry , and a t one stage found wor k on the staf f o f Memmius, a dry, egotistical civil servant. To Memmius was dedicate d one of the greatest texts to survive from the classical world: De return natura by Lucretius. Lucretius speaks our language. Titus Lucretius Carus was an out-and-out materialist. Fo r him, not only objects but also ideas and sense impressions wer e material, Thus I can see my dog because he sheds a n excruciatingly thin layer of atoms (not e the word) that penetrate my eyes and end up somewhere in my brain. The explanation ha s distant echoes of the corpuscular theory of light, the "atoms" of light being reflected by an object into the observer's eyes. With suitable modification it is also not a bad description o f how I smell my dog . Because man had constructed the idea of the gods, they existed somewhere—because ideas are material. However, in complete variance with contemporary dogma, Lucretius avowed that the Gods had no interest in us whatsoever. Lucretius was on e of the earlies t publicists o f the ide a o f atoms. He believed, as few di d i n hi s day , in th e experimenta l metho d o f determining facts ; h e was end lessly curious about nature and courageously antiestablishrnent. An d he knew how to write. In 60 B.C. Lucretius published hi s masterpiece, "On the Nature of Things," in the six book s o f whic h h e explaine d th e universe . H e leave s almos t nothin g un touched: how th e univers e wa s formed , how th e star s an d th e planet s move , the origins of man and speech , the nature o f politics and religion, the discover y of fire, the beginnings of music, and s o on, and s o on. He frequently goes into great detail. There are seventeen listed reasons why the soul must die when th e body dies . Almost everythin g tha t h e wrot e wa s wrong . Ther e jus t weren' t enoug h fact s available t o him. H e was a propagandist fo r atoms, but h e had absolutel y no evi dence for their nature or even their existence. Why concern ourselve s wit h a would-be scientist? Partly because we owe him a debt. He was a poet, a thinker standin g out against the irrational, but not the mysterious; against superstition, but not against awe. He is the counterpart of Pythagoras. Lucretius's writings, like those o f Catullus, are powerful and direct . They speak to the feeling, rational man, to HMS. Here is a loose modern-language version of the famous lines in which he extols his spiritual father , the Alexandrian Epicurus, who died 20 0 years before Lucretius wrote3: When human life was still oppressed , suffocated wit h the dea d weight o f Re3 Those with a morbid tur n of mind might be interested t o know that Lucretius's Elizabetha n translator, Thoma s Creech, hung himself. He was given to toying with a rope while reading Biathanatos, John Donne's sympatheti c stud y o f suicide.

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ligion, which had come down from the Heavens, terrifying and hovering over mortal men, it was then that a Greek had the courage to raise his eyes, mortal eyes, and look Religion boldly in the face. He was cowed neither by the reputations of the Gods , nor the thunderbolts o f Heaven; their threats onl y sharp ened his resolve to smash down the gates that guard the secrets of the Natural World. And his drivin g energy carried him throug h to victory. He passed beyond the fier y regions surrounding the Earth and roamed in thought through the immeasurabl e universe. And he returned i n triumph, bringing bac k the spoils o f victory, explaining wha t i s possible an d wha t i s not, what governs the potentialitie s o f matter, and wha t ar e the dee p an d inheren t limit s tha t dwell i n all things. And Religion was trampled underfoot. One man's victory put us on a level with the Gods. Lucretius made littl e impressio n on the Romans, probably because he admired Epicurus. In later centuries, Epicurus' s philosophy wa s ofte n wrongl y taken to be an enticemen t t o la dolc e vita, a hedonistic respons e t o the gods ' indifferenc e to man. The Romans saw it correctly, as a search for peace of mind by living the quiet life, devoi d o f excessive desires . Horac e called i t th e happines s o f a pig i n a sty . This philosophy , wit h which Lucretiu s sympathized , was avers e to excessive , or even moderate, wine, women, and gladiators, and didn't at all suit the Roman mentality, which wa s basically action-oriented. In contrast, Lucretius's writings revea l him as a man to whom melancholy was familiar. Like Camus, he seemed to see man standing alone, but proud, in a hostile universe. Democritus, and his conviction that there was "nothing but atoms and the void," was the other great influence in Lucretius's thought. Reading Lucretius, one senses that h e would have made a name as a physicist ha d h e been born a few centurie s later. He was an observer , and h e had th e curiosity , intuition, an d skepticis m o f a good scientist. Lucretius wa s effectivel y forgotte n fo r 150 0 years , until th e sam e spiri t wit h which he swept aside obscurity and superstition, mysticism and rites, tore through Renaissance Europe. Lucretius was on e o f the source s o f the atheis m that, no t al ways overtly , underlay th e thinkin g o f many o f the ne w me n wh o overthre w th e moldy dogma of the Middle Ages. He spoke to a generation only too willing to discard th e inheritanc e o f Aristotle, Christianized b y Albertus Magnu s and Thoma s Aquinas, and fossilized in a way that Aristotle himself, the probing, questioning inventor of logic, would probably have hated. Lucretius was widely read in the Enlightenment. The philosophes sympathize d immediately wit h hi s rejectio n of mysticism an d hi s vigorou s attack o n religion . They sa w in him a n ech o of their ow n Newtonian belief that observation an d reason would provid e an understanding o f the workings of the universe . Exactly 1600 years afte r Lucretiu s published th e never-finishe d De rerum natura, Giambattista della Porta founded the firs t recorded scientific society, in Naples in 1560. And in 1960 , men sen t up the firs t weather satellite and Lt. Don Walsh together with Jacques Piccard descended 35,80 0 feet into the Pacific near Guam. If we have journeyed outward t o the planet s an d downwar d t o the floo r o f the ocean, if we think th e wa y we do , a way s o different fro m tha t o f pre-Renaissance man, i t i s partl y becaus e o f me n lik e th e pre-Renaissanc e poe t Titu s Lucretiu s Carus.

¥ Cracks in Newton's Pedestal

A nineteenth-century scientist would find this part deeply subversive. For two centuries, Newton's mechanical univers e dominated the way that both scientists and laymen thought about the workings of nature. Newtonian-Galilean mechanics hinted strongl y at a deterministic framework fo r the cosmos, a conclusion that had dee p psychological, moral, and religious implications. But the seeds of scientific heresy were germinating in the quiet fields. The nature of light and o f heat— problems that occupied Newton, Hooke, Huygens, and their contemporaries—were to eventually split asunder the analogy between the universe and a well-oiled clock. It is a mistake to think that the downfal l of the Newtonian universe started in the twentieth century , with the development of relativity and the quantum theory. The rot started long ago, and in fact there is almost nothing in this destructive part that falls outside the realm of classical physics. Newton would not be amazed if he read this part, but he might be very perturbed by some of its conclusions. H e would find a fundamental la w of nature that should follow fro m his laws but doesn't, and he would find that in practice there are many situations where his laws should give an answer but are completely impotent.

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15 Making Waves

My mothe r taugh t m e t o enjo y ligh t waves , my fathe r t o enjo y soun d waves . My mother wa s th e eldes t o f four sister s bor n a t the tur n o f the centur y in Gomel , in what is now called Byelarus. Her earliest memory was of being hidden under art inverted tin bath in the house of an old colonel, during an attack by cossacks engaged in their national sport of slaughtering Jews. Years later, in London, I found ou t that when my father went to work in the East End, and I had gone to school, my mother would ofte n tak e th e Undergroun d t o centra l Londo n an d wande r aroun d th e pricey, fancy art galleries. Once, as a university student, I cut through Dover Street, near Piccadilly , an d unexpectedl y caugh t sigh t o f her throug h th e windo w o f a dealer. She looked small, shy , and shabby amongst the real and would-be connoisseurs. Sh e could never affor d originals , but sh e brought home catalogues and purchased postcards in the big public galleries like the Tate. She had almost no forma l education, bu t he r taste s wer e extraordinaril y sophisticated : Kandinsky , Klee , Miro, Chagall, Marino Marini. And she loved Vermeer and Turner. Color fascinate d me as a child. My father , o n th e othe r hand , ha d ver y conventiona l visua l tastes . H e loved music, whereas m y mother was tone-deaf. He felt uneasy with Chagall's blue cows floating above the roof s o f Vitebsk. I remember as a boy arguing with him whe n h e told me that colors vanished i n the dark and would no t exist at all if there were no animals t o see them. H e quoted Bacon: "All color s will agree in the dark. " He listened to Bach in the dark , and I discovered th e Chaconri e in D Minor. My mother picked up reddish golden autumn leaves and put them by his bedside. Light and sound , color and music , Chagall and Monteverdi , were onc e all considered t o be manifestations of waves. That sound is a wave phenomenon i s indisputable, but ligh t i s a far more complex creature, as it showed a t the beginnin g of the twentieth centur y when it came out of the closet and revealed a particulate nature. Newton had always suspected that light was corpuscular; Huygens said it was a wave phenomenon. Neithe r offere d convincin g experimental evidenc e fo r their guesses, althoug h experiment s i n th e nineteent h centur y strongl y supported th e wavelike nature o f light. However, as a result of certain observations in the twentieth century , Einstein wen t agains t conventio n (a s usual) and opte d fo r particles. The position at the moment is that it is very convenient for purposes of calculation to regard light as wavelike in some cases, but the particle-picture seems to be closer to realit y an d ca n als o accoun t fo r phenomena tha t ar e inexplicabl e i n term s of waves. The reasons for all this will become apparent later. In this chapter we will speak the language of waves.

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The Messenger of the Gods Luz vertical, luz tu alta luz tu luz oro ; luz vibrante, luztu. Yyo la negra, ciega, sorda, muda sombra horizontal. —Juan Ramon Jimenez, "Luz Tu"1

There ar e fe w word s mor e evocativ e tha n light. Th e wor d itsel f ha s becom e a metaphor fo r happines s an d understanding . I n Franci s Bacon' s Afe w Atlantis (1627), the remot e island kingdo m of Bensalem engaged in externa l trad e in onl y one commodity: light. The export-import agencies dealt in the light of understanding—the "knowledge of causes and the secret motion of things."2 Light is a basic component in the functioning of this planet. The light of the Su n maintains lif e on Earth. The mental world of most of us is based heavily on the content o f light signals, and ligh t acts as a time cu e (zeitgeber ) for the biological clock in mammals. Man manipulated light long before the nature of light or vision was understood . The ar t o f constructing optica l instrument s wa s highl y develope d b y th e seven teenth century. As for vision, it was believed for centuries that light issued from th e eye of the observer, a Pythagorean idea that was taken up by Plato. Newton was deeply interested in the nature of light and particularly in color. He made notes on nearly forty recipes for mixing paints, mainly reds. His best-known experiment was the splittin g of a ray of sunlight b y allowing it to fall o n a prism. "Light," he wrote, "consists of Rays differently refrangible," meaning that they were bent by different angle s when they passed through his prism. 3 To this statement we can trace the beginning of the modern technique o f spectroscopy, th e analysi s of light signals into their components—and by "light" I mean any kind of radiation. It is to this ability to separate the different frequencies in electromagnetic radiation that we owe much o f modern physics and chemistry. It is this that allows us to detect the chemical elements in the stars, to analyze complex mixtures o f materials, to measure the vibrations and rotations of molecules, to probe the electronic cloud of atoms and molecules and to detect tumors by magnetic resonance. Light, in fact an y electromagnetic radiation, has many wavelike characteristics; sound is a wave phenomenon. All waves have certain common properties, and it is to these that we now turn. 1

Vertical light / you, light / tall light / golden light / vibrating light / you light. / And I, the black, the blind the deaf, the dumb horizontal shadow. (Translation: Eleanor Turnbull) 2 It was Bacon's fictional Salomon's House on Bensalem, the original model for the modern research establishment, that was almost certainly in the minds of the founders o f the Royal Society. 3 When Goethe read of Newton's experiment, he interpreted it as showing that light was in fac t homogeneous and it was only the interaction of light with matter that produced colors—they were not there to start with. This was a perfectly acceptable interpretation, but it runs into difficulties wit h Newton's demonstration that a second prism, placed in the path of the light emerging from the first, can recombine the colored rays to give white light.

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5

Waves: Periodicity

The beatin g o f our hearts , the circlin g o f the Sun , the danc e o f the seasons , menstruation, metronomes, the tides, marching feet, Gen e Krupa, and Ravel's Bolero— all thes e ar e reminder s o f natural o r man-mad e temporal periodicity . Wallpaper patterns, tiled roofs, Greek decorative patterns, Arabic tiles at the Alhambra or Isfahan, th e scale s o f a fish, th e arrangemen t of atoms i n crystals , are al l example s of spatial periodicity . Ou r through-space interactio n wit h th e univers e i s primarily mediated b y periodi c movement—soun d wave s an d ligh t waves . Bot h soun d waves and light waves are scientific constructions. If our sense organs could directly detec t light and soun d a s waves, it would no t have taken ma n s o long to show their wavelike nature. If we defin e a wave as a moving periodicity (Figur e 15.la), then ther e are three simple characteristics tha t are possessed by all waves: the velocity, the wavelength (or it s frequency) , an d th e amplitude. Tw o of these propertie s ca n b e see n ver y clearly for ripples spreading across a pond. If we fix our eyes on one crest, we ca n define th e velocity of the wave as the velocity of the crest . The wavelength is simply the distance between two neighboring crests. A quantity that is directly related to the wavelengt h i s the numbe r o f waves that pas s a given point i n on e second. The number o f ripples that pass a reed in a pond i n one second is the frequenc y of the wave. For waves traveling at the same speed, the frequency increases as the distance between crests , the wavelength , decreases. If one cres t passe s by ever y second, we say that the wave has a frequency o f 1 hertz, written 1 Hz, which some people would write as 1 cycle/second. The frequency , v , wavelength, X, and velocity , v, of a wave are related by: v = vX. Velocity = frequency x wavelength, which is the sam e as saying that the spee d of a train i s equal to the numbe r o f carriages which pass yo u in on e second, times th e length between th e fron t end s o f two adjacen t carriages (or any two similar point s on adjacent carriages). In a vacuum all electromagnetic waves (visible light, UV, X-rays, etc. ) travel a t the "spee d o f light," c, which i s about 30 0 million meter s pe r second, or about 186,00 0 miles per second. To and Fro versus Up and Down Put a cork in a pond, on a windless day, and then throw a stone into the pond an d watch th e cor k as the waves pass it. The cork moves up an d down . All the movement is perpendicular to the direction in which the waves appear to move. For this reason, waves in water are termed transverse waves (Figure 15.Ib). If you rhythmically wave one end of a rope while someone holds th e othe r end, you are creating transverse waves. In this case it is very clear that the rope is neither moving toward nor away from you . Its only movement is perpendicular t o the motion of the wave, as you can check by tying a red ribbon o n the rope. In transverse waves in matter, the movemen t o f the wav e in a given direction is no t a movement o f matter but a

Figure IS.la. A simple wave. This could be a rope or a line drawn on the surface of the sea.

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Figure IS.lb. A transverse wave. The ribbon oscillates vertically. A cork far out t o se a behaves similarly provide d the waves are gentle.

movement o f form; th e movemen t o f matter i s onl y transvers e t o tha t direction . Watch a "Mexica n wave " i n a footbal l stadium . Ligh t waves ar e als o transvers e waves, but they are harder to visualize than waves in a rope or in a pond. In contrast, sound waves in air are longitudinal. I f you could observe the air molecules i n th e pat h o f a soun d wave , you woul d fin d tha t the y oscillat e bac k an d forth, but this time in the direction that the sound moves (Figure 15.Ic). Nevertheless, on the average they stay where they are because, although longitudinal waves carry molecules in the air forward, they carry them back again. You can see what a longitudinal wave looks like by holding one end of a "Slinky" (thos e tightly coiled metal springs sold in toy shops) and lettin g the sprin g hang dow n vertically. Now move your hand up and down, and you will see vertical longitudinal waves. Obviously, since the spring remains in your hand, there is no net movement o f metal in the direction o f the wave. Simple waves do not permanently displace matter. Velocity A baritone and a soprano produce notes with differen t frequencies . Can we choos e the velocity of a wave in a given medium, a s we can choose the frequency? Not really. The velocity is overwhelmingly determined for us by the medium, although it is mildly sensitive to changes in conditions. The speed of sound waves in dry air at 20°C is abou t 112 5 fee t pe r second . Changing the ai r pressur e ha s n o significan t effect o n this value . Temperatur e has a small effect . A t 0° C the spee d i s 108 6 fee t per second and a t 100°C it is 1266 feet per second, whether you are singing bass or soprano. The speed of sound depend s o n the medium through which the waves are traveling. The "stiffer " th e medium , th e faste r th e wave . The speed i n water i s abou t

Figure IS.lc. Th e wave travels along the axi s of the Slinky. At any given point above the ground, the closeness of the coils varies periodically.

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1500 feet per second; in iron it is about 5160 feet per second. Similarly, the speed of sound throug h th e groun d i s muc h faste r tha n i t i s i n air . That' s wh y th e Lon e Ranger's faithful Tont o put hi s ea r to the ground to get early warning of the galloping hooves of the bad guy's horses. The velocity of electromagnetic waves in vacuum has been measured for wavelengths ranging from abou t 6 meters t o less than 10 0 million milliont h o f a meter (10"14m), an d foun d to be effectivel y th e same , as Maxwell predicted. Thi s inde pendence of velocity on wavelength is not true for light traveling through matter. The velocit y o f electromagneti c wave s i n a give n materia l mediu m i s slowe r than i n vacuum and depend s slightl y o n the frequenc y o f the wave , which i s the cause of the splittin g o f "white" ligh t into differen t color s (frequencies) b y prisms, lenses, and raindrops. The velocity of a wave is not dependent o n the velocity of its source. For example, if I wave my hand in water , I create waves that mov e forward a t a velocity of about 150 0 fee t pe r second . If, while movin g my hand bac k and fort h I also walk forward, th e wav e fron t wil l stil l trave l at the sam e speed. The disturbanc e tha t I create, once it has established itsel f in the water, is no longer affected b y my hand. However, although there is no affec t o n the velocit y of the waves , my walking forward means that I will partially catch up with the first wave by the time that I make the second one. I am compressing the waves, so that their peaks are closer together. I have shortene d the wavelengt h o f the wave . If I continually walk forward at the same speed as the waves, then I will be movin g forwar d o n the cres t o f the firs t wave, an d ever y new wav e will b e produce d a t th e wav e front , whic h neve r es capes fro m me . Thi s extrem e bunching , whe n i t occur s in air , i s terme d a sonic boom, which i s heard when a plane travels at the speed of sound. Frequency

Light waves an d radi o waves exhibi t a range of frequencies; otherwise we woul d see only one color and hea r onl y one radio station . Th e light that come s fro m th e stars, the Moon , and the Su n is a mixture of different frequencies . I t is rare that we see light o r hear soun d that is of one frequency. Tr y joyously singing two differen t notes. If you sin g middle C you are producing waves having a frequency o f 256 Hz. Now listen t o this note when i t is made by a tuning fork . I t sounds different . Th e note tha t yo u ar e singin g i s no t pure . Al l musica l instruments , includin g th e human voice , emit note s contaminated by other frequencies . I t is this contamination that allows our ears to differentiate betwee n instruments an d gives them thei r character. Light from almos t any natural source is a mixture of very many frequencies. Th e invention of the laser allows us to produce light that is almost pure (monochromatic) in that i t contains effectivel y onl y one frequency, whic h als o means on e wavelength. Ye t even a laser doesn' t produc e absolutel y monochromati c light. Thu s a krypton laser produces light with an average wavelength o f 605.78021 nanometers and a sprea d o f abou t plu s o r minu s 2 nanometers . B y ingeniou s instrumenta l tricks, thi s 4-nanomete r spread i n wavelengt h ca n b e reduce d by a facto r o f 100 million to give almost pure light.

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The Electromagnetic Palette

Until th e nineteent h century , what wa s calle d "light " wa s radiatio n wit h a very limited range of frequencies, th e range detectable by the human eye . Maxwell predicted that ther e was radiation that the human ey e failed to see. His equations predict that i t is possible to generate electromagnetic waves o f almost an y frequenc y that, when i n a vacuum, all travel at the spee d of light. As it should do , theory resulted i n previously disconnecte d an d puzzlin g phenomen a droppin g int o place . Thus Maxwell' s theory made sens e of some observations mad e by the astronome r William Herschel in 1800. He attempted to measure the heating effect i n the differ ent color s o f th e visibl e spectru m b y placin g th e bul b o f a thermomete r i n th e patches o f different colo r obtained when sunlight passe d through a prism. He noticed that when he placed the bulb of the thermometer in the dark area just outside the re d en d o f the spectrum , th e mercur y als o rose. He concluded tha t th e caus e was invisible radiation. Since the frequency o f this radiation was apparently lower than tha t of red light , he called i t infrared (IR) . In 1801, Johan n Ritter had als o detected "something " jus t outsid e th e other , violet, end o f the visibl e spectrum . H e found tha t photographi c salt s wer e blackene d b y thes e invisibl e ultraviolet (UV) rays. Maxwell' s theor y shepherde d I R and U V into th e electromagneti c fold . I n 1886, Hert z created radio waves. Marconi was waiting in the wings. 4 The yea r afte r Hert z died , Roentge n discovere d electromagneti c radiatio n a t much highe r frequencie s tha n eithe r radi o o r light waves . Thi s radiatio n i s stil l called after hi m in some countries but is more commonly known by the name that he gav e it: X-rays. The English satirical weekly Punch wa s highly amuse d b y the penetrative propertie s o f X-rays. The followin g uninspire d verse s wer e par t o f a poem it published o n 25 January 1896: O, Rontgen, then the news is true, And not a trick of idle rumour, That bids us each beware of you, And o f your grim and graveyar d humour. We do not want like Dr. Swift, To take our flesh off and t o pose in Our bones, or show each little rift , And join t for you to poke your * * * * i n . . .. (Nose i s a four lette r word.) In 190 1 Roentge n was th e recipien t o f the firs t Nobel Prize awarded in physics . In 1900 the French scientis t Paul Villard detected y-rays from radioactive material. They were shown to be electromagnetic radiation, with frequencies even higher than those of X-rays. A whole universe of waves was opening up. The propertie s o f natural an d man-mad e electromagneti c wave s hav e revolu 4

Even long after "th e radio" became a standard household item , it aroused amazed hosannas, being described b y one author, in 1938, as, "the miracle of the ages. . . . Every vision that mankind has ever entertained, since the world began, of laying hold upon th e attributes o f the Almighty, pale into insignificance besides the accomplished fac t of radio."

Making Waves

Figure 15.2. The known range of electromagneti c waves .

tionized scienc e an d technology . Th e know n sprea d o f frequencie s i s show n i n Figure 15.2. Walk out on a dark night, far from the city lights. Darkness is the name we give to the inabilit y o f our eye s to detec t any other tha n visibl e light . Bu t the whol e uni verse is teeming with electromagnetic radiation. We see only wavelengths between about on e si x millionth s o f a centimete r an d on e 1 2 miilioriths o f a centimeter, which, as you ca n see from Figur e 15.2 is but a tiny fraction of the known range of radiation. Radiatio n over the complet e range o f frequencie s show n occur s in na ture; ye s X-rays , microwaves , an d radi o wave s ar e detecte d comin g fro m space . They are in no way evidence of intelligent life. Nature has her ways, and in fact our Sun sends out IR, visible, UV, X-rays, and y-rays, although the last two fail to penetrate the atmosphere. Man creates a wide variety of radiation.5 Some of it is involuntary, as in the case of the IR radiation arising from the jiggling of the molecules in our body, and whic h can be detecte d an d photographe d wit h suitabl e equipment . Deliberatel y created radiation such as that from lightbulbs, neon lighting, and lasers all result in the end from electrons moving, either between o r within atoms, and thereby creating electromagnetic waves. Cat Whistles? As for sound, human ear s can respond t o frequencie s i n th e rang e of 16 to 20,00 0 Hz. Dogs hear u p t o about 50,00 0 Hz, cats to 65,000 Hz, and moth s have a hearing range from 3000 to 150,000 Hz. By way o f comparison, the range of the pian o is 30 to 4100 Hz. The human ea r is remarkably sensitive . No t only ca n it distinguis h somethin g like 400,00 0 differen t sounds , but i t can detec t sound s s o quiet tha t th e vibratory movement induced i n the eardru m is not much mor e than th e width of a calcium atom. Intensity Velocity and frequency (o r wavelength) are not enough to completely characterize a wave; we also need t o specif y it s intensity. When waves rock a boat, we fee l intu itively tha t the forc e the y exert i s related to their height , the distanc e between th e 5 He is not unique in this respect. There are several organisms that produce light, such as the glowworm, biolumiiiescent bacteria, and certain deep-sea creatures.

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peaks and valley s o f the wave , as measured perpendicular to the wave. We could measure this distance, th e amplitude, b y watching a cork bobbing up and down in the water and noting its maximum and minimum height . If I walk in the su n and fee l its heat on my shoulders, I know that the heat originated 9 3 million mile s awa y an d reache d m e acros s a n effectiv e vacuum . Wave s undoubtedly transfe r somethin g fro m plac e t o place : waves transfer energy, a s Joshua demonstrated at Jericho. We live in a huge energy bath. In th e cas e o f water waves , th e energ y transferre d t o a floatin g cor k fro m th e point a t which a stone strikes the water is connected to the amplitude o f the vertical motion of the cor k (Figur e 15.1b) . It can be shown that the amoun t o f energy transferred by a water wave, or any wave, is proportional to the square of its amplitude. I f the amplitud e i s increased, say , threefold, the n th e energ y transferred increases by a factor o f nine. Waves have curious characteristics tha t arise from thei r periodic nature. Tw o of these hav e playe d a n outstandin g par t i n th e genera l histor y o f science: interference and the Doppler effect . Interference The great Dutch scientist Christiaan Huygens (1629-1695) realize d that two waves can mutually interfer e in suc h a way as to annihilate eac h other . Suppos e you simultaneously, and with th e sam e force, thro w two identical stone s into a pond, at separate, closel y space d point s (Figur e 15.3) . Wave s sprea d ou t fro m th e tw o points. Both waves will have identical speeds, frequencies, and amplitudes. Tak e a point P , equidistant fro m thos e a t whic h th e stone s entere d th e water . Th e tw o waves pas s throug h P like a pair o f synchronized swimmers . What on e does , th e other does . If a crest of one wav e passes throug h P , then a crest o f the othe r wav e will pass through at exactly the same time. If a valley of one wave passes through, a valley o f the othe r wav e accompanie s it . I n short , th e tw o wave s reinforce eac h other; they exhibit what the aficionados call constructive interference. To rub in the superiority of the exper t to the layman , they will also tell you that the two waves are in phase. Now consider the point Q . We choose it so that exactly as the cres t of one wave passes, the valley of the other arrives. Put a cork at that point. It goes neither up no r

Figure 15.3. Tw o identica l stones land in the wate r simultaneously at points A and B, which are equidistant from point P. At P the wave s arrive in phase: when one wav e is at it s peak (or trough) so is the other. This is known as constructive interference. A t point Q, the distance s from A and B are such that when the peak of one wave passes through it coincides with the trough of the other. The waves cancel each other out. This is destructive interference. W e can find a whole range of points similar to P or t o Q. This is the basi s of the nex t figure.

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down as the waves pass it, because there are no waves at this point. They have canceled each other out—they are exactly out of phase. The name of this phenomeno n is destructive interference. Interference ca n be demonstrated easily for water waves because they are obviotis t o the eye . But what abou t electromagneti c radiation? Maxwel l had claime d that light consists o f waves. If light coul d b e show n to exhibi t interference , tha t would be convincing evidence that Maxwell was right. Which brings us to Thomas Young, who preceded Maxwell. A Famous English Experiment I learned history when the map of the world was heavily splashed with red—representing the British Empire. History, as taught at my first school, was a succession of dates on which "great events" occurred: 55 B.C., Caesar lands; 1066, William of Normandy lands ; 1215 , Magna Carta; followed b y a string o f dates o n which Englis h armies won battles abroad . Scienc e was taught on the sam e principle: larg e numbers of clever Englishmen and importan t (mainl y English) experiments. The great event method is a terrible wa y of learning history but a fairly good way of learning science. On e o f the grea t events i n scienc e wa s undoubtedl y an experimen t performed by Thomas Young. Young (1773-1829) was a man of diverse talents who read at two years old. His hobby wa s Egyptology , and h e wa s on e o f the tea m tha t deciphere d th e Rosetta stone. He was trained as a physician, and his medical interest in the senses resulted in his discovery of the cause of astigmatism in 1801, an d the correct suggestion that we have three types o f color detector s in ou r eyes . His particular interes t i n light led him to perform one of the more famous experiments in scientific history. 6 Young guessed that light was wavelike and that the waves were not longitudinal but transverse; the vibrations, whatever they were, were perpendicular to the direction o f the light ray (Figure 15.1b). You can replicate his experimen t by shining a strong, reasonably monochromatic light at a screen pierced by two slits, each not. much more than about a thousandth o f an inch across, and spaced about one-hundredth o f an inch from eac h other (Figure 15.4a). Observe the image produced on a second screen, placed about 1 yard behind the first. You should see not two lines of light but a roughly elliptical patch crossed by parallel dark lines. This is what Young saw, and he realized that he had demonstrate d the wavelike behavior of light.

Figure 15.4a. Young' s experiment. The light waves from the two slit s give alternate bands of dark and light on the screen. 6

If there are any engineers reading this and you have ever used Young's modulus in the study of the elasticity of a material—it's the same man.

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The explanatio n o f the dar k line s exactl y parallel s tha t fo r the interferenc e of water wave s (Figur e 15.3). A t point s lik e P o n th e secon d screen , th e tw o ligh t waves coming from th e slits will be in phase. The waves reinforce eac h other an d give a bright area; this is constructive interference. If we now move to a point lik e Q, we see that the two waves travel different distances , and we can account fo r the dark line by supposing that the point Q is so situated that the two waves are exactly out of phase at that point, annihilating each other; this is a case of destructive interference. If we move to other bright areas, we can explain their brightness by supposing that, although the two waves travel different distances , they arrive in phase again. If you reduce yourself to sub-Lilliputian dimensions an d go for a walk along the second screen—fro m poin t 1 to point 2 in Figure 15.4b—you will find tha t the light intensity o n your path falls and rises periodically. O n the basis of Young's experiment, it is difficult t o quarrel with his conclusion tha t light is wavelike. Newton believed that light consisted of corpuscles, from which he deduced tha t light could be attracted by gravity: "Do not bodies act upon ligh t at a distance, an d by their actio n bend it s Rays, and i s not this actio n (caeteris paribus) stronges t at the leas t distance? " Bu t no on e ha d see n ligh t ben d i n respons e t o gravitationa l pull. And now Young's classic experimen t appeare d to utterly destro y the corpuscular theory of light. How could one possibly look at the striped pattern o n the second scree n an d explai n tw o corpuscle s o f light producin g darkness ? Tw o waves might be able to annihilate eac h other, but how can two bullets? (The final hope of the revolutionary physics student facing the firing squad?) A dramatic example of constructive interference is the laser. Traditionally, light is produced by heating or burning something, say , a lamp filament o r oil. The light originates i n th e movement s o f the electron s in th e atom s o f the ho t body , an d a simple pictur e sees the electrons oscillatin g and thereby producing electromagnetic waves. No w it is highly improbable tha t al l the electron s responsible fo r radiation will be oscillatin g i n phase . I n general eac h electro n wil l be "doin g it s own thing" quite independentl y o f the others. Thus the waves emitted b y the body are not i n phase; they are a disorganized jumble of waves. Furthermore, the ligh t i s a mixture o f frequencies, s o that th e wave s don' t "fi t together." If you stoo d i n th e path of such ligh t an d could se e the individual waves , their peak s would no t pass you together. If, however, they all did, if all the waves had th e same frequency and were in phase , you would expec t to feel a very strong effect. I t is as though man y people were simultaneously shakin g you such tha t the y al l pushed an d pulle d i n the same direction together. That's how laser light acts; all the waves in the light are effectively o f the sam e frequency , an d the y al l trave l i n phase . Th e effec t o f thi s army of simultaneous shakers can be dramatic. Lasers can burn through steel . As obvious as the implication s o f Young's experiments appear , his conclusion s

Figure 15.4b. Th e variation of ligh t intensity i n walking along the line from point 1 to poin t 2.

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about the wave nature of light were greeted with ridicule by his compatriots. Who was an upstart physician t o argue with Newton? The strength of the paradigm prevailed. In France, primarily because o f the confirmator y experimental work of Dominique Arag o and Augusti n Fresnel , Young' s ideas wer e quickl y accepted, and the doubtin g English scientific establishment eventually ha d n o choice but t o follow suit. Notice that i n the explanatio n o f Young's experiment i t was assumed that ligh t emerging from a narrow slit spreads out slightly. If this were not so, then the image of th e tw o slit s woul d simpl y be tw o narro w line s o f light. Thi s spreadin g out of light when i t passes through a narrow orifice i s termed diffraction. I n fact it occurs for orifice s o f any siz e but i s not usuall y noticeable , being manifested by a slight fuzziness at the edge of shadows. Diffraction i s a property of all waves, and you ca n observe it for water waves. In Young' s experimen t th e spacin g o f the patter n o f lines tha t h e sa w o n th e screen depended on the wavelength of the light and also on the spacing of the slits . In fact th e best, most readily detecte d diffractio n pattern s ar e produced when th e spacing between th e slit s is roughly the sam e as the wavelengt h of the light . This fact i s th e basi s o f one o f the mos t powerfu l method s w e hav e t o determin e th e shapes o f molecules and th e interna l arrangement s of atoms in crystals . We jump forward a century. The Microscopic Young Experiment Without X-ray crystallography and related diffractio n techniques , we would never have know n th e structur e o f the DN A molecule, an d moder n molecula r biolog y would have been a stunted flower . We owe the idea to Max von Laue (1879-1960). Aware of Young's experiment, von Laue realized that the wavelength of X-rays was of the sam e order of magnitude as the spacin g between the nuclei of atoms in crystals or molecules. Since the atoms in all crystals are arranged in very regular arrays, von Laue guessed that they might diffract X-ray s to give simple patterns that would depend o n th e spacin g o f th e atoms . H e an d hi s collaborator s passe d X-ray s through a crystal of copper sulfate an d obtaine d complex diffraction patterns . Th e "slits" in crystals are usually complicated , and so is the connection between the m arid th e for m o f the patterns . Onl y i n th e cas e o f certain simpl e type s o f crystal, such a s sodiu m chloride , wher e atom s ar e arrange d i n ver y simpl e ways , i s th e analysis of the pattern s i n terms of the structur e o f the crysta l relatively easy. The early analysis of the patterns given by many crystals was usually long and tedious, but toda y they ca n b e analyze d rapidl y by compute r technique s s o that eve n for crystals o f large complex molecules suc h a s proteins, we ca n work back fro m th e diffracted patter n to find the arrangement of atoms in the crystal. The method should no t be confused wit h the medical use of X-rays to examine the interior o f the body. This use is based on the fac t tha t X-ray s usually penetrate noncrystalline matter in straight lines just as light penetrate glass, so that we are essentially lookin g at X-ray shadows. Diffractio n woul d b e a nuisance fo r this pur pose, since we rely on the X-rays traveling in straight lines to give sharp shadows . If, a s Young seemed to have proved, light was indeed wavelike, then certai n interesting phenomena coul d be explained o r predicted. One of these was to be th e tool by which , i n th e twentiet h century , i t became clea r tha t th e univers e i s expanding at a frightening rate .

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The Redshift

When, in 1924 , it was proposed that our universe is expanding, the conclusion relied o n wor k publishe d i n 184 2 b y th e Austria n physicis t Christia n Dopple r (1803-1853), Th e well-known Doppler effect come s into play whenever a source of waves and an observer are moving relative to each other. Let's throw another stone into the pond. On the surface of the pond there is a stationary pond skater. As the wave passes, he takes out his stopwatch and counts the number o f times pe r secon d that a crest pushes hi m upward. He is measuring th e frequency o f the wave , as he sees it. Now suppose that w e repeat the experimen t but that thi s time we are dealing with a cowardly pond skate r who, o n seeing th e stone strike the water, skates rapidly away from the stone. Cowardly, but still cooperative enough to take out his stopwatch and measure the number o f crests that lif t him upwar d eac h second. Sinc e he i s running awa y from th e sourc e of the wave, fewer waves will pass him i n a second than will pass his stati c friend. Yo u can see this very easily if you think o f a special case: a surfer riding on a wave. He is traveling at exactly the spee d of the wave, and therefore no waves will pass him; and for him, accordin g to the definitio n of frequency, th e frequency of the wave is zero. In general, if you mov e away fro m a static source of waves, you observ e a lower frequency than i f both you an d th e sourc e are static. I f you thin k for a moment, yo u will see that if you are static and the source is moving away from you, you will also observe a lowered frequency. All these closel y related effect s ar e included unde r the headin g of the Doppler effect. Th e exampl e of the Dopple r effect usuall y given to undergraduates is that of an ambulance or anything with a horn or siren on it. As such a vehicle passes you, the pitch of the note that is heard suddenly drops as the source of the sound moves away from the listener. If a source of light of known frequency i s moving away from you, the frequency , as you observe it, will be lower than when th e source is static. Since red light is at the low-frequency end of the spectrum of visible light, we can say that the light we are observing displays a redshift. Suc h shift s hav e been observe d in the ligh t emanating fro m certai n heavenl y bodies . A s earl y a s 1814 , Fraunhofe r observe d th e light of the Su n and detecte d a large number o f different frequencies . Whe n he di d the same thing with light fro m the stars, he found very many frequencies that were almost identica l t o those from the Sun , but slightly red-shifted. He did not realize the huge significance of this discrepancy, which i n the twentieth century was a key factor in the development of our theories about the birth o f the universe. Polarization

More "proof " that ligh t i s wavelik e and , mor e specifically , that i t i s a transverse wave, comes from experiment s which showe d tha t ligh t exhibite d a property that was onl y known t o be associated with transvers e waves: the propert y of polarization. Take hold o f one en d o f a rope an d as k a patient frien d t o tak e the othe r end . Move your arm up an d down . Yo u will produce a transverse vertical wave along the rope . Now chang e t o a side-to-side motion o f your hand. Yo u will produc e a transverse horizontal wave . In fact , yo u ca n produce a wave in an y direction tha t you like, which i s what we mean when we say that transverse waves can be polar-

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ized. This is something you can't do with a longitudinal wave, where the motion is always along one line, the direction of the wave. Recall the Slinky . Normally the light we experience, from eithe r natural or artificial sources, is unpolarized. Perhaps a better word would be multipalarized, sinc e such light consists of a mixture of light in very many planes. Each radiating atom gives radiation in an arbitrarily oriente d plane. However, there are natural an d artificial substances that can polarize suc h light. What they do is to cut out all wave motion that is not in a certain plane. Som e crystals have this property. They have a plane, which w e will refer to as the polarization plane, such that unpolarized light shone onto the crystal emerges polarized in that plane. You can do much the same by waggling your rope through a slot (Figure 15.5). Only a waggle in the plane of the slot will pass through.7 If you vertically waggle a rope through a vertical slit, the wave will pass through, but i f you now pu t a second slit , oriented horizontally , after th e firs t slit , you will kill the wave . Similarly, you ca n extinguish a beam of light by passing it through two polarizin g crystals , wit h thei r polarizatio n axe s arrange d perpendicularly . Later o n thes e simpl e conclusion s wil l lea d u s t o doub t whethe r w e understan d reality. Movers and Shakers

Electromagnetic waves interac t wit h matter, which accounts fo r photography, the mechanisms of sight, Sun-induced ski n cancer, bleaching by the Sun, the mutation of genes, the greenhous e effect , th e destructio n o f the ozon e layer, and photosynthesis. All these phenomena hav e something in common. Water wave s mov e thing s lik e ship s an d pon d skaters . Soun d wave s mov e eardrums and shatter crystal decanters. What do electromagnetic waves move? The answer follow s directly from their nature: the varying electric field acts on electric charges; the varying magnetic field act s on magnets. Th e electric interactio n i s far stronger and is the only one that we will consider, although magnetic interaction s cannot be ignored in certain important areas of medical instrumentation an d scientific research . Since all atoms contain charge d particles, the doo r is open for electromagnetic waves to act on matter. The net result of absorbing light is always seen in a rearrangement , however small , o f the molecule' s electro n cloud . I f this re arrangement is sufficiently drastic , the molecule may change shap e o r even fall to pieces. LT V light can d o this to a large number o f molecules, which brings us to the ozone layer. Much attention has been given recently to the depletio n o f the ozon e layer arid the consequen t increas e i n th e quantit y o f UV light reachin g th e Earth' s surface . The frequenc y o f UV light i s higher tha n tha t of visible light . Very crudely put, it

Figure 15.5. Th e polarized light passes through the first slit but i s "killed" by the second.

'Strictly speaking, if the waggle is at any angle to the slot except perpendicular to it, part of your waggle will pass through, but the rope on the far side of the slot will only waggle in the plane of the slot.

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can shake the electrons even more violently than visible light, so violently, in fact , that the electronic "glue" holding the molecule together can be disrupted an d the molecule falls apart . The resulting fragments ar e usually very chemically reactive. In the living cells of humans, the best scenario that can be hoped for, following this molecular disruption, i s that the two fragments shoul d joi n together to reform th e shattered molecule. The worst scenario is that the active fragments attack other cell components. This can happen when sunlight falls o n the skin and ca n be the firs t stage in the development of malignant melanoma. The molecules use d in pressurized spra y cans include a group called CFC s for short. CFC s contain chlorin e atom s bonded t o carbo n atoms, and th e U V light i n the Sun can break this bond and liberate free chlorin e atoms. These attack and disrupt the ozon e molecule. Now atmospheric ozone absorbs much o f the UV light of the Sun , and the depletio n of the ozone layer in the Southern Hemisphere, caused by CFCs and othe r gases, has given rise to what ha s become known as the "ozon e hole" throug h which UV light streams almost freely . Th e numbe r o f cases of skin cancer has risen significantly in Australia. It should be pointed ou t that nature itself is not alway s on our side in regard to the atmosphere. Volcanic eruptions ca n result in the emission of harmful chemicals that circle in the stratosphere for three years or more. From what was said earlier about laser light, it is understandable tha t when laser light falls o n matter it zonks the electrons around so violently that there is a strong rise in temperature, which explains why lasers can burn their way through metals. For well ove r a century , the ligh t generate d by heatin g differen t material s ha s been used as a means o f identifying them. In 1860 a German chemist noticed tha t when he placed a small quantity of common sal t on a platinum wir e and put th e wire int o th e flam e o f a Bunsen burner, the flam e burne d yellow . Why a Bunsen burner? Becaus e he wa s th e ma n wh o invente d it : Rober t Bunsen (1811-1899) . Piped gas, generated from coal , had becom e newl y available as a consequence of the developmen t o f the Germa n chemical industry . Bunse n put othe r salt s i n th e flame. Coppe r salts burne d green , potassium salt s gav e lilac , lithiu m gav e a re d flame. His colleague Gustav Kirchhoff (1824-1887 ) suggested that they let the ligh t from th e incandescent salts fall on a prism. The emerging light was thus split into a spectrum o f frequencies, each spectrum being characteristic of the substanc e they were heating (Figure 15.6). These spectra were one o f the firs t piece s o f evidence for th e internal structure of atoms, the once supposedly indivisible unit s of matter. Bunsen an d Kirchhof f ha d n o mean s o f answering th e obviou s questions : Wh y these frequencies? Where does this light really originate? But their work provided a powerful empirical method of identifying the components of a sample of matter, although it was primarily limited to substances containing metal ions. In 186 0 Bunse n and Kirchhof f discovere d a new element , cesium, which the y

Figure 15.6. Th e wavelengths of the visible light emitted by hydrogen atoms that have been heated by an electric discharge. Many more wavelengths are emitted, which are invisible to the huma n eye.

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first detected by its unfamiliar spectral frequencies and. subsequently isolated fro m their sample by chemical methods. In 1861 they found rubidium, another metal. Analysis o f the ligh t fro m th e star s provides a means o f detecting chemical elements i n th e heavens . I t is true tha t w e ca n lan d o n som e cool heavenly objects , such a s th e Moon , and actuall y tak e sample s t o analyze , bu t onl y spectroscop y reaches to the farthest galaxies. More about Waves: Wave Packets Unlike a particle, a wave has no position. Yo u cannot point at a specific spot on a wave and say , "That's wher e it is." However , interesting things happe n whe n you start to mix waves of different frequencies. Figure 15.7a shows what happens when two waves of slightly different frequen cies ar e mixed. As you ca n see , the intensit y o f the joint wave varies i n a regular way. Anyon e who ha s playe d the sam e note o n two differen t string s o f a slightly out-of-tune guita r wil l hav e hear d "beats, " a kin d o f throbbing th e frequenc y o f which increase s a s the differenc e betwee n th e tw o frequencie s increases. Figures 15.7b and 15.7 c show what happens when several waves of different frequenc y are mixed. The result is known as a wave packet. It is a traveling disturbance that, compared with a pure wave, is comparatively localized; at any given time it has a "position," which ca n be defined by the point of its maximum intensity . The spatial spread of a wave packet depends o n the range of frequencies use d to make it . I f all th e wave s tha t contribut e hav e prett y muc h th e sam e frequencies, then the wave packet will be fairly long , as in Figure 15.7b. If a wider range of fre quencies is used, the packe t is narrower, as in Figur e 15.7c. If an extremely wide range of frequencies i s mixed, the packet narrows so much that we can attribute to it a ver y wel l define d position, a s thoug h i t wer e a particle . These ar e no t idl e games. The y touch o n th e ver y nature o f reality and wil l be o f deep significanc e when we come to talk of quantum mechanics .

Figure 15.7a. Th e superposition of two wave s of different frequencies produces "beats."

Figure 15.7b. Th e combination of many waves of slightly different frequencies produces a broad traveling wave packet.

Figure 15.7c. Th e combination of man y waves of widely varying frequency produces a narrow wave packet.

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The Problems Start

So far, so good. Huygens's waves have triumphed ove r Newton's corpuscles. But in the hour of Maxwell's tour de force, doubt was seeping through the Victorian floorboards. Maxwell had shown that light was a wave, but a wave in what? Water waves trave l in water; sound wave s travel in gases, liquids, o r solids. In what d o electromagneti c wave s travel ? Unlike an y othe r kin d o f waves tha t w e know of, they can travel in a vacuum. What is waggling in a vacuum? It would in a way be easier if light consisted of corpuscles. Bullets have no trouble going through a vacuum . Bu t Youn g seeme d t o hav e kille d tha t possibility . Hert z said o f Maxwell's equation s that "Maxwell's theory consists of Maxwell's equations." In other words, use the equations, don't ask too many questions. Maxwell's laws allow us to calculate the strengt h of the electri c and magnetic fields fo r any system, including light waves . The y giv e th e righ t answers , an d i t i s o f n o practica l importanc e whether w e have a reassuring physica l pictur e o f electromagnetic waves . Logical positivism ignores awkward questions. The idea of waves-in-nothing was deepl y disturbing t o the scientifi c establish ment. W e noted previousl y tha t th e "stiffer " th e mediu m throug h whic h soun d waves travel, the faster waves travel through it. It is possible to quantitatively relate the velocity of a wave to the stiffnes s o f the medium; if this is done for light waves it turns ou t that they must be traveling through a medium that has the stiffnes s of steel. Where is this medium ? Why aren't we and the planet s continuall y hackin g our way through it ? In order to salv e their consciences , the physicist s invente d a universally presen t medium, dubbe d i t the ether, and hemmed an d hawe d whe n they were asked to explain its properties. HMS might well regard this a s a step of dubious morality . No one had th e slightes t evidenc e fo r the ether. 8 Moreover, the required properties of the ether were a bit too much to swallow. Apart from havin g the stiffness o f steel, it was also supposed to penetrate transparent substances, so as to provide a medium in which light could waggle. Not too credible. Scientists realized that if the ethe r existed it might provide an answer to an old problem: Is there an absolute space, a framework fixe d in the universe to which all motion shoul d b e referred ? I f the ethe r wa s motionless, then perhap s th e Earth' s motion through the ether could be measured. The attempt was made in 1887 in Cleveland, by two Americans, Albert Michelson (1852-1931), born i n Prussia, and Edwar d Morley (1838-1923) . They argued that if we were drifting through a sea of ether, like a fish i n water, then, if light wa s a wav e i n th e ether , a ligh t bea m shinin g i n th e directio n o f the Earth' s motio n should behave slightl y differently fro m a beam traveling at right angles to the motion. Usin g extremel y sensitiv e methods , the y foun d n o differenc e whatsoever . This was one of the great null experiments of all time. If the ether was there, it gave no sign of it. The result induce d instant migrain e i n the physic s community . Michelso n regarded the experimen t as a failure, an d Lor d Kelvin (1824-1907 ) pronounce d i t a real disappointment. I t is an interesting sidelight on the dynamic s o f scientific respectability that when the experimen t was repeated thirty-five years later by D. C. 8 Descartes had postulated an omnipresent ether, not to carry waves but to satisfy his belief that there could not be a vacuum in nature. The idea was rejected b y Robert Boyle, since he could fin d no experimental evidence for it.

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Miller, his positive result was rejected. By that time the special theory of relativity was s o firmly establishe d tha t th e existenc e o f an ethe r was n o longer compatible with accepte d theory. Anyway, his result s late r turne d ou t t o be experimentally suspect. Despite the fac t that Maxwell's equation s worke d for most purposes, the physi cists knew that all was not well with the world of physics. But the ether was not the only problem with light. The Problems Continue

Why is it pleasant to kiss a lipsticked mouth but not a red-hot poker? Both are red. The answe r become s eviden t i n a darkene d room . Al l visibl e ligh t originates in very hot bodies, but what we normally see is reflected light . Lipstick is not a source of visible light; it's not hot enough . The light given off by a body depends on its temperature. Heated bodies give off a range of electromagnetic waves, due t o the motio n o f the charge d particles fro m which the y are made. At normal temperatures this radiation i s rather low-frequen cy; if you like , you ca n imagin e that th e movement s o f the particle s ar e leisurely. Almost everythin g in you r surrounding s is at about room temperature. These objects are giving off a range of frequencies, mostly in the IR, which is invisible to the naked eye. If your temperature goes up, the distributio n of frequencies will change slightly. The light at the lowest frequencies will decrease in intensity and the higher frequencies will increas e i n intensity. I n general the distributio n o f frequencies looks like a hill (Figur e 15.8a), and a s you warm up, th e peak of the hill moves toward higher frequencies. You are unlikely to get so hot that the hill starts to encompass visible frequencies . Th e Sun, of course, is hot enough , and give s off not only visible light but also radiation of much higher frequencies, in the UV. The Earth, on the othe r hand, has an average surface temperatur e of about 8°C and th e top o f the frequency hil l is in the IR range of radiation. In the ninteent h centur y a peculiar fac t emerge d about th e radiation produce d inside a closed heated container. The way that this radiation is analyzed is to construct a hollow cavity, which can be maintained a t various temperatures, and dril l a tin y hol e i n i t to allo w a beam o f radiation t o escape . This radiatio n i s termed blackbody radiation. We can construct a graph showing the distributio n o f the intensit y of the differ ent frequencies that are detected in blackbody radiation (Figure 15.8b). This graph,

Figure 15.8a. Th e distribution of the frequencies of the radiatio n emitted by a body at different temperatures;. As the temperature increases, the radiation moves to highe r frequencies.

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of course , depends o n the temperatur e at which the cavit y is maintained, hut th e intriguing finding is that, for a given temperature, the curve is quite independent of the material from which th e container is made; it depends onl y on the temperature of th e container . This rathe r out-of-the-wa y observatio n eventuall y produced th e greatest revolutio n in scienc e since Newton. The problem was that no one could explain the shape of the curve that showed the distributio n o f the intensities o f the different frequencies . I t was not that ther e was a poor fit between observatio n an d Maxwell's theory—there was no fit. Here we have an example of the periodical impotence of established science , th e failure that smashes the paradigm and prepares the ground for the next revolution. It was evident , a s the nineteent h centur y dre w to a close, that, as far as blackbody radiation and the problem of the ether were concerned, Newton and Maxwell were of no help; ther e was something very wrong with th e basic physics. Ther e was far more wrong than the scientists o f the time could have known, but before a new paradigm wa s constructed , Newto n ra n int o mor e dee p trouble . T o appreciate hi s posthumous tribulations, we must firs t say a word about molecular motion.

Figure 15.8b. Th e distribution of radiatio n emitte d by a blackbody at two temperatures .

16 The Ubiquity of Motion Shake it, baby, shake it! —Marvin Gaye

The Ubiquity of Motion In 1827 , as Beethoven lay dying, the Scottis h botanis t Rober t Brown observed a n aqueous suspensio n o f pollen grain s unde r th e microscop e an d foun d tha t the y were in continual motion , not in smooth waltzlike trajectories but in sudden, break dance-like jumps in al l directions . H e concluded tha t thi s motio n wa s displayed only by the mal e sexua l cell s o f plants. (I n those day s women move d more decorously than men. ) Later he found that polle n fro m long-dea d plants exhibite d th e same phenomenon, a s did unambiguously nonlivin g systems, such a s tiny specks of dus t derive d fro m crushe d stones . Brown was , o f course, not observin g molecules, but unknowingly he had stumbled across the visible consequences of molecular motion. Brown was not the firs t t o observe what ha s sinc e become known a s Brownian motion, but he was the first to study it seriously. He volunteered no explanation. It was anothe r fift y year s before th e correc t explanation wa s pu t forward—tha t th e pollen grains were being battered on all sides by the endlessly scurrying, but invis ibly small, molecule s of water. Pollen grain s are far smaller than the averag e dust particle; they are small enough to be detectably pushed aroun d by molecular bombardment. In a dense crowd you would no t expect to be simultaneously and sym metrically bumpe d int o b y al l you r neighbors . Similarly , th e chance s ar e tha t a pollen grain in water will be hit unevenly, in the sense that at any given moment its surface will not be subjected to equally strong simultaneous molecular blow s fro m all sides. Any imbalance i n the blows will push th e grain into movement. That is why it jumps around. Brownian motion provided the first direct evidence of the immortality of molecular motion: Brownian motion does not die out. If you observe a suspension o f fine particles unde r th e microscope and preserv e the sample , your descendants to the nth generation will see exactly what you see. The inference is that the water molecules are exhibiting perpetual motion. Furthermore, even the average length of the jumps exhibited b y the particles will remain the same—provided the temperature at which th e observations are made is always the same. This strongly suggests that the average strength of the blow delivered by a water molecule is unaffected by the passage o f time, whic h i n turn implie s tha t th e averag e speed o f the wate r molecules, at a given temperature, is constant. A similar statement was made about the average speed of our molecules-in-a-box, and you can look upon Brownian motion as very strong circumstantia l evidenc e fo r the validit y o f that statement , which I previously asked you to take on trust.

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The central idea of this chapter is that all the microscopic components of matter are jumping around; that gases, liquids, and solid s ar e characterized by ceaseles s microscopic motion. In a gas, molecules move in straigh t lines unti l they bump int o each other . All molecules except those fe w that hav e only one atom, like helium, also exhibit in ternal motion; they can rotate and vibrate, twist and shake. This may seem to be an out-of-the-way professorial bit o f information, but w e will see that the greenhouse effect i s largely due to the existence of internal motions in the carbon dioxide and methane molecules . Gas molecules are fre e t o mov e wher e the y will , whic h i s consisten t wit h th e fact tha t a sample of gas released into a container will immediately spread ou t and fill the entire space. In liquids the molecules attract each other enough to keep very close together. However, they still move about, but in a manner resembling people in a dense crowd. Their motio n is akin to the mixing of the tightly packe d partici pants in a crowded cocktail party. If molecules stopped moving in liquids we would all drop dead. Within the living cell , material s hav e t o b e move d fro m plac e t o place ; otherwise , substance s coming into the cell would not reach the molecules that they have to meet for the life proces s to continue. The movement of molecules in the cell is in general sim ply a result of their inherent inabilit y t o remain stationary. The movement of molecules into the cell is not always so simple, and may involve their being carried by other molecules. In solids, atoms or molecules generally occupy permanent sites from which they rarely stray, but they can be crudely envisaged as a gospel choir, each singer swaying, wobbling, and bobbing up and down, but remaining tethered to their places as a consequence o f the close proximity of their neighbors. Motion in solids is thus almost entirely vibrational. You can't see or feel these vibrations; they are too small. Movement of molecules from plac e to place, so-called translational motion, occurs continually in gases and liquids but can occasionally occur in solids, although it is generally very slow. One manifestation occurs in old color films. The different ly colored dyes in a cinema fil m were originally confined to certain areas . However, in ol d film s th e border s betwee n thes e areas ar e sometime s blurred because , over th e years , dy e molecule s slowl y migrat e acros s th e film , smearin g Jeanette MacDonald's lipstick and Gable's razor-sharp moustache. This is an example of diffusion, the slow spreading of one substance through another by molecular motion. Molecular motion is universal. It underlies almost every kind of change found in the inanimate and animate world. The explanation of molecular motion, how molecules mov e and wha t th e consequence s o f that motion are , has grow n into a sophisticated an d highl y successfu l theory . Theory grows from observation , and al though i t i s no t eas y t o se e molecules , ther e i s a wealt h o f readily observabl e macroscopic phenomen a tha t depen d o n microscopi c molecula r motion . I t wa s from th e stud y o f these phenomen a tha t th e unifyin g them e o f molecular motio n emerged. Th e first suc h stud y was conducted Robert Boyle. In Chapter 1 we saw that if a sample of gas is kept at constant temperature, then th e product o f its volume and the pressure exerted on it remains constant , no matter what the pressure. The correct model for the explanation of Boyle's Law was given by Daniel Bernoulli, who guessed that the molecules are in motion. The discover y of Brownian motion subsequently supported his guess.

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What Molecular Motion Can Do Mark off, i n your imagination, a square inch of skin. Every second this area will he subjected to 2 x 1024 blows from the molecules in the air. This incredible and ceaseless bombardment affect s ever y surface expose d to the air . The human bod y is not sensitive enough to detect the tiny individual blows delivered by gas molecules , but nevertheless a very significant observable effect arise s from this bombardment. Imagine a vertical meta l plate welded t o a wheeled platfor m standin g o n a railway track. The plate is perpendicular to the direction of the tracks. Fire a few shots at the plate from a revolver. The effect o f each impact is a ping and a very slight jerk forward o f the wheele d platform , whic h the n come s to res t afte r eac h shot . (I n a frictionless world , and in a vacuum, the plate would of course roll on forever, condemned to do so by Newton's first law of motion.) Now take a submachine gun an d fire a prolonged, continuous, very closely spaced stream of bullets a t the plate. The platform accelerates smoothly. According to Newton's second law, acceleration implies tha t ther e i s a net forc e actin g o n the body . Wha t i s happenin g i s tha t th e storm of very closely spaced impacts appears to create an effectively constant forc e on the plate. If the point s a t which th e bullets strik e are fairly equall y distribute d over th e whol e surfac e o f the plate , then th e forc e i s evenl y sprea d ou t ove r th e whole area. In this case we can work out the force du e to the bullets striking a unit area (sa y 1 square inch ) o f the plate . Th e definitio n o f pressure i s forc e pe r uni t area. The ballistic bombardment results in pressure. Now replace the bullets with molecules and it is believable that what we call air pressure is merely the macroscopic effect o f a microscopic molecular bombardment. The atmosphere presses on everything, not because of its "weight" but because of the ceaseles s movement of its component molecules. The first person to differenti ate between th e weigh t o f a sample of air and th e pressur e that i t exerts was th e Frenchman Pierr e Gassend i (1592-1655) , th e atomis t an d mechanis t wh o is attacked, along with Descartes, in Gulliver's Travels. Gassendi realized that the weight of the air in a container had nothing to do with the pressure that it could exert. A 50liter compressed air cylinder usually contains about 200 gram of gas, but the internal force acting on 1 square centimeter of the container is about 5 kilogram weight. If the cylinder is heated, the weight of the gas remains unchanged but the pressur e rises. The explanation o f gas pressure in terms of molecular motion was first clear ly stated by the Swis s Daniel Bernoulli, one of seven distinguished Bernoullis. The Inquisition Pursues the Inquisitiv e The Bernoullis were originally based in Antwerp, but when that town was taken by the Catholi c Spanish force s o f the duk e o f Alva, th e Protestan t famil y prudentl y packed their bags and fled to Switzerland, to avoid the Inquisition. The y settled in Basel in 158 3 an d produce d thre e generation s of mathematicians, physicists, an d astronomers holdin g academi c position s i n Basel , Berlin , an d St . Petersburg . Daniel (1700-1782) , perhap s th e mos t distinguishe d membe r o f the clan , taugh t mathematics, physics, botany, anatomy, and, in the end, philosophy a t the University of Basel. In Basel, the Bernoulli' s were fre e t o worship a s they wished an d t o publish their scientific thoughts. In 1738 , Danie l Bernoull i published hi s mos t importan t an d influentia l book, Hydrodynamica. I n i t h e suggeste d tha t invisibl e microscopi c bombardmen t ex-

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16.1. Wh y Bernoulli's piston did not fall.

plained som e commonl y observe d macroscopi c phenomena . I n particular , h e asked why i t was that, even in the absence o f significant friction between cylinde r and piston, the piston in Figure 16.1 didn' t immediately fall to the floor. His explanation assumed that the molecules (he called them particles) were in continual motion. I f the pisto n fell , th e molecule s woul d b e crowde d close r togethe r an d th e number o f hits per secon d o n each squar e inch o f the pisto n woul d increase . The pressure of the enclosed air on the walls of the container, and on the piston, woul d increase an d resis t th e fal l o f the piston . Thin k o f 1000 dim-witte d houseflie s i n Carnegie Hall, bumping int o th e walls . No w reduce the hal l to the siz e o f a cigar box. Ther e woul d b e a huge increas e i n th e numbe r o f collisions pe r secon d o n each squar e inc h o f wall. In othe r word s th e fly-pressur e o n the wall s woul d in crease tremendously. Bernoulli showed tha t Boyle' s law followe d fro m hi s mode l of a gas. His explanation is better than Newton's because Bernoulli's model of moving as opposed to static molecules can be used as the basis of explanation for many other properties of gases. Establishment Inertia, Again New Opinions are always suspected and usually opposed, without any other reason but becaus e they are not alread y common. —John Locke

Bernoulli's correct hypothesis about th e origin of gaseous pressure, which wa s th e first exampl e of modern theoretical atomic physics, was published i n 173 8 and ignored until 1821. Onl y then di d on e Herepath dig it up, in the year that Napoleon was buried . Th e eighty-yea r neglec t o f Bernoulli's hypothesi s i s ye t anothe r re minder of the all-too-frequen t conservatism of the scientifi c establishment . Thu s i t was that, when an important equatio n in the theory of gases was formulated by the Englishman Joh n Waterston , an d submitte d t o th e Roya l Society , i t declare d th e manuscript t o be "nothin g bu t nonsense. " Poo r Waterston decide d t o publish hi s paper in an obscure railway magazine of which he was the editor. Not surprisingly, the pape r did no t attract a huge amount o f attention. Eventuall y its merit wa s recognized and, in a pitiful attemp t to make amends, the Royal Society published th e paper i n 1892 . Thi s wa s a n exampl e o f scientific pie i n th e sky—Watersto n ha d died nine years earlier. The Jimmy Connors Effect If the concep t of perpetual molecular motio n in gases is accepted, a whole range of

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phenomena can be rationalized. We concentrate on one, avoiding math, but showing that extremel y simpl e idea s ca n explai n a phenomenon tha t puzzle d generations of wise men. A tennis ball hits a vertical wall. It leaves the wall with (roughly ) the same speed it had whe n i t struck . Now replace th e wal l wit h Jimm y Connors, making his famous two-hande d forehan d drive. A s the ball hit s the racket , it meets the string s coming the other way. The ball leaves the racket at a greater speed than that whic h it ha d whe n i t hi t th e string s (Figur e 16.2) . No w chang e th e tenni s cour t int o a closed container, convert the tennis ball int o a molecule, and let a piston pla y the part of the tennis racket. Molecules in a container into which a piston is moving forward will rebound off the piston at higher speeds than that at which the y hit. This is the Jimmy Connors effect, whic h result s i n a rise in th e averag e speed o f molecules i n th e container . But we know that increased average molecular speed corresponds to a rise in temperature, and thi s i s exactly what i s observed. If you compres s a gas, its temperature rises. Those of you who grew up wit h a bicycle will remember that when you vigorously pumped up a tire the pump heated up. That was the Jimmy Connors effect. Molecular motion is not a fiction. The Newtonian Picture Becomes Blurred It should b e noted tha t we have not the slightes t possibility o f describing the motion o f a single molecule in a gas, in th e way that w e can describ e the pat h o f the Moon. W e can't se e molecules , an d the y mak e to o man y collision s pe r second . What predictive limitation s aris e fro m ou r ignorance of the movement of individual molecules ? How can w e quantitativel y predic t anythin g abou t a collection of trillions of wildly careering particles? Our present, and probabl y eternal , inability t o predict th e motio n o f single gas molecules ca n b e (ver y imperfectly ) compared t o ou r inabilit y t o predic t th e lif e span of a given individual. Thi s latter limitation doesn' t worry life insurance companies. The y wil l giv e yo u a goo d estimate o f the probability o f a certai n clien t dying reaching, say, age forty-seven. They can't poin t t o a specific Joe Bloggs an d tell you that he will be battered to death at the age of forty-seven, but, after examin ing his medical and other records, they can say that he has a 22% chance of dying

16.2. Th e Jimmy Connors effect.

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before he is forty-seven; that is the best that they can do, but it is good enough—life insurance companies don't ofte n go broke. For many systems , probabilitie s ca n be predicte d wit h great accuracy. No one, except Fat Louey, can tell you that the firs t card that you are going to select from a n unmarked pack of cards will be the king of clubs, but the probability tha t yo u will do so is exactly 1 in 52. We often use the language of probability when we speak of the properties of large collections o f molecules. No one can predict the velocity of a given molecule i n a gas at a given time, but you can get an excellent estimat e of the average velocity and o f the probability that a molecule has, at any time, a given velocity, say 2.65 or 4.76 times th e averag e velocity. These estimate s com e fro m th e kinetic theor y o f gases, a theory t o whic h man y mad e contributions , non e mor e than th e grea t James Clerk Maxwell. This theor y deals almos t entirely i n term s of probabilities. Th e reason that it works is the same reason that insurance companies remain solvent . The y hav e enoug h customers . Whe n yo u dea l i n larg e numbers , probabilities are almost the same as certainties. I wouldn't be t my life on the toss of a single coin, but I would, with grea t confidence, bet on heads appearin g betwee n 49% and 51 % of the throws of a coin if the number o f throws was 1 billion. There is a subtle and fateful change in going from the language of Newtonian laws to the language of probability, and i t is a change that will hound u s on and off until the end of this book. In the meantime, we ask another question about molecular motion and get an awkward answer . Perpetual Motion Most moving objects i n the familiar , commonsens e world eventuall y com e to rest, and if they don't do so of their own accord we can, in principle, stop them dead in their tracks. Thus water roaring over Niagara Falls can be collected in a bucket and will in a few seconds come to complete rest—except for the microscopic motion of its molecules. We all eventually come to rest—except for the microscopic motion of the molecules of our skeletons. Under what circumstances does this molecular motion cease completely? Under no circumstances! It i s eas y t o sto p th e translational movemen t o f molecules. Freez e a bottle of olive oil, and the molecules stop moving from place to place. Any rotational movements they may have had in the liquid stat e are also frozen out . But they don't stop moving. They vibrate in complicated patterns . The amplitude o f the vibrations can be reduced by lowering the temperature. Can the amplitude be reduced to zero, so that the vibrations are killed? No! At the lowest temperatures attainable in the laboratory, or theoretically attainable, all molecules are still vibrating. We say that they have "zer o poin t energy. " Fo r reasons tha t wil l appea r later , there is no way in which molecules, or atoms, can be stopped from vibrating. Molecular Motion, Violent Encounters, and Chemical Change Molecular motio n i s a prerequisit e fo r chemical interactio n betwee n molecules . The piece o f magnesium metal i n a flashbulb cannot burn i f oxygen molecules d o not someho w arrive at its surface. Th e fact tha t molecules usually hav e to meet to react is trivial, but molecular motion has another indispensabl e rol e in most chemical reactions. Chemical reaction s almos t invariabl y involv e th e rearrangemen t o f molecules.

The Ubiquity of Motion |

For example, if you put a match to a mixture o f hydrogen an d oxygen , you will get a joltin g explosion , an d th e ne t resul t o f the reactio n wil l h e th e productio n o f water. In the process , the atom s o f the oxyge n molecules an d th e hydroge n mole cules become rearranged to give molecules of water, which, as we know, consist of two atom s of hydrogen linke d to one atom of oxygen. Now you ca n mix hydroge n and oxyge n gas and nothin g a t all will happen. Yo u can warm u p th e mixtur e by placing the containe r i n boilin g water. Nothin g happens. W e know, o r can guess, that molecules of hydrogen and oxyge n are bumping into each other at a staggering rate, an d ye t water i s not formed . The y have t o meet t o react, but meetin g i s not enough. That is because they are not bumping int o eac h othe r sufficientl y violent ly. It is rather lik e two Rolls-Royce Silver Clouds hitting eac h othe r head-on whe n both are traveling at 2 mph. At worst the chauffeur s wil l vibrate slightly . Nothing gets broken, even if the champagne slop s around a little. This is what usuall y hap pens when two molecules i n th e ai r meet at room temperature. The way they vibrate may be slightl y altered , bu t nothin g muc h els e occurs . If you want a visual model yo u ca n thin k o f a "molecule " mad e o f a few metal ball s hel d togethe r by short springs , bumping into another suc h "molecule " a t moderate speed . Plenty of wobbling, but no real damage. When two cars, each traveling at 100 mph, collide frontally, there is major structural damage . When tw o molecules smac k into eac h othe r at high enoug h relativ e velocity, there is a breaking of existing bonds and the formation of new bonds. Th e molecules that com e out o f the encounte r ar e not those that cam e in. If there is no reaction, we can guarantee to produce one by raising th e temperature. For a pair of any given makes of car, there is a minimum relativ e velocity below which no damage occurs on contact. Something simila r i s true for reactions between simple molecules. There is a certain critical relative velocity, specific for each reaction, below which no reaction occurs . In general , raising th e temperatur e encourage s chemica l reaction s t o g o faster . That's why you put foo d i n the refrigerator, t o slow dow n the chemical reactions— usually induced by bacteria—that we call decay. Motion is the key to reactions o f another kind—reactions between nuclei. In the Sun, radiatio n i s generate d by th e collisio n o f protons. Protons , being positivel y charged, will repel eac h other, and at close quarters this repulsion i s so strong that the chance o f two nuclei getting close enough to "touch" is very small. This disin clination to get to grips can be overcome by giving them high velocities. In the Sun the temperature varies from abou t 15 million degree s Celsius at the center to about 6000°C at the surface. At the higher temperature the average speed of the protons is over half a. million kph , about 100 0 time s th e averag e velocity o f an oxyge n molecule a t room temperature. Tw o protons approachin g on e another a t these speed s have sufficien t momentu m t o overcom e thei r electrostati c repulsio n an d smas h into each other, forming a deuterium nucleus an d two unstable particles—a neutrino and a positron. This is the firs t ste p in the production o f the solar energy which I hope is warming you now. An average proton in the Su n can rush aroun d colliding for a billion years before it reacts with another one . That is why the Sun is burning slowly,1 which suit s us fine . *Per kilo, a human being produces 10,000 times the energy produced by the Sun in the same time. But (bi g but) the mass of the su n is 10 19 times that of the total mass of the population of the Earth, so the Sun produces 10 15 times the heat energy produced by the whole population of the Earth in the same time.

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For the kind of temperatures prevailing on Earth there is a huge range of rates at which chemica l reactions occur. Some reactions appear not to go at all. The nitrogen in the air doesn't burn in the oxygen of the air , even when I light a match. You can imagine the consequences if it did; the firs t man to have made fire would also have been th e last . On the othe r hand, pu t a small piece of phosphorus i n a jar of chlorine gas and a violent reaction occurs, lasting no more than a few seconds. Life, at least in the for m tha t we know it, would be impossible if all chemical reactions were either very slow or very fast. I n fact, man y of the reactions that take place in the living cell take place extremely slowly when w e try to reproduce them i n th e test tube , even thoug h w e kno w that th e rat e o f collisions betwee n molecule s i s colossal. What is it about the internal environment of the cell that makes the differ ence? There was a time when the answer to that question would have included th e "Life Force, " the magi c ingredient tha t was suppose d to distinguish livin g matte r from dead . The real answer is that all living cells contain catalysts. A catalyst is a substance that speed s up th e interaction s between molecules or atoms. Often i t does this by holding dow n on e of the reacting molecules while the other one attacks, rather like a "heavy" holding someone by the arms while his boss delivers blows to the victim's belly. The interaction with the catalyst alters the fin e details of the molecule's structure enough to either break it on the spo t or soften i t up t o attack by molecules that would no t otherwise be able to react with it at that temperature. The essential feature o f most catalysts is that they are built in suc h a manner that their shape, or part of their structure, is adapted to the shap e of one or both o f the molecule s betwee n whic h the y ar e attemptin g t o induc e a reaction . There are something like 1000 catalysts in each living cell. We call them enzymes, and they speed up the reactions that keep life going. Another example is the catalysis of the reaction between hydrogen and nitrogen, which is carried out industrially t o produce ammonia. This reaction can be speeded up enormousl y by the presence of a piece of platinum metal . The reaction takes place on the surfac e o f the metal. The German chemist Fritz Haber developed this process, which saved the German cordite (explosive) industry in World War I.2 The British munitions industr y a t the time was saved by Chaim Weizmann, later to be the firs t presiden t of the Stat e of Israel. He invented a novel process for manufacturing acetone. In 1934 Haber died on his way to Israel to take up a position as head of the Sief f Institute, later to be called the Weizmann Institute. It ha s bee n estimate d tha t abou t a quarte r o f the GN P of the Unite d State s i s based on the sale of products the manufacture of which involves catalysts. Chemical chang e is impossibl e withou t molecula r motion , but molecula r motion has another string to its bow: it lies behind the idea of heat.

2 Haber strongly objected to the Nazis' requests that he dismiss Jewish employees in his research institute. In a letter of protest he wrote, "For more than 40 years I have selected my collaborator s on the basis of their intelligence and their character, not their grandmothers. "

17 Energy A man meet s a woman on a bitterly cold, windy Chicago street corner. Her hands are freezing, his are warm. He presents her with a bunch of faded flower s and then , humming, "You r tiny hand s ar e frozen, " warm s her hand s wit h his . Ther e hav e been three very different kind s of transfer between them. One was material and tangible: the flowers. The other two were intangible and involved no material transfer: the heat that went fro m hi s hands to hers, and the information that went from his mouth and eyes to her brain. There are very many intangible transfers between animate an d inanimat e objects , transfer s that appea r at first t o have nothing in common but in fact are closely linked. Throw a ball. Come to rest afte r th e ball leaves your hand. Th e ball i s moving; you ar e not moving, but you were. An observer could summariz e what h e saw by saying that motion had bee n transferre d from yo u to the ball. A falling column of water impinges on the blades of a turbine i n a hydroelectric station, and the whee l turns. Again , motion appear s to have been transferred from on e body to another. When the attentiv e wimp warms his companion' s col d hands, nothing material is transferred, but somethin g has obviousl y moved from one body to another. It was only in the middle of the nineteenth centur y that the transfer of heat and the transfer o f molecular (or atomic) motion would have been jointly recognized as involving the transfer of energy. Energy, like force , i s a concept that unifies a host o f phenomena. In discussin g energy it is convenient to use the concept of work, so let's immediately define work as force times distance. Suppose you take an apple that has a weight of 2 newtons. This is the force that you have to exert on the apple to hold it up. Now lift it to your mouth, a distance of about half a meter. The work that you have done in lifting th e apple is 2 newtons x 0.5 meter = 1.0 joules. The joule is a unit of work, named afte r the nineteenth-centur y Lancashir e scientist Jame s Prescott Joule (1818—1889). We all have a feeling for the meaning of work, but what about energy? Energy, lik e work , i s a n abstract , man-made concept. Yo u can't se e energ y or work. Beware of common usage here. You can see someone work, and yo u may be able to see the results of his work, but you cannot see the work itself. Energy can be thought of as something that enables work to be done. Thus a waterfall has the ability to do work by virtue of the fac t that the water is moving. This is true of all moving bodies, and we call that ability kinetic energy. A body moving with a velocity v has kinetic energy equal to one-half of the mass of the body times the squar e of its velocity: KE =(1/2) mv2. In the case of the waterfall, the kinetic energy of the water can be converted into the kinetic energy of a spinning turbine, which in turn is converted into the electric current produced by the dynamo, which can be used to run an electric motor, doing work. On the othe r hand, a n immobile boulder perched o n the edg e of a cliff ha s th e stored ability to do work. It too could fal l on a turbine blade, not a particularly ele-

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gant arrangemen t but sufficien t t o prove that it s store d energ y can be turned int o work. We call stored energy of this kind potential energy. In countless case s a body is not movin g but ha s th e potentia l t o do work, provided tha t i t ca n move i n response to the forces acting on it. In the case of the boulder the force that in the en d produces the work is gravity, as it is in the case of the waterfall. The potential energy of the boulder, its ability to do work, clearly increases with its initial height . As the boulde r falls , i t i s continually losin g potentia l energ y and speedin g up , thu s gaining kinetic energy. There ar e many kind s o f potential energy . A twisted rubbe r ban d i n a toy airplane can potentially do work if it is released. The stored chemical energ y in your muscle cells ca n d o work if released. S o can the store d chemical energ y in petrol . There i s n o singl e simpl e expressio n fo r potential energ y except i n th e cas e o f a body that can do work by virtue of the fact that it can fall. In this case, the work, in joules, that it can do by falling throug h a height differenc e o f h meters is given by mgh (m x g x h), where m i s its mass i n kilograms and g is the acceleratio n du e to gravity, which appeare d in Chapter 4. On the Moon g would have to be replaced by g/6. The languag e o f daily lif e assume s tha t w e nee d energ y to perfor m wor k an d that, a s we d o work, energy gets used up . W e cannot us e th e sam e coa l twice. It looks a s though energy—kineti c o r potential—and work are differen t face s o f th e same thing. This statement includes any kind of potential energy , including chemi cal potential energy. Suppose we lift a boulder onto a ledge. In doing so we do work and also lose part of th e stor e o f chemica l potentia l energ y containe d i n certai n molecule s i n ou r muscles. So kinetic energy, all forms o f potential energy , and work are all intercon vertible. Daily life tells us that we have to extend this statement . Consider a coal-fired railway engine. When the engine is moving, work is being done, since the engine is certainly exerting a force an d thereby moving something . This tim e th e immediat e sourc e o f the wor k seem s t o be th e hea t o f the burnin g coal. It appears as if heat can also be changed into work. Are heat and work also the same kind of thing? Are they two face s o f energy? The Return of the Fat Sumo

Two hundred year s ago, heat wa s believed t o be a n invisibl e indestructabl e flui d called caloric, a word coined by Lavoisier. Caloric is another exampl e of a theory that fit s som e o f the facts . Th e particle s o f caloric wer e suppose d t o repe l eac h other. This explained why heat had a tendency to spread from on e body to another. It also explaine d wh y a body expanded upo n bein g heated ; the mor e particle s of caloric i n the body, the greater the interna l repulsiv e forc e pressin g the body outward, and so on. The fat sumo was alive and well. The first rea l advance in burying Lavoisier's caloric was made by the man wh o married Lavoisier's widow. The highly colorful, an d moderately obnoxious American, Benjami n Thompson , Count Rumford, appear s to have live d abou t te n live s (some simultaneously) , a s scientist , diplomat , spy , philanderer , philanthropist , military adviser , creator of the Roya l Institution, an d others . Thompso n observe d that hea t wa s produce d durin g th e borin g o f canno n barrels—fo r th e Bavaria n armed forces. It was clear to Thompson that a s long as the dril l was turning i n th e

Energy

block o f metal, heat wa s being produced . Calori c was suppose d t o be conserved , and yet here was an endless strea m of caloric coming out and none going in. In the paper tha t h e presented t o the Royal Society, Thompson suggeste d that hea t was a form o f motion. Humphr y Dav y adde d t o th e evidenc e b y showin g tha t i f tw o pieces of ice were rubbed together, they melted. No one took much notice. Around about 1840 , James Joule set out to prove quantitatively tha t mechanica l work could b e converted int o heat an d tha t work and heat were therefore equiva lent, tw o aspect s o f the sam e thing . Hi s apparatu s i s show n i n Figur e 17.1 . Th e falling mas s i s subject t o a force—its weight , which is mg (see Chapter 4). As th e mass falls , th e paddle s sti r th e water . Th e mas s fall s throug h a distance , h, say . From th e definitio n o f work a s "forc e time s distance, " thi s mean s tha t th e wor k done by the attractio n o f the Eart h is mg x h = mgh joules. You may be unused t o the ide a of the Eart h doin g work, but i f you stic k to the scientifi c definition , yo u will see that a mass is being moved through a distance by a force. That's work! The mass come s to rest o n the floor . Whe n i t was suspende d abov e the floo r i t had the potential to do work; on the floor that potential has gone. We can say that it has lost its potential energy . But if you measure the temperature o f the water at the end of the fall, as Joule did, you will find that it has risen. Joule concluded that mechanical work , done by the falling weight in turning the paddles, could be converted into heat. The farther th e mass falls , the greater the rise in water temperature: a certain amount of work was equivalent t o a certain amount of heat. Another way of looking a t i t i s tha t w e starte d wit h a certai n amoun t o f (potential ) energ y an d ended u p wit h the sam e energ y in anothe r form : heat . Joule had show n quantita tively that: work an d hea t wer e tw o side s o f the sam e coin . I n modern nomencla ture, 4.184 joules of work is equivalent to 1 calorie of heat. Once again the concep t o f moving molecules simplifies everything : the moving paddles hit the water molecule s and , like a tennis playe r returning a ball, they increase the speed of the molecules that they hit. The Jimmy Connors effect i s working, (Th e blow s wil l als o increas e th e violenc e o f the interna l vibration s o f th e water molecules an d the vibrations o f the atoms in the paddles.) We know that increased motio n i s associated wit h a rise i n temperature , whic h i s exactly what i s observed. All that Joule had don e was fin d a complicated wa y o f transferring the motion o f the fallin g mass t o the water molecules. Nothing material has gone fro m the mass to the water; only energy has been transferred. In fact an y collisio n o f macroscopic moving objects results i n the productio n of heat, because part of the translatory motion of the moving bodies i s converted int o the rando m motio n o f their atoms . Joul e spen t hi s honeymoo n i n Switzerland ,

Figure 17.1. Joule s experiment.

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where it occurred to him tha t water fallin g ove r a waterfall shoul d war m both th e Earth and the water slightly when it hit the Earth. He spent part of his honeymoon confirming this prediction. Mrs. Joule's comments have not been recorded. Joule presented the results o f his paddle experiments to the British Association in 1843 . Th e receptio n veere d fro m skeptica l to frigid . H e tried agai n two year s later, thi s tim e addin g hi s ide a tha t wate r a t th e botto m o f Niagar a shoul d b e warmer than at the top. No one cared. In 1847 he returned, but this time there was a genius sittin g i n th e audience . Willia m Thomson , twenty-si x year s old , realize d what hi s elder s faile d t o see: that Joule had mad e one of the great advances in th e understanding o f nature. Thomson, later to become Lord Kelvin, sparked the interest of the scientific establishment. The stubbornness of the scientific world in the face of Benjamin Thompson's observations and Joule's experiments were not the only examples of mental inertia i n the embarrassin g histor y o f heat. Th e equivalenc e o f heat an d mechanica l wor k was also stated by the German physician Julius Mayer (1814-1878) in a paper that was rejected a s worthless by the Germa n scientific journal Annalen der Physik. A modified versio n o f the manuscript was published by another prestigious journal, but it left the readers cold. The acceptance of Mayer's ideas was probably hindered by the obscuring influence of Naturphilosophie i n his writings and the fact that he did not have Joule's clear conception of the meaning of energy. In 1847 the distinguished physicia n an d scientist Hermann von Helmholtz sent a manuscript t o Annalen der Physik presenting his conclusion that heat and work were equivalent an d that energy was conserved in any process. You guessed it: rejected. Th e autho r subsequentl y presente d hi s idea s a t a scientifi c meetin g i n Berlin and paid for the article to be published privately . It was this article that was the majo r influenc e in persuadin g th e res t o f the scientifi c worl d tha t hea t an d work were interconvertible and quantitatively related. The idea of the conservatio n of energy was to become a cornerstone of science. To get a feel for the units of work and energy , lift Newton' s apple to your mouth. You are doing very roughly 1 joule of work, which is equivalent to a little less than a quarter of a calorie of heat. To warm an average cup o f water to boiling, you nee d about 16,00 0 calories . To get this amount o f heat by doin g mechanical work , you would hav e to d o work equivalent t o tha t neede d t o rais e 64,00 0 apples t o your mouth, or a 13-ton barbell from th e floor to hip height . Heat and Motion The perceptive Robert Hooke guessed the truth: "Heat is a property of a body arising from the motion or agitation of its parts, and therefore whatever body is thereby touched must necessaril y receive some part of that motion, whereby its parts will be shaken. " Although the exac t connection betwee n molecula r motion , heat, an d temperature too k a long time t o gel , when i t wa s finall y establishe d i t provide d simple, transparent explanation s o f countless phenomena—such as making a cup of tea. Fill th e containe r wit h water , plu g in , an d switc h on . Electron s begin t o flo w through the heating coil. They bump into the vibrating atoms from whic h the wire is made. The blows that the atoms get from the rushing electrons induce them to vibrate more violently. This enhance d movemen t conveys itself to the atom s in th e

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ceramic coating of the wire. The atoms of the cerami c beat upon th e metal base of the water container, thereby increasing th e vibrational motio n of the metal atoms. You can guess th e nex t step : the enhance d vibrationa l activit y o f the meta l o f the container i s passed o n again, this time t o the molecule s o f water. The blows tha t they receive affect them mainly by increasing the average velocity with which they move and by increasing their internal vibrations. There are two effects tha t can be easily measured. The water expands. This is because the increased motion of the molecules tends to push them farther awa y from each other. They need more lebensraum, more elbowroom. The other effec t i s that the temperature rises. How do I know? I can put m y finger in . The enhanced molecular motion of the water molecules is now transferred to the molecules of my skin and progressivel y works inwar d unti l it reaches nerv e endings , the molecule s of which als o begin to vibrate more vigorously. I hope that I'm not yet at a temperature where I'm doing physical o r chemical harm to my cells. Somehow the increased vibration is converted to an electrical signal to rny brain, and I "feel that the temperature o f the water has risen." Th e phrase doe s not indicat e what actuall y happens in m y brain; I am merely usin g conventiona l languag e to describ e th e sensation . Of course I could put a mercury thermometer into the water. Again the heightened movement o f the wate r molecule s i s conveye d by collisio n t o the glas s tube an d via the glass to the mercury of the thermometer. The mercury atoms consequently also nee d mor e lebensraum , an d th e mercur y expands , risin g u p th e ste m o f the thermometer. Notice that we have described the heating of water without mentioning the word heat. What has happened t o the water is that i t has "augmented its molecular motion by being at the receiving end of a succession of collisions, startin g with the galloping electrons in the heating element." In everyday, macroscopic language: "The water absorbed heat from the heating element." To heat an object is simply to make its atoms or molecules move more violent!}', whether by placing the object in contact with a hotter body or by exposing the object to radiation. No substance is transferred in either case. "Heat" i s a macroscopic concept. Almost every time we use th e wor d heat we can replace it with the idea of molecular motion. However , normally i t is far more convenient t o us e th e macroscopi c concep t o f heat rathe r tha n th e microscopi c concept of molecular motion. The realization that heat an d wor k are aspects o f energy, and tha t wor k can be converted into heat, is one of the unifying principle s that underlie the complexit y of nature. The Conservation of Energy

In Joule's experiment, when the mass can fall no farther i t can do no more work. It had the ability to do work before i t fell, and it has now lost that ability; we say that the potential energy of the mass is lost. On the other hand, the water has gained energy, th e molecule s ar e movin g faster ; the y hav e increase d thei r kineti c energy . Joule believed that the loss of potential energ y of the mass was equal to the gain in the kinetic energy of the water. He was very nearly right. In fact the string connecting the mass to the paddle passes over a wheel, and a small amount of heat is produced by tltie friction between the axle of the turning wheel and its suspension. The

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loss of energy of the mass was in fact eqiial to the total amount of heat produced by friction ari d by the movemen t of the paddles . No energy was lost in the process. If we want to be pedantic, w e have to admit tha t the water that heated u p i n Joule's experiment also heated the air surrounding the apparatus . A nit-picking summin g up o f the experiment is that the loss of potential energy of the mass is exactly equal to the total heat release d int o th e environment . Nothin g has bee n lost ; energ y i s conserved. The idea of energy as being something that was conserved was formally stated in the 1860 s by the Germa n physicis t Rudol f Clausiu s (1822-1888) . Today we speak of the first law of thermodynamics. In its most general form, the law says that ther e is a certain amount of energy in the universe an d that we can never increase o r diminish it. We can transform it from on e form to another—work to heat, or potential energy to kinetic energy, or chemical energy to heat, and s o on, but w e never gain by these processes; we are merely changin g currency (with no commission costs). The law is based on experience, and on the exact definition of what we mean by energy. It was not derive d from a simpler law. All that we ca n say about i t is "That' s the way the universe is," as far as we know. This is our third conservation law, after thos e for charge and mass. In each case the laws put restraints on the way the universe behaves. In each case the law is deduced fro m th e behavio r o f nature. W e noted tha t because o f Einstein w e ha d t o modify th e la w of conservation o f mass to take into account the interconvertibilit y of mass and energy . Obviously the same applies to the conservation of energy. If we want t o be correct , we shoul d spea k of the conservatio n of mass plu s energy , bu t since the conversion o f one to the other is not something tha t happens i n everyday life, it is far more convenient to use the two laws separately. We will run acros s situations where that cannot be done. If the firs t la w says that the amoun t o f energy in th e univers e i s constant, then why shoul d w e worry about how much energy we use? When a car engine works , part of the energy of the fuel is turned into heat, which warms the air. Why not take all that heat and reuse it? Better, consider all that kinetic energy in the molecules of the water of the ocean. Since Joule took the potential energy of a body and used it to raise the kinetic energy of water molecules, why can't we reverse the process? Let's turn the kinetic energy of the molecules in the ocean into work. This brings us to the next chapter, the contents of which ar e really bad news for Newton.

18 Entropy: Intimations o f Mortality So far as scientific evidenc e goes, the univers e has crawled b y slow stages t o a somewhat pitiful result on this earth, and is going to craw l by still mor e pitiful stages to the condition of universal death. —Bertrand Russell

Open a can o f petrol i n a closed room . Th e room is als o thermall y isolated ; heat cannot enter or leave. The smell of petrol will slowly spread through the room. The mechanism i s simple: molecules leave the can and meander across the room. Why do the y leav e the can ? Because, in th e can , i n th e spac e abov e the liqui d petrol , they ar e moving. Som e of them will , purely by chance, fin d thei r way ou t o f the neck of the bottle. It is absolutely essential to realize that they d o not purposefully make thei r wa y to th e opening ; remember th e blind , deaf , radarless , unsmellin g flies o f Chapter 1 ? In fact , som e o f the molecule s tha t hav e lef t th e ca n ma y fin d their wa y back, not because of a homing instinc t bu t purel y by chance. Molecules have no will. It would be a scary world i f they did. In time the petrol will distribute itself evenly over the whole room. This process is spontaneous—nothin g pushe s th e molecule s around . The y ar e condemne d t o eternal motion. Because this motion always seems to result in their spreadin g out, never i n thei r al l going back to the can, th e sprea d o f petrol through the roo m is termed an irreversible process. A larg e number o f randomly moving molecules woul d b e expecte d t o en d u p uniformly distribute d inside a container.1 At any given time, we d o not expec t exactly the same numbers to be in each half of the room; there will be small fluctua tions in the numbers as the molecules rush around . All the same, we do expect the numbers t o be very nearly equal, and on the average, taken over a period o f time, we ca n confidentl y predict the m t o be equal , This predictio n i s based o n experience. You wouldn't expect all the molecules in the air of the room in which you are sitting now to accumulate on the other side of the room, thus leaving you in a vacuum and wantonly snuffing ou t your life. And yet there is nothing in Newton's laws that says that this cannot happen. I n principle it could. Why doesn't it? Why d o we neve r fin d tha t al l the petro l molecule s hav e returne d t o the can ? Most people would instinctivel y say , "Because it's very unlikely, isn' t it? " Other s might reply, "Yes, but why?" a

We can neglect the fact that, because of gravity, there would be slightly more molecules in the bottom half of the room than the top. This increase in density nearer the Earth is displayed by the atmosphere. However, the density of molecules would be equal in the left an d right halves of the container. We also discount cases where the molecules condense to form a liquid, for example, the perfume i n a closed bottle or the petrol in a closed can.

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Where do we proceed from here ? We could go along the path labeled "Newton " and try to prove that the molecules never return to the bottle by using th e laws of motion. Instead, we'l l tr y something mor e intriguing; we will follo w th e pat h la beled "probability. " We have taken a fateful ste p here. We are going to use probability to explain th e workings o f nature. This is not th e wa y that Newto n spoke. The implication s for our understanding of reality are not trivial , an d i t is advisable fo r us t o stop fo r a moment and define what we mean by probability. We need to do this because probability is another of those words that is shared by science and everyday language. If I state tha t th e probabilit y of throwing a "four " wit h a fair di e i s on e i n six , what d o I mean? What is a "fair" die? I could define it as one in which the chances of throwing a "four" are one in six! Another way to say what I mean is to claim that for a physically symmetrica l die there is no reason to suppose that the di e will fal l on on e sid e mor e o r les s tha n an y other . W e believe thi s becaus e w e don't , o r shouldn't, believe in occult influences. I do believe that a perfectly symmetrical die should fall on any of its faces with the same probability. In a simple syste m w e ma y know enoug h to stat e probabilitie s exactly . Thus, with a pack of unmarked cards the chance of picking out a given card is exactly 1 in 52, provide d the ma n holdin g th e card s i s no t a cardsharp . I t turns ou t tha t th e probabilities associate d with the behavior of molecules can often be stated exactly. We are going to use probability to see why the petrol vapor will eventually spread evenly throughout a room. We go back to our molecules-in-a-box. Suppose that there is one molecule of oxygen in an otherwise empt y box. What are the chances, at any given moment, of finding it in the left-hand sid e of the box? A gambler would say "fifty-fifty," b y which he means that there is an equal chance of finding it in the left-han d sid e or the right-hand side. We can say that the probability of finding it in the left-hand sid e is one-half. Now suppose that there ar e two molecules in the box, and assum e that neithe r molecule affects th e behavior of the other. This is a crucial assumption. Thus if you put a man into an empty room, the chances are "fifty-fifty" tha t he would be found in the left-han d side . If you put a heterosexual man and a heterosexual woman i n the room, the chance s are very high that they would be found i n the sam e side of the room. This is not true of, say, nitrogen molecules; they behave effectively inde pendently of each other as far as their location is concerned. What is the probability tha t both molecules wil l b e foun d i n th e left-han d sid e o f the box ? We can assume tha t eac h molecul e individuall y ha s a probabilit y o f 1/ 2 o f being i n th e left-hand side. The rules of probability are quite clear on how to continue: if two independent events each have probabilities of one-half, then the chance of the event s occurring together is 1/2 x 1/2 = 1/4. This is exactly the same reasoning that makes the chanc e o f throwing tw o "heads, " i n tw o throw s o f a coin , equa l t o 1/4 . Th e chance of throwing three heads, one after the other, is equal to 1/2 x 1/2 x 1/2 = 1/8. We ca n writ e 1/ 2 x 1/ 2 x 1/ 2 a s (1/2) 3. In a box containin g thre e molecules , th e chance o f finding al l thre e o n th e left-han d sid e (o r the right-han d side ) i s als o (1/2)3, that is, one in eight. The generalization is obvious. If there are n molecules in a box, the chance of finding them all in the same half of the box is (1/2)". This becomes a very small number for even moderate values of n. Thus suppose that there were only ten molecules in the box; the chance that they would all be on one side is (1/2)10, which is equal to a little less than 1/1000 . The chance of finding all twenty

Entropy

molecules in a box on one side is a little less than one in a million. Now let' s conside r th e chance s tha t yo u are going to be suffocate d becaus e al l the gas molecules in the room in which you are sitting spontaneously collect in the other half of the room. (Remember that Newton's laws of motion do not forbid this happening.) The number of molecules in a modestly sized room is about 1028. It follows that the chance s of all the molecules being on one side of your room is about (1/2) multiplied b y itself 10 28 (10,000 trillion trillion times ) times. You would ap pear t o be safe : yo u ca n trus t th e calculations . The y als o indicat e wh y i t i s that, once th e petro l vapor i s sprea d evenl y throughout th e room , unlike th e genie , it doesn't go back in the bottle; it's just too improbable. What is the probabilit y o f finding some other arrangement of air molecules besides the extrem e case of all being in on e half of the room? To answer this we consider a much simple r case : the box with ten molecules in it. We work out the probability that there will be nine molecules in one half and one in the other; eight on one side and two on the other, and so on. The probabilities, as gamblers should know, are exactly the sam e as throwing a given number o f heads i n ten throws. The y are plotted in Figure 18.1, wher e it can be seen that the maximum probability is associated with 5/5, that is, equal numbers of molecules in each half. This is intuitively expected . If you had a box with many gas molecules in it, you would expect t o find th e gas equally distribute d throughout the box. The least probable distributio n i s that in which al l the molecules are on one or the other of the two sides. Again, this is a reasonable result. To bolster our belief i n our new method of approaching the world, let's consider a cocktail party problem: two sets of guests socializing. Mingle! We go back to our box and place twenty molecules in it, ten oxygen on the left-han d side, ten nitrogen on the right. Again, for later purposes, I want the box not only to be closed but als o to be thermally isolated . Obviously, the separatio n o f the gases will not last, because the molecules are in motion. We can guess that the most probable distributio n i s tha t i n whic h ther e ar e equa l numbers o f molecules o n eac h side of the box, and we will suppose that this is the case. But within the limitatio n that there are ten molecules on each side, there are several possible distributions of oxygen and nitroge n molecules. I n the initia l stat e the separatio n i s complete: ten oxygen on the lef t an d ten nitrogen o n the right. Without going into the math, I ask you t o believ e that th e mos t probabl e distributio n o f molecules i s tha t i n whic h each half of the box contains fiv e nitrogen and fiv e oxygen molecules. Again, with-

Figure 18,1. Th e probabilities of finding different distributions often molecules in a box. Two of th e probabilities are too lo w to appear on the scale of the figure.

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in th e restrictio n tha t ther e ar e equa l numbers o f molecules o n either sid e o f the box, the least probable distribution is when all the molecules of one type are on one side and al l those of the other o n the opposite side. This confirms us in our belief that we will not be sitting in a recital in a concert hall and suddenly fin d that all the oxygen molecules hav e lef t th e singe r and concentrate d around the audience . It is possible, jus t no t ver y probable. 2 Th e probabilit y o f finding all te n oxyge n molecules together on one side, right or left, i s about one in a hundred thousand . When mixing is complete, experience shows that the system has no tendency to stray away significantly from tha t condition. W e say that the syste m is at equilibrium, a term we apply to any system that shows no spontaneous urge to change. We can sa y of our system of two gases that it started of f from a state that ha d les s tha n maximum probability an d arrived at a state with maximum probability—the equilibrium state. Time Makes Its Appearance There is a road that turning always Cuts off th e country of Again. Archers stand there on every side And as it run s time's dee r is slain And lie s where it ha s lain. —Edwin Muir, The Road

We expect the spreading of perfume through a room and the spontaneous mixing of two gase s to be irreversible; we never observ e the evenl y spread o r evenly mixe d molecules revertin g t o thei r origina l arrangements . Likewise , w e neve r observ e the Worcestershir e sauc e i n th e Blood y Mary unstirring itsel f and separating . We believe that such processes go only one way, and our belief is based on 10,000 years of experience . The concept of irreversibility drags time into our picture of the world. When we sa y that the sprea d of perfume i s irreversible, we are picturing in our mind s a proces s tha t develop s wit h time . Suppos e w e tak e a vide o o f th e process o f two gase s mixing, which coul d be don e fo r chlorine an d oxyge n sinc e chlorine i s colored green. If we run the video in reverse, we would immediately realize that time was going backward. Time could not, in our experience, possibly be running forwar d if molecules spontaneousl y unmixed, or if a perfume returne d t o its bottle. Why I s Time a One-Way Road? Now consider a box in which all the molecules are in one half of the box. They will, of course , spontaneousl y sprea d out . I f we coul d observ e a fil m o f this process , there i s an excellen t chanc e tha t th e molecule s will mov e progressively throug h more and mor e probable states—moving fro m lef t t o right i n Figur e 18.1—until it arrives at the most probable state. You will never observe the opposit e behavior, a set of evenly distributed molecules spontaneously working their way through a series of less and less probable states until they arrive at the least likely state, that in which al l the molecule s are on one side of the box. In making this statement I am 2

It would be a God-sent response to the wish of Coleridge: "Swans sing before they die—t'were no bad thing, / Should certain persons die before they sing."

Entropy |_2]9

assuming that you have a frame o f reference, a n everyday world in which th e concepts of "before" and "after " ar e agreed by everyone. Unfortunately, there is no law based on the behavior of individual molecules that indicates that mixed gases cannot spontaneously unmix. And yet there seems to be a natural directio n fo r spontaneous processes . N o on e i n th e histor y o f the Earth ha s observe d spontaneou s unmixin g o f th e molecule s i n th e air . Mixin g processes o f this kin d always go in on e directio n only . Any san e scientis t woul d tell you that there must be a physical law behind this universal directionality. And there i s anothe r point : the direction of spontaneous, irreversible processes is always the same as that in which we think that "time" develops. Are we justified i n jumping to the thought-provokin g statement tha t the direction of time is determined by probability? Let us pause to see where we are. What we have suggested is that, in describing a basic property of nature, we ca n dispens e wit h physica l law s o f cause an d effect , such a s the law s o f motion. We are also hinting tha t th e directio n o f spontaneous processes is determined b y probability, and that the directio n o f time is tied to the direction of increasing probability . Is it? Are the law s of motion impotent whe n it comes to describing the natural direction o f microscopic physical processes? We have betrayed mechanics and taken up a passionate liaison with probability. Yet mayb e w e hav e give n u p thos e law s to o quickly ; maybe ther e i s somethin g missing in the probabilisti c explanatio n of the wa y in which large groups of molecules behave . Ther e certainl y is . Ou r assumptio n tha t a syste m moves fro m les s probable to more probable states is all very well; it fits in with the facts, but it doesn't sa y how, or why, th e syste m doe s this. A childless coupl e livin g i n a country where th e averag e number o f children pe r coupl e is 2. 2 is in a less probabl e state than a couple with 2 children. Th e probabilistic approac h i s to say that the y will probably procee d to have one chil d an d the n a second one . But it doesn' t tel l u s how they will make these steps. The frustrating fac t is that there is no way of using our probabilitie s fo r molecules-in-a-box , t o prov e tha t th e s}?ste m mus t g o "forward" rather than "backward. " Probability in itself gives no preferred direction for a system to evolve. This may be hard to accept, since we might expect that a system would move from a less probable to a more probable state. In general we are right; it does, but i n the case of molecular motion we don't know why. And for small numbers o f molecules it i s easy to se e that th e syste m can obviousl y move fro m mor e probable to less probable. An extreme example: If you have two molecules in a box and the y ar e i n differen t halve s o f the bo x (th e mos t probabl e arrangement) , it would b e no great surprise t o find bot h o f them i n the sam e half (les s probable) a second later. Newton Disappoints Let's give mechanics another chance. Let's make a videotape of the spreading of the petrol vapor and run i t backward. In our case it will have to be an imaginary film , since we can't see the molecules. If the reversed video shows a process that contradicts Newton's laws , then we have to assume that onl y the forward proces s is possible. The opening scene in our box office sellou t is a box containing an evenly distributed collectio n of molecules. As the reversed film proceeds, the molecules drif t toward one half of the box, finally leaving a vacuum at the other half. Is this impossible; does it defy th e laws of motion? The disturbing answe r is that, at every stage

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of thi s process , each individual molecule behaves according to Newton's laws. There is nothing happening to any given pair of colliding molecules tha t would in duce a scientific observer to say "This is unnatural. " According to a therom of Henri Poincare, a system obeying Newton's equations of motion will, if left t o its ow n devices , inevitably return agai n and agai n to an y state that we care to specify. I want to specify the unmixed stat e of two gases. Poincare assure s m e that thi s stat e will return . Wh y doesn' t experienc e confir m tha t prediction? Neither Newton nor Poincare helps us. The reverse video leaves their laws invi olate, in othe r words the laws ar e obeyed by the syste m even if we know that i t is going backwards in time. Nevertheless there is something terribly wrong about the reverse film. The total process which i t depicts is unnatural—gases do not unmix— or collect in one half of a container. Our conclusion at this stag e is that there is something about the behavior of the mechanical universe that is not contained in Newton's laws. The laws do not contain withi n the m anythin g tha t predict s th e irreversibilit y o f processes suc h a s those that typify the natural world. We hav e looke d a t th e behavio r o f a ga s fro m tw o completel y independen t points o f view: mechanical law s and consideration s of probability. We believe that the mechanica l law s mus t b e obeyed, but the y are obeyed whether th e processe s through which th e gas goes run backward or forward. It is only probability that appears to control reality. For the scientist this is a frustrating situation—the laws that control the movemen t of individual bodie s should , hopefully , b e sufficien t t o explain completel y the behavior o f collections o f such bodies. And yet they seem to be insufficient . Th e directio n o f mechanical processe s involvin g molecule s is , i n the rea l world , governe d b y a differen t principle : the y generall y move fro m th e least probabl e state , throug h increasingl y probabl e states , t o th e mos t probabl e state. Let us consider anothe r example of irreversibility, one that threatens us with extinction. Place some cold water i n a perfect thermo s flask , on e that neither let s in nor let s ou t an y heat whatsoever . Nex t throw i n a heated lum p o f iron. Clos e the flask. Ope n it after a half an hour. The contents, iro n and water alike, will be at the same temperature. The iron has cooled, and the water has warmed up. We can say that heat has passed from th e iron to the water. Or, in the microscopic version, we can say that the average molecular motion of the iron atoms has decreased and that of the water molecules ha s increased. Why? Why shouldn't th e water have coole d down and frozen , an d give n part o f its molecular motio n t o the atom s of the iron , warming the lum p o f iron to an eve n higher temperatur e than i t had before ? Th e first reason is that all our experience since childhood proclaims thi s process to be idiotic; but that is not a demonstration that a scientific law is being broken. Maybe the firs t la w o f thermodynamics has been violated? No! The firs t la w merely says that energy is conserved. It is conserved in the thermos, even if the water got colder and the iron hotter. All that would have happened i s that energ y would hav e gone from th e colde r body to the hotte r body. The total amount o f energy is neither de creased nor increased. Admittedly such a process contradicts our common sense , but tha t doe s not explai n wh y i t doesn' t happen . I f we tak e a microscopic view point, the passage of heat from a hot body to a cold body just involves the loss of kinetic energ y (motional energy) by the atom s or molecules o f the ho t body and th e

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increase in kinetic energy of the constituents of the cold body. This comes about by collisions. I f a fast-moving body hits a slow-moving body, then the faster body usually slows dow n and the slower body speeds up. One might think there was no alternative but fo r heat to pass fro m hot to cold. The problem is that if you took a (hypothetical) video of the process and ran it backwards, each individual microscopi c collision woul d satisf y Newton' s law s an d yo u coul d no t tel l tha t anythin g wa s wrong until you suddenly realized, looking at the whole system, that in the cooler part o f it th e molecule s wer e actuall y slowin g dow n an d i n th e hotte r par t the y were getting faster. Of course it's wildly improbable, but it contradicts no law of nature that we have spoken about u p t o now. A slowly moving body hitting a fastermoving bod y can giv e up par t o f its kineti c energ y to th e faste r bod y an d slo w down, if they hit a t the right angle. So what's going on? Equilibrium The common factor tha t connects al l our examples is that we started with systems that were, in our experience, inherently unstable and they all moved spontaneously to states in which ther e were no further macroscopi c changes: the petrol vapor remains evenly spread, the two gases remain perfectl y mixed, the iron sits silentl y in the water, both of them at the same unchanging temperature. The systems evolve spontaneously but eventuall y sho w no tendency to change: we say that they have reached equilibrium. Eve n if they fluctuate slightl y about that state , they show no macroscopic changes whatsoever. There is something else that the systems have in common. They are all what are technically know n a s isolated systems , wher e th e wor d ha s thi s ver y specifi c meaning: they are closed to the transfer o f matter o r heat, in or out. They were deliberately chosen this way because there is one mightily important isolated system: the universe. It cannot exchange heat or matter across its borders because by defin ition it includes everything that exists. What we have learned about little boxes applies to the cosmos: Isolated system s move toward equilibrium and stay there.

So the entertaining thing that we have learned is that the universe is spontaneously moving toward equilibrium. In simple words, we are going to end up in a universe where there will be no further macroscopic changes. This condition, of course, precludes life of any kind. This is too dramatic a conclusion t o be left lik e that. The Problem of Time We see that th e innocuou s molecules-in-a-box , with which w e starte d thi s book, have led us to a dismal prediction an d to this nasty problem: what physical la w determines th e spontaneou s direction o f natural processes ? Where is the directio n of time built into the laws of science? If scienc e i s suppose d t o giv e a rational explanatio n o f the physica l universe , then i t must surel y be abl e to account fo r the passag e of time. Pu t anothe r way , if our descriptio n o f the univers e is to be crystallized i n a number o f basic physical laws, such as the laws of motion and Maxwell's laws, then one would hope that the use of these law s would allo w us to predict unequivocall y the directio n in whic h all natural processe s proceed with time. Our hope s ar e no t fulfilled . Th e law s o f motion an d Maxwell' s law s ar e un -

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changed by reversing time. Any process described by these law s ca n be run backwards without violating the laws . In summary, we can say of nature that if you ru n the fil m backwar d it may look ridiculous, but everythin g will procee d strictly according to the laws of nature. Except one. There is one law in nature that ensure s that processe s like the mixin g o f gases, the spreadin g o f Chanel No . 5 , the passag e o f heat fro m th e war m hand s o f th e flower-bearing man to the col d hands of his beloved are all irreversible. They only go one way: they only go forward wit h time, and i n doing so they obey the secon d law of thermodynamics. The Second Law

There are a number of equivalent ways of phrasing the law, the simplest of which i s the statement that : Heat does not flow spontaneously from a colder to a hotter body.

The mor e combativ e amon g you wil l declar e tha t I have bee n cheatin g becaus e what I have done is to observe what happen s in nature an d then declar e that it is a law of nature. From which it follows that what happens in nature can be explained by science, by the secon d law of thermodynamics in fact. You are right. It is a law based purely on observation—as all fundamental laws are. The secon d la w o f thermodynamic s i s o n a standin g wit h Newton' s an d Maxwell's laws. It is one of the cornerstones o f the scientific attempt to explain th e universe. It is the onl y law that gives a direction t o time and thus "explains" why spontaneous natura l processe s ar e irreversible . Incidentally , neithe r th e law s of quantum mechanic s no r relativity can do this because they, too, are unaffected b y reversing time.3 The law was not derive d fro m fanc y theory ; it did no t com e out o f a professor's study. The opposite is true. It was put o n the road by a French army engineer who had mad e a stud y o f steam engines , particularl y those bein g buil t i n earl y nine teenth-century England . A logica l analysi s o f the wa y suc h engine s operat e le d Sadi Carnot (1796-1832) t o formulate a law that looks very different fro m th e wa y we have stated the second law but can be shown to be completely equivalent : It is not possible to construct an engine that operates in cycles and whose only effect is to convert heat into an equivalent quantity of work.

I am going to leave this definition , sinc e i t is not a s obvious a s the previou s one . You might see other definitions of the second law in your wanderings; they can all be shown t o be equivalent. For now, we have everythin g we need i n the previou s definition and our ideas on probability, but I stress that both forms are based on observation of the way the world behaves. Carnot's law is not derived from othe r laws or from theoretica l axioms. In the end , all our physical laws have come from som e kind o f observatio n o f th e "real " world , includin g th e law s o f motio n an d Maxwell's laws. We do not have to be ashamed of this. The second la w does not allo w natural spontaneou s processes to reverse, even 3

One of the forces withi n the nucleus, the weak force (se e Chapter 31), i s not time-reversible, but it is not considered to interfere with the workings of the atomic world.

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though they would not be breaking any other law. Because the second law has time built int o it , an y derivatio n o f the la w fro m th e othe r laws , whic h ar e time-reversible or time-independent, i s extremely suspicious. 4 Entropy Here is another statement of the second law : The entropy of the universe is continually increasing.

Entropy is a convenient concept, allowing us to use short sentences instead of paragraphs. Changes in entropy can often be measured, which allows us to use it to make quantitative predictions abou t the behavior o f systems. We can readily make the transition fro m probability to entropy because entropy is probability in disguise. Which i s more probable, to find a room with normal air in it or a room with al l the oxyge n o n on e sid e an d th e nitroge n o n th e other ? We already have tw o an swers, one based on our experience and the other on considerations o f probability. Both lead u s to expec t the mixe d state . We can say of the unmixe d stat e that i t is more ordered tha n th e mixed state . Thus i f your girlfriend's T-shirts are mixed u p with he r sweater s an d yo u unmi x them , you ar e bringing mor e orde r t o her cup board. We can extend this idea to the case of the molecules clustere d i n one corner of the room. They are more ordered than if they were all over the room, just as picking up the scattered trash in a public park and bringing it to one corner is an act that increases the order in the park. Recall the water and the iron. At the beginning, one part of the system, the iron, contained al l the violently moving particles. This is an ordered state; it is as though someone has taken kinetic energy from on e part of the system (the water) and pushe d i t into the other par t (th e iron). The kinetic energy, like the pape r i n on e corner o f the park , is ordered . When th e temperatur e i s th e same everywher e and th e averag e kinetic energ y of all th e molecule s throughou t the syste m is equal, the system is less ordered than it was; the paper is all over the park. Notice that in all the preceding examples the ordere d state is les s likely (unless you have an orderly girlfriend). In general, order is less probable than disorder. But you knew that. The terms order and disorder are qualitative, but i t is possible to give a number to the disorder in a system. We can say not only that the disorder in a system has increased; we ca n sa y by how much . Th e clu e lie s i n th e probabilitie s tha t w e attached t o differen t state s o f a spreading ga s and t o a system o f mixing gases. Both systems went from orde r to disorder, and on the way we were able to give clear estimates o f the probabilitie s o f the intermediat e state s through whic h they passed. This can be done for any physical syste m in theory, and for very many in practice. In general we do not use probabilities bu t a very closely related quantity: entropy . In thinking o f entropy, think of order and disorder : The statement that the entropy of the universe is continually increasing is equivalent to th e statement that the disorder in the universe is increasing. 4

That profound Austrian thinker Ludwig Boltzmann (1844-1906) thought that he had derived the second law from the kind of probabilistic arguments we have been using, but there is a flaw in his reasoning.

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The T-shirt s an d th e sweater s ar e mixin g mor e thoroughly ; th e pape r i s bein g blown all over the park. Why use entropy when we can use probabilities? Because for all but simple systems i t is impossibl e i n practic e to measure th e probabilitie s tha t w e need, but i t has been shown that we can measure a quantity that is closely related to these probabilities. Tha t quantit y i s entropy , an d t o measure changes i n entrop y it i s quit e often sufficien t t o measure the amount of heat entering or leaving a system, and th e temperature at which this process takes place. We will not go along this path. The central point to be grasped at this stag e is that in naturally occurring spontaneous processes (fo r example, the spontaneou s mixin g o f two gases ) we ca n make three equivalent statements: • Th e univers e ha s change d t o a stat e tha t i s more probable tha n tha t whic h preceded it. • Th e disorder in the universe increases. • Th e entropy o f the universe increases. In all our examples we can say that the entrop y of an isolated syste m increased. It stopped increasin g onl y when th e system s reache d equilibrium. Ther e wer e no states mor e probabl e than th e equilibriu m state , and s o that i s the stat e o f maximum entropy , for isolated systems. If you prefer, you can say that in an isolated system the equilibrium stat e is the state of maximum probability. Clausius Coins a Bon Mo t To summarize some simple facts that Newton never knew: 1. Isolate d systems spontaneously mov e toward states of higher entrop y (probability) and stop changing when they reach an equilibrium state, which is characterized by maximum entrop y (maximum probability). 2. Thi s spontaneou s process , for isolated states , is irreversible. The syste m never stops i n an y stat e tha t i s no t th e mos t probabl e state , that is , th e equilibriu m state. 3. Becaus e the universe i s an isolated system , the preceding conclusions appl y to it. The total entrop y of the universe i s increasing continuously , thus hastenin g not the day of judgment but the night of silence. Clausius, wh o ha d invente d th e ter m entrop y i n 1865 , summarize d th e hear t of thermodynamics in the famous sentence: The energy of the universe is a constant: the entropy of the universe always tends to a maximum.

The Autonomy of the Second Law No one has yet succeeded in deriving the second law from an y other law of nature. It stands on its own feet . It is the only law in our everyday world that gives a direction to time, which tell s u s tha t th e univers e i s moving toward equilibriu m an d which give s us a criteria fo r that state , namely, the poin t o f maximum entropy , of maximum probability . The second la w involves n o new forces . O n the contrary, it says nothing specifi c about forces whatsoever. It migh t see m possibl e t o explai n th e unidirectiona l progres s o f spontaneou s

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processes by supposing that there is a mechanism that drives systems from states of low probabilit y (say , all te n molecule s o n on e sid e o f the box ) to state s of higher probability (nine on one side, one on the other). No one has found a logical basis for such a supposition. Our molecules-in-a-bo x mode l suggest s tha t th e secon d la w i s a la w o f large numbers. Take a box with only four molecules in it. "Equilibrium," the most probable state , occurs whe n ther e are tw o molecule s o n eac h side . Th e probabilit y of finding this state is 3 in 8. This is not very much greater than the chance of finding three on the left-hand sid e and one on the right—namely, two in eight. If a given observation showed the box to be "at equilibrium," then I would be prepared to bet on finding the system well away from equilibriu m (thre e times as many molecules on one sid e a s the other ) at the nex t observation . Thi s would contradic t th e second law, which say s that whe n yo u get to equilibrium in an isolated system , you stay there. In fact, if someone gave me good odds, say 200 to 1,1 wouldn't mind putting money on finding all four molecules on the left-han d side ; the probabilit y of finding that state is 1 in 16. 5 Thus for small numbers of molecules, we can say that the second la w holds very weakly. Systems don't mov e inexorably to maximum entropy (probability ) and sta y there. I n fact , eve n i n system s containing enormous numbers o f molecules we don' t expec t the syste m to remain exactly at equilibrium.—because of fluctuations . For hug e number s of molecules thes e fluctuations are, percentage-wise , very smal l compare d wit h thos e i n system s wit h ver y few molecules. The second law predicts that the available energy of the universe, that which i s available for work, is being continually degraded int o heat, becoming unavailable for work. This can also be seen as a move from order to disorder. Thus the atoms of the fallin g boulder ar e all moving downwar d togethe r in th e sam e direction , despite thei r rando m vibrations . Lik e the dancer s in th e Ri o carnival, the y wobble and twirl within the boulder, but their collective movement is forward and can easily be converted into mechanical work. When the boulder hits the ground, the column o f dancers disperses . Each atom and dance r goe s he r ow n way , the Kin g of Disorder rules. The boulder and the ground are static, the atoms in the ground vibrate more vigorously, the heat oozes away, the atomic and molecular motions are completely random, not directed along one line. And even if the boulder hits a turbine blade and thereby does some useful work, the blade and the boulder still steal some of the kineti c energy of the boulder an d warm up. Useles s heat. The second law is a lav; of irreversibly lost potency. Ashes to ashes, available energy to heat. As the blue s ma n says , "Ther e ar e thirteen goin ' t o th e fun'ral , ' n onl y twelve men coniin' back." The reason we can't us e the kineti c (heat ) energy of the wate r molecules o f the ocean to get work (the opposite of Joule's experiment) is that to run a machine (a car or a stea m engine) heat ha s t o flo w fro m a higher t o a lowe r temperature . If you have a bathful o f water at the temperature of the room, you can't get the heat to flow out of the bath. There have been plans to use th e temperature difference betwee n equatorial and polar seas, but not practical plans. What does all this mean for the universe? 5 If you want a really good bet, try putting a few dollars on the chance of finding three molecules out of four o n either the left-hand or the right-hand side. The combined probabilit y is one half.

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The Big Bang

The second law implies that the universe, throughout its history, has been continually driftin g towar d equilibrium , a s doe s an y isolate d syste m i n whic h change s occur. This drift does not preclude local islands of decreasing entropy (increasin g probability), bu t the overal l entrop y increase s inexorably. I t follows that the uni verse starte d i n a state o f comparatively low entropy—i t was highl y improbable . We will retur n to this topic, but on e point is worth makin g here, especiall y sinc e the molecules-in-a-box model has been so prominent. Don't b e tempte d t o pictur e the univers e a s a huge box, ful l o f molecules, for which th e state of highest entropy , the equilibriu m stat e to which w e are journeying, is that in which al l the molecules are spread out over the box, like perfume i n a room. The molecules in our box were presumed to have no force s between them , and in fact these forces are so weak for most gases that we can ignore them for many purposes. How do we know, qualitatively, how t o take the presenc e o f forces int o account when asking what equilibrium stat e we expect? It is not a bad principle to trust the world when it comes to asking in which directio n entropy leads us. To appreciate that forces can make a difference to the equilibrium stat e of an isolated collection o f molecules, yo u just have to conside r a thermos flas k partl y filled wit h water. Th e molecule s ar e certainl y no t sprea d ou t evenl y throughou t th e bottle; most o f them ar e in the liqui d water , and som e are in th e spac e above the liquid . (This would be true even if there were no air in the bottle.) It is the comparatively strong force s betwee n wate r molecules, as compared t o the molecule s i n air , that pull them together. The system is certainly at equilibrium—it will not change if left alone. It s state of equilibrium is very different fro m that of air in a box, although if you cool the air enough you will find that the equilibrium state at low temperatures will als o consist o f a mixture o f liquid an d gaseou s air, the mixtur e yo u ge t in a commercial container o f liquid air . What happens a t low temperatur e i s that th e molecules ar e moving so slowly tha t th e wea k force s o f attraction betwee n the m succeed in holding most of them together as a liquid, against their tendency to rush off int o the space above the liquid. All this is relevant to the fat e of the universe. The force that we forgot is gravity, which must be taken into account when considering a system containing as much mass as the universe. The upshot i s that the equilibriu m stat e of the universe wil l not be a state in which matte r is evenly distributed . Rather , it is more likely to be typified b y the gravitationall y induced clumpin g togethe r o f all the matte r i n th e universe int o on e horrifying black hole. S o the fat e o f our universe ma y be to en d up as a clump of matter at equilibrium, i n which no further chang e takes place. Depressing, but notice that we slipped i n the phrase "loca l islands of decreasing entropy" a couple of paragraphs back. Where and what are they? Life versus the Second Law

The most spectacula r exceptio n (bu t only apparent!) to the secon d la w is a living organism. There are two puzzles: the origin of life and the maintenance o f life. Both appear to be wildly improbable . Is this a sign that the supernatural is at work? I am not being flippant; there are those who would answer yes. When a living organism dies it decomposes, which jus t means tha t the extraor-

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dinarily comple x molecules of which it is made break down into far simpler components. Ther e ar e few systems mor e ordere d than th e living cell an d it s components. Just ask yourself what the probability is of finding all those atoms linked u p to giv e the highl y comple x molecules o f the cell , an d th e probabilit y o f findin g those molecules arrange d in the wa y that the y are . The process of decompositio n goes th e wa y tha t th e secon d la w predicts : th e complex , highl y ordere d syste m breaks u p int o a highl y disordere d mess . Th e structur e o f the cel l collapse s (becomes disordered), and the molecules tha t i t contains disintegrate , destroying the miraculous orde r and leaving the fragment s t o wander abou t in a disordered man ner. Som e o f the smal l molecule s ar e incorporate d int o low-entrop y large molecules i n the bacteria tha t caus e mos t decomposition , but th e overal l result is still that the entrop y (alias disorder, alias probability ) of the univers e increases . That' s what the second law predicts for any real process. And if they are left without food , the bacteria will also die, and their molecules will be degraded by the atmosphere. Living matter would much rather be dead. Living matter is a curiosity. So, the (entropic ) question tha t has to be answered wit h respect to the origi n of life, is : Is it possible to defy the second law and spontaneously create an ordered, low-entropy, low-probability system out of a disordered, high-entropy, high-probability system, that is, the primeval oceans, which contained no large molecules or highly ordered structures?

The second question arises from the stability of most organisms. They show no tendency to change, at least over time periods short compared with their lifetime . We could say that they show all the signs of equilibrium. And yet, as we just remarked, they are not really at equilibrium; equilibrium fo r an organism is attained when it dies an d spontaneousl y disintegrate s int o a final, genuinel y unchanging, high-entropy, unordered state. A living organism is apparently not in its state of highest entropy and yet it manages not to move in that direction, at least in the short run. So we have a second question : How do living organisms avoid spontaneously increasing in entropy until they reach their state of maximum entropy? In other words, how can life maintain itself in a state of low entropy? How does an improbable state avoid becoming more probable?

First o f all, let i t be clea r that , contrar y to th e claim s o f the creationists , ther e i s nothing i n the law s o f thermodynamics that prevents the spontaneou s creatio n of organized (entropy-poor , low-probability ) system s o n th e primeva l Earth . Th e statement that entropy has to increase in a spontaneous proces s applies onl y to an isolated system . The Earth is an open system, since both matter and energ y can arrive and leav e the Earth. Huge amounts o f energy stream toward us fro m th e Sim, and w e radiate comparable amounts o f IR light back into space. The arrival of matter is in amounts too small to be of any great significance, but the exchange of energy with th e rest o f the universe mean s that the Earth, and it s flora an d fauna , i s at the very least what i s called a closed system, one that can exchange energy but not matter with its surroundings . There i s n o theoretica l reaso n wh y entropy-poor , ordered , system s canno t b e formed in an open or closed system, and we will subsequently illustrate this claim. Unfortunately, pseudoscientific babble fro m a variety of sources has suggested that science i s o n th e sid e o f the creationists , sinc e th e secon d la w supposedl y pre -

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eludes the spontaneous formation of organized systems. Ergo, life required a supernatural hand . The creationists have also carelessly dragged the second law into the question of evolution. Evolution has, on the average , led to increasingly complex living forms . The complexity of the higher apes, let alone man, far outdoes that of the unicellula r organisms that were presumably the first, or near-first, life-forms. This can be interpreted in terms of a spontaneous evolutionar y decreas e in probability. (Remember that complex , highly organize d systems ar e Ves s probabl e tha n simple , compara tively les s organize d systems.) The creationists , thos e who den y evolution , hav e jumped o n this a s proof tha t evolutio n coul d no t hav e happene d sinc e i t woul d have required a spontaneous decreas e in entropy (probability). The flaw in the creationist argument is again simple: the Earth is not an isolated system ; a closed system can spontaneously produce islands of order, that is, low entropy. Science doe s not disprove the creationist thesis , but it does not support i t either. It just makes it look infantile. Regarding the Creation, I feel that i t is necessary to give at least on e example of the spontaneous decreas e in entropy (that is, the creatio n of order) in a comparatively disordered system . The Spontaneous Creation of Order

We have seen that natural processes spontaneously move from more ordered to less ordered, whic h appear s t o rul e ou t th e spontaneou s creatio n o f ordered system s and forc e u s back to magic if we want to create life. Ther e is, however, a way out , and it is suggested by simple experiments tha t can be performed with simple materials by a layman. What is common t o these experiment s an d makes them s o relevant to the nature of living matter, is that (1 ) they start with a disordered mixture of molecules and self-organize, (2 ) the ordered state survives only as long as either energy or material is continuously fed into them, and (3 ) the systems are not isolated . Dynamic Equilibrium

Mechanical equilibriu m i s ofte n observe d an d readil y comprehended . A child' s swing a t rest an d a motionless tabl e ar e at mechanical equilibrium , b y which we mean tha t if we d o not exer t forces o n these bodies the y will maintai n thei r posi tion. But the equilibrium of these bodies is of a special kind. It is a stable equilibrium; a smal l disturbanc e wil l caus e a smal l chang e i n th e stat e o f each system , which move s to a new equilibrium state. Thus if I push gently on the swing, it will move to a new position , ou t o f the vertical, where it will remain a s long as I maintain my pressure. Furthermore, if the smal l disturbin g forces ar e removed, the systems retur n t o thei r origina l positions . Thi s i s obviousl y no t tru e o f all systems . Thus a stationary billiard bal l resting on a table will not return to its original position if it is temporarily subjected to a force—it is in a metastable state. Now consider an adult human being. In the healthy state , the organs of the body function fro m da y t o day , fro m yea r t o year , withou t an y significan t chang e i n shape, size, or function. I f the body begins to overeat, its size and th e siz e of its organs can be affected, but the system is in stable equilibrium i n the sense that smal l disturbances, which could mean one too many hamburgers, bring it to a new equilibrium position, specifically, a state in which the total mass of the body is greater.

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Now there is something different abou t the stabl e equilibriu m o f living organisms and th e stabl e equilibrium o f chairs. Th e equilibrium o f the chai r i s a state it ca n maintain without any help from its environment. To maintain their state of equilibrium, living organisms need a n input of material an d energy , without whic h the y drift rapidly awa y from thei r equilibrium towar d another, highly disordered, equilibrium state—a state of decomposition preceded by death. The maintenanc e o f lif e i s a n exampl e o f a dynamic equilibrium, th e syste m being maintained i n a n equilibrium stat e removed from it s "real " equilibrium , by the input of energy. If you are not convinced that this can happen, I ask you to consider a very simple physical system in a similar state. Picture a horizontal tub e containin g heliu m gas . The tube i s divide d int o two equal halves by a partition that contains holes a little larger than the atoms of helium. The partition is there to stop bulk movement of gas from on e side of the tube to the other; it's like having two rooms connected by a very narrow door. At equilibrium, as we well know, there will be the same number of molecules on either side of the tube, a state we ca n refer t o as "normal." Now , wrap one side o f the tub e i n a heating coil through which you pass a steady current so that the temperature of that side is higher than that in the other. Maintain this temperature difference a t a constant value. You will find that a new equilibrium will be established in which there are more molecules o n the cold side of the tube than on the hot side. Provided you maintain th e temperatur e difference , th e numbe r differenc e wil l remai n un changed. The point i s that you have managed to keep a system in an "unnatural " state, and the way you are doing it is by putting energy through the system: heat energy flows int o the ho t en d o f the tube , from a source of heat, and flow s ou t a t th e other end. The moment you stop this flow, the system starts to revert to its original equilibrium state—it "dies." In terms of the probabilistic models that we have been playing around with, the state of dynamic equilibrium, with its unsymmetrical distribution of molecules, is more ordered and less probable than the normal state—it has a lower entropy. We agreed that in nature systems tend to move in the directio n that increase s th e entrop y o f the universe , an d her e w e hav e a syste m tha t ha s moved from a more probable state (befor e heating ) to a less probable state (during heating), but there is no paradox. The second law says that the entropy of the universe increases i n all natural processes, and although the entropy in the tube may have decreased, it can be shown that the entropy of the tube plus its surroundings, increases becaus e heat i s spontaneousl y flowin g fro m th e ho t heatin g coi l to th e cooler air. The dynamic equilibrium i s maintained by a flow o f energy through the system. Such a system is too simple to provide a convincing model for life, but i t shows that molecular ordering, and a lowering of the entropy of the system, can be created from disorder by nonsupernatural means. There is no need for a life force . Dissipation Life i s a curiosity . I t built itsel f ou t o f a high-entrop y (disordered ) world an d i t maintains it s low entropy (order), against the overall tendency of the universe to go to eve r higher tota l entropy . Life's mott o is "Ordnun g muss sein! " Except fo r the living world and some of the artifices that it constructs, the universe appears to be universally disorderin g itself . Livin g organism s are island s tha t swallo w matte r and energy from thei r surroundings an d use them to keep themselves i n a state of

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ordered dynamic equilibrium, a state that collapse s and becomes disordered when they die . Structure s that us e th e resource s o f their environmen t i n thi s wa y have been called dissipative structures by the Belgian Nobel Prize winner Ily a Prigogine (1917-), a theoretician wh o has been largely responsible for initiating th e stud y of such structures. So even the holiest of us, the nondrinking, nonwenching saint , is a dissipative structure. And so is Earth, which receives a continuous input o f energy from th e Sun . This energ y comes from on e direction onl y (at . any one time) but radiates i n all directions. We are in approximate dynami c equilibrium, th e temperature remaining stable within fairl y narrow limits. If the energ y source were cut off , it would result in a drop i n temperature of at least a couple of hundred degree s as we rushed toward a new equilibrium . There is, as your priest wil l tel l you, a price to pay fo r dissipation. Th e heate d tube o f gas describe d earlie r illustrates a basic fac t abou t dissipativ e structures . They ma y hold thei r ow n entrop y constant , bu t the y increase th e entrop y o f the surroundings. In the end we can't win; the total entropy of the universe increases . By the generality of its implications, and their doomsday aura, the second law of thermodynamics, or at least the vague statement tha t entropy condemns the uni verse to death, has attracted the attention o f nonscientists, man y of whom were, or are, otherwise completel y uninterested i n science. Oswald Spengler (1880-1936), another of the prolific Continental school of obscurantists, wrote in his best-selling Decline of the West (1918) , apropos the secon d law, "Something Goetheia n has en tered into physics—and if we are to understand th e deeper significance of Goethe's passionate polemic agains t Newton in the Farbenlehre w e shall realiz e the ful l weight of what this means. For therein intuitive vision was arguing against reason, life against death, creative image against normative law." Which is about the level of stuff that the second law has inspired among those who don't understand it . Henry Adams expressed a more human an d understandable sentimen t whe n he wrote to William James: "The universe has been terribly narrowed by thermodynamics." The prediction that the universe will edge inexorably closer to dead equilibriu m speaks of a time possibly billions o f years in the future , ye t we sometimes fee l as if we hav e t o cance l nex t month' s ticket s t o th e Met . There i s somethin g repellen t about that final silent sea , a sea alive only in the sense that the kinetic energy of its component particles will neve r cease. There are a variety of scenarios tha t offe r a way out. The though t o f the Suprem e Architec t gallopin g ove r th e hil l t o rewin d th e spring of the great clock is comforting, but you wouldn't ge t very good odds on it at the loca l betting shop. S o perhaps w e should tr y those cosmological theories tha t see the universe eventually collapsing to the size of a golf ball, only to reappear like a phoenix, born again to repeat its history in a series o f endless cycles . This is the Big Crunch, followe d b y anothe r Bi g Bang—and wh o say s that ou r Bi g Bang was the first ? Unfortunately, cosmology offers n o clear way out of the grip of the secon d law. The problem with thermodynamics is its generality—the first and second laws don't as k anythin g whatsoeve r abou t the detaile d natur e o f a system. 6 If the uni verse is an isolated system, which i t clearly is, then the second law leaves us with 6 There is a third law. The second law allows us to calculate only differences i n the entropy of a system when something happens to it. The third law allows an absolute estimation of the entrop y of a system.

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no alternative : we ar e heading fo r equilibrium howeve r man y cycle s of bang an d crunch we go through. Some scientists have suggested another loophole. What if the law s of thermodynamics are valid onl y in certain parts of the universe? There is as yet no evidenc e for this hypothesis, which echoes one explanation o f suffering—that Go d is in control of only part of the universe—and it isn't our part. Another lifeline is the fluctuatio n theory. As we saw, even at equilibrium ther e are fluctuation s that tak e the syste m awa y from equilibrium , whic h i s where w e want to be taken, O Lord. Even in a universe that on. the average was at equilibrium, there could conceivably be one or more places where there were significant deviations fro m equilibrium , i n othe r words, where thing s ca n happen ! O r is that just wishful thinking ? Entropy for Beginners

The reader should be on guard against books in which entrop y appears without a definition, o r with a faulty definition , and i n which i t is used i n relation to undefined system s to give heartwarming results. I won't take up spac e unpicking thes e balls o f wool, o f which perhap s th e outstandin g exampl e i s Jerem y Rifkin's Entropy: A New World View (1980), in which ca n be found th e fourt h law(!) o f thermodynamics: "I n a close d system , the materia l entrop y mus t ultimatel y reac h a maximum." The term material entropy is meaningless; it has not the slightest connection wit h entropy , or indeed science . Th e "law" i s the brainchild o f an economist, Nicholas Georgescu-Roegen. It is a child that should have been left o n a bleak Thracian mountainside, a fate that shoul d als o have befallen the essays written i n the lat e nineteenth centur y by the American historian Henry Adams in which h e maintained that history should be "scientifically" based on the laws that governed energy an d entropy . The objectio n to suc h text s i s not tha t the y challeng e established science . We are all for that, I hope. The problem is that they use very welldefined concepts in situations to which they do not apply, and in a way that reveals that the authors have misunderstood th e meaning of both entrop y and the secon d law. Entropy is one of the buzzwords in the realm of pseudoscience, being blamed for crime s tha t i t neve r committed an d praise d fo r deeds it never did . On e of the problems with peopl e who writ e books like Rifkin' s i s that i f you questio n thei r concepts, they tur n their bac k on you, face th e audience , an d proclai m that onc e again the blindnes s of conventional scienc e is revealed. They are sometimes right, but neve r whe n thei r "innovations " ar e based o n the gros s distortion o f well-defined concepts. What Use Is Entropy?

Because we are concerned more with ideas than with their application, we will not discuss the practica l use of the secon d law. A law that deal s in the entrop y of the universe might seem somewhat remove d from th e marketplace. It isn't. Chemists, chemical engineers , mechanica l engineers , an d biologist s ar e amon g the peopl e who us e th e la w a t thei r place s o f work. I t ca n hel p u s t o decide , fo r example, whether o r not a certain potentia l manufacturin g process fo r a chemical wil l b e economically feasible.

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We see m t o b e makin g excellen t progress . W e have Newto n an d Maxwel l t o cover the mechanical and electromagnetic aspects of matter, and the second la w to help us deal with huge assemblies o f molecules. Are we at last in a position, except for some niggling problems with light, to explain an d predict, the course of nature? No, often we are not. In the following chapter we are going to be humiliated .

19 Chaos I tell you: one must have chaos in one, to give birth to a dancing star. —•Nietzsche, Thus Spake Zamthustra

Is prediction possible ? When the astrologer confidently tells you that you will meet a tall dark man this year, she is merely exploiting the fact that about 5% of the population fall int o that category , and if you leave the house there is almost no chanc e that you will not meet a tall dark man within a year. But what abou t prediction i n the inanimate world, or the world of nonhuman life-forms where cold physical law operates? Newton and Maxwell gave an unambiguous answer: given the initial condition s of an inanimate system, and assuming that the laws apply to them, the future o f the system can be mapped out exactly. And, if need be, as in the example s of the preceding chapter, we can call on the second law to help us out. In classical physics the present determines the future. I t is said of classical physics that it is deterministic. So that there is agreement about what we mean when we say that a theory is deterministic, we will defin e ou r terms. A theory may be sai d t o be deterministi c if , using only the theory and a complete description of the state of a system, every subsequent state of the system is logically inevitable. Newton's equations are certainly deterministic in this sense. A body acted on by forces has no choice at all about its behavior; if Newton's laws hold, its future is absolutely certain. Another way of expressing the creed of extreme determinism i s to say: For every event there must be a cause, and so , given the condition s precedin g the event , and th e law s o f nature, every event must i n principle b e predictable and i n practice be inevitable. T o be a little mor e pedantic, which never hurts i n this kind o f argument, I should replac e "cause" by a "set o f causes," the complete collection o f circumstances whic h guarantee tha t a n even t wil l occur . Thu s th e predicte d pat h o f an artiller y shel l de pends, amon g othe r things , o n atmospheri c conditions , the position s o f al l th e heavenly bodies, and s o on. And o n the fac t tha t ther e is not a faulty detonato r in the shell. We can see planets and missiles, but are we so sure that the microscopic world is a deterministic system ? It certainly i s if we agree that the sam e laws of motion that Newton declare d t o hol d fo r the sola r syste m als o hold fo r molecules. Whe n w e wrote F = ma, we didn't pu t upper o r lower limits on the size of m, the mass of the body. Newton's laws, i/they hold fo r molecular motion, tell us that the movement of a molecule after a collision, either with another ga s molecule or with the wall of the container, is completely determine d by the laws of motion. In Newton's world the future stat e of all particles in the cosmos, great or small, is determined only by their present condition s an d those laws . We should b e able to

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predict exactly the future o f any physical system—given complete knowledge of its present. The Inexorable Gears The grea t eighteenth-centur y mathematicia n Laplac e dreame d u p a n ambitiou s project. Since , sai d he , Newton' s law s completel y determine d th e motio n o f all bodies, if we could at any given moment measure the position and velocity of every particle in the universe, we could use the laws of motion to determine their futur e movement completely . Thus th e futur e o f the univers e i s i n principl e calculabl e from it s presen t state , just as the futur e positio n o f the plane t Mar s is completely predictable given its position and velocity at any given moment. More than this, we can use the laws, together with the present state of the universe, to calculate where everything was, and ho w fas t i t wa s moving , at an y tim e i n th e past . And , say s Laplace, there i s n o roo m for uncertainty, eithe r i n th e pas t o r i n th e future ; th e birth, life, and death of every physical object, including humans, can be unambiguously plotted. The future i s completely predetermined.1 Laplace had taken Newton's science and turned it into philosophy. The universe was a piece o f machinery, it s histor y wa s predetermined , ther e wa s n o roo m for chance or for will. The cosmos was indeed a n ice-cold clock. Maxwell leaves this conclusion unchanged . H e merel y adde d additiona l deterministi c law s t o th e game. All we have to do is include the human brain in this strait-jacket and we have a depressing bottom line: the whole history of the cosmos, including human history, was fixed a t the moment of Creation. There could have been only one possible history for the cosmos—the history that happened—and there is only one future history, which, if I had enoug h information and a big enough computer, I would be able to calculate. Everything is predictable. To which Newton would cry: "Wait, I didn't mean that at all!" What we intend to show here is that even in the deterministic Newtonian world, prediction can be impossible. Determinism or Fre e Will? The determinis m tha t th e Principia engendere d wa s a t th e cor e o f the threa d o f ironclad certainty that ran through science until the nineteenth century . It supported the Deism of the Enlightenment and created a breed of materialistic determinist s such as d'Holbach and La Mettrie. Although determinism was not invented i n th e seventeenth century , fro m Newton' s time unti l th e en d o f the nineteent h centur y few scientists doubted that the inanimate world was deterministic. But what about man? In its extreme form, the doctrine of determinism includes man. If man is a part of nature, is he not also bound by its unbreakable laws? If so, this has the profoundest implications for man's self-image and his attitude toward religion. Are we destine d a

lf we could predict the future, would it be avoidable? This is the oft-considered parado x of the time traveler who jumps into the future an d sees his own life story. If I perform a Laplacian calculation that shows that I am going to drink a Heineken tonight, can I perversely choose to drink a Budweiser instead?

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to do what we must do ? Is my every thought fixe d b y the movemen t of molecules and charges in my brain, movements and charges that, in turn, are completely predestined by the previous physical history of my body? Is there no free will? Are we just immensely sophisticated automata ? So though t th e Englis h philosophe r Thoma s Hobbe s (1588-1679 ) wh o pub lished his treatise s De corpore an d De homine (O n Matter and O n Men), in 1655 5 and 1658. Newton was still at school, but Galileo's mechanics had reached Hobbes, and h e fel l fo r the sam e deductive reasoning that h e had foun d i n Euclid, Deeply influenced by mathematics and mechanics, Hobbes stated that philosophy shoul d only be concerned with the action of contiguous moving bodies on each other and that th e result s o f suc h actio n wer e t o b e obtaine d fro m th e law s o f dynamics . Hobbes realized that the mentally directed actions o f humans were different i n nature fro m th e movemen t o f inanimate bodies , but h e deeme d the m no t differen t enough to take them outside the realm of mechanics. Hobbes provoked fierce criticism, and twice in his lif e he chose discretion rather than valor and slipped across the Channel to live in France. It is good to know that he was clear-minded and active to the end , dying at the age of ninety-one. Paradoxically, his agnostic negation of free will was backed by religion. Religion and Science Agree Any system of belief, like Christianity, that include s a n all-knowing deity can ru n up agains t the followin g dilemma: if God knows and ca n forese e everything, then he know s exactl y what i s t o com e an d h e canno t b e mistaken . "Qu e ser a sera. " Boethius, the sixth-century thinker, explains: "If God beholdeth all things and cannot be deceived, then what H e forseeth must inevitably happen. Wherefore if from Eternity He doth foreknow not onl y the deed s o f men but als o their counsel s an d their will, there can be no free will." As Karl Popper comments, an omniscient God would be impotent, since his actions would be completely determined by his prior knowledge of them. The religious problem of free will was intensified by Galileo's and Newton's deterministic physics , althoug h Newto n himself make s i t clea r that h e leave s room for Go d to modif y th e operatio n o f his cosmos , thus breakin g the iro n chain. Bu t did he consider the paradox of the all-knowing God? Man I s Not an Exception Unlike Hobbes, many who were prepared to accept determinis m i n the nonlivin g world made an exception of man, but sinc e it has now been demonstrated beyond any reasonable doubt that living material, including th e human brain, is constructed from molecules that obey the same laws as any other molecules, there seems reason to suppose that the behavior of human beings can be explained o n the basis of deterministic, chemica l an d physical processes . Ma x Macho might thin k tha t h e chose to chat with tha t attractiv e barmaid, but he ha d no choice; it was predetermined. It was in their stars. At least that's what he's trying to tell her. It looks as if our personal live s hav e alread y been punche d ou t o n the pianol a scroll. Like the intricate clockwork dolls that amused the baroque courts of Europe, the only tune we can play is the tune that we will play; there is no free will. This chilling conclusio n in fact preceded modern biochemistry and biophysics; as we saw, several Enlightenment thinker s viewed man a s a machine. Diderot ex-

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pressed the consequence in general terms: "Look closely and you will see that the word liberty is a word devoid of meaning; that we are no more than fit s in with the general orde r o f things, th e produc t o f ou r organization , our educatio n an d th e chain of events." Voltaire, as usual, speaks with more bite than most: It would be very singular that all nature and all the stars should obey eternal laws, and that there shoul d be one animal fiv e fee t tal l which, despit e these laws, could always act as suited his caprice . It would ac t by chance, and we know tha t chanc e i s nothing . W e have invente d thi s wor d t o expres s th e known effect o f any unknown cause. Note the Newtonian assumptions (an d the average height for a man). The scientifi c backing for determinism sharpened the philosophical debate on ethics and particularly on punishment, a debate that continues to this day. Diderot, like Hume, concluded that the concepts of vice and virtue were meaningless; there was no point in apportioning praise or blame for any action, since all actions were inevitable. Criminals shoul d no t be punished bu t shoul d b e eliminated , preferabl y o n the publi c square. In this century Bertrand Russell expressed related sentiments : "If, when a man writes a poem or commits a murder, the bodily movements involved in his act result solely from physica l causes, it would see m absurd to put up a statue to him in one case and to hang him in the other." A deterministic univers e in which all effects come inexorably from previous physical causes has no room for morality; it is a universe with facts but not values. Is ther e a n escap e fro m thi s claustrophobic , flypape r world , o r ar e w e reall y trapped by unbreakable chains of cause and (completely predictable) effect? I don't want to believe that my actions are controlled by a rigid chain o f cause and effec t going back to the Big Bang; but d o I have a choice? And if I don't believe, is my disbelief inevitable ? This conclusio n ha s been strongl y rejected b y most thinkers. A common attitude is to accept the determinis m o f the natural worl d but t o exclude man fro m th e dictate s o f physics. Thi s liberate s history , whic h become s unpre dictable. There could hav e been a multitude o f histories. Thi s conclusio n ma y be an illusory victory of wishful thinking. The Impossibility of Prediction

The idea that, in principle, the futur e o f the universe is completely determined by its present state is usually associated with Laplace, but in fact it had been previously put forward by the Croatian scientist Rudje r Boskovic in 1758 and had als o been hinted at by Newton in the Principia. Boskovic, however, was the only one to qualify hi s statement , admitting that "we do not know the number, or the position and motion of each of these points." Boskovic's comment kills the project . I t is clear that no one will eve r be able to do Laplace's calculations. Go back to Chapter \ an d you will see that if we want to "do a Laplace" on a spoonful o f air we will need to know, at a given moment, the position and velocity of something like 10 20 molecules. One minor difficulty arise s here: How can anyone possibly obtain this information? Furthermore, we saw that, on th e average , molecule s i n th e ai r bum p int o eac h othe r an d chang e velocity about 6000 million times per second. This means that we would hav e to complete

Chaos | our 10 20 measurements in one 6000 millionth o f a second to have any hope of measuring the position and velocity of most of the molecules before they were changed by collision. T o be honest, the problem is worse than I have presented it . Even for a simple gas like helium, i n which eac h molecule is a single atom, we need, for each atom, three numbers to specify its position and another three to specify its velocity, because velocity includes a specification of direction. For a calculation o n a sample o f helium containin g 100 0 atoms we need 600 0 pieces o f data. At the presen t time, the task of measurement alone is well outside the capabilities o f mortal rnan. But supposing i t were not . Ho w are we going to d o a calculation tha t involve s registering and then manipulating dat a on 10 20 molecules? At present, no way. To complete ou r calculations befor e th e futur e caugh t up wit h us, we would nee d to repeat th e calculatio n abou t 600 0 million time s pe r secon d t o keep u p wit h th e changes induced by collisions. No t even Aristo the Human Calculator , whom a s a child I saw in a fair, could cope with that.2 But th e proble m o f prediction i s i n fac t fa r deepe r tha n Laplac e or Boskovi c knew. To begin to see why, let us lower our sights and tackle what appears to be a far simple r problem . The succes s o f the Newtonian-Galilea n laws o f motion lay in their abilit y to explain and predict with great accuracy the movement of some mechanical systems. If we take the classic Newtonian system, the Earth and the Moon, we can solve the equations of motion exactly, using the law of universal gravitation to tel l us what forc e t o take. Any two bodies can be treated in the sam e way. Thus one body coul d b e the Eart h and th e othe r a cannonball. The expression s fo r the paths an d velocitie s o f the bodie s involve d ca n be expresse d i n analytica l form , which means as simple mathematical expressions. Thus if I throw a body vertically into the air with a velocity of VQ meters per second, then its velocity, v( , after t seconds is given by the simpl e expression : v ( = vo-gt meters per second . And i f necessary I can take air resistance int o account. Now let us do one experiment too many. Take three bodies, say Mars and its two moons, Phobo s an d Deimos . Can we work out th e path s o f these bodies? Yes and no. We can predict th e paths o f the moons quite well, but not exactly. The strange truth is that we cannot solv e the equations . We can solve them approximately, b y first assumin g tha t th e plane t i s a stationar y objec t aroun d whic h th e moon s re volve independently, no t interacting throug h their mutual gravitational attraction. Any attempt to treat the problem in its entirety has in the end to resort to a computer to produc e approximat e paths . N o analytical expressio n ca n be found . Thi s i s not a weakness in our mathematical techniques . No w that we have started sowin g doubt, let's keep up the good work. Let's take the mos t famou s exampl e of Newton's success an d niggl e away at it. The pat h o f the Moo n is describe d b y a simple (analytical ) mathematical expres sion, which appear s to work beautifully and ha s been working for more than 300 years. Or has it? The model used to calculate the Moon's motion, involves two bodies: the Earth and the Moon. The laws are the laws of motion and the law of universal gravity, But we have neglected the fact that the Moon is attracted by the Sun. We feel justified i n this because the calculated and observe d paths o f the Moon are ef2

I have simplified the problem by assuming that all molecules collide simultaneously at intervals given by the average time between collisions. By definition of an average, a substantial number of molecules will collide within a shorter interval.

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fectively identical , bu t i n principl e w e shoul d tak e into accoun t the influenc e of the Sun and work out a new more correct equation for the Moon's path. We should be treating the problem as that of the motion of (at least) three interacting bodies. In 1889 , Henr i Poincar e startle d th e worl d o f the mathematica l physicist s b y showing that in principle ther e i s n o analytica l solutio n t o the three-bod y problem.3 The best we can do is to obtain approximat e answers. Fo r a problem involving three, or more, interacting moving bodies, there is no closed solution , n o simple mathematical expression. We are lucky that in many cases a problem that really involves the interaction of three or more bodies can be simplified by taking physical facts int o consideration. Thus the path of a baseball is influenced by the Earth, the Moon , the Sun , the planets , an d s o on. But the influenc e of the Eart h so outweighs that of the other bodies that we can ignore them for a problem that involves a path o f a couple of dozen yards. We assume that the Eart h is stationary and tha t the onl y moving body i s th e baseball . Likewis e the pat h o f the Eart h around th e Sun i s given to an excellen t approximatio n by ignoring the effec t o f other planets and the Moon. But we have no exact solution. Is Determinism Dead?

Not yet. At this point we can say that although nature may obey deterministic equations in principle, in practice it is impossible to find an exact solution to the general problem of the movement of three or more bodies. We have run int o tw o type s o f difficulties. On e i s a matter o f principle: Poincare's proo f tha t th e three-bod y proble m ha s n o analytica l solution , whic h ca n sometimes be surmounted by simplifying the physical problem and getting an analytical, and approximate, solution as in the cases of the baseball and the Earth. The other problem, which i s practical, i s that typifie d b y Laplace's problem: an enormous an d inaccessibl e quantit y of data. 4 Despit e our inabilit y t o fin d exac t solu tions to these two types of problem, we still believe that the systems are governed by deterministic laws. W e believe tha t Newton' s law s hold . W e can sa y tha t al though determinism holds in principle, practical determinism is somewhat shaky. Nevertheless, since w e hav e better computer s ever y month, ther e seem s to be no significant limitatio n o n ou r abilit y t o obtai n extremel y goo d approximation s to any problem involving the classical laws of motion. At this point we can say that not only is determinism unchallenged but, for any systems in which the quantity of data is manageable, determinism (possibly helped by a computer) allows us to make very good predictions. This is an illusion. The Uncertainty of Measurement Suppose tha t yo u ar e godlike and coul d know the positio n an d velocit y of every molecule in the box at a certain time. Concentrate on one molecule. I n principle , 3 The three-body problem is not a problem if all the bodies are nailed to the wall; it is a simple matter to calculate the forces acting on each body, from th e law of universal gravitation. It is only when at least two of them can move that we get into trouble in trying to predict their paths. 4 The three-body, or many-body, problem is not applicable to our simple model of a gas since, between collisions the molecules are supposed to be traveling in the absence of mutual forces.

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we can work out its future pat h because we have the deterministi c law s of motion to help us. The three-body trap doesn't worry us because in our model there are no forces betwee n the molecule s betwee n collisions , an d i t is the force s tha t usuall y create the difficulty . Ignor e for the moment tha t you couldn't possibl y have all the knowledge that you need, and suppose that you have actually performed the calculation of the molecule's pat h for the next second. You can tell exactly where it will be in the box at the end of the second. Now someone comes up to you and tells you that th e initia l directio n tha t yo u were give n for the molecule' s motio n wa s very slightly inaccurate. What can you say about the fina l position o f the molecule afte r one second? Obviously, it will not be where you calculated it to be. Will it be near where you calculated it to be? Very unlikely, even i f the initia l data tha t you used for it s direction were in fact very close to the truth. In one second a molecule in the air makes several billion collisions ; a tiny change in the directio n o f our molecule at the beginning of its journey may only slightly alter the way in which i t makes its first collision, but that will slightly alter the direction and speed with which i t carries on after th e collision, and slightl y alte r the subsequent movemen t o f the molecule tha t i t hits. Afte r ver y few collisions ou r molecule , an d th e molecule s in it s vicinity, wil l hav e entirel y differen t position s an d velocitie s fro m thos e tha t w e predicted. After 4 billion collisions the molecule is likely to be in an entirely differ ent place from that originally calculated. It is easy to believe that the effect o f an extremely smal l chang e i n initia l condition s wil l hav e a n effec t whic h i s ou t o f all proportion. What we are seeing is an extremely simple example of the fact that : There are systems in which the outcome of a series of events is very sensitive to the initial conditions. So sensitive that the behavio r o f the system may be unpredictable in practice, even if it is predictable in theory.

It was Poincare who firs t pointe d ou t thi s sensitivit y i n gaseou s systems. H e was also the firs t t o realize that the difficult y o f making meteorological forecast s wa s a consequence of the same sensitivity. A n extraordinary illustration o f this sensitivity is provided by the calculations o f the physicist Michae l Berry, who considered a collection of oxygen molecules at atmospheric pressur e and room temperature. He placed an electron at the edg e of the know n universe (abou t 1C) 10 light-years away) and asked: After how many collisions would a given molecule miss a collision tha t it would have had i f the electro n were not there? Now the electro n i s supposed t o act only via its gravitational field, which a s you know must be so incredibly smal l that an y right-thinkin g scientis t woul d completel y ignor e it . Ba d mistake! Afte r fifty-six collision s the molecule misses a collision. I find this result to be almost incredible, but you can see why any attempt to predict the microscopic future of molecular systems requires a macroscopic amount of optimism. The next step is to realize that I may never be able to specify th e initial positio n of th e molecule, not because of instrumental limitation s bu t because of the way th e 'world is . Suppos e I use a ruler i n orde r t o hel p m e specif y wher e th e molecul e starts. I choose a tiny point at the center of the molecule and line it up with a point on the ruler. Is this possible i n principle? Yes, but onl y if I'm prepared t o approximate. Let us see why. The ruler is marked with numbers, the integers, 1, 2, 3 , . .. If I want to specify a point, I can estimate where i t is with respect t o the two nearest integers . But how

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many points ar e there between zero and one , or between one and two? An infinite number. Som e ar e rational; they ca n be expresse d a s the rati o of two integers , for example, 1/2 , 9/74, 260/513. But there are, nestling between the rational numbers, an infinite number of irrational numbers: V(7/9), V(9/ll), and s o on. These numbers cannot be expresse d a s the rati o o f integers, and the y presen t a n insurmountabl e difficulty. Whe n a n irrationa l numbe r i s expresse d i n decima l for m (i n orde r t o allow me to say exactly where I want to put a molecule, and give the information to a computer) , th e ro w o f digits, whic h i s randoml y ordered , stretche s t o infinity . Thus V(7/9 ) i s 0.29397236 7 . . . and s o on, forever. The numbe r o f such irrationa l numbers being infinite, I am almost certain of putting the molecule on one of them. If I want to put th e number into a calculation, 1 have to cut it off somewhere. If I cut off the number, say V(7/9), after 9 digits, as I have in the example, I will get a differ ent answer to my calculation o f the molecule's path than if I had taken 12 digits, or 27 digits, or ... I can never get an exact answer for the path. Computers have a limited numbe r o f places t o whic h the y ca n work . A long multistage calculatio n o n two differen t computer s can predict entirely differen t behavio r fo r a physical sys tem. Now, suppose that the number that I start with is an irrational number, like the square root of two, which canno t be expressed as a decimal with a finite number of digits. There is no finite computer that ca n accommodate such a number, and anything less than that coul d lead to trouble. If I cut of f the infinit e row o f integers i n the decimal after 10 0 places, and my calculation involve s many steps, I could get a very differen t answe r fro m tha t whic h I would ge t if I took 10 1 places. Problems that on the face of it should be soluble turn out to be insoluble. The problem of predicting th e molecule's flight i s an example of two principle s that are gathering in importance in modern science: the impossibility o f completely specifyin g th e initia l stat e o f a system (i n ou r cas e the positio n o f a molecule) and th e extrem e sensitivity o f the futur e developmen t o f a system (the path o f the molecule), to its initial stat e (the position of the molecule). It is important t o realize that ou r inabilit y t o predict the behavio r o f such systems is not a refutation o f determinism. Th e path o f a molecule, in ou r Newtonia n model, is completely determined by the laws of physics. Predictability is the problem, not determinism. We just don't have an accurate enough description o f its initial state , an d i f we wer e t o improv e ou r measuremen t device s t o excruciatingl y high standards, we would stil l run up against the problem of irrational numbers . An importan t objectio n can be made to ou r pessimistic analysi s o f the motio n of a molecule i n a gas. It is tru e tha t th e behavio r o f a singl e molecul e i s unpre dictable, requiring an impossible accurac y in the initial condition s o f all the molecules i n the box ; but th e behavio r o f the whol e sampl e o f gas is very predictable, and this i s of far greater practical import. Thu s ther e are laws that tel l us how th e pressure of the gas changes if we heat it or compress it. The results of such calculations are quite insensitive t o small error s in ou r initial conditions , fo r example, in the assumed pressure and volume in the box. An error of one millionth o f a percent in th e initia l positio n o f one molecule i n th e ga s will giv e a completely differen t final position after on e second. A 10% error in the initial volum e will caus e only a 10% erro r i n th e calculate d value o f the fina l pressur e o f the ga s after i t has bee n heated. Thus, all is not lost—there are predictable quantities in nature.

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Chaos: The Ubiquity of Unpredictability Chaos umpire sits Arid by decision more embroils the fray By which he reigns. —John Milton, Paradise Lost

We have looke d at a syste m tha t i s deterministi c an d whos e developmen t i s extremely sensitive to its initial state. In addition, in practice it is impossible to specify th e initia l condition s wit h sufficien t accurac y to avoi d considerabl e unpre dictability in the developmen t of the system . These are the characteristic s of what are called chaotic systems. Chaotic systems occur all over the place. Ecological Chaos

We will take two basic systems that have had an important role in the history of the development of chaos.51 am going to slip in a simple equation here. The equation is based o n a naive model for the numbe r o f animals in a given locale, in our case the numbe r o f rabbits i n Sherwoo d Forest . Suppos e that w e star t of f at a certai n time with NQ rabbits and tha t on the averag e each rabbit gives birth to A , offspring a year, so that the value of A, is a measure of the breeding rate. For convenience in ou r calculations, we scale NQ s o that it has a maximum value of 1. We can always multiply our results at the end to get the real numbers. All births occur at the sam e time of the year, and th e parent rabbits die soon afterwards. JVj, the numbe r of rabbits in the first generatio n is given by AJV 0, which i s just the average number of offspring pe r rabbit times the number of parents. All the first generation grow up fi t and well, because this is a rabbit's paradise; there is an ample supply of food fo r everyone, and ther e are no predators. The number o f rabbits in the second generation will be AJV^ , which is the number of rabbits in the firs t generation times the average number of offspring tha t they have. Notice that this is a linear relationship; th e numbe r o f rabbits i n an y generatio n i s directl y proportional to the number in the previous generation. However, life is not like this. In the real world there is a limited amoun t of food in the forest, and, because there is competition fo r food, th e weakest rabbits perish an d w e have to reduce the estimate d number of rabbits surviving in each generation. We do this by multiplying the ideal number of rabbits in an y given generation by a factor o f less than one . How do we choose this factor ? Sinc e it is less than on e we can write it as (1 - something). One simple way to decide on the value of "something" is to realize that the more rabbits there are in the forest, the tougher the food situatio n becomes , and the smaller proportion of those born will survive. So we want a "something" that gets larger as the number of rabbits increases. Taking all this into account, for the first generation, instead o f AJV 0 rabbits, we writ e AJV 0 multiplied b y (I - NQ), whic h i s written XJV Q(1 NQ). Notic e that the more rabbits there are at the beginning, the bigger NO is and th e smaller ( 1 - NQ) is . This make s sense since the mor e rabbits there are initially, th e more the pressure there is on food, and the smaller the fraction that will survive in the first generation. 5

I was first made aware of the fascination o f chaotic systems hy an article on the pendulum written by David Tritton, which was published in the European Journal of Physics in 1986, and which I recommend.

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e Ascent of Science So, according to our admittedly simpl e model, the number o f rabbits surviving in the secon d generation will be N2 = WV3(1 - N^, and s o on. This is not a linear relationship; the number that survive in a given generation is not directly proportional to the number in the previous generation. It is this nonlinearity that will produce the unexpected effect s tha t await us.6 (By the way, the equation is known to professionals in the field as the logistic map.) It is extremely informative, from the point of view of learning about the nature of chaos, to see what happens t o this population of rabbits under a variety of circumstances. We will start all our ecological experiments wit h the sam e number o f rabbits, 0.2 . As we note d earlier , this doesn' t mea n one-fift h o f a rabbit. Fo r conve nience we have just scaled the number o f rabbits s o that the maximum number i s one. Thus we star t with Ng = 0.2 and var y A, , the averag e number o f offspring pe r rabbit. We plot the number of rabbits that survive in each generation. 1. A. = 2. Each rabbit o n the averag e produces 2 offspring. Th e results are shown i n Figure 19.la. As you can see, the population in successive generations grows but levels out at a constant value of 0.5. This leveling out could have been expected on two counts . First , that' s ho w th e mathematica l equatio n behaves , independently o f whether i t refer s t o rabbits o r company shares. Second , at th e beginning of the experiment there is more than enough food in the forest and the population grows , but i t canno t increas e indefinitel y because the foo d i s limited . Where is the chaos in Figure 19.la? There isn't any, yet. 2. _A , = 2.9. Figure 19.Ib shows that the populatio n again settles down to one value, a higher one than previously. Notice, however, that the population oscillates for many generations before i t settles down . The larger number of offspring tha n in the previous case gives a baby boom that depletes the food suppl y faste r an d results in a lower number of survivors in the following generation. This is still not chaos; there is nothing unexpected here. Forward. 3. K = 3. Figure 19. Ic shows that the population oscillates for many generations but appears t o very slowl y approac h a constant value . Th e baby booms ar e bigger and the following shortage of food more severe than in the previous case. 4. A . = 3.2. Figure 19.Id reveals something entirel y new, although on e migh t have guessed what was going to happen afte r seein g the last two graphs. The population oscillate s forever . I t is a s though th e tim e durin g which ther e ar e oscilla tions has been getting longer as A , increases and ha s finall y become infinite. The population settle s down to two fixed values. We say that there has been a bifurcation, a splitting int o two . Afte r a generation with a high populatio n a smal l generation follows, forever . W e say that the populatio n has a period of two. For values of A, up t o about 3.4, this behavior continues, alternate generations of rabbits hav e only one of two possible sizes , but th e differenc e betwee n th e value s grows if A . is increased. 5. A , = 3.5. Again something new happens . The populatio n agai n oscillates foreve r but settle s down to four fixe d values : the population has a period of four. Ever y fourth year the value for the population returns. Each of the two previous values 6

If you multiply out the expression, to give N2 = \Nt- XN 22, you can see that there is a term in the square of the previous generation. That is why this is not a linear expression. A linear expression would include only N .

Chaos

Figure 19.1. The population of rabbit s in a forest. The initial population is 0.2, and X. is the averag e number o f offspring (see text for explanation) . In graphs (g) and (h) the crosses and/or dotted lines indicate the populatio n changes for an initial population of 0.202.

(for A = 3.2) splits into two: there are two bifurcations. It begins to look as though we may be heading for a doubling process as A , increases. Ther e is, but w e will not work our way along a series of values of A,. If we did , we would fin d ou t that as A , increased, for certain ranges of values of X the value of the populatio n would settle down to oscillations between 8 values, then 16 values, then 3 2 . . .. The results are plotted in Figure 19.le, and you should read the caption at this point. 6. / I = 4. There is absolutely no pattern discernibl e in Figure 19.If. The size of the populati on of one generation seems to have no connection with that of the previous generations. We have reached a state of permanent instability. I s this chaos? Let's see if it obeys one of the essentia l requirements . We have said that on e of the basic characteristics o f a chaotic system is that it s development with time is extremely sensitive to initial conditions. We can test this by doing all our experiments again but slightl y changing the initial rabbi t population. Let's make a 1% increase, from 0.200 to 0.202. From Figure 19.Ig, we see that this change makes almost no difference to the behavior o f the population s fo r A , up t o 3.5 , a range in which th e behavio r was non chaotic. We have plotted the results up t o the tenth generation , but after a few generations ther e cease s t o b e an y significan t differenc e betwee n th e population s based on the two different initial values. In fact, the results in the nonchaotic range, far fro m displayin g oversensitivity , show almost complete insensitivity t o the initial population. No matter what initial population is chosen, after a few generations the numbers settle down to values determined only by A, . The moment w e go to A , = 4, chaos takes over. After th e firs t fe w generations, i n which it appears that nothing untoward has happened, the population numbers for Ng = 0.200 o r 0.20 2 diverge . Ther e i s n o connectio n betwee n them . Th e smal l change in initia l populatio n ha s a very strong effec t o n the numbe r o f rabbits observed in following generations (Figure 19.Ih). This is a sign of chaos. How sensi-

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tive is the pattern of population? Instead of making a 1% change in the initial num ber of rabbits, we make a change of 1 in 100 0 and pu t Ng= 0.2002 . Predictably, the population remain s clos e t o tha t fo r AT fl = 0.20 0 fo r more generations tha n i n th e case of Ng = 0.202. But at the tent h generatio n the patter n als o breaks away completely, again confirming our statement that in a chaotic system the evolution of the system is very sensitive to the initial conditions . In practice these results simply mean that if you are asked to predict the way in which the rabbit population changes in a forest, then fo r the first few generations it doesn't matter much if you make a slight error in estimating the initial population, and i n th e lon g run i t doesn' t matte r a t all— provided you are in the nonchaotic range. If you aren't in that range, then there is little hope for you, unless you have a cast-iron method of counting rabbits exactly. You can solve the equations using the observed value of the breeding rate, A,, but that doesn't help, because the values that you get for the successive populations are so sensitive to the initial population. We see that a nonlinear system, as shown by our example, can be perfectly well behaved for some conditions but switc h ove r to chaos a t others. And, by the way, the scheme given in Figure 19.1 contain s undisclosed riches, but you will have to go elsewhere to enjoy them . I return to a vital point: the system is deterministic, it is not outside the laws of nature. In this case , the initia l information involves onl y integers (th e number of rabbits) o r rational number s lik e A, . I f you hav e th e exact initia l information , you can always calculate the results exactly, even in the chaotic range. If you haven't, it doesn't matter much provided the system is in its nonchaotic mood. Otherwise you would be well advised not to start the calculation. Again, distinguish between chaos and unpredictability: chaoti c processes are by definition unpredictabl e in practice because of their oversensitivity t o initial conditions, but unpredictabl e processes need not be chaotic. Consider a series of four flips of a coin. The final result cannot be predicted. We can only state probabilities, for example , the chance of throwing three heads and one tail, is one in four. But the process o f flipping a coin i s no t chaotic , because the fina l resul t o f flipping fou r coins has nothing to do with the initial conditions. Each flip is absolutely independent of the previou s flip. Thi s is not true of the fligh t o f our molecule. Th e path of the molecul e afte r eac h collisio n depend s o n th e position s an d velocitie s deter mined by the previous collision, and this chain of cause and effec t goe s back to the initial condition of the molecule as it set out on its odyssey. Similarly, in the region in which th e rabbit population behaves chaotically, the successive populations do depend on the initial population—very sensitively. Attractors We are going to put som e foxes int o Sherwood Forest. For simplicity w e will sup pose that the only factor that controls the number of foxes is the number o f rabbits, because the rabbits are their only food. It is also presumed that in the absence of the foxes, the breeding rate of the rabbits is such that they would settle down to a single value fo r their population ; A , is 2 , say. We will not writ e dow n th e equation s thi s time; the y ar e know n a s Volterra's equations. Qualitatively , i t i s clea r wha t wil l happen. Suppose that we have introduced a small number o f foxes. The y find plent y of rabbits to eat, they reproduce, and their cub s likewise enjo y eas y hunting. The fox

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Figure 19.2a. Rabbit s and foxes. The populations at successive times are given by a succession of points that when connecte d make up the graph.

Figure 19.2b. Th e population graph for a number of differen t starting populations.

population grow s a t th e expens e o f the rabbits , wh o ar e defenseless . In dealin g with chaos, you will fin d tha t pictures ar e invaluable, so let us make a graph (Figure 19.2a) . Along the horizonta l axi s (x) we plo t th e numbe r o f rabbits; along th e vertical axi s (y), th e numbe r o f foxes. Th e zero marks the initia l populations . No w since th e numbe r o f foxes increases , we move upward o n the y axis , and w e also move lef t alon g the x axis , because the numbe r o f rabbits i s decreasing. We move away fro m th e initia l populatio n a t poin t zero , alon g th e arro w an d towar d th e point labele d 1 . The res t o f the curv e ca n als o b e understoo d qualitatively : th e number of rabbits decrease s an d th e numbe r o f foxes increases , bu t graduall y th e foxes star t to find i t hard to find rabbits—the y have eaten most of them. Th e foxe s start to get short o f food an d som e die o f starvation because, as Darwin says , only the stron g survive. The number o f foxes decreases , and because it does so the rab bits find i t easier to live a full an d rewardin g life. I n short, as the numbe r of foxes falls, the number of rabbits grows. We are at point 2 on the curve. The continuation is inevitable: as the rabbit population grows, the foxes find hunting easie r and, afte r reaching a minimum, thei r populatio n grow s again an d the y star t decimatin g the rabbits. We are back to where we started. Both the populations oscillat e when plot ted against time. In the model system the cycle goes on forever. Furthermore, different set s of initial populations can give different cycles (Figure 19.2b) . A more realistic model of the predator-prey system reveals two important difference s fro m the simple Volterra model (sometimes known as the Lotka-Volterra model). The plot does not return

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Figure 19.3. A slightly more realistic model of the animal' s histories gives a graph that converges onto a single "attractor" no matter what the starting populations.

on itself except for certain initial condition s (Figur e 19.3) Only plot A in the figur e shows this behavior; any starting population numbers that correspond to a point on this plo t wil l resul t i n th e population s followin g th e plo t an d returnin g forever . Any other starting populations tha t li e off this plo t will result i n populations tha t follow a spiral path. Startin g points lik e B will result i n plot s tha t spira l outwar d until the y reach plo t A, which the y will then follow . Startin g points lik e C, which lie outside plot A, will result i n a plot that spiral s inward unti l it reaches plo t A. Plot A can be called a limit cycle, since in the limit of long times the other plots all end u p there . I t is also very natural t o cal l plo t A an attractor. The plots that w e have drawn are deterministic, and there is nothing chaotic about them. Their evolution i s almost the opposit e of chaotic—they are very insensitive t o initial condi tions, since they all predictably arrive at plot A. There is one further poin t before we carry on to chaos. Going back to the simpl e situation illustrated in Figure 19.2b, we realize that by suitably choosing the initia l populations w e can get smaller an d smalle r cyclic plots. There must be a point, P, in the interior, which i s the limit where the plots collapse. If the initial populations correspond t o this point , the y will sta y there. Th e foxe s won' t increas e becaus e there i s n o surplu s o f rabbits; the rabbit s won' t decreas e becaus e ther e ar e no t enough foxes to reduce their numbers. Point P is also an attractor in its modest way. We could call it a steady-state attractor , because the stat e of the population s neve r changes. The value o f this exampl e i s that we have introduce d th e ide a o f an attractor, a cycle t o whic h th e syste m wil l gravitat e whateve r th e initia l conditions ; o r a steady-state point a t which th e syste m start s and wher e i t remains. Bu t where i s chaos in all this? First we must remind ourselve s that al l these plots are of mathematical expres sions, like those for the rabbits alone. It has been shown that great numbers o f very diverse types of mathematical equation , when plotted, demonstrate the presence of attractors. Wherever you start plotting the equation, it develops in such a way that it ends up being confined to a certain path, like path A in Figure 19.3. We now extend the idea of an attractor. We add a third beast to the forest, a group of stoats, say. We set up a model for the changes with time i n th e populatio n o f all three beasts , but no w w e would nee d three axes on our graph and we might expec t a series of plots i n the three-dimen sional space, each plot representing the changes in all three populations fro m gen-

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eration to generation. We would hop e that in on e of these plots the behavior o f all three populations would be cyclic, going through the same succession o f numbers again and again. This plot would be a three-dimensional attractor , and in principl e there could als o be a point attractor in there somewhere, a set of starting values for fox, rabbit, and stoat that would sta y unchanging . In general, for a three-animal forest, we can picture the attractor as an imaginary three-dimensional surface . A s the syste m develops i n time , it traces a line on th e surface o f the attractor . Now such a line ca n wander i n a closely wrapped coi l of enormous lengt h unti l i t return s o n itself . I n ou r three-beas t forest , thi s woul d mean that if the initial populations were represented by a point outside the surfac e they would eventually zoom into it and then move over the surface, running over a very large range of sets of values until they started repeating their tour. This is still not chaos. The path taken by the point is not very sensitive to the initial conditions. Visually what this means is that if you take two points, representing slightly differ ing set s o f initial populations , they will follo w eac h othe r a s they mov e over the surface. Both paths are completely predictable, and they do not diverge. Next stop, chaos. There ar e attractors tha t hav e a n infinite surface , an d yet , as we will see later, this surface ca n be packed into a finite space. Such surfaces ca n often b e regarded as being infinitely folded upo n themselves , not a series o f separate surfaces . Th e difference ca n be appreciate d b y takin g all th e pape r o n a new toile t pape r roll, stretching it out, gluing the two ends together and then crushing it up. The surface is not infinite, but you get the idea; it is continuous, and i n principle a journey on the surfac e ca n cover every point i n the surface. 7 I t is very different fro m th e Sun day New York Times, which i s a stack of independent sheets . There are sets of starting values for the thre e animals whic h generate such infi nite attractors and for which two closely spaced points that start moving on the surface ca n easil y ge t separate d i n a ver y shor t distance . Th e tw o point s represen t slightly differen t initia l populations of the three animals. Th e two paths, showin g the developmen t o f the thre e population s wit h time , ar e extremel y sensitiv e t o their initial conditions; the slightest alteration in this position can result in the system following an entirely different path . This is the hallmark o f chaos—we cannot know the initia l condition s accuratel y enough to predict th e system' s future . Th e points may occasionally come close together after being separated. This means that: starting with slightly different populations , they diverge greatly but can come close to each other after a number of generations and then diverge again. What is the nature of these new, infinitely surfaced, attractors? They are fractals. Fractals

One of the mos t delightful meetings i n scienc e has been between chao s and fractals. An important idea that links the two concepts is that of an infinitely long line contained withi n a finit e space . Th e classi c exampl e i s the Koc h snowflake, the construction o f which i s describe d i n th e captio n t o Figur e 19.4 . Tw o points ar e worth noting : the shap e o f the lin e look s the sam e a t all magnifications, and th e length of the line can be increased indefinitely while stil l remaining within the circle. Afte r 100 steps performed on a triangle with 1-centimete r sides , the lengt h of 7

If you twist the strip once to make a Mobius strip, you can travel over both sides.

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Figure 19.4. A Koch snowflake. Eac h successive shape is obtained by mentally dividing each straight segmen t into three and then building an equal-sided triangl e o n the center segment .

the line is about 93 million kilometers. After 24 0 steps, the line has a length of over 1011 light-years, about the distanc e o f the farthes t object visibl e i n th e universe — with the corrected Hubble telescope. And the line never crosses itself. The concept of an infinitely long line within a finite area may be qualitatively justified if you accept what we were taught at school: a line has no width. Now imagine a surface tha t never crosses itself, never ends, and can be extende d indefinitely bu t neve r leaves a finite portion o f space, just as the Koc h snowflake sits within a finite area . Since a surface ha s n o depth , presumably thi s i s also allowed. I f you progressivel y shrin k yourself , examining th e surfac e i n fine r an d finer detail , what you see is basically the same at all magnifications, like a wanderer inside the snowflake. Such a surface is a fractal, a term invented by Benoit Mandelbrot, who is the best-known name in this field . A lin e i s one-dimensional , a n are a i s two-dimensional. I f you allo w th e Koc h snowflake to go on forever, although you will still have a line, there is a feeling tha t this infinitel y closely packe d objec t i s a n honorar y area . Thi s statemen t ca n b e quantified: one can define a "fractal dimension" fo r fractals, an d the Koch line has a dimensio n o f 1.2618, mor e than a line but les s tha n a n area . For most o f us th e concept can only be appreciated intuitively via the imagination, but fractal dimen sions have their importance i n solving certain problems. A s you might anticipate , fractals constructe d in three dimensions have fractal dimension s tha t vary between 2 and 3 ; they are, in a way, more than surface s but les s than solids . Many physica l processes , whe n modele d i n mathematica l terms , giv e chaotic behavior, which i s demonstrated by the fac t tha t the y have attractors that ar e frac tals. In other words, if you plot the history of the system, it wanders ove r an infinite surface, an d th e histor y o f two system s starting off close to each other ca n diverge to an extent ou t o f all proportion to their initia l differences . Tha t is chaos—an extreme sensitivit y t o initia l conditions . Thes e fracta l attractor s ar e th e so-calle d strange attractors. Two points place d in close proximity o n a fractal ca n easily get separated very quickly i n the infinit e maze through which they travel. We have a situation i n whic h a chaotic syste m move s throug h a series o f states tha t appea r completely random, never repeating in our lifetime, always finding a new place on the infinite surface o f the strange attractor, and ye t limited to a certain range of values for whatever parameters we are measuring. If you traveled along the edge of the infinite Koc h snowflake, you woul d g o through a n infinit y o f positions, bu t yo u would never leave the very limited area enclosing the snowflake. Fractals are shapes that can be generated by mathematical expressions o r by geometrical operations—a s fo r the snowflake . It is obviou s wh y th e Koc h snowflake looks the sam e at all magnifications—it wa s built tha t way. However, not al l frac tals hav e this property of self-similarity on all scales, and i n fac t many o f the frac tals associated with chaoti c natural phenomena hav e a different geometr y at whatever magnificatio n you loo k a t them . Th e stud y o f fractals ha s attracte d popula r attention because of the amazing forms tha t can be generated by the mathematica l

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expressions that give fractals. I well recall the strange, entirely mathematically generated landscape s tha t Benoi t Mandelbro t brought t o m y office , landscape s tha t were a cross between Swis s calendar photographs and the dream landscapes of the surrealists. An d i f you as k the compute r t o zoo m in o n th e detaile d structur e of these scenes, it reveals more and more structure, whatever magnification you go to. Practical Chaos

Of wha t practica l significanc e i s th e stud y o f chaos? Th e distinguishe d Belgia n physicist Davi d Ruelle , th e "inventor " o f th e strang e attractor , ha s said , "Th e physics o f chaos , however , i n spit e o f frequen t triumphan t announcement s o f 'novel' breakthroughs, has had a declining outpu t of interesting discoveries." Th e initial excitemen t ha s coole d slightly . Th e realization that natur e i s replete wit h nonlinear system s an d tha t som e o f them displa y chaoti c behavio r encourage d those in the field t o think that chao s theory could be fruitfully applie d to an enormous range of problems. It is possible that it can, but althoug h it has had som e fas cinating successe s i n som e fields, th e complexitie s o f many system s frustrat e th e easy application of theory. But the general feeling is that it will find more and more applications. Th e scientificall y importan t field s i n whic h attempt s hav e alread y been made to use the theory include weather prediction, astronomy, certain chemical reactions, the nature of turbulent flow , medical statistics, electronics, mechanical engineering , and the behavio r of biological systems. It is eve n intrudin g int o economics, where I suspect tha t it has a natural home. The movement o f some asteroids (se e Chapter 33 ) has bee n show n t o b e chaotic—thei r orbit s ar e unpre dictable. Th e sam e i s tru e o f the plane t Pluto , and i n a very muffle d wa y o f the whole solar system. The physical reaso n is the fac t tha t the paths of all the bodie s in the solar system are affected by several other bodies. We have seen that an attractor can be localized in a region of space. Our luck is that the attractors for the chaotic motio n o f the planet s ar e quit e limite d i n extent . I n th e past , som e asteroids, which circulate mainly in a dense belt between Jupiter and Mars, seem to have had large attractors; in othe r words, their orbit s were "wild." The spatial spread of the attractor depend s o n the force s o n the asteroids, and those whose orbit s were in a certain relationshi p t o tha t o f Neptune displaye d chao s dramaticall y enoug h t o have lef t thei r companions , most of whom continu e to circulate in reasonably settled paths. Their original orbits are empty, and the asteroid band has gaps in it that were previously a mystery but are no longer. There is a modest number o f convincing applications of chaos theory to real systems, including cardiac rhythms and certain chemical reactions. The theory is here to stay, and as computers become more powerful, it will be possible to tackle an increasing number o f problems usin g model s that are nearer to reality than ou r rabbits in Sherwood Forest. The Significance of Chaos

The problems fo r those wh o believ e i n scientifi c predictability hav e mounte d i n this chapter. If we canno t solv e the three-bod y question, if we canno t specif y th e state of some simple systems accurately enough to prevent chaotic solutions, what hope have we of predicting the behavior o f complex systems?

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Does this mean that determinism is dead? It may be, but if it is, chaos didn't kill it. The fact that we have no hope of predicting the behavior of chaotic systems does not mean that they are not deterministic . I f I can put i t this way: we may never be able to predict the behavior of a chaotic system, but the universe "knows" what its future is . The fact that I can't measure a length doesn't mean that that length has no objective existenc e (a t least that's what most nonphilosophers believe). Nevertheless, in practice, fo r chaoti c system s determinis m i s a fiction . Th e mai n conse quence of the developmen t of the theory of chaos is the collaps e of practical determinism and the realization that there are insoluble problems within the framewor k of deterministic science . They are not theoretically insoluble, if we still believe i n the laws of motion and in cause and effect . Bu t for many real systems, we can never specify th e initia l condition s accurately enough to obtain a believable prediction. This finally puts an end to the seventeenth-century belief that all aspects of nature could be, in principle, the subjec t o f quantitative analysis and reliable prediction . The scientist has been humbled, and not for the only time in this century. Some have seen chaos as a road by which to escape the mechanistic universe of Hobbes and La Mettrie. This seems to me to be grabbing at straws. Unpredictability and determinism are, as we have seen, completely compatible bedfellows. It is also difficult t o see how chaos provides support for the operatio n of free will. The argument is that the brain may include chaotic processes in its working, thus freeing u s from determinism . It doesn't—chaos can be deterministic. At least that is what th e present physicochemical state of my brain cells has forced me to write. The unwillingness to include man in a deterministic universe, the hope that free will really operates, is symptomati c of our wish t o be qualitatively different fro m the rest of the universe. This is one of the drive s behind creationism. Unfortunate ly, the mor e we learn of biology, the mor e it seems that man i s just a particularly complicated exampl e of organized matter, firmly withi n th e anima l kingdom . Or maybe you believe that Bonzo has an eternal soul.

VI Life Life is anything that dies when you stomp on it. —Dave Barry

The most complex systems of molecules in the universe are probably on this obscure planet. Living cells are by far the most organized form of matter that we know. Here is matter that can reproduce itself and, in the case of man, examine its own structure and workings, and ask why it exists. It is possible that you hold the vitalist belief that there is a qualitative differenc e between living and nonliving matter; that the laws of physics and chemistry, on their own, plus a little feedbac k theory, cannot explain th e phenomenon of life. I am not on your side, but I am not going to unleash a stream of polemics. What I ask is that you, likewise, have patience and accept that science has found rational reasons for a host of once mysterious phenomena associate d with life , and that these findings have proved themselves i n combat. All living forms are partially the products of their genes. We are going to examine the genetic basis of inheritance. We will be discussing great science, absorbing science, useful science—an d disturbing science. As well as delving into the nature of life, we will be reviewing the current state of research into the origin of life. Here we are on shakier ground than any we have trodden on to date.

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20 The Slow Birth of Biology Sir Nicholas i s discovered practicing swimming on a table: Longvil: Have you ever tri'd in the Water , Sir? Sir Nicholas: No, Sir; but I swim most exquisitely on Land. Bruce: Do you intend to practis e in the Water, Sir? Sir Nicholas: Never, Sir; I hate the Water , I never come upo n the Water , Sir. Longvil: Then there will be no use of Swimming. Sir Nicholas: I content myself with the Speculative Part of Swimming; I care not for the practick . —Thomas Shadwell, The Virtuoso

For centurie s n o are a o f scienc e flaunte d suc h a smal l rati o o f meaningfu l "practick" to empty theory, as biology. The early history of biology was a catastrophe because of man's inability to put "practick " before authority and "speculative " thought. Observation was downgraded to an irrelevancy. It is difficult t o excuse the immense durabilit y o f Aristotle's descriptions o f the for m an d functionin g of animals an d plants . Ther e is very little in his writings on biology that has stood th e test o f time, an d muc h o f what h e wrote coul d have been show n t o be wrong by simple us e o f the nake d eye . But no on e dare d t o seriousl y challeng e the maste r until the late Middle Ages. Unfortunately, he was not the only sacred bull. On the kitche n wall o f my home hangs a large, luxuriant drawin g of a lavender plant. Beneath the proliferating roots are the words Mattioli, Venezia 1565. Pierandrea Mattioli (1501-1577) published a best-seller in 1544: the firs t translation int o a modern European language of the classic De materia medico of Dioscorides. Dioscorides, a first-century A.D. surgeon in the servic e of Nero's armies, used hi s spare moments to make drawings of plants and to list their real or supposed medicinal effects . Th e resultin g herbal , writte n i n Greek , wa s t o influenc e European botany fo r the nex t 150 0 years. It became a holy text, repeatedly copied. Lik e th e story whispered fro m ea r to ear at a party game, the illustrations drifte d farthe r and farther awa y fro m th e originals , and fo r fifteen centurie s peopl e were reading an d teaching from books that contained drawing s of plants removed from the reality revealed to them by their own eyes. Dioscorides was the standard text in many European universitie s unti l th e middle 1500s . Onl y then di d three Luthera n Germans produce a trio of herbals that were illustrated by accurate, and ofte n very beautiful, drawings. Th e accompanyin g texts , however , stil l borrowe d heavil y fro m Dioscorides. Th e most successfu l o f these herbals wa s Leonhar d Fuchs's Historia stirpium (1542) , which cam e out i n a German translation the followin g year. The fuschia was named after Fuchs . The fossilization of botany was paralleled by the stagnatio n o f zoology. For centuries Aristotle was the accepted textual authority, but it was the bestiary of Physiologus, a second-century Greek, that was the prototyp e of the immensel y popular

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medieval bestiaries. Physiologus's descriptions of animal behavior were rather low on fact. Everything was buried in a morass of mythology, theology, and popular beliefs. The animal kingdom was apparently created to provide Aesop with material for his tales. Every beast illustrated a moral lesson. A totally unreliable bestiary does not threaten the health of the average armadillo, but a surgeon could be letha l i f he worked fro m a Renaissance tex t o n human anatomy. Of Apes and Pigs and Amateur Surgery

If you are in Uppsala, visit the seventeenth-century anatom y lecture theater in th e Gustavatium. The benches are arranged in elliptical tiers , to form a steep funnel at the botto m o f which stoo d th e tabl e upo n whic h th e dissectio n wa s performed. Climb the narrow steps up to one of the upper benches and imagine yourself in the world o f a seventeenth-century student : the crowded , exclusivel y male gatherin g looking down at the waxen, gashed corpse as its inner architecture was revealed by the dissector, to the accompaniment o f a commentary read by the professor. Usually it was a male corpse, since most of the corpses were those of criminals. Ofte n th e dissection took longer than a week and so winter was the preferred seaso n because it was colder and the nauseating stenc h that rose through the theater was reduced. When I sat in that theater an d looke d down t o the table, I knew that blindness , literal and metaphorical, had prevailed. First, it was impossible at that distance for the student to see anything but the coarsest detail. Second, in the seventeenth century, the commentary of the learned professor of anatomy was taken from an unreliable text written fiftee n centurie s before the dissection . Galen (c. 130-200), a Greek born in Pergamos, learned much of his anatomy as a physician to gladiators. He settled i n Rome and became the court physician t o the philosophical emperor , Marcu s Aurelius . H e turne d ou t torrent s o f treatises o n everything from physiology to philosophy. Galen was worth y o f his reputatio n a s the greates t physician afte r Hippocrate s (c. 460-377 B.C.) . I n accor d with twentieth-centur y trends , he favore d preventio n over cure. He was a brilliant experimenter , amon g othe r things demonstratin g th e pulse that spread alon g the arterie s from th e heart . Dissection of the huma n body was forbidde n in Rome . Galen had t o content himsel f wit h the dissectio n o f pigs and Barbar y apes, an d th e examinatio n o f a coupl e o f human skeleton s tha t h e came upon by chance. 1 The extraordinary fact i s that the anatom y o f two animal s was regarded as part of the definitiv e source of information on human anatomy for about 150 0 years. In the dissectin g theaters o f sixteenth-century Padua and seventeenth-century Uppsala, the dissector did his work while the professor stood to one side and read from second-centur y Galen. Galen, like Dioscorides, had emphasize d the importanc e o f observation and th e dange r of being overly influenced by exist ing texts . T o 110 avail . H e survive d throug h th e Dar k Ages, and, lik e man y othe r 1 The dissection of human bodies for teaching and anatomical research was practically unknown in Europe before 1300 , when it was revived by the Italian Mondino de Luzzi. The ancient Greeks had performed occasional human dissections, but the Church effectively shu t down such work for centuries. Medieval Islam also forbade dissectio n of the human body, as does orthodox Judaism today.

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Greek authors , hi s reputatio n blossome d a t the tim e o f the Renaissance . H e was first published i n a printed Latin translation by the famous Aldine Press in Venice, in 1476 . The text sprea d ove r Europe, and i n mos t universities i t was considere d near heres y t o questio n anythin g tha t Gale n wrote. An y difference s betwee n th e anatomical finding s o f a dissecto r an d Galen' s tex t (an d there wer e many ) were pushed unde r the carpet. One o f th e very fe w t o publicl y revol t wa s th e grandiloquentl y name d Theophrastus Philippu s Aureolu s Bombastu s vo n Hohenhei m (1493-1541) , known as Paracelsus. He was a wanderer for most of his life , a practicing physician without a n officia l qualification , a professor a t the Universit y of Basel. His early success depended o n the patronage of the humanist Desideriu s Erasmus and the fa mous printer Johann Froben, both o f whom were apparently gratefu l patients . His self-confidence flourished , and i n 152 7 he thre w a copy of Galen into a student' s bonfire. Fro m now on , he announced , h e woul d teac h onl y what h e had learne d from hi s own patients. That year his main backer, Froben, died. The establishment took its revenge, and Paracelsus had to leave town. He was pushed ou t of practices in other towns and died in Salzburg in 1541. He believed that, at the Creation, God had supplie d a remedy for every ill, an d th e onl y reason for a physician failin g to find a cure was his own ignorance. He spoke in the language of astrology; he left n o school. Vive Leonardo! One man might have saved anatomy at that time, the man who i n his lette r of selfrecommendation to Lodovico Sforza wrote, "My work will stand comparison wit h that of anyone else." It could, but Leonardo da Vinci was not systematic, and in any case hi s anatomica l drawing s di d no t reac h th e printin g pres s i n hi s time . Dr. William Hunter , the distinguishe d eighteent h centur y anatomis t wh o introduce d the dissectio n of cadavers into British medical education, said that "Leonardo was the best anatomist a t that time i n the world. He certainly knew more than the doctors." Hi s anatomica l drawing s ar e amazing . H e invente d th e cross-sectiona l method of presentation. He made the first drawin g to show the proper relationshi p between th e smal l an d larg e intestines, an d h e mad e wonderfu l drawing s o f the veins o f the live r an d o f a dissection o f the heart , "Tha t marvelou s instrumen t in vented by the Supreme Master." Leonardo rarely mentioned Go d directly. Da Vinc i wrote, "Th e mor e thoroughl y yo u describ e th e mor e thoroughly yo u confuse. I t i s necessar y t o draw. " Th e seein g ey e o f the artis t wa s ofte n i n thos e days more reliable tha n the tradition-boun d scholasticis m o f the learne d doctors . Da Vinci' s drawing s o f flowers wer e miracle s no t onl y o f art bu t o f accuracy, as were Diirer's. But even da Vinci was under Galen' s spell. Hi s drawings of muscles and bones were the frui t onl y of observation, but th e drawings of some of the deep er organ s o f the bod y wer e a cros s between wha t th e ey e saw an d wha t Galen' s books described . The Truth at Last The man wh o finall y sa w through his ow n eyes, arid not thos e o f others, was Andreas Vesalius (1514-1564), who established a reputation when dissecting for medical students, while he was stil l a teenager. In 1537, at the age of twenty-three, he was alread y given the chai r o f surgery and anatom y at Padua. Early in hi s career ,

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Vesalius realized that there was a gap between what he saw and what Galen wrote. He entered a period of intensive activity , it being rumored that his enthusias m fo r dissection reache d suc h height s tha t h e dissecte d bodie s befor e the y wer e dead , like those overzealou s waiters wh o remov e your plate befor e you'v e finishe d eating. H e employe d artists , som e fro m th e schoo l o f Titian, t o prepar e anatomica l drawings an d woodcuts . Befor e h e wa s thirty , Vesaliu s had publishe d on e o f the most handsome an d influential texts ever printed: De humani corporis fabrica (O n the Structure of the Human Body) (1543). By 1600 it had become the standar d textbook throughout Europe, and thus it was that, in the sixteenth century, the life sciences finally mad e a serious break with the error-ridde n past. Th e living eye had vanquished th e dea d word—although no t everywhere . Avicenna's translation s o f Galen into Arabic were still the basis of medical practice in late-nineteenth-centur y Teheran. Appropriately, the Fabrica came out in the same year as Copernicus's De revolutionibus orbium ccelestium. One author had described man better than he had ever been described; the other had moved man fro m th e center of the solar system. Naturalists bega n t o examin e natur e throug h thei r ow n eyes , unprejudice d b y medieval herbals and bestiaries. One of the great questions that they asked was this: Is there any order, any sense, in the multitude o f living forms ? The Spectrum of Life

A few years ago, ten tree s i n the Brune i rain fores t wer e spraye d with insecticid e and th e dea d insect s collected . I n round numbers , 20,00 0 insect s wer e foun d be longing to 2500 different species . In the whole world, about 1 million specie s of insect have been described, but entomologists believe that there are at least another 5 million t o be discovered , and i t i s estimated tha t i n al l there ar e between 1 0 and 100 million livin g species as yet unnamed. Wha t is a species? Is a poodle a differ ent species from a dachshund, a cat from a puma? Is every mongrel a new species ? Ideally, systematic classification should allow biologists to immediately plac e a species in the anima l o r plant hierarchy, simply fro m th e nam e o f the species . On what principle s d o we carry out this classification? How would yo u classify a collection o f coins o f differen t years ? You could, fo r example, group all th e coin s of any given year together, or you could grou p all the nickel s together, all the dime s together, an d s o on. Th e classificatio n depend s o n wha t i s most suitabl e t o you. There is no best way. Is there a choice i n classifyin g livin g forms , o r is there on e "true" way? On my sixth birthda y m y father bought me a Bible and a pair o f boxing gloves. The gloves were "because you're a Jew." He should have said that abou t the Bible, not the gloves, but my father was a realist. At the age of seven, if I had been asked to classify th e huma n rac e I would hav e starte d of f by askin g i f you wer e a heavyweight, a middleweight, a bantamweight, and s o on. After tha t woul d hav e com e color. Thus I had a binary classification system and, if pressed, would hav e classified Jo e Louis as Heavyweightus blackus. If you thin k thi s system is idiotic, I suggest that you compare it with those used to classify animal s u p to the seventeent h century. Aristotle divided the animals into those that had red blood and those tha t were bloodless. In many bestiaries, the only attempt at classification was to list the animals alphabeticall y unde r th e name s the y ha d bee n give n fo r centuries. Th e

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order differed i n different languages . So how d o you classify animal s and plants? The man who first laid down rational general principles of classification was the Swedish naturalist Carolus Linnaeus (1707-1778) . H e used two concepts to guide him: the idea of distinct species and the concept of a hierarchy of living forms. The supposed hierarchical structur e is a cornerstone of the theory of evolution. The ide a o f specie s ha d previousl y occurre d t o th e Englishma n Joh n Fla y (1627?-1705), for whom a species was a collection of individual animals or plants that reproduced among themselves to give individuals similar to themselves. Reproduction ha d als o bee n pu t forwar d b y Aristotl e a s on e possibl e criterio n fo r grouping animals. Ray believed tha t specie s were fixed, o r very nearly so, but no t everybody did. Today the concept of species seem s so obvious that it is difficult t o understand wh y i t took so long to be established , until w e recall that, apar t fro m the confusin g result s o f crossbreeding, those reading medieval bestiaries an d folk tales found that there were beasts that gave birth to utterly different beasts and animals that wer e generated spontaneously . Th e mutabilit y o f species was take n for granted, but not in the evolutionary sense. Animals didn't chang e and adapt, they just changed. In such a world, Ray's definition of a species was controversial. Linnaeus accepted Ray's concept of species, but h e went further, envisagin g an animal an d plant worl d united b y common characteristics. Th e one on which he laid specia l emphasi s wa s the sexualit y o f plants; h e was th e Georgi a O'Keeffe of his day, and the invento r of the commonly used signs < J an d 9 for male and female . He saw animal genital s everywhere i n the plant world, and his description s wer e not inhibite d b y th e pri m convention s o f the Dutc h tow n o f Leyden, where, i n 1735, he published hi s seven-pag e summary of a classification scheme fo r plants: Systema Naturae. The organizational framewor k that Linnaeus introduce d was to classify plant s into class, order, genus, species, and varieties. The basis of the classification scheme, for flowering plants, was the form of the stamens, the male "genitals." He observed the number of the stamens and their length and grouped flowering plants int o twenty-thre e classes. The remaining, nonflowering plants , such as mosses, were put into a single class, the Cryptogamia. Classes were divided into orders depending o n the structur e of the stigmas , the female "genitals, " of the flow ers. The calyx, the supporting structure for the flower , wa s referred t o as a nuptial bed, s o tha t th e poppy , fo r example , wa s describe d a s havin g "twent y o r more males in the same bed with the female." This might have been considered as merely "naughty," but one wonders what his readers made of his comparisons of certain structures in the flowe r to labia minora and majora. To name a class of flowers Cli toria was askin g fo r trouble and di d no t escap e the censur e o f solid citizens , bu t Linnaeus could point to more blatant examples of the description o f nature in suggestive terms . Conside r th e followin g vers e fro m a poe m o n th e lamprey , b y William Diaper (16867-1717): At length with equal Hast the Lovers meet, And strange Enjoyments slake their mutual Heat. She with wide-gaping Mouth the Spouse invites, Sucks in his head, and feels unknown Delights. 2 2

I would like to put in a plea for the little-known Diaper, a country parson who, if not a major poet, is often a lively and fresh alternative to the stereotyped nature poets of his time. Diaper wrote i t as he saw it.

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Having named the main classes of plants, Linnaeus, after some experiments, settled o n a binary syste m o f nomenclature fo r individual species. B y 1758 h e ha d named 4236 species. Then he turned to the animal kingdom. A century later, Agassiz and Brow n had classifie d 129,370 animals an d plants . We still use Linnaeus' s binary system of Latin names. The whole living world is classified into five kingdoms: th e Monera, which ar e single cell s withou t nucle i an d includ e bacteri a an d som e algae ; the Protista , which ar e also single-celle d bu t hav e nuclei ; th e Plantae , th e highe r plants ; th e Fungi, plants such as mushrooms that do not have the capacity to use sunlight a s a direct sourc e o f energy; and Animalia , th e animals . Th e kingdom s ar e spli t int o classes, as we have alread y seen fo r plants. Th e mammals, mammalia , ar e one of the classe s o f the Animalia . Classes are split int o orders. The rabbits an d tailles s hares belon g t o th e orde r Lagomorpha . Orders ar e spli t int o families. Thu s th e family Leporida e contains those member s of the Lagomorpha that have elongated hind limbs, long ears, and short , curve d tails. Families ar e divided int o genuses. Rabbits belon g to th e genu s Oryctolagus. Genuse s ar e divide d int o species. Th e different specie s of rabbits ar e differentiated fro m eac h othe r on the basis of their average size, their color , length of hair, and s o forth. Mos t common or garden rabbits ar e labele d Oryctolagus cuniculus. The officia l nam e consist s o f the genus , written wit h a capital letter , and the species , written wit h a small letter . There is no need to write more; the professional biologist will know from th e genus wher e to fin d th e organis m i n th e tre e o f life. Thi s i s the grea t advantage o f systematic classification. There was no place for evolution, or transformism as it was then called, in Linnaeus's scheme . The hierarchy of living forms, so strongly suggested by his classifi cation, did not in his eyes imply that lower forms had developed into higher. As he said, there ar e as many specie s a s God created. But the doctrin e o f evolution wa s stirring in the brain o f an aristocratic French contemporary of Linnaeus. Buffon

As a youngster, Georges-Louis Leclerc, Comte de Buffon (1707-1788 ) was a dueler, and like Tycho Brahe he had to leave his university for this reason. He did not like Linnaeus and was not averse to saying so. Unlike Linnaeus , Buffo n sa w the natura l world , anima l an d plant , a s an everchanging unified whole i n which the differenc e betwee n forms wa s often difficul t to perceive. This was the basi s of his objectio n to the rigid classificatio n int o un changing classes , an d th e backgroun d to his belie f in evolution . O f the forty-fou r volumes o f his enormousl y popular Histoire naturelle, thirty-six appeare d i n hi s lifetime. Thi s i s a treatise writte n by a man i n lov e with the natura l world , but a man who had th e clarity of thought of a mathematician. ( I like his way with words: "The as s is not a marvelous production." ) The drawing s i n hi s Histoire naturelle were to inspire a series of sketches of animals by Picasso. Buffon objecte d violentl y to the concep t o f families of species, deridin g "thos e naturalists who, o n such sligh t foundations , have establishe d familie s among animals and vegetables." He was referring obliquely to Linnaeus but was more specif ic and combativ e elsewhere: "This system , indeed, namely Linnaeus's, is not onl y

The Slow Birth of Biolog y |

far mor e vile and inferior to the already known systems , but i s further exceedingl y forced, slippery, and fallacious; indeed I would consider it childish."3 Buffon estimate d the age of the Earth to be 74,832 years4 and used this time scale to construc t wha t amount s t o an evolutionar y histor y o f the Earth . Instead o f the seven days of Genesis, Buffon propose d seven lengthy epoches. Animals emerged in th e fifth epoch , the continents separate d i n the sixth , and man appeared in the seventh. This elongate d time scal e is not par t o f the St . James version. When th e first volume of the Histoire naturelle was published, it was predictably attacked by a committee set up by the theology faculty of the University of Paris. Buffon issue d a thoroughly deviou s retraction . Bu t the seed s of evolution were stirring. Th e part s wer e slowl y comin g together: the hierarchica l structure o f the natural world as reflected in Linnaeus's classification; the work of the Danish Nicolaus Sten o (1638-1686), who explaine d th e stratificatio n of rocks by a process of successive depositio n (ove r a period of seven days!); and the realization, by Buffo n himself, tha t th e anima l worl d wa s involve d i n a competition for the inadequat e food resources of the earth. Classification was the necessary framework for the theory o f evolution, althoug h toda y we would sa y that evolutio n i s the tru e basis for classification. For many years classification was effectively a dead subject; the general outlines of a system had been constructe d b y Linnaeus, and there was not a lot more to be said. However , recently th e subjec t ha s bee n give n a sho t i n th e ar m by th e ad vances in molecular biology. The compariso n o f the DNA , the collectio n of genes, of different specie s has allowed family connections to be revealed. Species that are closer i n th e evolutionar y hierarch y wil l tend t o have mor e closel y related DNA maps. Similarly, analogous proteins in different specie s can be compared—they always diffe r somewher e in their amin o acid sequences, and the difference s ten d to be smaller the closer the species. Taxonomy, the study of classification, has moved from th e macroscopic to the molecular level. But we have run ahea d o f our story: before molecular biology, it was the optica l microscope that was at the leading edge of biological research. Macroscopic to Microscopic

The earl y single-len s microscope s o f th e Dutchma n Anton y va n Leeuwenhoe k (1632-1723) were capable of revealing the tiny inhabitants of pond water. 5 His best lens gave a magnification of about 500. His assistant, Johann Ham, managed to see single cells—huma n spermatozoa . Seein g the m swimmin g abou t vigorously , van 3

Compare the gentlemanly Robert Boyle, in the preface to The Sceptical Chymist: "A man may be champion to truth without being an enemy to civility, and may confute a n opinion without railing at them that hold it." 4 There is evidence that Buffon believed the age of the Earth to run int o several million years, He was wise enough not to make this guess public. His published estimate was off by a factor of roughly 50,000. It was also about thirteen times longer than the then widely accepted figure of Archbishop James Ussher who, in 1654, announced that, after years of research, he had fixe d th e date of the Creation as 26 October 4004 B.C., at the distinctly civilized hour of nine o'clock in th e morning. 5 Leeuwenhoek was a friend of Jan Vermeer, who used light in a somewhat different way.

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Leeuwenhoek was s o impressed tha t h e declare d the m t o be th e rea l creator s of new life, rathe r than the egg. Nevertheless, the concept of the cell di d not occur to him. When he communicate d hi s finding s t o the Royal Society, his descriptio n of "little animals" i n water created a sensation. Leeuwenhoe k and his compatriot Jan Swammerdam (1637-1680 ) wer e largel y responsibl e fo r th e no w defunc t preformistlheoiy, whic h states that the sperm contained a minute replica of the grown organism. A variation of the theory places the replica i n the ovu m rather than th e sperm. Swammerda m wa s th e firs t ma n t o se e red bloo d corpuscles , bu t h e als o failed to be led to the conclusion that life came in small packets. In England, Robert Hooke constructed a compound microscope, with tw o lenses, and produced exquisite drawing s of parts of insects and othe r natural objects. It was he who discovere d the multi-len s structur e o f the fly' s eye . His work was frequently met with the same skepticism that met Galileo; it was imputed that he was studying optical illusions. H e did not escape the barbed pen o f Thomas Shadwell, who in the play The Virtuoso (1676) was referring to Hooke when he wrote: "A Sot, that ha s spen t £200 0 i n Microscopes , t o fin d ou t th e Natur e o f Eels i n Vinegar , Mites in Cheese, and the Blu e of Plums, which h e has subtill y foun d ou t to be living Creatures." Hooke was the firs t t o employ the term cell in the contex t of living matter. He examined a cross section of cork and describe d the arra y of roughly circular hole s a s "cells," usin g th e word i n analog y to prison cells . He invented th e nomenclature, bu t h e to o wen t n o furthe r wit h th e idea . Marcell o Malpigh i (1628-1694) used both single-len s an d two-lens microscopes. H e was the founder of microscopic anatomy , and his work on the lungs, in which he discovered capil laries, was the real beginning of our understanding of respiration. H e drove himself hard: "I have sacrificed almos t the whole race of frogs, something that did not come to pas s eve n i n Homer' s savage battle between frog s an d mice. " Lik e the wor k of Hooke and Galileo, his optical devices were held by his contemporaries to be falsifiers of reality. It is pleasant to think that in 1684, when he lost his microscopes in a fire a t hi s house , th e Roya l Societ y ha d som e lense s mad e fo r hi m an d sen t t o Bologna. Again, Malpighi missed the significance of the cell. Frangois-Vincent Raspail (1794-1878), politica l activist, friend o f Flaubert, and unqualified bu t successfu l medica l practitioner , prepared th e way for the modern concept of the cell theory, stating that "the plant cell, like the animal cell, is a type of laborator y of cellular tissues. " H e realized tha t th e membran e aroun d th e cel l acted as what h e called a "sorter," selectively allowin g onl y certain substance s t o pass. Even so, the origi n o f the cel l theory i s conventionally attribute d t o the German scientist s Theodo r Schwan n (1810-1882 ) an d Matthia s Jako b Schleide n (1804-1881), both unusual characters . Schwann wa s the founde r o f the mechanistic schoo l of medicine. I n contrast to the overwhelmin g feelin g a t the time , Schwan n considere d that livin g organism s were not produced by a directing will, aimin g at a predetermined goal , but rathe r by th e law s o f chemistry an d physics . H e sa w al l organism s a s being buil t fro m cells, a "cell" fo r him being "a layer around a nucleus," the whole structure being covered by a membrane. The cell nucleus had been discovered in 1830 by the Scots botanist Rober t Brown , who w e me t i n connectio n wit h Brownia n motio n (se e Chapter 16). Schwann als o made the pivotal suggestion that organisms develop by the differentiatio n o f the origina l clump o f undifferentiated cells . This i s the basic axiom o f embryology, which should be compared with Leeuwenhoek' s preformist

The Slow Birth of Biolog y |

theory. Schwann's whole scientific career lasted only five years, from 183 4 to 1839, after which he forsake materialistic rationalism and drifted into mysticism.6 About the same time that Schwann was singling out the cell as the central concept i n biology , his countryma n Jacob Schleiden wa s bringing ou t simila r state ments, particularly i n an article writte n i n 1838 , and i n a subsequent textboo k in which he writes that the cell is "the foundation of the vegetable world." Schleiden, like Schwan n i n his earl y days, adopted a straightforward physical an d chemica l approach to living matter, rejecting the vague wafflings o f Naturphilosophie.7 The cel l theor y neede d th e prestig e o f anothe r German , Rudol f Vircho w (1821-1902), t o firml y establish i t a s official dogma . In 1860 , Virchow coined th e classic motto: Omnis cellula e cellula, All cells arise from other cells. The cel l i s the universa l uni t o f living matter . The concept of the cell was the great turning point in the history of biology. It was the microscope that was the in dispensable instrumen t neede d t o detec t object s tha t ar e generally no mor e tha n one five thousandth of a centimeter across. From the middle of the nineteenth century, the cell theory established itself firmly at the center of the biological sciences. Different types of cells were characterized, their internal structure examined as best as could be, by the optical microscope, and their components separated out. This work was to lay the foundations for the astonishing advances in cell biochemistry and molecular biology that were, in the twentieth century, to sweep biology into the realm of the exact sciences. Biology, chemistry, and to a lesser extent physics have met within the living organism. The metamorphosis of biology into a science came to full fruition with the elucidation of the natur e o f genes and thei r mod e of action. The stor y began in a quiet Austrian garden.

6

S(:hwann realized tha t alcoholic fermentation was caused b y yeast cells, but he came under a n extraordinary attack from Wohler on this count. Wohler wrote a satirical article suggesting that yeast cells in sugar solution chang e into small animals, which eat the sugar and expel carbo n dioxide from their urinary organ s and alcohol from their anus. Their bladders are shaped lik e champagne bottles . 7 Schleiden was an individualist. At a time when the tide of anti-Semitism wa s rising in German universities, h e wrote a complimentary articl e on the Jews, singling out their role in conveying knowledge to the West in the Middle Ages.

26 1

•M1 A

In a Monastery Garden He's the spitting image of hi s dad. —About one-quarter of the visitors to maternity hospitals.1

Gregor Johan n Mende l (1822—1884 ) bre d pe a plant s i n a monaster y i n Brno , Austria, because he was interested i n inheritance. Mende l concentrated on the inheritance o f a very smal l numbe r o f characteristics, an d thos e on e a t a time . H e started of f with plant s tha t ha d bee n inbre d s o as t o giv e a uniform population . Thus Mendel took plants with long stems, that had been inbred for at least two generations unti l al l offsprin g ha d lon g stems . Similarly , h e bre d "pure " short-ste m plants. Only then did he cross short-stemmed and long-stemmed plants, taking the pollen fro m on e plant an d transferrin g it to the other . In a large set of experiments he observe d ste m length i n th e progen y of his pur e plants , an d foun d that all the stems were long, eve n thoug h on e o f the "parents " wa s short-stemmed . The n h e took that firs t generation of long-stemmed plants and crossbred them among themselves, agai n documentin g ste m lengt h amon g thei r progen y (Figur e 21.1) . H e found that both long- and short-stemmed plants appeared in the second generation. He carried out experiments o f this kind to observe other singl e properties: color of seeds, see d shape , pod color , pod shape , flowe r color , and flowe r position o n th e stem. He observed something like 28,000 results o f crossbreeding . What woul d we expec t fro m thes e experiments ? W e know tha t insid e almos t every living cell there is a well-defined, roughly spherical bod y called the nucleu s and within th e nucleus there are elongated bodies called chromosomes . The chromosomes are basically strings of genes, the entities that control the differen t physi cal characteristics o f our bodies. Gene s are passed fro m generatio n t o generation, and i n th e cas e of sexual reproduction th e offsprin g receiv e half o f their chromo somes from their mother and the other half from their father . In peas chromosomes come in pairs, each member of the pair carrying the same kind o f genes but not necessarily identical genes. For example, both chromosome s of a pair may carry a gene for color, but one may be the gene for yellow peas and th e other the gen e for green. In human being s eac h chromosome may carry about 2 to 3000 different genes . In the normal human cell there are twenty-three pairs of chromosomes, forty-six chromosomes in all. In the female, each member of a pair, as seen under the microscope, is apparently of equal length. In the male, one of the pairs consist s o f a long chromosome (labeled the X chromosome) and a short on e (th e Y chromosome). In the pea plant there are seven pairs of chromosomes i n each cell. Assuming that about hal f the babies are female, and about half the visitors to a male birth think that junior looks like his mother .

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Figure 21.1. Mende l breeds peas.

One o f the gene s in the pe a plan t control s the lengt h of the stem ; another controls the colo r of the seeds . When crossbreedin g take s place, the gene s of the par ents ar e passed to the cell s o f the offspring . I t is the way that the y mix that is th e clue to Mendel's findings. To simplify ou r explanation w e will look at a hypothetical plan t that ha s onl y one pair of chromosomes in each cell (Figur e 21.2). We will concentrate on the in heritance o f color. We assume that the gene that controls color has two forms, tw o alleles, as they ar e called. On e allele result s i n a yellow pea , the othe r in a green pea. In the cas e o f "pure" yellow plants, the pai r of chromosomes that carrie s th e color genes each has an identical "yellow " gene. Likewise for the "pure " green variety (Figure 21.2). The reproductive cells—the gametes—of the plant, like the sperm and the ovum of humans, contai n onl y half th e numbe r o f chromosomes o f the norma l cell , bu t they ca n contai n eithe r chromosom e fro m eac h pai r i n th e norma l cel l (Figur e 21.2). In our hypothetical case , since w e have onl y one pair o f chromosomes, th e gametes o f a "pure" yellow plan t al l hav e a yellow gene . Now th e singl e pai r of chromosomes in the normal cell ar e not necessarily identical, eve n if both carr y a yellow gene: for example, one chromosome may carry the short-ste m gene and th e other the long-stem gene. Thus in the present hypothetical cas e all gametes carry a yellow gene, but there are two types of gametes. Next take the pollen fro m a pure yellow plant and pollinat e a pure green plant. In principal th e reproductive cells in the receiving plant will also be of two kinds, but in the case of a pure green plant every gamete will have a green gene. Since the meeting o f gametes i s random , an y on e o f the tw o type s o f pollen ha s th e sam e chance o f meeting an y on e of the tw o "receiving " gametes . The consequence s ar e

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Figure 21.2. The inheritance of color. For example, a pure green plant crossed with a pure yellow plant gives all yellow offspring, but they contain (recessive) green genes.

shown in the figure , fro m whic h i t is evident that there are four possible combina tions—two things with two things. In other words, there are four types of fertilized egg, each containing a pair of chromosomes. What will be the colo r of the seeds of each of these egg s when it develops into a plant? Mendel would have guesse d tha t they would al l be yellow. This is because all o f them hav e a yellow gen e in thei r cells , an d i f there i s a yellow gen e an d a green gene, the yello w gene is dominant an d force s th e plan t t o be yellow. Thus , even though the cell s o f a yellow plant may contain gree n genes, they ar e not evident i n it s color. We say that the y ar e not expressed—the gree n gen e is recessive. All of us carry some recessive genes. Now tr y crossin g tw o o f these first-generatio n yellow plants , tw o plant s tha t both contai n on e gree n an d on e yello w gen e (Figur e 21.2) . Th e gamete s o f both plants are now divided int o those that contain a yellow gene and those that contai n a green . W e combin e the m a s before , tw o object s wit h tw o object s a t random . Mendel found that three-quarters of the progeny were yellow and one-quarter were green. We can get this result i f we assume that in a second-generation plan t carrying two yello w genes , th e plan t wil l b e yellow ; if there ar e two gree n genes , th e plant will be green. If there i s a yellow and a green, the yellow dominates an d w e get a yellow pea. As you can see, three out of the fou r fertilize d combinations have at least one yellow gene, giving a ratio of 3:1, for yellow to green, as Mendel found. The fact that a real pea plant has another six pairs of chromosomes is irrelevant to the result; it is only the chromosomes carrying the color genes that control the color of the nex t generation . Thu s th e matin g o f two yello w plant s can , if they ar e no t "pure," give some green progeny—a scandal in the family . Mendel kne w nothin g abou t genes , but b y attributing th e inheritanc e o f single characteristics to a "factor" that could take on a dominant or a recessive character, he coul d explai n th e statistic s tha t emerge d fro m hi s painstakin g work . Th e founder o f genetics publishe d hi s work in 1865 , i n a minor scientific journal, and also wrote to some eminent biologists . You've guessed it—his work was either dismissed or ignored. Mendel was crushed; he gave up trying to publish hi s results . Mendel had read Darwin's Origin of Species, but, strangely, did not appear to see the relevance o f his ow n work to evolution. Darwin is known to have see n a book published i n 1881, citing Mendel's work, but he never referred to Mendel. Mendel's work appeared to have died. And then, in 1900, three scientists independently pub lished result s that completel y confirmed Mendel' s work. De Vries in Holland, von Tschermak in Austria, and Correns in Germany had carried out their work unaware

In a Monastery Garden |

of each other and o f Mendel. All three went to the library to write their papers, and all thre e discovere d tha t Mende l ha d scoope d them . Al l thre e acknowledge d Mendel's prior claim, but he had die d sixteen years before. In 1904, Walter Button, in the United States, realized that genes (he didn't use that word) and chromosomes carne in pairs, and he voiced the suspicion o f several other investigators that genes, which were invisible unde r the microscope, were located on chromosomes, which were visible. Genetics was blossoming. Mendel had created one of the central field s of modern science. His sole honor in his life was to be made abbot of the monastery, not the last time that a scientist ended up as an administrator . The eminent statisticia n an d geneticis t R. A. Fisher ha s suggeste d that Mendel thought up his theory before he did his experiments, and gently cooked his results so as to conform to his expectations . There are reasons for supposing that exact ratios of 3:1, for example, should not be observed. If Mendel did massag e his result s slightly, his confessions must have been rather unicaie for a monk. Interesting Complications We have considere d a n extremel y simpl e cas e o f heredity, the inheritanc e o f one characteristic, determine d b y one gene (for color) with two alleles (green and yellow). Inheritance is often more complicated than this, and the study of inheritance at the genetic level is a major discipline . Her e we will content ourselve s by pointing out some of the simple r basic ideas that are part of the geneticist's armory. We supposed colo r to be simpl y determine d b y tw o alleles , one o f which, th e dominant allele , overrides the actio n o f the recessive allele. There are cases when this dominance i s incomplete, and the various characteristics expressed in the organism ar e a mixture o f those du e t o the tw o alleles . I n th e cas e o f the pea , this would mean that we could breed yellowish green peas. Another complication is that there are characteristics tha t depend on more than one gene. Whatever part of our intelligence is inherited, it is almost certain that it is not due to a single gene, and neither i s skin color. In the case of man, as compared with pea plants, there is an additional compli cating factor tha t has t o be taken into account . Human s exis t i n two sexes. As we mentioned earlier, in the cells of the male there is one pair of chromosomes that is not symmetrical . On e chromosome , the Y chromosome, i s considerabl y smalle r than it s partner, the X chromosome, and carrie s less genes. This asymmetry holds for most animals, although there are a few in which it is the male who has two complete, X, chromosomes, and the female who has one asymmetrical pair. A disagreeable consequence o f the chromosomal difference between the sexes can be appreciated by considering the cas e of a gene that is defective . Suppose the gen e responsible fo r directing the synthesi s o f a certain protei n is located on the X chromosome, which implies that for a woman the gene is on both members o f the X pair (Figur e 21.3). Now suppose that a certain woman has a defective gen e on on e of her X chromosomes. This gene is incapable o f directing th e synthesis o f the protein in her cells. However, we have supposed that she has a corresponding norma l gene on the othe r X chromosome, and therefor e sh e will produce th e protein . If a man ha s a defective gen e for this enzyme o n his X chromosome, there is a chance that he will not have a normal gene on his Y chromosome because th e Y chromosome i s muc h smalle r an d ha s fa r fewer genes ; i t ma y no t even carry that gene. This man wil l suffe r fro m whateve r symptom s follo w from a

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Figure 21.3. Sex-linke d inheritance. The recessive (black) gene in question does not appea r on the short male Y chromosome but i s carried by the female on one of he r X chromosomes.

Figure 21.4. Th e production of mal e gametes, called sperm i n the case of man. The organism in this illustrative case has only one pair of chromosomes.

lack of that protein. Notice that the woman is a carrier; although not suffering fro m the disease herself, she is carrying a defective gene that she can hand on to her children. If it goes to a male child, he ma y suffe r fro m th e deficienc y disease. If it goes to a female child who is unlucky enough to inherit a defective gene from her father , then the child wil l have two defective genes and will certainly suffer fro m the dis ease. Hemophilia is a classic case of a "sex-linked" geneti c disease , and the classi c example is Queen Victoria's progeny. She was a carrier, not sufferin g fro m th e dis ease herself but passing on the faulty gene to some of her offspring . There ar e a variety o f abnormalities associate d with a small percentag e o f hu mans who carry more than one Y chromosome. The best known are XYY individuals, havin g forty-seve n chromosome s an d bein g popularl y dubbe d supermales . Such men appear to have an above-average chance of being violent. Another complicating facto r i n heredity, one that occur s throughout the anima l and plan t kingdoms , i s recombination o r crossing-over. It play s a vita l par t i n heredity. The Gene Blender It is obvious that sexual reproduction mixes the genes of a given population. This is one o f the thing s tha t worr y th e minuscul e brain s o f racists. However , genes get

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In a Monastery Garden

Figure 21.5. Crossin g over. The letters s, t, b, and d stand, respectively, for short, tall, blond, and dark; see text for details.

mixed up i n another way even before fertilization of the egg. They get mixed up i n the cel l of the parents, durin g meiosis, the proces s that results in the formation of the gametes from their precursor (germ ) cells. Let us take a simple example and follow the proces s of sperm productio n in an anima l wit h onl y one pair of chromosomes (Figure 21.4). In the firs t stag e of meiosis, each chromosome is replicated to give four chromosomes in the cell . Thes e crow d together to form a tetrad, which subsequently, via two cell divisions, breaks up to give four sperm cells, each containing one chromosome. I f the tetra d merel y breaks u p t o giv e the origina l fou r chromosome s tha t made it, then there ar e no surprises. The chromosome in each sperm is exactly the same as one of the chromosome s in the origina l germ cell, which mean s that the y are th e sam e a s on e o f those i n ever y cell o f the father . W e have single d ou t tw o genes to illustrate wha t happens . On e is a gene for hair color (dar k or blond) an d the othe r for height (lon g or short). In our example , then, father' s sper m will con tain chromosomes of two types: tall, blond-haired sper m (Scandinavian) and short, dark-haired sper m (Celtic) , so to speak. If there is what is termed crossing-over the situation is more interesting . In crossing-over , two chromosome s temporaril y joi n togethe r an d whe n the y separate, swap pieces of each other, as can be seen from Figure 21.5. This can result in new combinations o f characteristics bein g exhibited i n offspring . I n our case, as you can see, two new kinds of sperm are produced: tall, dark-haired (Scandinavian Celts) an d short , blond-haire d (Celti c Scandinavians) . I t i s becaus e thi s kin d o f shuffling aroun d that a couple can have two children who look very different fro m each other. The last complication that needs mentioning is the most newsworthy: genes can undergo changes in their chemica l structure . Mutations are , as we will see, one of the reasons life developed from a primitive, single-cell organism into a higher for m of life: the drunken , beer-bellied soccer fan.

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Evolution For when he takes his prey h e plays with it to giv e it a chance. For one mous e i n seven escapes by his dalliance. —Christopher Smart, "Jubilate Agno," (My Catjeoffrey)

One day in 1956, during the Sue z crisis, I was summoned to the offic e o f Professor J. B. S. Haldane, the famou s geneticist, biometrist, and ex-Marxist . I was an undergraduate at University College London, and Haldan e was for me an awesome personality. Hi s room was littere d wit h books, random objects , sheet s o f notepaper, and wha t seeme d to be fossil bones . There was a box o f germinating potatoes beneath his desk. "Sit down, Silver." "Thank you, sir." "I'm told you're a leader among the students." He went o n to outline a plan for bringing dow n th e governmen t o f Anthony Eden , whose polic y i n regar d to th e Suez Canal he objecte d to. The plan involve d thousand s o f students, arme d with pennies, phoning government offices i n Whitehall from public telephones. "Whe n the phone rings, replace the receiver immediately. That way you can use the same coin repeatedly." The idea was that this continual tying up of the phones in Whitehall would induce the government to resign. He elaborated, and I sat there amazed at this zany, professorial plot coming from someone who was one of my intellectu al heroes. When the plan had been fully explained , Haldane chatted with me on science. It was, of course, more of a monologue than a chat. At one point I ventured a standard question: "I've always wondered i f life ha s existe d long enough for one-celled organisms to evolve into human beings." He smiled from under his bristly eyebrows, "It took you exactly nine months. " Was there time for an amoeba to be transformed into Frank Sinatra? Is Darwinian evolution credible? There have been two major battles concerning living matter. One has been over the questio n o f the uniquenes s o f living matter: ar e the livin g an d th e nonlivin g worlds separated by what in the nineteenth century was called "vital force," an undefined, occul t "something"? The second, and longer-lasting, altercation, has been over the reality of evolution. The two controversies are connected. In both cases the argument is between those who believe that lif e and , more specifically, the emergence of man, can be explained by the law s that govern the behavior of the inani mate world, and those who don't. The belie f tha t livin g creature s contai n molecule s tha t canno t b e mad e fro m nonliving precursors, or that living matter contains a "vital force," die d down (bu t not out ) i n th e nineteent h century . Evolutio n remains a n are a of controversy, al-

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though the arguments agains t it have the nature o f a desperate, hopeless rearguard action. I n this chapte r I will attemp t t o demonstrat e open-mindedness , but ther e will certainly b e those wh o will condemn m y scientifically conventiona l conclu sions as wrong-minded a t the best and satanic at the worst. Those wh o se e Ol d Nick' s han d behin d th e theor y o f evolutio n stil l tak e o r threaten cour t actio n ove r th e plac e o f evolution i n th e schoo l syllabus . O n th e strictly scientific front ther e are sharp difference s o f opinion betwee n professional research workers as to the exact mechanisms of the evolutionary process in specif ic cases. For example, there is no consensus o n the cause of the so-called Cambrian explosion, the sudden emergence , about half a billion years ago, over the comparatively shor t perio d o f about 2 0 million years , of a great variety o f bigger animals . Nevertheless, the scientific world overwhelmingly believes in the principle o f evolution, an d it is the current , broadly accepte d pictur e tha t will be presented here . The fact that all the detail s have not yet been fille d in is a reflection of the infinite variety of nature, not a sign of a basic weakness in the theory. The Evolution of Evolution First, forms minute, unseen by spheric glass, Move on the mud, or pierce the watery mass; ""hese, as successive generations bloom, New power s acquire, and larger limbs assume. —Erasmus Darwin, "The Temple of Nature "

"Evolution" invoke s Darwin . An d ye t there ar e few ideas that ca n be ascribe d in thei r entiret y t o on e individual. 1 Darwin wa s precede d by Jean-Baptiste de Lamarck (1744-1829), wh o was preceded by Erasmus Darwin (1731-1802) , who was preceded by many eighteenth-century scientists, amateur biologists, and writers, including Diderot . No one who observed the animate world could fail to notice the similarities between differen t species , and to realize that even in the absence of the fossi l record there was a rough hierarchy o f living forms , a steadily increasing complexity that was bound t o suggest the idea that the simpler were the biological antecedents o f the mor e complex. As far back as 1699, the English physician Edward Tyson (1650—1708) had publishe d a n account of the dissection of an orangutan and had pointed out that chimpanzees were anatomically close r to man than to the other primates. Linnaeus, in 1735, commented, "It is remarkable that the stupides t ape differ s s o little fro m th e wisest man , that the surveyor of nature has yet to be found who can draw the line between them." It was he who gave us the name Homo sapiens, making us another species in the animal kingdom, but he also avoided suggesting, or did not dare see, the evolutionary link between man and ape. Over a century befor e Darwi n published hi s ideas , Benoi t de Maillet ha d pro posed tha t bird s ha d evolve d fro m flyin g fis h an d lion s fro m se a lions. I n 1751 , Maupertuis suggeste d tha t ne w specie s coul d b e forme d since , "th e elementar y particles" whic h for m th e embry o "ma y no t alway s retai n th e orde r whic h the y 1 As an ex-rugby player, it is clear to me that the invention o f the game by the immortal William Webb Ellis catching (rather than kicking) the football, and then running with it, is perhaps the only example in human history of a stroke of genius unaided by any other mortal.

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present i n th e parents. " Th e endlessl y curiou s Goeth e suggeste d tha t al l plant s were descende d fro m on e primitive plant , t o which h e gav e the rathe r inelegan t name o f Urpflanze. Ther e wer e other s wit h simila r ideas , includin g Charle s Darwin's own grandfather, Erasmus Darwin, a doctor and inventor, friend o f Benjamin Franklin and o f Josiah Wedgwood. However, Erasmus Darwin based his concept of evolution on a mistaken belief in the inheritance of acquired characteristics, a theory that implies that environmentally induced change s in the parent are passed on to its offspring. Incidentally , the term Darwinism, as applied to evolution, was firs t used in reference to Erasmus Darwin. It was Charles Darwin who summe d u p hi s own and others' ideas to propose a convincing theory of evolution. A ma n wh o undoubtedl y ha d a majo r effec t o n Darwi n wa s th e Reveren d Thomas Malthus (1766-1834), who in his seminal Essay on the Principle of Population (1798 ) propounde d th e thesi s tha t grea t masses o f humanity perishe d be cause they faile d t o compet e for limited availabl e food . Thi s wa s surviva l o f th e fittest. Listen to Darwin: In October 1838, tha t i s fiftee n month s afte r I had begu n m y systemati c en quiry, I happened t o read fo r amusement Malthus on Population, an d bein g well prepared to appreciate the struggle for existence which everywhere goes on from long-continue d observatio n o f the habits o f animals and plants , it at once struc k m e tha t unde r these circumstance s favorabl e variation s woul d tend to be preserved and unfavorable ones destroyed. The result of this would be the formation of new species . Malthus himself had already considered, in the spirit of natural selection, the lowered chances of survival of physically handicapped members of the American Indian community. Darwin took Malthus an d applied his analysis of human histor y to all God's creatures: "It is the doctrine of Malthus applied with manifold force to the whole animal and vegetable kingdoms." Darwin was a candidate for Holy Orders when, twenty-two years old, he set sail on th e HM S Beagle i n Decembe r 1831 . W e probabl y hav e t o than k th e grea t Swedish botanist Linnaeu s for the fac t tha t the commande r of the Beagle was prepared to take a scientist aboard. Almost exactly a century before Darwin stepped on deck, the young Carolus Linnaeus, then a medical student, had joine d an expedi tion to Lapland to examine the local way of life an d to bring back biological specimens. B y the tim e Darwin sailed, i t was commo n practice fo r naturalists, a s they were called, to travel the world on sailing vessels. Darwin's five-year journey to South America changed his life, revolutionized biology, and united man with the natural world. When he set out, he believed in the immutability o f species; when h e returned , afte r observing and collectin g a huge number of biological and geological specimens, he had become convinced that the only rational explanation of the facts was that species evolved into new species. He believed, as most open-minded scientists still do, that all life forms developed fro m one or a few very primitive organisms, although he di d no t speculat e abou t their origin. Darwin was convinced of the realit y of evolution but ha d t o find a mechanis m for it , and this he did in the theory of natural selection, sometimes termed the sur vival of the fittest. Had he lived today, he would have published hi s ideas immedi-

Evolution |

ately, t o establis h priority—an d ge t tenure. I n fact , h e worke d fo r nearly twent y years collecting new facts , thinking, and analyzing, until on e summer da y in 185 8 he receive d a lette r fro m Alfre d Russe l Wallace, a naturalis t workin g i n th e Fa r East. While goin g through a n attac k o f malaria, Wallace lay dow n t o think abou t "any subject s then particularl y interesting me." It occurred to him that "th e fittes t would survive. " Wallace, incidentally, ha d also read Malthus. His letter containe d a shor t descriptio n o f his idea s o n evolution . The y wer e practicall y identica l t o Darwin's. Darwi n ha d t o publis h o r perish , bu t hi s sens e o f fairnes s mad e th e thought of publishing befor e Wallace repugnant: "I would fa r rather burn my whole book than that he or any other man should think that I had behaved in a paltry spirit." In fact, Darwin had a copy of a letter that he had written to Asa Gray at Harvard in 1857, and also possessed the 1844 version of a manuscript tha t he had originall y prepared in 1839. These documents establishe d hi s priority. His friends convinced him to present them, together with Wallace's letter, at a meeting of the Linnean Society in London on 1 July 1858. Neithe r author was present, and no discussion followed the reading of the communication . Th e annual report of the president o f the society for 1858 include d th e following words: "This year has not been marked by any o f those striking discoverie s which a t once revolutionize, so to speak, the de partment of science on which they bear." Oh well. The dat e 24 November 1859 sa w the publicatio n o f On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. A fe w day s befor e th e boo k cam e out , Darwi n wrot e t o Wallace : "God knows what the public will think." Wallace must be given his due, but Darwin not only preceded him, he provided the bul k o f the massiv e bod y o f biological and geologica l evidence tha t gav e th e theory o f evolution it s credibility. Fo r this reason, Darwin i s considered to be th e authentic fathe r of the doctrine of evolution through natural selection . Darwin had hoped to gloss over the inflammatory question o f man's place in the evolutionary ladder , which he barely mentions i n his book, but i t was inevitabl e that most of the fus s aroun d the book was centered o n the questio n o f the origi n of man: Was he part of the evolutionar y saga or wasn't he ? One has the feelin g that if Darwin ha d unequivocall y exclude d ma n fro m hi s theory , the boo k migh t hav e passed almos t unnoticed b y the genera l public. A s it is, there ar e still thos e wh o would like to burn it. The Darwinian Evolutionist's "I Believe"

Those who believe in Darwinian evolution generally believe that life on this planet originated by chance, although that is not an official par t of the theory of evolution. They all believe that the first recognizably living forms were tiny unicellular organisms living i n water, and tha t ever y single species , extant or extinct, is connected by an unbroken chain o f intermediate species to these firs t life-forms . Al l species, here or long gone, belong to one biological family. In Darwin's own words, they can be arranged on "the great Tree of Life, which fill s with its dead and broken branches the crust of the earth, and covers the surfac e with its ever-branching and beautiful ramifications. " Historically, the reasons for believing in this scenario were firs t and foremos t th e possibility , fo r any given species, of finding close relatives. The relationship ma y express itself in a similarity of structure and function. The notori-

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ous example, of course, is Homo sapiens and his similarity to the higher apes, but a child at the zoo can sense the kinship o f the tiger and the puma to her pet cat. That these similaritie s exist , that rough plausible chain s of structural evolutio n can be constructed by examining living species, is undeniable. I t is not true that all living species can be arranged in a branching tree. In the cours e of evolution some of the branches have ended up "dea d and broken"; there are species that have developed from a common, long-extinct ancestor. This is where the fossi l record often fill s i n the gaps. The remains of prehistoric species have been dug out of layers of rock that can be dated. I n broad outline , the olde r the rock s in which a fossil i s found, th e simpler the species. Taken as a whole, the fossil record, which stretches over a geological time scale of billions o f years, reveals an unmistakable, if incomplete, progression of living forms , a slow evolution from simpl e t o complex. How is the evi dence t o b e interpreted ? Thos e wh o believ e i n th e litera l trut h o f th e boo k of Genesis believe that every individual species, plant and animal, was created in one gigantic fait accompli , on Wednesday, Thursday, and Frida y of Creation week. The Darwinian theory of evolution provides a rather different explanation . The Bare Bones of Evolution

At the root of the modern theory of evolution is the genome, the collection of genes that determin e th e physica l characteristic s o f ever y individua l livin g organism . Differences i n th e genome s o f parents an d thei r offsprin g ca n resul t i n mino r o r major physical differences betwee n consecutive generations. The mechanism o f evolution i s based o n the appearance , i n ever y new genera tion, of variants—individuals or groups of individuals o f the sam e species that differ geneticall y fro m eac h othe r to a lesser o r greater degree. A huge amount o f experimental evidenc e show s tha t ther e i s a wid e rang e o f variants i n an y give n generation, althoug h most o f those variation s ar e not particularl y dramatic . Thus even in a fairly homogeneou s isolated societ y like a remote tribe, there ar e variations in height, age of balding, facial structure , and s o on. Some variations may be due t o environmenta l cause s suc h a s better diet , bu t ther e ar e alway s variation s that can more or less confidently be ascribed to genetic differences . There ar e two methods b y which specie s ca n produc e variants : mutation an d sexual reproduction. In the earl y history of life, mutatio n may have been the onl y method. Some basic points: 1. A "mutation " o r "mutant " originally meant an y variant , a n organis m o r smal l group of organisms that differe d i n some observable way, in either form or func tion, fro m th e majorit y o f the member s o f the previou s generatio n o f a give n species. Wit h the birt h an d advanc e o f molecular biology , it became clea r tha t variations i n th e form , appearance , or functionin g o f the member s o f a singl e species are (except in the case of noninherited diseas e and obvious environmental factors ) cause d b y variation s i n DN A composition. (A n "obvious environ mental factor " coul d be, fo r example, th e compan y barbe r responsible fo r th e crew-cut appearance of enlisted men.) It also became apparent tha t som e mutations were created by chemically and physically caused damage to the chemica l structure of DNA. We shall adopt the current usage, which is to confine the term mutation t o a chang e i n DN A caused b y a n externa l agen t o r a n interna l re -

Evolution |

arrangement o f the DN A molecule. Variant s caused by sexual reproduction are not terme d mutants . Nonbiologist s ofte n overloo k the rol e o f sexual reproduc tion, unjustifiabl y assumin g tha t onl y mutatio n ca n creat e th e wid e rang e of variants tha t i s the basi s o f natural selection . Th e mixin g o f genes that occur s during fertilizatio n is by far and awa y the main cause of the variants that occur in any one generation in species that reproduce sexucilly. 2. Ove r a geological time period, multitudes o f variants have appeared. 3. I n the natural environment o f a colony of a given species, there will occasionally be cases in which one or more variants have characteristics tha t enabl e them to survive or to multiply mor e efficiently tha n all other variants present . 4. Th e advantage possessed by such a "superior" organism , and which ensures its surviving longer and/or breeding faste r tha n othe r variants, normally results i n that organis m becoming the majorit y varian t afte r on e or more generations, if it is not threatened by subsequent, even more superior, variants. This is natural selection, the survival of the fittest. This, in the barest possible outline, is the mechanism o f evolution: natural or induced variation s i n ever y generation, plus natura l selectio n o f the fittest . Darwi n did no t hav e the benefi t o f our knowledg e o f the molecula r mechanism o f evolution; this is how he expressed his general conception of evolution in a critical passage from Chapte r 4 of his book: Can it, then, be thought improbable, seeing that variations useful to man have undoubtedly occurred, that other variations useful i n some way to each being in the great and complex battle of life, should sometimes occur in the course of thousand s o f generations? If such d o occur , can w e doub t (rememberin g that many more individuals ar e born than can possibly survive) that individ uals having any advantage, however slight , over others, would hav e the best chance of surviving and of procreating their kind? On the other hand, we may feel sur e that any variation in the least degree injurious woul d be rigidly destroyed. This preservation of favorable variation s an d th e rejectio n of injurious variations, I call Natural Selection . It i s essentia l t o realiz e tha t evolutio n i s a n automati c process ; i t involve s n o "will" on the part of the organism involved, and the occurrence and type of a given variation, unles s huma n being s deliberatel y intervene , i s governe d b y chance . There is no instinctive driv e in a living organism to create "higher" form s o f life. It is the combination o f chance variation and the environmen t that gives evolution a direction. A well-known example of the evolutionary process, which has taken place within you r lifetime , i s tha t o f the adaptatio n o f certain bacteri a t o antibiotics . I n a colony o f bacteria dose d with penicillin, i t is quite possible tha t ever y single bacterium will perish. However, it is difficult t o find a colony that is genetically homogeneous, because mutations resul t i n bacteria whos e geneti c makeup differ s fro m that o f the majority . Ther e could be many kinds o f mutants, and i t is possible that most o f them wil l peris h alon g with th e majorit y variant , bu t i t i s eviden t fro m medical records that ove r the years certain strain s (mutants ) have flourished even in the presence of penicillin. Thes e are the mutants whos e genetic makeup confer s

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on them the ability to resist the fatal actio n of penicillin tha t kills off their less talented brethren. We have selected a new "species" that, because it is fitted to its environment, will become the dominant mutant in the colony as long as the threat of penicillin i s present. The appearanc e of a completely penicillin-resistant typ e of bacterium need no t be accomplished by a single mutation. It is quite possible that none of the mutants in a given generation is particularly resistan t but that ther e are a few that, though all but wipe d out , are sufficientl y resistan t to be the majo r specie s afte r th e mas sacre. Thes e mutants ar e no w th e origi n o f further mutants , some o f which ma y well be less resistant and some more. And so on. Mutations are chance events, and there is frequent misunderstandin g of this point. The bacterium does not know in which "direction" it is supposed to mutate; it has no will; it does not size up the situation, gird its genes, and hea d fo r the pass . If it i s unlucky, none o f the mutant s will stand up to penicillin, and that colony will perish. Was There Enough Time?

If Homo sapiens had develope d from one-celled organism s over a period o f a few thousand years , one could b e forgiven fo r saying, "This couldn't hav e happened , that fast , by a chance series of variations." Sexual reproduction doesn't usually result in marked differences betwee n generations, and a s for mutations, the chang e per mutation would have had to have been too big to be believable to create a man from a n amoeba in a million years, let alone a few thousand. Evolution is not a science fiction film ; ants don't mutate into elephants in one step. But we are not talking about a million years. Evolution has been taking place over a time scale that is so huge as to be beyond our ability to grasp. Was there enough time? If one looks at human history, the living species that are familiar to us appear to have changed negligibly over a period o f several thousan d years. Is such a slow rate of change sufficien t t o get from one-celle d organism s t o man over the span of time for which lif e has been estimated to exist? Furthermore, both i n natur e an d i n the laboratory , when w e d o observe mutational changes in species, these changes are small, at least in comparison with th e differences betwee n a cockroach and a gorilla. Was there enough time for a succession of such small changes to result in a cockroach, let alone a man? How muc h tim e wa s available ? Thi s wa s a problem that worrie d Darwin , because i n hi s da y the estimate d ag e of the Eart h was embarrassingl y short . I n th e eighteenth centur y Buffon deduce d a figure o f 74,832 years, not exactl y what Darwin wante d t o hear . I n 185 4 th e Germa n scientist Helmholt z calculated tha t th e Sun could not have been shining for more than 20 million years . This helped, bu t not enough; 20 million years was far too short for Darwin's purposes. Darwin had allie s in the geologists, in particular James Hutton (1726-1797) and Charles Lyell (1797-1875). Hutton , in his Theory of the Earth (1795), had conclud ed that the rock structure of the Earth had require d a n immense stretc h of time to form, an d tha t th e Eart h revealed "no vestig e o f a beginning—no prospec t o f an end." Lyell warily avoided discussing the origins of the Earth, but it was clear fro m the tex t that he believed the ag e of the Eart h to be immense. Darwi n should hav e listened t o Kant , who i n 175 4 publishe d a n essa y with a most un-Kant-like title: Whether the Earth Has Undergone an Alteration of Its Axial Rotation. His estimation of the Earth's age was in the range of hundreds of millions o f years. In the end,

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Darwin sidestepped the problem, not hazarding a guess at the date of the Creation. We now believe that the Earth came into existence about 4600 million years ago. The earliest signs of life that we have date to about 3. 6 billion years ago, with animals emergin g perhaps over 1 billion year s ago. For much o f life's history , the or ganisms that flourished were unicellular o r very simple, and such organisms usiially have a very small "turnover" time. A colony of bacteria can easily produce a new generation withi n twenty-fou r hours , a s agains t twenty-fiv e years fo r humans . Thus the number of generations between the first recognizably living organism and Homo sapiens can be very conservatively estimated at 1,000 million. Now, even before sexual reproduction weighed in as a contribution to the production of variants, each generation almost certainly produced mor e than one new mutant. Simpl e organisms, and even such complex forms as insects, exist in huge numbers, and this means that very large numbers of different mutant s coul d have occurred in a given species in quite a short time. Some of these must have been steps "up " th e evolutionary ladder. And think of how many generations there have been! We have not formally demonstrated that there was time for man to have evolved, but we can see that the number of possible step s between th e earliest and most recent species was unimaginably large . This i n itsel f doe s not prov e that evolutio n took place, but it allows us to believe in its possibility. We could shorten the time estimated for the evolution of man by supposing that among the mutations occurring in any one generation, there are always one or more that result in a major chang e in the for m an d functio n o f the next generation. This is a highly unlikely scenario. First, we have almost no evidence for such mutations. Second, the ver y smal l amoun t o f evidence that ther e i s show s tha t a n organism that i s drastically differen t fro m th e res t o f its specie s is unlikely t o survive as an individual or to breed. As we see with humans, very significant genetic changes are almost always classified as "defects," because they make life harder, not easier. Man-rnade Evolution The evolutionar y proces s i s not uniqu e t o nature. Ma n has carrie d ou t processes that mimic natural evolution. The best known is the breeding of animals for a specific purpose, the commonest examples being the breeding of racehorses and sho w dogs. All the element s of evolution ar e present. Horses that are fast runners are selected fo r mating , and th e successfu l runner s amon g thei r progen y can expec t a similar fate. Th e selection process and th e characteristi c (speed ) for which th e selection is performed are, of course, entirely controlled by man, who i n this case is part o f the horses ' "natural " environment . Th e differenc e betwee n thi s environ ment and nature is that nature automatically selects for survival, while in the case of human selectio n the "losers " (th e slower horses) are not doome d to become extinct. The same is true of dog breeding, in which it is the look of the dog that is the selection criterion. The dog world is in no danger of being overtaken by fancy-looking poodles; they do not compete for food with the average mongrel, who hopeful ly has a good home.2 In bot h thes e example s o f animal breeding , ma n ha s dippe d int o a heteroge2 Animal breeding was another of Darwin's triggers: "I was brought to my view by consideration of that which was practised in domestic animals, artificial selection." Letter to Sir Charles Lyall, 25 June 1858.

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neous genetic pool and the characteristics sought (i.e. , speed and good looks) are at least partially under geneti c control. If they were not, it would be a fruitless exer cise to attempt to encourage the desired characteristics by breeding. An exampl e o f man-made evolutio n a t th e molecular leve l i s provide d b y th e work of Spiegelman in the lat e 1960s, a condensed accoun t of which i s appended to this chapter . In short, molecules of ribonucleic aci d (RNA ) were isolated fro m a virus. These molecules can ac t as a template, on which copies of the RN A can be assembled b y the linkin g together of smaller molecule s present i n th e sam e solu tion (Figur e 22.1). Some of these copie s are defective—a mutan t has been created. These mutant s wil l themselve s for m template s fo r a furthe r generatio n o f RNA, which wil l als o includ e som e mutants. In the cours e of the experiment , th e RNA mutated to give a succession o f different forms . Each form copie d itself at a differ ent rate. After seventy-fou r successiv e generations, the specifi c RN A that survive d was tha t whic h copie d itsel f fastest . Th e "fittest " RN A had survived . Ther e wil l doubtless be useful application s of this type of procedure, and much wor k has followed Spiegelman' s experiments , bu t th e poin t fo r us i s that th e mutation s wer e completely random; no one told the mixture to try to produce faste r breeding mutants, no will was involved. In fact, at any particular stage there may be no new mutant formed tha t is copied faste r tha n the fastes t mutant at the previous stage . And yet the overall result wa s that the syste m produced "species" that bred faste r tha n both their ancestors and their less well-adapted companions. That's how evolution works—by chance , no t b y will. I stress thi s because ther e are , amon g thos e wh o have accepted the phenomeno n o f evolution, many who have suppose d tha t will , or somethin g aki n to it , i s the drivin g force . I t is difficul t t o se e how a system of molecules in a test tube can have will. The Superfluousness of Will The wil l t o surviv e i s a universa l huma n characteristic . I t i s also , apparently , a characteristic o f nonhuman life-forms , "apparently " becaus e there i s very seriou s doubt that the patterns that such forms exhibi t in life-threatening situations are the product of will. There is no evidence that anything except man demonstrates will.

Figure 22.1. Spiegelma n demonstrates molecular evolution; see text for details .

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The fact that an animal fights for its life is not evidence o f a will to survive. It is evidence of Darwinian evolution. Those foxes that live today are overwhelmingly the descendants o f thos e whos e lifesavin g behavio r favore d thei r survival . Foxe s whose behavior di d not help them surviv e i n life-threatening situations wer e mutants that were weeded out by natural selection. Thei r unsuccessful genes were not handed on. The concept of will as a driving force inherent in human beings has appeared in many guises. George Bernard Shaw invoked the life force, and h e was not the firs t or last writer to seek an undefined spiritual fuel fo r th e living world. In the prefac e to Back to Methuselah, Sha w writes: "The will to do anything ca n an d does , at a certain pitc h o f intensity, . . . create and organiz e new tissu e t o d o it with." Elsewhere in the same preface he typifies Darwinism as a "rotten myth." One can sympathize: creation myths are usually replete with charismatic god s or goddesses, supernatural transformations , an d al l the brillian t scener y o f an Italia n opera . And here comes Darwin with his prosaic mutations . Shaw echoes Nietzsche's concept of Will (wit h a capital w), a kind o f animate force directin g nature. Nietzsche was not a Darwinian: "The influence of the envi ronment is nonsensically over-rated in Darwin... the essential factor in the process of lif e i s precisely the tremendou s inne r power to shape an d creat e new forms , which merely uses, exploits 'environment.' " Schopenhauer sa w unconscious Wil l as the ultimate reality , a purposeful, irrationa l forc e that manifests itself in the phenomena of the natural world. He became intoxicated with his own ideas and ended up believing that it was will that drov e the evolution o f the cosmos, the geological history of the Earth and biological evolution. The hidden assumption behind th e myth o f the will or the lif e forc e i s that th e living noiihuman world i s somehow consciously pressin g in th e directio n of perfection, or at least better adaptation to its environment. This concept is wrong. Evolution is based on variants, including mutants, and it stretches credibility to accept that th e molecula r processe s responsibl e ar e unde r eithe r consciou s o r uncon scious control. The fact is that many mutations result in an organism becoming 7ess well adapte d to its environment . Th e deat h force ? I t is far simpler t o assume tha t those who are better adapted, adapt better. The fac t tha t th e formatio n o f mutant gene s in natur e i s a questio n o f chance does not mean that al l types of mutation are equally probable, like all possible sequences o f thre e card s draw n fro m a ful l pack . Mutatio n involve s a chemica l change, and suc h change s do not all proceed at the same speed. Certain mutations will be favored because they occur through relatively easy chemical changes. It is worth stressin g yet again that within th e range of variants foun d i n a given population, on e canno t automaticall y expec t a preference fo r those tha t hel p th e species to survive better. Thus if a certain mutant has properties that confe r o n it a greater chance of survival than its parents, that is pure chance—it has nothing to do with purpose. How Is Evolution Studied?

Evolution can be studied in the natural worl d an d in the laboratory. Under laboratory conditions it is advantageous to work with organisms that breed rapidly, thus allowing ne w variants t o develo p int o significan t populations by reproducing for

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several generation s i n a shor t time . Bacteri a an d certai n insect s ar e convenien t from this point of view. Darwin himself took the natural world as his laboratory, observing animal form , function, coloration , and distribution . H e began by observing living species rather than fossils, an d as a result of his (an d Wallace's) theories, th e way in which anatomists looked at animals changed . Of course, similarities between the forms of different specie s had been noted before Darwin . Lamarck had use d suc h similaritie s t o arrive at a primitive theor y of evolution, and he must be given credit for emphasizing the vital significance of fossil remains, which are , after all , the only evidence we have for the temporal ordering of living forms over the past few billion years. Rocks originating nearly 4 billion years ago are the firs t to show any remains of living organisms, and these fossils are of microscopic forms o f life. It was anothe r 2 billion year s before vertebrate fossils began to be laid down , and lan d animal s only appear i n the fossi l record in rocks formed les s tha n abou t 60 0 million year s ago . The progressio n o f form s i s very clear.3 After The Origin of Species, n o on e coul d compar e tw o simila r livin g form s without lookin g for the origin s o f the more complex species in the anatom y of the simpler, o r searching for a joint origin for the tw o species . Anatomy , first externa l and then internal, remained for many years the main lens through which evolutio n was scanned, and under anatomy must be included the structure of fossils. The tools that have become available to study evolutio n have multiplied sinc e Darwin's day . Unde r th e microscope , anatom y become s morphology , an d fro m comparing thighbones , evolutionary biologists turned t o comparin g the structur e of cells and their components. With the coming of molecular biology, the investigation went dow n to the most intimate leve l at which on e can expect difference s between species . Sinc e genes control the natur e o f all the molecules produce d by a given species, we can attempt to find evolutionar y connections between species by examining variation s i n th e structur e o f th e molecule s tha t the y possess . I t i s known that the molecular makeup of a protein molecule in one species may diffe r in detai l fro m tha t of a molecule performing the sam e function i n another species . Thus th e hemoglobi n molecule , whic h latche s o n t o oxygen , differs i n it s exac t structure between different mammals . This variation does not apply to simple molecules; you wouldn't expec t the water molecule in the cell s of catfish to be differ ent from that in the blood of zebras, and the structure of the small molecule glucose is th e sam e i n yeas t an d i n man . However , for large molecules, particularl y proteins, it has been found tha t the detaile d compositio n o f molecules with the same function ca n diffe r betwee n species because there are parts o f such molecules that are essential an d parts that are not. Thus enzyme molecules, which ar e invariably very large, have regions known as "active sites" (see Chapter 13), which are responsible for the actio n of the enzyme . Changing the natur e of the sit e destroys the en zyme's ability to perform it s task, but there are other regions that are far less sensi tive fro m thi s poin t o f view an d ca n b e slightl y change d withou t affectin g th e action o f the enzyme , just as the performanc e of a concert pianist is , or should be, unaffected b y his or her having a haircut. Enzymes that have exactly the same func3

Possibly the first person to sense a correlation between geology and paleontology was Robert Hooke who, in the seventeenth century, suggested that fossils be used to establish the chronology of rock formations.

Evolution |

tion i n differen t specie s almos t alway s hav e simila r activ e site s bu t diffe r i n th e ammo acid composition of the rest of the molecule. In general these differences are smaller the nearer we consider two species to be in terms of evolution. Thi s is exactly what we woul d expect . Thu s th e enzym e superoxid e dismutas e appear s i n the cells of higher animals but als o in organisms dow n to the level of bacteria. The amino acid sequence in the enzyme differ s fro m species to species, but the general similarity i s unmistakable an d th e difference s ten d t o be smaller , the smalle r th e evolutionary distance between any two species. A powerful means o f linking specie s is DNA analysis. Ou r DNA contains all the information responsible for our basic physical appearance. This being so, we might expect that , paralle l t o the visuall y obviou s similaritie s betwee n certai n species , we will find similaritie s betwee n thei r DNA, and that it might be possible to trace the evolution of DNA just as we trace the evolution of wings or eyes. Much work of this kind has been done. Much remains to be done, but the similarity o f the DNA of species tha t hav e been related o n other criteri a i s unmistakable. Th e general picture emerging from thi s researc h i s entirely consisten t wit h the premise that relatively small changes in DNA form the basis for the evolution of the marvelous variety of living forms. We see that not only is there a more or less continuous evolution in the visibl e forms of animals and their organs, but there also is a trail left by the molecular variations tha t w e fin d i n chain s o f related species . Th e creationist s wil l have to explain why Satan took a freshman course in molecular biology. Evolution is studie d i n fa r subtler way s than th e simpl e observation o f macroscopic o r microscopic variation . Fo r example, animal behavior, a fascinating and complex subject, is revealing som e extraordinarily interesting behavioral determi nants of the selection process. An area that has attracted much attention i n recent years is sexual preference. Why does an animal prefe r to mate with on e member of the opposite sex, and not another? Among humans the situation i s complicated by considerations tha t ar e foreig n t o th e res t o f the livin g world . Mercenar y femal e chimpanzees ar e no t attracte d t o wealthy , cigar-smokin g males. Bu t animal s d o show preferences, and many of these ca n be shown to be genetically determined by the genetic constitution o f both male and female. This is clearly a selection process in the Darwinian sense . It is too specialized a subject for us, but i t does hint at the complexity o f the evolutionar y process , which tend s t o get simplified i n popula r science text s t o talle r giraffe s winnin g ou t agains t shorte r giraffe s i n th e figh t fo r leaves on trees. Cherchez la Femme

Among the component s o f animal cell s ar e small structure s calle d mitochondria, whose functions ar e discussed late r (see Chapter 26). Mitochondria ar e unusual i n that they are one of the very few cell components no t produced on orders from th e DNA i n th e chromosome s withi n th e nucleus ; the y -contain their ow n DNA. Furthermore, whe n cell s divid e an d proliferate , thei r mitochondri a reproduc e inde pendently; their DNA replicates an d is inherited entirel y independently of the nuclear DN A in th e chromosomes . Thi s mean s tha t mitochondri a hav e thei r ow n proliferation mechanism , a kind o f segregated priesthood. No w mitochondria ar e too big to get inside sperm , which mean s that the origi n of all the mitochondria in

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every cel l o f your body is the handful of mitochondria tha t were in your mother' s egg when it was fertilized. What this means is that your mitochondria! DNA is a gift from your mother; your father had nothing to do with it. Furthermore, since she got her DNA from her mother, and so on, it is apparent that you can trace the history of your mitochondrial DN A through the female line of your family. Analysis o f the mitochondria l DN A of differen t huma n race s no t unnaturall y shows clos e similaritie s within eac h rac e an d greate r diversit y between differen t races. By comparing the nature of these similarities an d differences , i t has been inferred tha t al l th e mitochondria l DN A was derive d ultimatel y fro m a commo n source—Africa. This research is part of the ongoing search for the origin, or origins, of moder n man . It s conclusion s have , however , bee n challenged , especiall y b y those who rel y more on the evidenc e o f comparative studie s o n fossils. The skep tics present evidenc e supporting their claim that modern man appeared in severa l places o n th e globe , mor e o r les s independentl y evolvin g fro m mor e primitiv e forms. Bot h side s clai m t o b e right , bu t neithe r sid e ha s th e slightes t doub t tha t Homo sapiens i s the end product o f evolution.4

Appendix: Molecular Evolution The bacterium Escherichia coli is a common resident in commercial foods prepared under unhygieni c conditions . Thes e bacteri a themselves can become infected by a virus, th e Q B bacteriophage. This virus , like all living forms , contain s th e gene s essential to its reproduction. However, viruses are extremely simple forms of life with a very limited, if efficient, rang e of structures and functions. Sinc e the physical characteristics of an organism are genetically controlled, the rathe r short strip of RNA that acts as QB's genetic material contains only four genes . The RNA strand is composed of a chain o f small molecules called ribonucleases. In principle a solutio n o f these could be assemble d to give a strand of RNA by using an alread y existing strand as a template. This can be done using the good offices o f an enzyme—"replicase" (Figure 22.1). One of the virus's genes provides the cell with the information needed to synthesize this enzyme. It is possible to disintegrate the QB virus and isolate its RNA and the enzyme replicase. Spiegelman found that if a sample of this viral RNA is placed in a solution containing a mixture o f the righ t ribonucleases (th e building block s of the RNA ) and a touch o f th e enzym e replicase , ne w molecule s o f RN A ar e manufacture d (Figure 22.1). However , replicase ha s a ba d wor k ethic ; i t frequentl y produce s imperfect copies—mutants. These mutants differ fro m th e origina l RNA in th e exac t sequence of the different nucleosides in the strand. It is as though the sentence written with nucleosides had ha d it s words scrambled, so that, for example, a section of RNA might "read" . . . bda . . . instead o f . .. dab. . . . Now this first generation of new RNA , mu tants and all, can be replicated again, using replicase and more nucleosides. However, not surprisingl y each mutant is reproduced at a different rate, depending on it s constitution. 4

Just to complicate matters , there has been a claim, by Sir Alister Hardy in 1960 , that we are descended fro m aquati c apes.

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Spiegelman mad e a mixture o f the origina l RNA, nucleosides, and replicas e an d left i t for twenty minutes. Durin g that time a variety of mutants were produced. Suppose that on e particular mutant , sa y mutant A , is copied faste r tha n th e other s an d than th e origina l RNA . Its proportion will increas e a t the expens e o f the othe r mutants. After twent y minutes Spiegelma n transferred a small portion of the mixture to another test tube containing fres h nucleoside s an d replicase. The replicase will continue to produce new copies, favoring mutant A, the proportion of which will furthe r increase. However, replicase continues t o make mistakes and produce new mutants. Some o f these wil l replicate slowe r than mutan t A , but possibl y on e will replicat e faster. Cal l i t mutan t B . The proportio n o f B will increas e a t the expens e o f all th e other species, including mutan t A. Spiegelman repeated this transfer fro m on e tube to another seventy-fou r times. At each step there was a chance, but no guarantee, that at least one of the mutants would grow faste r tha n an y o f its predecessors . The mutan t tha t gre w fastest di d s o at th e expense o f the others . A t the en d o f the experiment , there wa s a dominant mutan t that was being copied a t about fifteen time s the replicatio n rat e of the origina l RNA strands. It is reasonable to suppose that the shorter a mutant is, the quicker it is replicated, and in fact the mutant RNA that survived was only about 550 nucleotides long, compared with the origina l 4500. In the languag e of evolution, the RN A had "bred " for man y generations, during which tim e a large number of mutations had occurred . The mutant tha t dominate d a t the end was that whic h survive d because i t bred th e fastest in its (man-made) environment.

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23 The Descent of Man Man is descended from a hairy tailed quadruped probably arboreal i n his habits . —Charles Darwi n

Copernicus and Galileo moved the Earth from the center of the solar system and invoked the wrath of the Church, because they had removed man fro m th e center of the universe.1 An earlier heliocentric hypothesis , put forward by Aristarchus in the third century B.C. , was greeted by a demand that the author be indicted o n a charge of impiety. Darwinism was worse; evolution not only denied th e literal interpreta tion o f Genesis but als o questioned th e uniqueness o f man. The record shows tha t the main irritan t was Darwin's attack on man's status, although th e truth i s that in the whole o f The Origin of Species ther e is only one passing, although admittedl y provocative, reference to man. On page 488 of the first edition the hope is expressed that "ligh t will be thrown o n the origin of man and his history." It was only in his Descent of Man, published twelve years later in 1871, that Darwin specifically stated, "He who i s not content t o look, like a savage, at the phenomena of nature as disconnected, cannot any longer believe that man is the work of a separate act of creation. . . . [M]an is descended fro m som e lowly organize d form." To rub i t in he wrote, "My object in this chapter is to show that there is no fundamental differenc e between man and the higher animals i n their mental faculties. " The lighted matc h had been thrown into the petrol tank. No scientific text since the Principia has had such a widespread influence on thinkers, poets, writers, and society in general. It did not help Darwin that he made no bones about his agnosticism. The ex-candidate fo r Holy Orders wrot e tha t th e Ol d Testament "wa s n o more t o be truste d than th e sacre d books o f the Hindoos , or the belief s o f any barbarian." H e was n o kinder to the New Testament, and he was also not the first to have trouble with the problem o f a God who stoo d by and watched suffering : "I t revolts our understand ing to suppose that his [God's ] benevolence is not unbounded. " The agnosti c Darwi n was burie d i n Westminste r Abbe y on 2 6 April 1882 . Hi s Origin of Species remain s the most widely talked abou t and controversia l book in scientific history , and eve n if the Churc h would not burn him , it could not ignore him. O n readin g hi s book , the wif e o f the bisho p o f Worcester had appeale d t o heaven: "Le t us hope i t is not true, but i f it is, let us pray that i t does not becom e generally known!" The good lady's pious plea was not answered. The battles started within month s o f the publication of the book. The first skirmish took place at Oxford on 30 June 1860 between the redoubtable 1

In 1990, a third of the adults in England believed that the Sun went aroun d th e Earth (fro m a survey reported i n the Lancet).

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T. H. Huxley (wh o coine d th e ter m agnostic to describ e himself ) an d th e estab lished Church , a s represente d b y th e bisho p o f Oxford , Samue l Wilberforce . Wilberforce, whose credentials wer e bolstered by the fac t tha t he was a competent ornithologist, had taken advice from Richar d Owen, a paleontologist and ex-frien d of Darwin, who not only bitterly resented the attention tha t Darwin was getting but also ha d bee n challenge d b y Huxle y in a n argument ove r the differenc e betwee n the brain of man and that of other animals. Owen had claimed that only in man was there a certain area of the brain calle d the hippocampus minor . Huxley's denial of this claim annoyed Owen intensely. Huxley, who was a loyal friend o f Darwin, had been converte d from hi s skepticis m regarding natural selectio n by Darwin's book. At Oxfor d h e wo n th e debatin g due l wit h Wilberforce . A t th e sam e meetin g a lengthy defense of Darwin was delivered by Joseph Dalton Hooker, a distinguishe d naturalist who, lik e Huxley, had initiall y bee n ver y critical o f evolutionary ideas but ha d see n th e light . Year s later Bisho p Wilberforce grudgingly conceded tha t there was some merit to Darwin's ideas, but the themes of the Oxford encounte r remain t o haunt all the subsequen t confrontation s between impassioned reaso n and impassioned faith . Th e antievolutionist s retur n agai n an d agai n t o th e affron t t o man's uniqueness an d to God's omnipotence. Bishop Wilberforce's taunts as to the simian ancestr y o f Huxley have been echoe d a thousand time s i n th e Bibl e Belt. The attitude o f the "antis " is that man i s too important to have been a chance descendant o f a one-celled ancestor—he could only have been personally created by the Creator. Consistent with this belief are those whose objection s to evolution are predicated o n the existenc e o f an entit y calle d the soul , which is presumed t o be the unique possessio n of man. This problem was brought up te n years before Darwin's book, by Hugh Miller in Footprints of the Creator (1847). Miller pointed ou t that if the "development hypothesis" was accepted and Homo sapiens is supposed to have descende d fro m lowe r form s o f life, the n i t i s arguable that th e sou l als o evolved i n thes e forms . Wha t would b e lef t o f man's uniquenes s i f Bonzo ha d a soul? Miller concluded that man is not a continuation o f the animal kingdom. Science has advanced since Darwin's day. The evidence is now so strong that it would be almost impossible t o find, eve n among the most rabid antievolutionists , someone who denies the existence of mutations or the mixing of genes due to sexual reproduction. An d i f these phenomen a exist , then there is a mechanism for the creation of new specie s from old . A reasoned refutation of evolution has become so difficult tha t the opposition is now largely confined to fundamentalists, those who believe in the literal truth o f the Bible, and specifically in Genesis 1:27: "And God created man in His image, in the image of God He created him; male and female He created them." This leaves little room for argument. Genesis is a powerful an d brilliantly imaginative myth. As an account of the origin of the Earth and the creatures living on it, it is wildly improbable, but creationist s believ e that the theory of evolution is "simply the continuation of Satan's long war against God." Fundamentalists have found ingenious ways to discount the scientific evidence for evolution . The classi c exampl e i s the suggestio n that fossils wer e deliberatel y concocted and place d i n the Earth by Satan himsel f in orde r to deceive man, an d that on e ca n eve n detect a devilish whif f o f sulfur a t the site s o f fossil remains . In fairness t o the proponent s o f such views, it must be conceded that they cannot be disproved, either by reason or by observation. They are just staggeringly improbable, which is why I will ignore them.

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Nevertheless, the argument over the theological validity of evolution is depressing. A world i n whic h i t too k a Vatica n committe e thirtee n year s t o grudgingl y come to the conclusion (i n 1992!) that Galileo had been wrongfully condemned by the Church in 1633 is a place where reason needs as many friends as it can get. Darwin's Fan Club

It was predictabl e tha t par t o f the oppositio n t o Darwi n woul d com e fro m orga nized religion. On e of the few clergyman who bucked the trend was Charles Kingsley, whose best-known work, The Water Babies, contains references to the controversy ove r evolutio n an d t o th e mai n antagonists . I n particular , h e refer s t o Huxley's spat with Owen over the hippocampus minor , writing that the victory in the grea t hippopotamus debat e ha d gon e t o th e well-know n exper t i n necrobio neopalaeonthydrochthonanthropopithekology, Professo r Ptthmlmsprts . I n th e spirit of the Deists, Kingsley considered Darwin to have disposed o f "an interfering God." He made no impressio n o n his clerica l colleagues , perhaps becaus e he declared that in Heaven the saved indulged in continuous sexual intercourse. Whic h is one way of making converts. It is often forgotten that, at the time, not everybody regarded Darwin as the spearhead of the threat to faith. A couple of months after The Origin came out, a collection of articles on religion appeared, entitled Essays and Reviews (1860). Written almost entirely by Anglican clergymen, this adopted a very liberal stance . Miracles were downplayed and reason lauded. Th e uproar was, if anything, more impassioned than the response to Darwin. The Church was being attacked from within. Unsuccessful attempt s were made to have the authors prosecuted for heresy. Likewise, despite the high-profile debate at Oxford, it is a mistake to suppose that the resistance to Darwin came solely from the Church. Darwin's own professor of geology at Cambridge declared that his forme r pupi l was plunging humanity into " a lower grade of degradation than an y yet recorded." Darwin, he said, was "deep i n fallacy." Other devout scientists fel t similarly . One of them was the fundamentalist marine biologist Philip Gosse, whose son Edmund describes his father's reaction to natural selection , in a classic and moving autobiography, Father and Son (1907). Philip Goss e had alread y been shake n b y Lyell's suggestion that the Eart h had developed ove r a very long time perio d durin g whic h new specie s ha d appeare d and other s ha d becom e extinct . "Her e wa s a dilemma! " wrot e his son . "Geolog y certainly seemed to be true, but the Bible, which was God's word, was true." Philip Gosse spoke to Darwin in 1857 and was informed, in advance of the publication of Darwin's book, of the theory of natural selection. His son Edmund Gosse wrote, It wa s thi s discovery , tha t ther e ar e tw o theorie s o f physica l life , eac h o f which was true, but the truth of each incompatible with the truth of the other, which shook the spirit o f my Father with perturbation . .. he allowed the turbid volum e o f superstition t o drow n th e delicat e strea m o f reason. He took one step in the servic e o f truth, an d the n he dre w back in a n agony, and accepted the servitude of error. Philip Goss e went a s far as publishing a book, Omphalos (1857) , which claimed , "When the catastrophi c ac t of creation took place, the worl d presented , instantly ,

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the structural appearance of a planet on which lif e had long existed." The book was hammered by both atheist s an d Christians . Charle s Kingsley wrote t o the autho r that he could not believe "that Go d has written o n the rocks one enormous and superfluous lie. " Darwin's dramatic vision o f man's evolutio n from th e primeval seas stimulate d many o f the writer s an d thinker s o f the lat e nineteent h century . On e who wa s swept of f his fee t by The Origin of Species was th e autho r of The Way of All Flesh, Samuel Butler. Again the revolt against religion was lurking in the background, but this time Freud would have had got his notebook out. Butler did not get on with the authoritative figur e o f his father , a clergyman , a headmaster , an d eventuall y th e bishop o f Lichfield. Th e so n found i n the theor y of evolution a convenient crutc h for hi s rejectio n of Christianity and God . But eventually Butle r returned t o a personal God of his own , rejected Darwin , and proceede d to write a number of books on evolution in which the theme was that Darwin was mistaken in his suppositio n that the variability in one generation of a species was just a question of chance. Darwin had removed will from nature ; Butler wanted to restore it by postulating tha t living form s striv e to overcome the difficultie s i n thei r environmen t and tha t because o f thi s effor t the y develope d better-adapte d organs , o r mode s o f action , which the y passe d o n t o thei r offspring . Butle r succeede d i n annoyin g both th e Church and th e follower s of Darwin. For those o f you who fea r th e dominatio n of the computer , try reading Darwin among the Machines, i n which Butle r sees machines competin g successfully with man , threatenin g t o be the fittes t t o survive . Butler's convictio n tha t evolutio n wa s drive n b y wil l ha d a dee p influenc e o n George Bernard Shaw, another one of those who liked to conjure up th e life force — whatever that may be. The poet Alfred Tennyson was an acquaintance of Darwin and was far more than averagely intereste d in science . Thoma s Huxley said o f him that he was "the firs t poet since Lucretius who has understood the drif t o f science." Tennyson wa s strongl y affected b y Lyell' s Principles of Geology, especiall y b y the suggestio n that the histor y of the Earth was far too long to be compatible with the traditional biblical account. Tennyson accepted Lyell's thesis and was a convert to the general idea of evolution before Darwin wrote his book. Tennyson was clearly concerned over the antireligious implications of evolution, and he was the prime instigator behind the formation in 1869 of the Metaphysical Society, a collection of eminent scientists , writers , an d cleric s whos e ai m wa s t o attemp t t o "unit e al l shades o f religiou s opinio n agains t materialism. " Th e group , whic h include d William Gladstone, the duk e of Argyll, two archbishops , two bishops, the dea n of St. Paul's, th e criti c John Ruskin, the famou s economist Walter Bagehot, Thomas Huxley, and others, discussed such topics as "What is matter?" "Is God knowable?" "What is death?" and "Has a frog a soul?" They had their lighter moments such as a proposal to test the efficac y o f prayers—a "prayer-gauge"—by seeing how effectiv e prayer was in a hospital ward. The society faded awa y in 1880. Tennyso n whimsically explained: "Becaus e after te n years of strenuous effort n o one had succeede d in even defining the term 'Metaphysics.'" Tennyson saw man evolving into a more perfect being, the "crownin g race" referred t o in his great poem In Memoriam.2 I n 2

It has been amply commented on that this poem contains passages that read like paraphrase s from Chambers's Vestiges of the Natural History of Creation (1844), mentioned earlier .

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the same poem it is also possible to find the influence of the geologist Lyell, for example, i n thes e line s referrin g t o th e erosio n o f th e Eart h an d th e subsequen t process of sedimentation: The moaning of the homeless sea, The sound of streams that swift o r slow Draw down the Aeonian hills, and sow The dust of continents to be. Although Tennyson probably rejected the biblical account of the Creation, he final ly convinced himself that science and religion were compatible. He firmly believed that science was a major facto r i n countering the superstition tha t he sa w as darkening civilization. There were those who were only too happy to have found i n Darwinism an ally against religion and the Church. The notorious pagan, masochist poe t Swinburn e (known as Swineburne to his detractors ) accepted evolution immediately. It spoke to a man who could write the line: "The supreme evil, God." The philosopher John Stuart Mill, who also saw Christianity as a failure but was loathe to say as much i n public, was deepl y affecte d b y The Origin of Species and th e controvers y that followed its publication. His impression was that Darwin had weakened the image of religion to such an extent that the time was right for Mill to risk offering a n alternative, in the for m o f the humanistic philosoph y embodied in the thought o f Jeremy Bentham. Mill's fathe r ha d instille d i n him th e Benthamite doctrine tha t "th e exclusive test of right and wron g [is] the tendenc y of actions to produce pleasure o r pain." Directl y influenced by what h e sa w a s the beneficiall y disruptive effec t o f Darwin's work on Christianity , Mill wrote one o f his majo r book s for the genera l reader, Utilitarianism (1863) . Utilitarianism i s usually glibl y summarize d as "th e greatest happiness for the greatest number," a phrase coined by the eighteenth-century English philosopher Francis Hutcheson. Mill did not see evolution as a direct basis fo r utilitarianism. Indeed , it is difficul t t o see how th e surviva l o f the fittes t can in general be compatible with the greatest happiness fo r the greatest number . The point is that, for Mill, Darwin appeared to have engendered in England a social environment sympatheti c t o a secular approach to morality, which utilitarianis m is. He miscalculated. Benthamite humanism di d not sweep England. Darwin's greatest champion was Thomas Huxley, who as a young man had also collected biological specimens, while spendin g three years as a medical officer i n the South Seas on the HMS Rattlesnake. The famous educator, who believed in the abolishment o f slavery an d th e educatio n o f women, deserves a book of his own . His attitude toward life i s best summed up i n his ow n words: "We live in a world which is full o f misery and ignorance, and the plain dut y of each and all of us is to try and mak e the little corne r that he can influence somewhat les s miserable an d somewhat less ignorant than i t was before h e entered it. " Huxle y had written an d spoken in support of evolution from the appearance of Darwin's book. When asked to giv e th e prestigiou s Romane s Lecture at Oxfor d i n 1893 , h e chos e a s his titl e "Evolution and Ethics." His theme was that natural selection does not automatically lead to ethical progress; that the fittest , a s defined by Darwin, did not mean th e best a s judged o n ethica l grounds . Thi s perhap s seem s obvious , but ther e wer e weighty intellects , notabl y the philosophe r Herber t Spencer , wh o though t other-

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wise. Spence r saw natural selectio n i n the anima l world as a model fo r the workings of human society, so that those who survive d the human ra t race were necessarily th e fittes t i n all senses. Huxley , the grea t freethinker and liberal , wa s concerned to show that societ y should not be dominated by those who survive the rat race. The criti c an d poe t Matthe w Arnol d wa s anothe r wh o wa s disturbe d b y th e clash between science an d religion. He realized tha t it was up t o religion to make some concessions , o r it would ris k losin g many o f its followers . In particular, he pressed th e opinio n tha t i t wa s aki n t o idolatr y t o tak e th e Bibl e literally. Ho w could one, after Darwin? Darwin's fam e soo n spread to Europe and America . His prime discipl e in Germany wa s th e biologis t Ernst Haeckel, who i n hi s Riddle of the Universe (1899) , went wel l beyon d Darwi n in applyin g the principl e t o "th e motio n o f heavenly bodies," to the "growt h o f plants an d th e consciousnes s o f man [which ] obey one and th e sam e great law o f causation," producin g " a vast, uniform , uninterrupte d process o f development. " Moreover , h e bestowe d upo n atom s a primitiv e con sciousness o r soul , accountin g fo r th e upwar d clim b o f matte r t o livin g forms . Naturphilosophie wa s alive and well. Of the scientifically active countries of westem Europ e only the French , excep t for their anthropologists , generally ignored or disparaged Darwin. The amoun t o f literature generate d b y th e philosophica l aspect s o f evolutio n was greater than tha t stimulate d b y any scientifi c theory since Newton . This wa s because, of all the revolutions caused by science, Darwin's struck most dangerously at the self-imag e of man. Apart from attacking the literal truth of Genesis, he ha d shown ma n t o b e a n integra l par t o f the anima l kingdom . Thi s histori c turnin g point i n ou r inne r worl d i s th e factua l justificatio n fo r the increasin g numbe r of people who believe that we are not so much masters o f this planet as part of it. The Wrong Theory One canno t help bu t b e sorr y for Jean-Baptiste de Lamarck . He clearly suggested the concept of evolution, half a century before Darwin. The trouble was that Lamarck's mechanism for evolution was completely wrong. The man who invented the word biology apparently was the first person to sense the rea l significanc e of the similaritie s betwee n fossil s an d th e livin g specie s t o which the y bor e mos t resemblance . Lamarck was a carefu l observer ; he guesse d that living forms had evolved from simpler organisms, and he tried to explain thi s in terms of an, at first sight, reasonable mechanism. Lamarck believed in the inheritance of acquired characteristics. Accordin g to this theory, if you keep cutting off people's left hands for generation after generation, eventually a time will come when children will be born without lef t hands . More over, Lamarck held that, in nature, animals ha d an instinctive driv e to improve themselves. The striving of individuals for improvement was the mechanism of evolution, when combine d with the inheritance o f those improvements. Conside r giraffes. Lamarck would say that the evolution of the giraffe's lon g neck was due to the striving of each individual giraff e t o reach the leave s on the trees . The effort s o f a given giraffe le d to a lengthening o f its neck, and this acquired characteristi c wa s passed on to its offspring. Darwin's explanation is completely different. H e held that

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in every generation of giraffes ther e were those that had longer necks than the average because they were genetically favored i n this respect. Sinc e they had a better chance than the others to feed wel l o n the trees , over the generations the longernecked giraffes survive d better—and passed on their favorable genes to their kids. Condorcet, one of the outstandin g figure s o f the Enlightenment, believed in th e Lamarckian theory o f the inheritanc e of acquired characteristics and argue d that, apart from the value of education for the individual, th e parents' education was, in some degree, inherited by their children s o that there could be a cumulative educational effect throug h the generations. At the turn of the nineteenth century , a test of the inheritanc e o f acquired characteristic s wa s carrie d ou t b y August Weisman n (1834-1914), perhaps the firs t perso n to realize that the "germ plasm," what today we would call the genes, is not normally affected by damage to the whole organism. Weismann cut of f the tails of several generations of mice—to no effect . Non e of the offspring o f this line of martyrs was born tailless, or even with a significantly shortened tail. He might have spare d th e mice their sufferin g i f he had just noticed tha t after hundred s o f generations, Jewish boys are still bor n with foreskins. Acquired characteristics are not inherited. Contrar y to Lamarck' s theory , simpl e physica l modifications o f the parents are not inherited b y their children. Damag e to the parents' reproductive cell DNA will, of course, affect th e nature of their offspring . Lamarck's belief in th e inheritanc e o f acquired characteristic s was anticipate d by Charles Darwin's grandfather Erasmus, and has in fact persisted fo r centuries. It is part of the folklore of many societies and has been around too long to be killed by ugly facts. On e example of the effec t o n their offsprin g o f what thei r parents see is about 400 0 year s old . Genesi s 30:37-3 9 reads : "Jaco b the n go t fres h shoot s o f poplar, and of almond and plane, and peeled white stripe s in them, laying bare the white of the shoots . The rods that he had peele d he set up, i n front o f the goats, in the troughs , the wate r receptacles, that th e goat s came to drin k from . Th e mating occurred when they came to drink, and since the goats mated by the rods, the goats brought forth streaked , speckled, and spotted young." The Greeks were equally inventive; they believed in telegony, a theory, supported by Aristotle, which says that i f a woman ha s a child by her secon d husband i t will have som e of the characteristic s o f her firs t husband , i f he consummate d th e marriage. It should b e eas y to discredi t thi s ide a by studying the childre n o f film stars. It i s no t ofte n appreciate d tha t Darwi n himsel f accepte d th e ide a o f inherite d characteristics. H e was les s concerne d wit h th e detaile d mechanis m o f heredit y than with what happened t o the heterogeneous collection of individuals i n a given generation. Neither he nor Lamarck could have known that the physical mutilatio n or modification of an organism (as against chemical or radiative damage ) did not affect th e DN A of the reproductiv e cell s and tha t it is only through thes e cell s and , more specifically , their DNA , that informatio n i s transferre d fro m generatio n t o generation. The doctrin e o f the inheritanc e o f acquired characteristic s stil l ha s a few sup porters. Its last great (if that is the word) promoter was the distinctly unpleasan t Soviet charlata n Trofi m Lysenko . Thi s apparatchi k declare d tha t gene s didn' t exis t and tha t i t wa s th e whol e organis m tha t contribute d t o heredity . B y subjecting plants to a variety of environments, he proposed to modify the m so that when they were bred they would have certain desired characteristics, for example, greatly im-

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proved resistance to extreme cold. Lysenko was supported by the political authorities, not for idealistic reasons but because they expected practical results i n terms of improved yields. Only Lysenko's version of genetics was acceptable in the Soviet education system . Since no genuin e case of the inheritanc e o f an acquire d characteristi c has eve r been documented, Lamarckism shoul d have died long ago. Its survival as an explanation for evolution is a tribute to the strength of folk mysticism. The Perversion of Evolutio n The Comt e d e Buffon , i n th e eighteent h century , declared—incorrectly—tha t chemical affinity wa s governed by a law similar to the law of universal gravitation. In the field o f political science, Montesquieu saw the idea l king as being similar to the Sun , hi s gravitationa l forc e attractin g t o hi m th e politica l institution s o f his kingdom. Newtonia n mechanic s wa s dragge d into totall y inappropriat e fields . I t was thus predictabl e that ther e would b e those who would se e Darwinian evolution as a general principle, a means of classifying all human activities and explain ing their development. Everything that changes smoothly with time "evolves, " but this is merely a case of verbal echoes. It is not apparen t how Darwinia n evolutio n can fruitfull y b e applied to art, literature, or philosophy. A n early attempt of this kin d wa s containe d in a lecture by Huxley: "The struggle for existence holds as much in the intellectu al as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals." Karl Popper has expressed similar ideas, and the American pragmatist G. H. Mead declared that "th e scientific method is, after all, only the Evolutionary process grown self-conscious," which is a neat thought. But the cold facts are that in the real, nonscientific, world, "fitter" theorie s do not necessaril y eliminate les s fit theories. In any case, the ide a is sterile , predicting nothin g of importance that coul d not hav e been deduce d by common sense. Darwin never used the phrase "the surviva l of the fittest." The man who did was Herbert Spencer. In the 1870s the name Spencer was synonymous with intellectua l vision an d powe r an d profoun d philosophical insigh t int o th e working s o f man and nature . Bu t history ca n be cruel. Today, the man who starte d his professional life as a railway engineer and ende d as the author of the massive multivolume System of Synthetic Philosophy i s a footnote. Spencer's writings had a deep, if not lasting, influenc e o n th e wa y i n whic h societ y viewed science . Whethe r o r not on e agreed with him, h e brought scienc e a s a whole, an d hi s concep t of evolution i n particular, int o th e intellectua l worl d o f Victoria n England an d post-Civi l War America. He was an evolutionist a t least a decade before Darwin , as shown by hi s first book , Socia7 Statics (1850) . In 185 2 he published a n article entitled "Th e Development Hypothesis," in whic h h e strongl y backed th e concep t o f evolution a s against the biblica l accoun t o f special creation . The article attracte d considerable attention an d Spencer' s impositio n o f evolution o n the natura l world wa s soon to be given a huge boost by Darwin and Wallace, who both admired Spence r greatly. Spencer frequentl y brough t attentio n t o the fac t tha t h e ha d precede d Darwin, so much s o that someone remarked that he "seems to wish to take out a patent for the invention o f the theory."

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The more controversial par t of Spencer's philosophy was his application of evolution to human history and institutions. Since , in his eyes, religion had lost its authority, ethics no longer had a spiritual basis. S o Spencer melde d scienc e with social science and ethics, thu s secularizing ethics and giving it, or so he thought, the authority o f science. Spencer's idea s were well received in England and i n Japan, but it was particularly in America that his writings and his visits boosted his reputation to guru status. His promotion of the concep t of the surviva l o f the fittes t wa s welcome, if in practic e superfluous, support fo r the rapidl y growing class o f millionaire entrepreneurs that was to typify American society from then on. Spencer wa s a Lamarckian. In particular, he hel d tha t th e menta l exertion s of parents were genetically transferred to the brains o f their children . Th e reason for his belief in this totally false premise is clear. He saw social development as an evolutionary proces s i n whic h eac h succeedin g generation learne d fro m th e experi ences of its predecessors. This process was not genetic, but it was Lamarckian; each generation inherite d th e acquire d characteristic s o f its parents . Similarly , h e sa w personal development a s a kin d o f Lamarckia n evolutionar y process , involvin g change throug h experience . I t would hav e spoile d hi s gran d thesi s t o admi t tha t one component , namely , biological evolution, wa s no t Lamarckia n and therefor e fell outsid e his scheme . Of course, he was right to suppose that social and cultura l evolution are, in a broad sense, Lamarckian processes. We can improve on the legal systems of past generations by observing what was good and what wa s bad and rejecting the bad. But this "evolutionary" process has certainly nothing to with genetics and everything to do with consciou s learning . Almost no one reads Spence r anymore, unless the y have to. Today the most interesting aspec t of his life is perhaps hi s affai r wit h the novelist George Eliot. Spencer wa s not th e las t to use Darwin' s name to pus h evolutio n int o history . When, in 1883 , Engels delivered th e oration over Marx's grave in London, he said , "Just a s Darwi n discusse d th e la w o f Evolution i n organi c nature , s o Mar x dis cussed the law of Evolution in human history." 3 Another who used the language of evolution in dealing with society was Walter Bagehot, the English economist, in his book Physics and Politics: Thoughts on the Application of the Principles of Natural Selection and Inheritance to Political Society (1872). Several misguide d attempt s to fin d evolutio n i n unlikel y place s die d a t birth . Thus Si r William Crookes's reference to Mendeleev's periodi c tabl e a s "inorgani c Darwinism" is rubbish. Th e elements d o not fight fo r survival, an d non e appea r to have become extinct. However, things d o become serious when a n attempt is made to impose the concept of natural selection on sociology or history. There were those who found justification for war in the argument that war was just a human exten sion o f the struggl e for existence foun d i n nature , an d the y coul d tur n t o Darwin himself, who wrote, "DeCandolle, in an eloquent passage, has declared that all nature is at war, one organism with another, or with external nature . Seeing the contented fac e o f nature , thi s ma y a t firs t b e wel l doubted ; bu t reflectio n will in evitably prove it is true." It is also easy to see how Darwin could be used as a justification for an uncaring, competitive society . Shigalov , th e mos t controversia l characte r i n Dostoyevsky's 3

The widespread belief that Marx wanted t o dedicate Das Kapital t o Darwin has no foundation .

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The Devil's, was based on the radical publicist Zaitsev, who used Darwin to defen d the enslavemen t o f blacks. One of the argument s agains t improvin g condition s i n slums, used by nineteenth-century reactionaries , was that concer n for the welfar e of the unfit went against the principle of competition that underlay evolution. Man should no t tamper with nature. On the other hand, there were those who wanted to help natur e i n th e nam e o f natural selection , an d wh o hel d tha t th e futur e o f the race came above individual liberty. Disturbing ideas issued fro m quie t professorial rooms. Karl Pearson, the renowned statistician , declare d that civilizatio n resulte d from "th e struggl e of race with race, and the survival of the physically and mentally fitter race." Francis Galton, a geneticist and a cousin of Darwin, coined the word eugenics for the policy of encouraging "good" human specimens to breed at the expense of the less "good. " He suggested cash grants to encourage marriage and chil d production among the "fit" and sterilization o f the "unfit." Social Darwinism, the applicatio n t o society of the principl e o f the surviva l of the fittest , attracte d many Wester n intellectuals . A little-known exampl e is H . G. Wells. Those who know Wells primarily through his science fiction might try reading his Anticipations (1901 ) an d A Modern Utopia (1905) . In both books racism, backed up b y eugenics, is explicit. Wells speaks of "efficiency." Race s that ar e not efficient wil l have to be kept unde r contro l by, among other measures , obligatory infanticide and abortion. Which races? That's an easy one: "the black... the yellow man . . . the Jew. " Wells was a n advocate o f sterilization. On e can hear Darwin in Wells's declaration that "the way of Nature has always been to slay the hindmost." The Fabian Society , to which Well s belonged, was heavily tainted by social Darwinism. One of the society' s outstanding spokesmen , Sidney Webb, warned of the national deterioratio n that would follow as a consequence o f the presence in Great Britain of Irish Roman Catholics, and Polish, Russian, and German Jews. We have sailed into dangerous waters. As applied to society, the "surviva l of the fittest" almost invariably means the survival of the thugs with the big sticks. Mental defective s and cripple s wer e doome d i n Naz i Germany, where th e surviva l of the fittest meant the destructio n o f the weakest, where the definitio n of fitness was determined b y the stron g and th e mean s o f selection wa s the truncheo n an d th e death camp. The final degradatio n of the human spiri t was reached by Dr. Meiigele standing at the head of a line of concentration cam p inmates and, with a gesture of the hand, directing the fitter inmates to one side, to work, and the ill and old to the other side to die. Natural selectio n i s a n unconscious process ; th e nonhuma n worl d doe s no t know tha t th e bette r adapte d wil l wi n out . Ma n can consciously hel p th e weak , knowing that th e surviva l an d comparativ e happiness o f our specie s depend s o n our control of our political an d ecologica l environment, not o n the eliminatio n of biological weakness. On that path there is no logical end. Why not execute diabetics and dyslexics , migraine sufferers, an d arthritics? Or the person who taught me so much of what I know about tolerance, my Down's syndrome son, Dan? We have evolved from the livin g world, and on e of the gift s that Darwin gave us was to place us in that world, not as conquerers with spoil s but as inheritors wit h responsibilities.

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24 The Gene Machine One might compare it to the most perfect machine that God ever made . —Diderot, on the Stocking Machine

In November 1895, Roentgen discovered X-rays. In 1912, von Laue showed that the diffraction o f X-rays could be used to determine th e arrangemen t o f atoms in crystals. I n 1952 , Rosalin d Franklin , workin g wit h th e physicis t Mauric e Wilkin s i n King's Colleg e London, shon e a bea m o f X-ray s at a crysta l o f DN A an d pho tographed the diffracte d rays . She obtained beautiful but comple x patterns. Ther e are recognized and well-tried mathematical method s use d t o analyze the pattern s in X-ra y diffractio n pattern s an d conver t the m int o informatio n o n th e spatia l arrangement of atoms in the scattering crystal. Rosalind Franklin's tendenc y was to appeal to these methods, but it was clear that the huge number of atoms in the DNA molecule was going to make her task extremely formidable, and in her da y powerful commercia l computer s were not available . James Watson, an America n i n hi s twenties, an d Franci s Crick , an English physicist , working together in the Cavendish Laboratory at Cambridge (yes again!) took a different approac h to the hunt for the structur e o f DNA. They opte d fo r intelligent guesswor k based o n wha t wa s known o f the chemical compositio n o f DNA. In practice they played with models, looking for a molecular conformation that was compatible with both th e chemica l and the X-ray evidence. They found the double helix. The adven t o f modern molecula r biology—th e understanding o f the molecula r basis of life processes , and arguabl y the mos t important scientifi c development i n the twentietht h century—date s fro m a one-page letter by Watson and Crick , published o n 2 5 April 195 3 in the Britis h scientific journal Nature: "We wish t o suggest a structure fo r the sal t of deoxyribose nucleic aci d (D.N.A) . This structure ha s novel features which are of considerable scientifi c interest." To say the least. Thei r elucidation o f the structur e o f DNA has had a profound influence on man's abilit y to understan d an d contro l the functionin g of living cell s an d th e mechanism s o f heredity. There is a certain injustic e in the proportioning o f fame for the DNA story. Many scientists have the feeling that at least one, and possibly two, of those who preced ed the discovery of the double helix were worthy of more recognition than they got, both fro m th e scientifi c establishment an d fro m Watson , in hi s boo k The Double Helix. Goethe once said, "After al l it's pur e idiocy to brag about priority, for it's simpl y unconscious conceit." Nevertheless, one can understand Watso n an d Crick' s ela tion at having discovered the structure of the DNA molecule before the famous California-based chemis t Linu s Pauling, who was working on the sam e problem an d breathing dow n their necks. It's very human t o want t o be first. I t is not s o easy to accept the oversight by which Watson neglects to mention th e crucial observation s

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of Fred Griffith, wh o in 1928 showed that genetic information could be transferred from on e type of bacteria to another. Watson mentions but underplay s the wor k of Oswald Avery , wh o i n 194 5 demonstrate d tha t DN A was th e materia l tha t trans ferred th e genetic information. The book is also distinctly ungenerou s to Rosalind Franklin. For example: "The thought could not be avoided that the best home for a feminist was in another person's laboratory." I t was at a seminar that Franklin gave in 1952 that Watson saw her X-ray photographs and realized that they might indicate a helix. In a footnote to a 1954 paper, Crick and Watson say, "We wish to point out tha t without this dat a the formulatio n of our structure would hav e been most unlikely, i f no t impossible. " The y didn' t sa y tha t the y ha d obtaine d he r pho tographs without he r knowledge . Watson also claime d tha t Frankli n rejecte d the double helix interpretation of her photographs, but this contradicts the evidence of her notebooks . I n The Double Helix, Watso n give s a n unflatterin g pictur e o f Franklin,1 but others have felt tha t sh e was a victim o f the "mal e club" syndrome . In 1962 Wilkins, Watson, and Crick shared the Nobel Prize. Rosalind Franklin died of cancer in 1958 , at the ag e of thirty-seven. Many think that she deserved far more recognition than she got, and that Avery deserved a Nobel Prize. DNA wa s discovere d i n 1869 , te n year s afte r th e publicatio n o f The Origin of Species. Ther e was n o suspicio n a s to its real importance. It is doubtful if Darwin was ever aware of the molecule isolated by Friedrich Miescher, a Swiss biochemist, from pu s stickin g to discarded bandages. To give Miescher his due , he di d venture the opinion that DNA had something to do with fertilization, but at the time no one followed up th e idea. The true significance of DNA was revealed by Oswald Avery. The next step belonged to the chemists . The Building Blocks of DNA Your DN A contains th e gene s tha t contro l th e structur e an d functionin g of your body. Human DNA contains o n the average something like a billion atoms , but it s structure is simple. I say "on the average" because your DNA is not identical to my DNA. They are very similar, but i f they were identical w e would be indistinguish able, apart possibly from duelin g scars. DNA is built fro m onl y fiv e kind s o f atom: hydrogen, carbon, nitrogen, oxygen, and phosphorus. If the DNA molecule is gently broken up, we obtain three kinds of small molecules: phosphoric acid , sugar molecules (th e sugar is ribose), and heterocyclic amines , whic h i n thi s contex t ar e commonl y dubbe d "bases " (Figur e 24.la). Ther e ar e fou r kind s o f bases i n DNA , and the y hol d th e livin g world i n their hands. Thei r structure s and name s are shown in the figure. The y are usually referred to by their initials: A, T, G, and C. It is not necessary to remember the structure of the bases to grasp the way in which DNA works. The General Structure of DNA All living forms, excep t viruses, which are hardly living, contain DNA. The structure of human DNA illustrates the principles on which all DNA molecules are built. 1

For a very different vie w of Franklin from that presented by Watson, see Anne Sayre, Rosalind Franklin and DNA (Ne w York: Norton, 1975).

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Figure 24.1a. Th e molecular building blocks of DMA .

Figure 24.1b. Puttin g the block s together. Phosphate groups are indicated b y the lette r P.

First link alternating ribose and phosphoric aci d molecules to form a chain containing about 100 million of each. The DNA of all species contains this chain. Now take you r stoc k o f bases an d star t attachin g the m t o th e chain , eac h bas e bein g linked to a ribose unit (Figur e 24.Ib) . In what orde r do I arrange the fou r kind s of base? Th e answe r t o that determine s th e differenc e betwee n m y generous brow n eyes an d m y ban k manager' s inhumanl y col d gra y eyes . Huma n DN A contain s about 100,000 genes, and eac h gene is essentially an ordered series of bases. Every gene has a different orde r of bases. Where i s th e doubl e helix ? It' s coming , but firs t w e nee d a pivotal discover y made by Erwin Chargaff, wh o i n the early 1950s publishe d th e results of chemical analysis o n DN A from a number o f species. Chargaff foun d that fo r every C (cytosine) molecule in a DNA molecule there was a G (guanine) molecule; if there were 74 million C s there wer e 7 4 million G s (within experimenta l accuracy) . And fo r every A (adenine) molecule there was a T (thymine) molecule. The Nobel Prize was knocking a t the window : Watso n and Cric k took Chargaff' s findin g and Rosalin d Franklin's X-ray hint and proposed that the DNA molecule consisted o f two strands lying sid e b y side . Eac h stran d ha d th e sam e backbon e o f alternating ribose an d phosphoric aci d units. Th e two strands were held togethe r by links between thei r bases, so that the tota l structure was reminiscent o f a ladder (Figur e 24.Ic)—but a twisted ladder—a right-hande d helix . An d the rungs that held th e ladder together were Chargaff' s pair s o f bases; every G held hand s with a C, every A grasped a T. The pairs o f bases are held togethe r by gentle links: hydrogen bonds (se e Chapter

The Gene Machine

Figure 24.1c. A schematic sketch of the double helix. The way in which thymine pairs with adenine is shown on the right.

13). Note that because of the fidelit y of G to C and o f A to T, if you know the orde r of the bases on one strand you can immediately work out the order on the other. So there it is. The structure o f the most important molecule on Earth. Your DNA, unless you are an identical twin , is distinct fro m everyon e else's i n the whole Creation, the differenc e being , as we said, in the orde r of the bases. Because the DNA molecule is so large, it can be seen with sophisticate d microscopes , appearing as a long wormlike structure . DNA carries all your genetic information, a collection of genes that contain a set of instructions fo r building you. Your chromosomes contai n you r DNA, and sinc e each chromosom e carries a differen t se t o f genes, eac h chromosom e contain s it s own kind of DNA, identical i n general structure with all the DNA in the cell nucleus but differin g fro m chromosom e t o chromosome in the orde r and number o f the different base s that go to specify the differen t genes. The Continuity of Science Science builds upon itself. The discovery of the structure of genes would have been impossible withou t th e discover y of X-rays, which allowed th e general molecula r structure of the DNA molecule to be unraveled. Also absolutely indispensable wa s the chemical knowledge that allowed the structure of the bases and the other components of the DNA molecule to be determined. Almost any scientist, i f he looks at his research , can trace a n indispensable lin e o f discoveries through to the seven teenth o r eighteenth century , i f not farthe r back . The doubl e heli x owe s muc h t o Lavoisier. How Does DNA Work? The livin g cel l builds mos t o f the molecule s tha t i t contains . Th e exception s ar e simple salts and a few small molecules that are absorbed from foo d and are used as building blocks for the constructio n o f large molecules. I n general the synthesi s of all molecules in the cell depends on catalysts, the enzymes, which ar e protein molecules. DNA, acting through the genes, is the master controller that is ultimately responsible for the synthesis of all proteins, not onl y enzymes. It is worth lookin g at

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the general scheme by which proteins are synthesized, if only to marvel at the ingenuity of nature. The secret is in the orde r of the bases. In human DNA there ar e about 6 billion bases, and it is this huge array that constitutes the collection o f genes, the genome, that control the functioning an d replication of all of us. (Don' t get overwhelmed by how many bases we have; the humble lily has about 600 billion.) Although at one time it was believed that each gene was a continuous stretc h of bases on the DNA molecule, in 1977 it became apparent that nearly all genes are split up into separate segments, the so-called exons, interspersed with other segments, the introns. If you need a mnemonic: introns ar e intruders. Thu s a typical gene may consis t o f anything fro m tw o t o fift y exon s (the rea l stuff ) separate d by intron s (th e intruders) . The intron s ca n be very long, running u p t o abou t 100,00 0 bases i n som e cases . Why ar e they there ? Functions hav e been uncovered fo r some introns, bu t man y appear to be useless, as reflected i n the nickname "junk." There is no firm answe r at present. When we refer to a gene we will mean a series of bases, ignoring the introns. Most human gene s contain 100 0 to 300 0 bases, without th e introns . A s we said, thei r task is to overse e the synthesi s o f proteins, an d w e will no w se e how they do it. Building Proteins

Each gen e is responsibl e fo r assembling a differen t protein . The gene itself does not do the work; it supplie s th e necessar y information on the compositio n o f the protein. Proteins are built by assembling amin o acids presen t in the cell , and the problem is to link the right amino acids together in the right order. The assembly of proteins is not don e directly on the surface of the DNA molecule. The relevant gene is first copie d an d sen t ou t o f the nucleu s int o th e extranuclea r interio r o f the cell . This is how that happens: 1. First a portion of the DN A molecule is attacked by a collection o f enzymes that "saw through" some of the rungs of the ladder so that the helix unwinds over the length o f one gene, including intron s (Figur e 24.2a). Since the rungs are hydrogen bonds (Velcro), they are comparatively weak. 2. Th e expose d bases o n a single strand o f the DN A direct the formatio n of a ne w single-strand molecule— not the protein. The principl e o f the assembl y line i s simple: base pairing again. The newly formed molecul e has the sam e backbone

Figure 24.2a. Unwindin g a gene.

Figure 24.2b. Th e formation of ptRNA.

The Gene Machine

as the DNA, namely, a sugar-phosphate chain (th e sugar this time being deoxyribose instead of ribose). Along the new chain the order of bases is completely determined by the fact that every base must "match " that opposite it on the single DNA strand. The only slight variation is that in the new stran d the place of the base thymine (T) is taken by another base, uracil (U ) (Figure 24.2b). Uracil pairs with adenin e (A) , and, as usual, G (guanine) pairs with C (cytosine). The ne w molecule, know n a s primary transcript RN A or ptRNA , ca n b e regarde d a s a complement to the origina l strand, consisting of complementary gene and complementary junk (or complementary exons and complementary introns). RNA stands fo r ribonucleic acid, and ptRN A is a shorthand symbo l for a whole class o f molecules. It s structur e (th e type, number, an d orde r o f the base s that i t contains) is determined completely by the gene that is being copied. There are thus as many kinds of ptRNA as there are genes, but their general structure is the same . Notice that when th e DN A is saw n through i t splits , fo r that par t o f its length, into two single strands. In principle bot h could be replicated, but only one, the socalled sense strand, carries genetic information, and it is the one that gives ptRNA. The replication of the other, antisense strand, would give nonsense, and in fact it is not replicated. It seems as though an enzyme involved in the replication process is involved in the decision not to replicate antisense strands . 3. DN A exists onl y insid e th e nucleu s o f the huma n cell . It is too large to get out through the membrane surroundin g the nucleus, but ptRN A i s a small enoug h molecule to escape. Once it is outside, in the cel l cytoplasm , an extraordinar y process occurs. Enzyme s cu t awa y th e complementar y jun k an d a smaller , smarter molecul e i s left : pur e complementar y gen e (Figur e 24.2c) . Thi s lean , mean molecule is known as messenger RNA, for short, mRNA. It is on the surface of mRNA that the desired protein will be constructed, s o the order of the bases on mRNA must contain the necessary information to ensure that the amin o acid s availabl e in the cel l ar e joined together in the righ t order to give that protein. Now we know that there are in the cel l something like twenty amino acids. We might assum e tha t wha t w e need i s at least twent y assembl y site s o n the mRNA , each site having the correc t shape to accommodate a different amin o acid , so that

Figure 24.2c. Messenge r RNA is obtained b y cutting out th e jun k i n ptRNA.

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they can be lined up side by side before they link to each other to form the new protein molecule . Yet there are onl y fou r kind s o f bases o n mRNA . Ou r assumptio n that we need twenty sites thus runs up agains t a difficulty: i f each base on mRNA was a site at which a specific amino acid could be held, this would, on a simple assumption, allo w us t o assemble proteins with onl y fou r differen t kind s o f amino acids, each one somehow brought to the surface of its corresponding base, where it would eventuall y link hand s with the neighboring amino acids to form a protein . This i s not goo d enough; in thi s scenari o the base s hav e provided u s with a language of only four words. Such a language might not limit certain rock stars, but i t is not enough to account for heredity. It turned out , in 1961 , that every amino acid is associated with a site on mRNA consisting not of a single base but of a group of three adjacent bases. Such a trio of bases is termed a codon, and ever y codon is an address, to which onl y one amino acid will somehow attach itself. As in a three-letter word the orde r of the letters — the bases—tha t compose the codo n i s important; differen t order s will giv e differ ently shaped surfaces , and i t is the fitting together of compatible surface s that controls th e "docking " a t th e codo n site . Thu s i n Englis h "ODE, " "DOE," "OED, " "DEO," an d "EDO " mean differen t things. 2 Th e codo n CA U is th e cod e fo r th e amino acid histidine, but CUA is the code for leucine. There are more than enough ( 4 x 4 x 4 actually) different permutation s of three letters chosen from C, G, A, and T to allow each amino acid to have its own codon. Actually, most amino acids have two to four codons. Thus glycine has the codon s GGC, GGU, GGA, and GGG. It is the order in which the codons are arranged on the mRNA that determines the order of the amino acids in the protein to be synthesized. Recal l that the orde r of the codon s in mRNA is completely determined by the DN A molecule that gave rise to it. Now no amino acid is the right shape to fit snugly on any codon, like a lock and key. What happens is this: 4. Amin o acids are brought to the codon s on mRNA by our last type of molecule: transfer RNA, o r tRNA for short (Figure 24.2d). This molecule has two "hands" ; one hand grabs an amino acid, the other holds on to the corresponding codon on mRNA. I t is this secon d han d tha t recognize s the codon . Thus, i n th e cas e of glycine, th e tRN A hold s o n t o glycin e with on e hand an d link s t o on e o f th e

Figure 24.2d. tRN A has two hands : one holds onto an amino acid, the othe r is the anticodon to th e amino acid's codon, which is on the mRNA. 2 EDO: ancient capita l of Japan; OED: Oxford English Dictionary. I haven't found a meaning for EOD, the sixth permutation .

The Gene Machine

Figure 24.2e. Ho w tRNA recognizes the sit e for histidin e on mRNA.

codons for glycine on mRNA on the other . There are many kinds o f tRNA; each one i s s o constructed tha t i t i s absolutel y specific , bindin g onl y to on e type of amino acid and to the corresponding codon. How does it know which codo n to bind to? Easy! It base-pairs. Thus the tRNA for histidine has to bind to the codon CAU, and w e alread y kno w that i n genera l C binds t o G, A binds t o U , and U binds to A. So to bind to the codon CAU the tRNA has a "hand" consisting of the three adjacen t bases : GUA, as you can se e in Figur e 24.2e. It is in this way that the twenty types of tRNA attach their specifi c amin o acids to the correct codon sites. The order of the codons thus completely determines the order of the amino acids in the assembled protein. The exact molecular square dance, on the surface of the EtiRNA , which eventually produces the linked amino acid chain which we call a protein, is merely hinted at in Figure 24.2f. Actually the process proceeds on an "assembly line," a cell structure called a ribosome that supports the mRNA. Also the protein is built up starting from on e end of its amino acid chain and working along to the other end, and there is a codon at the en d o f the mRN A that is a "stop" sign , terminating the assembl y process. I have merely outlined th e major player s in the production an d indicated thei r roles. Extraordinary as the mechanism is, all the known steps in protein synthesi s are explicable in terms of the familia r physica l and chemica l interactions o f molecules. Samples of DNA isolated from fossils show exactly the same general structure as modern DNA, and the same codons have been identified. The codons appear to be

Figure 24.2f. Linin g up amino acids , When the first two ar e in place, amino acid 1 transfers to amin o acid 2 by a procedure that is not describe d here. The linked amino acids then transfer t o the next amino aci d brought to the surface of the mRNA.

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universal in present-day species, from bacteria to man. Apar t from viruses , whos e genetic material i s RNA, the DN A double heli x i s the uniqu e geneti c informatio n carrier of the livin g world. The Way in Which Cells Multiply The fertilized egg develops into a fully forme d organis m by a process that is a long way fro m bein g completely understood. Th e essentia l fac t i s that full y develope d organisms, excep t fo r th e mos t primitive , ar e multicellular . A s a ne w organis m grows, after th e fertilizatio n o f the egg , it splits into more and mor e cells, about 10 trillion in the case of an adult human. Almost all known types of cell have a nucleus, an d ever y nucleus contain s exactl y th e sam e DNA, exactly the sam e orde r of bases, as all the other cells in the organism. The order of the bases in the DNA of the fertilized egg determines the order in all the other cells. Your parents ensur e tha t you have only one set of genes, one precious se t from which all the trillions o f others are derived . A t eac h cel l divisio n th e DN A of the paren t cel l appear s i n bot h daughter cells . Obviousl y ther e mus t b e a mechanism fo r replication o f the DNA molecule. "It has not escaped ou r notice," wrote Watson and Crick, "that the specifi c pair ing we hav e postulate d immediatel y suggest s a possibl e copyin g mechanis m fo r the genetic material." The mechanism b y which DNA is replicated i s simple: the DNA is split int o it s two component strands, each of which acts as a template for the assembly of a complementary stran d (Figur e 24.3) . Thi s i s reminiscent o f the mor e limite d process , described earlier , for producing ptRNA from one gene. The new strand s have thei r bases arranged in an order that is completely determine d by the orde r of the base s on the singl e strands o f the parent DNA. If, for the purpose of clarification, the tw o strands o f the paren t DN A are labeled 1 and 2 , it can be see n that th e ne w stran d built aroun d stran d 1 is bound to be identical to strand 2 , and the new strand built around stran d 2 is just a replica o f the origina l strand 1 . Base pairing ensure s tha t this i s so . I n thi s wa y eac h molecul e o f DN A generates tw o exac t copie s and , through billion s o f similar replications , th e origina l DN A of the fertilize d eg g is passed on to every cell that has a nucleus. Th e DNA of the fertilize d eg g thus contains the information needed to control the activities o f all the cells of the full y de veloped organism.

Figure 24.3. DM A replicates . After unwinding , the two separate d strands act as templates fo r ne w strands.

The Gene Machine |

On the pine tree outside my window there is a crow. She is a winged package of DNA, and her DNA will be given to her egg . The continuity o f life depends o n this flow o f information. Mutations The molecule ethanol (ethy l alcohol, C2H5OH) is completely specified by its name. The molecule DNA is not completely specified by its name. Since, identical twin s apart, everyone on earth has a different set of genes, one could say that there are several thousand million different molecule s that are all called DNA. And that is without taking into account the rest of the living world, the DNA of ants and oak trees, DNA i s a collective noun, like mankind. Furthermore, since man has evolved from hot soup, we see that DNA is an evolving molecule—it has the capacity to undergo change and yet, if that change is not too drastic, retain the ability to direct the development of a viable organism. The environment discourages the survival of those organisms whose DNA has given them characteristics which put them at a disadvantage compared to their colleagues. Thus, evolution is the evolution of DNA. In Chapter 22 we presente d mutants a s one o f the key s to evolution . Fro m th e viewpoint of this chapter, mutants are organisms whose DNA differs fro m tha t of their parents i n that on e or more genes have been modified; the y have undergone mutation. Mutatio n mean s a chang e i n th e chemica l structur e o f a gene ; som e chemical bonds in the molecule must be broken or new bonds formed. What agents can do this? The three most common are radiation, externally supplied chemicals , and cellular components . Radiation has been recognized as a mutagenic agent since the 1920s, when a variety o f organism s wer e irradiate d wit h X-ray s an d subsequentl y produce d offspring that differe d macroscopicall y i n som e way fro m thei r parents . Thi s i s th e origin o f the concer n about overexposur e o f human ovarie s and teste s t o X-rays . Greater public concern has been expressed ove r the danger s of exposure to radiation emanatin g fro m radioactiv e elements , eithe r i n nuclea r facilities , suc h a s Three Mile Island or Chernobyl, or from nuclear weapons. Of the three types of radioactive radiation, y-ray s are the mai n dange r fro m weapon s sinc e a - an d (3-ray s have rather short ranges in air or matter. On the other hand, the ingestion of certain kinds o f radioactive material can result i n sever e damag e to cells du e to the massive cc-particles. The damage incurred by the DNA of the reproductive cells can be so severe that the molecul e i s n o longe r capable o f functioning. At lowe r level s th e damag e to DNA is often sufficien t t o result in an embryo that is not viable. At very low levels, damaged DNA can be, and ofte n is , repaired by the cell itself. A genetic survey has been made of the children of parents who survived the two atomic bombs that were dropped o n Japan . Fo r parent s wh o wer e nea r th e explosions , thei r childre n showed onl y thre e mutation s i n a total o f 700,00 0 gene s examined . Fo r parent s who wer e well awa y fro m th e explosions , 500,00 0 genes examined i n thei r chil dren also showed only three mutations. Ther e is no statistically meaningful differ ence between these two figures . The chief source of radiation hazard for the averag e citizen is natural radon gas originating beneath the surfac e o f the Earth. Radon accounts for roughly half of the total natural radiation receive d by the body, but th e level goes up t o over 80% in

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some localities . Cosmic rays, which come from space an d ar e thinned ou t by th e air, normally account for 5% to 10% of the total radiation to which most people are exposed, but fo r those of us wit h frequen t flye r card s who fl y about 10 0 hours a year or more, the rays can constitute up to a quarter of the total. External radiation is an extremely clumsy way of inducing mutations. It is nonselective, tearin g throug h th e cel l lik e a crow d o f hooligans , indiscriminatel y smashing anything to hand. Many chemicals ca n cause mutations without completely inactivating the DNA. The firs t chemica l mutage n to be studie d wa s mustar d gas , used a s a weapon i n World Wa r I. Since the n man y substance s hav e been indicted , amon g them ciga rette smok e and oi l o f bergamot, the substanc e that give s certain tea s their flavor . As in the case of any mutagen, chemical damage will not usually be confined to the reproductive cells , bu t onl y the y ca n hand o n th e modifie d genetic information that produces mutant species. The Enemy Within DNA is a huge molecule that swims i n an immensely complicated environment. Is your DNA stable, even in the absence of environmental threats? Is a mutagen needed for mutation? The earliest evidence of the built-in instability of the DNA molecule, within the cell, came from the laboratory of Barbara McClintock, who in the 1940 s came to the conclusion, on the basis of breeding experiments o n maize plants, that some of the genes were mobile. They appeared to change positions on the chromosom e in th e transition fro m paren t t o offspring . He r unexpected finding s wer e regarde d with caution. When, in the 1950s and 1960s, the role and structure of DNA became clear, there stil l seeme d n o good reason to believe that th e molecul e was unstable. McClintock's results and her interpretation of them remained suspect, but her day was to come. It has bee n possible fo r some time t o determine the sequenc e o f the gene s in a DNA molecule—i n principle. I n the 1970 s the sequencin g of 1000 to 3000 bases, a typical number fo r one gene, would hav e taken ten to 30 years to complete. In the early 1990s the rate speeded up until roughly 10 million bases a year were being sequenced i n the human genome , out o f a total o f about 3 billion. A t this rate there would have been about another 300 years to go, but th e join t effor t o f hundreds of scientists i n dozen s o f laboratories so accelerated the sequencin g tha t b y 199 5 i t was clear that the project might be completed before the year 2005. Even the limited knowledg e o f gene sequence s tha t ha s bee n availabl e fo r th e pas t coupl e o f decades has been sufficien t t o show unequivocally that, in a variety of organisms, genes can change their positions on the DNA molecule, seemingly without any external prompting . Th e mobilit y o f genes is a n accepte d fact . Barbar a McClintock was awarded the Nobel Prize in 1983 . The ter m tmnsposon, o r more informall y "jumping gene," i s no w use d t o de scribe an y piec e o f DNA that moves to another locatio n o n the molecule . Thu s a child may inherit a certain set of genes from its father, but the order of the genes on the DNA helix may be very slightly different i n the child. Does this matter? It can. Anything that alters the environment of a gene can potentially act as a represser, preventing the gene from operating. Thus suppose that a certain transposon move s

The Gene Machine |

so that it is sitting next to a gene responsible for the production of a protein essential for the process of blood clotting. The gene may be so cramped by its new neighbor as to be put ou t of action, thus preventing the synthesis o f blood-clotting factor. Such a case has been recorded. The transposon tha t did the damag e was found i n the parents of the unlucky child , but at a different locatio n on their chromosomes. Transposons provide on e mechanism for turning genes off or modifying their effec tiveness. A variation of the jumpin g gene trick has been found i n certain bacteria. There are stretches of DNA, not necessarily genes or exons (bits of gene), typically several hundred base s in length, that are able to replicate themselves. Unlike the transposon, they themselves do not move, but the copy drifts awa y and forces its way into the DNA molecule a t another point . If it squats in the middle o f a gene, it can prevent that gene from performing its normal function. Alternatively, it could fall near a gene or on a gene regulator. Despite the disturbin g visio n o f pieces of DNA skittering aroun d from on e part of DNA to another, in general the standar d account of inheritance, based on a fairly stable DNA molecule subject to occasional local mutations, still holds. The Constant Codon

As far as we know, the codon s are universal. Thu s throughout that part of the ani mal kingdom for which dat a are available, the sequence CAU serves as the code for histidine. Research on the DNA of different specie s has revealed not only that ou r codons are identical but als o that the genes of different specie s are very similar. In other words, the total base sequences of analogous genes are very similar. In this respect we are very close relatives of slime mold, radishes, and armadillos. Of course a bacteria, for example, hasn't go t genes that control the color of its eyes; it has n o eyes. Bu t th e synthesi s o f simila r enzyme s t o our s i s controlle d b y gene s that , where their base sequences have been determined, are effectively th e same as ours. Thus i t has been foun d possible t o cur e yeast cell s containin g a mutant gen e by bathing them in a solution containin g human genes . Some of the yeast cells incorporate the corresponding "healthy" huma n gen e into their own DNA and proceed to function normally. Of course our DNA differs fro m that of other species, otherwise they wouldn't be other species; but the nearer a species is to us, the nearer its DNA tends to resemble ours. A s annoying as it ma y b e t o some , our set o f genes diffe r fro m thos e o f th e humble mouse by only about 2%. You are the inheritor of the firs t DNA to have been created, about 4 billion years ago. Tha t DNA molecule wa s much simple r tha n ours , but th e DN A of the mos t primitive organisms on Earth is recognizably related to ours. As evolution proceeded, DNA evolved, a firm an d continuou s threa d running throug h the whole of the living world. Why Don't Your Eyes Grow Nails?

Consider the followin g fact; w e have over 200 different type s o f cells i n ou r bodies—muscle cells , nerv e cells , leukocytes , ari d s o forth . Th e DN A in al l cell s i s identical, and therefore almost ever y cell contains all the genes responsible for the

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way w e are . (Som e cell s hav e n o DNA. ) Now let u s tak e on e specifi c gene , tha t which control s the synthesis o f insulin. It has been known for very many years that insulin is produced in the pancreas—and in no other part of the body. And yet the gene is distributed al l over our bodies, in our skin cells, our muscle cells , our gum cells, an d s o on. Why don' t al l ou r cell s mak e insulin? I n fact , wh y don' t al l ou r cells d o everything? Why don't ou r muscle cell s grow hair, or our brain cell s pro duce gastric juices? Because there is a repression mechanis m tha t close s down the operatio n of different genes in different cells . Usually an unwanted gene is literally covere d up by a small molecule , a represser. Thu s th e gen e for insulin is inoperative i n al l cells except thos e i n th e pancreas . Yo u may wel l ask , how doe s th e cel l kno w which genes to repress? We don't yet have a satisfying answer to that question . There is more: a mechanism ofte n exist s fo r canceling the repressio n i n time of need. For example, consider a bacterium that has a gene responsible for the synthesis of an enzyme that catalyzes the breakup of a certain sugar . If this sugar is not i n the bacteria's environment, th e gen e is switched off , covere d with a repressor. No enzyme is produced; if it were, it would have no role. However, if the sugar is fed to the bacteria l colony , ther e i s a n advantag e in havin g th e enzym e sinc e i t coul d break up th e sugar , providing the cel l wit h energy . What happens i s that th e firs t molecules o f the suga r enterin g th e cel l are chemically altere d s o as to produce a molecule, the inducer, which clamp s on to the repressor, altering its shape s o that it falls of f the gene. The exposed gene now starts manufacturing the enzyme needed to break up th e sugar . Th e proces s i s referred t o a s enzyme induction; th e en zyme i s manufacture d whe n i t i s neede d instea d o f being pointlessl y produce d when it s not wanted. Wonderfully subtle . Evolution or Creation? Please put your money on evolution. Why Sex?

We believe tha t w e understan d th e broa d outline s o f heredity, bu t problem s re main. We look at an important one . Why are there two sexes? A case can be made for the thesis that sexual reproduction is a less than optimal means of ensuring the survival of a species. Conside r this argument: Imagine an organism exists that has adapted itself exquisitely t o its environment, b y which w e mean that a significant proportion of the populatio n ha s a genome that coul d hardly be improved on from th e point of view of the survival of that species . The best thing for the continue d surviva l of the specie s woul d be for these "perfect " individual s t o produc e progen y who wer e exac t copie s o f themselves. No w ther e ar e organism s tha t bree d asexually ; w e sa y tha t the y ar e parthenogenetic. Many insect species reproduce by parthenogenetic females laying eggs withou t th e intervention , o r existence , o f a secon d sex . Reproductio n b y parthenogenesis, in the absence of mutations or copying errors, gives an exact copy of the parent' s genome in the offspring . A "perfect" genome would be reproduce d exactly—like mother , lik e daughter . Ha s this feminis t proces s a n advantag e ove r sexual reproduction ? Apparentl y yes , becaus e durin g sexual reproductio n th e whole populatio n i s involved an d the "perfect " genome of one part of the population ca n get spoiled by mixture wit h th e les s perfect genome s of another part . O n the fac e o f it, sexual reproduction i s against the interest s o f the "perfect " individ-

The Gen e Machine |

ual—and the species—because the genome that is most favorable for survival is on the average degraded. In parthenogenesis it is preserved. Note that if, in a "perfect population," ther e are mutations producin g less than perfec t genomes , these individuals cannot , in parthenogenesis, "contaminate " th e genom e of others and will presumably be eliminated by the environment faster than their perfect colleagues. If we believe that evolutio n is inseparable from th e surviva l o f the fittest , wh y has sexua l reproduction, an apparently inferio r method o f maintaining a species, evolved and survived? Evolution is supposed to weed out those characteristics that mitigate agains t the surviva l o f the species . I t look s a s thoug h t o b e successful, species should breed parthenogenetically. One fallacy in the argument is the implicit assumptio n that the environment is stable. A "perfect" genome is given this accolade because it is perfect fo r the environment in which it exists. Parthenogenetic species are all right as long as their environment is stable, but in relatively rapidly changing external conditions the very stability of the genome is a disadvantage because it prevents the genome from evolving so as to adapt to new stresses. Sexual reproduction is a far more efficient creator of ne w genome s because it mixe s th e parents ' DNA . The greate r the variet y of genomes pitched against nature, the more likely it is that one or more of them will be better adapted to new conditions than the previous genomes. This may apply particularly to the resistance o f a species to serious infection by microorganisms. Part of the defens e o f the body against bacteria depends on genetic factors. Bacteria have, on their surfaces, molecules (car keys) that are recognized by specific receptors (car locks) in the defens e systems of the body. This recognition process is the basis of the body's capacity to destroy the invaders. However, bacterial keys can change under the influence of mutation, which means that any given population of bacteria has a wide range of molecular "keys." Selection ensures that bacteria containing those car keys that are not immediately recognized by the body's receptors will flourish at the expens e of less successful variations . One way that the species can try to defen d itself against attack is to produce new receptor s (change the car locks to match the new keys). The receptors in the body are also under genetic control, which means tha t the mixing of genomes that occurs in sexua l reproduction will improve the chances that the offspring o f a particular generation will produce receptors to which the "successful " bacteria ar e not suited. However , the bacteria will start to adapt to the changes, since once again natural selection will encourage the (minority ) of bacteria that are not recognized by the new receptors. But sexual reproduction always aids the body to defend itself. The bacteria change keys, the body changes the locks , and neither sid e ever wins. Thi s situation i s a typical example o f the Re d Quee n theory , which ha s gaine d popularit y ove r th e pas t fe w years an d ha s bee n invoke d i n a numbe r o f contexts. Th e Re d Quee n i n Alice through the Looking Glass runs faster and faster but stays in the same place. By th e way , there i s som e evidenc e t o sugges t that specie s whic h mov e completely to parthenogenesis do not last very long on the time scale of evolution. Extreme feminists take note. The Wandering Gene

Genes ca n cros s fro m on e specie s t o another . Thi s happens , fo r example, in th e cross-pollination o f plants, bu t i t appear s that gene s can b e transferre d between

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species by a number of other natural mechanisms. For example, a virus may have a transposon (a jumping gene) in its RNA that could be transferred not to another site on the RNA but to the DNA of the organism whose cells it invades. This is a specific example of what may be a more general phenomenon in which genetic material, or even complete organelles, from on e species invades the cells of another. We saw in Chapter 22 that this may account for the origi n of mitochondria. Here's another example. It is believed by some biologists that very early in the history of life on Earth, relatively larg e complex cells firs t acquire d th e abilit y t o carr y ou t photosynthesi s when on e or more became fused wit h a photosynthetic bacterium . And that's how plants were born: the photosyntheti c apparatus of the plan t cel l is primarily concentrated in the chloroplast, which originated as a bacterium. In one of the most far-reaching developments in scientific history, man, emulating and surpassing nature, has also developed techniques for transferring genes between species . This is not a trivial accomplishment. There ar e dangers associate d with this power, and ethical questions have already arisen. In the following chapter we will see how science meets morality in the shadow of heredity.

25 The Lords of Nature ? ... an d thus render ourselves the lords and possessors of nature . —Rene Descartes, Discours de la methode

Our rapidly developin g ability to identify an d manipulat e gene s is creating problems, both biological and ethical, that we have never had to face before . Is Genetic Engineering Dangerous?

When th e Whize n famil y o f Lo s Angele s decide d t o donat e th e cos t o f a ne w biotechnology wing a t my university, ther e wa s on e condition: tha t there shoul d be an annua l serie s of conferences on "bioethics." Bruce Whizen was deepl y concerned wit h the ethica l implication s o f science. H e was well awar e that althoug h biotechnology could be used fo r "the relief of man's estate, " i t also had th e potential to be an ethical Pandora's box. He was thinking o f that componen t of biotechnology that we call genetic engineering. Genetic engineering is, broadly speaking, the art and scienc e of removing genes from the cells of one species and introducing them into the DNA of a member of the same or a different species . The primary commercial purpos e of genetic engineering is to induce another species to produce a substance which it would not normally produce, but whic h is useful t o man. Remember, the role o f genes is usually t o direct the synthesis o f specific molecules within the cell, Thus, in principle, if I put the gene for producing adrenaline int o a bacterium, then it will produce this vitally important substanc e fo r me, a substance tha t bacteri a never normall y synthesiz e since it is not part of their biology. The technique o f taking DNA from, say, human cell s and placing it in the cells of another organis m ha s becom e commonplace . Let's take a classi c exampl e to se e how this is done. We need to be able to obtain large numbers of the desire d gene (i.e., to clone the gene). This can be done by planting the gene in a helpless organis m and waiting for that organism to multiply rapidly . For this purpose it is usually best to use bacteria as the host organism, since they breed so fast. Certai n bacteria, including the ubiq uitous E. coli, carry their DN A in circula r for m i n their extranuclea r protoplasm. There can be several of these rings, or plasmids, i n one bacterial cell (Figure 25.1). Plasmids ca n be isolated an d treated with restriction enzymes, whic h have the ability to cut open the plasmid ring. If the solution in which this is done contains genes isolated from anothe r species, say man, it is possible for the exposed ends of the cu t plasmids to link ont o these foreig n gene s and reclose the ring, thus incorporatin g the visiting gene into the plasmid. This process is aided by another enzyme , DNA ligase. The resultin g rin g o f hybrid DN A is know n a s recombinant DNA. A t this

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Figure 25.1. Th e grafting of a foreign gene into bacterial DMA. The ring-like plasmids ar e removed from the bacteria , opened, and mixed with a foreign gene. They close, incorporating the gene, and are returned to the bacteria.

stage the plasmid , feeling lik e a nest with a cuckoo's eg g in it, can be induced t o reenter bacteria present in the medium. The excitin g but, to many , vaguely menacing fac t i s that the doctore d bacteria, containing recombinant DNA , reproduce, generating bacteria containing the iden tical recombinant DNA. A small number of bacteria can generate a huge number of offspring i n a matter of days. Furthermore, and this is the point of the exercise, the doctored bacteri a wil l synthesiz e no t onl y thei r ow n protein s bu t als o protein s whose synthesi s i s controlled by the foreig n gene, a gene that coul d be o f human origin. Here is an example. The interferons are a class of small proteins that are produced in minute quanti ties i n th e huma n bod y and ar e capable o f inhibiting the actio n of some viruses. The proble m i s tha t i t i s no t feasibl e t o obtai n th e amoun t o f human bloo d tha t would be needed to satisfy th e growing clinical need for interferon, and the cost of isolating useful quantitie s o f the protei n fro m bloo d would, in an y case , be enormous. Furthermore, the isolation process is lengthy, on the order of months. A few miles south of Tel Aviv there is a company that has taken the human gene responsible fo r the synthesi s o f an interfero n and place d i t i n bacteria. Interferon is no w produced relatively cheaply by these bacteria, the rate of production being several hundred time s as fast a s the conventiona l method. Using the sam e general princi ple, growth hormones, blood-clotting factor, insulin, vaccines, and a growing variety of polypeptides used i n medicin e ar e being produced in severa l countrie s by genetic engineering of bacteria or yeast cells. The bacteria that produce human in sulin d o so so enthusiastically tha t they bulge with product. The use s t o whic h geneti c engineerin g is being pu t ar e increasin g yearly . Enzymes are proteins, which makes them very suitable for production by genetic engineering. Among those enzymes successfully produced is a lipase, an enzyme that breaks up fa t molecules and i s added to detergents. It was just necessary to isolate the gene for lipase and induce it to link up with bacterial plasmids. Genes placed in plants ar e producing, among other things, pharmaceutica l peptide s an d melanin , the dark pigment of the skin, used in some sun lotions. Genes transferred to plants have conferred upon them heightened resistance to insects and disease. There appears to be no reason why we should no t be able to transfer any gene from a member of one species to the DNA of a member of the same , or any another, species. If this is so, then what was once unthinkable i s becoming feasible: remedying genetic defect s b y replacing faulty gene s with their health y forms . Th e advo-

The Lords of Natur e |

cates of genetic engineering see a future in which such transfers will eat away at the ills to which man's fles h is heir, a future i n which the blind cruelt y of nature will find its match in the laboratories o f the genetic engineer . Others are more wary. Another Viewpoint A doubt hovers in the background, a sense of the presence of deliberate or accidental evil. The ability to transfer genes has, as far as I know, been used only for harmless or beneficial purposes. Shoul d such work be more closely scrutinized and perhaps controlled ? I t i s no w commo n practic e t o inser t int o mice , gene s that ar e responsible fo r human diseases , such a s the gene associated with Wilms' tumor, a malignant growth causing kidney cancer in children. Mic e that carry the genes for human disorder s ca n be of immense help in studying such disorders. This medical breakthrough is seen in a rather different ligh t by those who support animal rights. Naturally, the transfer of genes to human beings has caused rather more concern. Gene Therapy Molecular biology has opened up the possibility of transferring genes to human beings, either from othe r human being s or from othe r species . HMS should be aware of thi s developmen t an d exactl y what i t implies biologically . The ethical implica tions are the subject of ongoing discussion. To put thing s i n perspective, it is worth notin g that i t is now possible to take a mouse an d replace any gene that has been identified, by a mutated version of that gene. The replacement sits in the same location as the healthy gene. The purpose is usually t o examine the role of a specific norma l gene in the working of the organism, but that is not the point I wish to make, which is to emphasize the rapidly increasing degree of precision with which th e genome can be analyzed and operated upon. There are two quite distinc t procedure s in gene transfer: transfer o f genes to the somatic cell s an d transfe r to the reproductive cells . T o clarify: th e somati c (nonreproductive) cells , suc h a s your muscl e cell s o r your blood cells , d o not han d o n their DNA to the next generation. Only your reproductive cells do this. If the gene for producin g comedian s is integrated into th e DN A of your liver cells , your children will not be the Marx Brothers. However, if there were such a gene and i t was incorporated int o you r ovu m o r sperm, then yo u migh t ru n th e ris k o f initiating generations of cigar-chomping, wisecracking babies. The effect s o f somatic gen e therapy ar e limited t o the individua l bein g treated; the invading gene does not appear in the sperm or ovum of the recipient. There are two possibl e motive s fo r suc h treatment . On e i s t o tak e a n ostensibl y norma l human being and attempt to improve her. A contrasting motive is to repair genetic shortcomings. An example follows . There ar e peopl e wh o ar e bor n withou t th e abilit y t o synthesiz e a n enzym e called adenosine deaminas e (ADA). This failure arises from a defect in the gene responsible fo r the synthesis o f the enzyme . Without ADA, there is a drastic weakening of the immune system , the body's defense mechanism agains t invaders. The resultant diseas e i s know n a s sever e combine d immun e deficienc y (SCID) . O n 1 September 1990 , W. French Anderson, then at the Nationa l Institute of Health, attempted t o treat a small girl from Ohi o who suffere d fro m SCID . His approach was to give her the gene that was responsible fo r synthesizing the enzyme ADA, which

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in her cas e was defective . Norma l ADA genes were transferred to a virus tha t ha d been rendered harmless. Cells were then taken from the girl's blood and exposed to the virus. The virus invaded the cells, to which they transferred their genetic material, including the ADA gene. The cells were then cultured so that they multiplied. They were the n infuse d int o th e girl' s bloodstream . They began producing ADA; they had the gene. A second child underwent the same treatment shortly afterward . Both children wer e partially cured. Every six months they return for an infusion, a small price to pay for a reasonably normal immune system. The general technique o f somatic gen e therapy will almos t certainl y become a standard for m o f treatment fo r some diseases arisin g fro m geneti c defects. Anderson's technique was suited to a disease of the blood—transfusion i s a standard procedure. Replacing the fault y genes in an organ such a s the kidney is far more diffi cult, in fac t practicall y impossible a t the moment, and the answer to most genetic diseases would see m eventually to lie i n reproductive cell gene therapy. Bu t this would help the children, not the parents. Whereas I can see no scientific, legal, or ethical objection to somatic cell therapy, I can understand wh y there have been objections in the cas e of genetic manipulation o f the reproductive cells . Thi s i s a n area in whic h th e issue s shoul d b e very clear to HMS because, although the techniques are not used at present, the possibilities are legion. Although reproductive cell gene therapy ca n be applied t o animals othe r tha n man, and her e on e may have to consider ecologica l and othe r consequences , th e ethical controversies in this area are naturally primarily centere d o n the applica tion to man. In Europe, in 1988, th e organization of Medical Research Councils put its stam p o f approval on somatic gene therapy but objecte d on principle t o reproductive cell gene therapy. In the same year, a similar position was taken at the Fift h Summit Conferenc e o n Bioethic s in Toronto . The objectio n centered aroun d th e point that the child-to-be would have had no say in the genetic manipulation tha t gave her her genes, and tha t i f the therapy had produce d undesirabl e effect s ther e would be no way back. If one wanted t o be awkward, on e could point ou t that at present there is no way back for almost any child that is born with a genetic defect, and that gene therapy performed on the ovum of a woman carrying a very undesirable gene could allow her to have normal children withou t the fear that they were going to inherit, say, cystic fibrosis o r Tay-Sachs disease. The British medical journal Lancet devoted an editorial to the subject of human gene transfer in January 1989, expressing the following opinion: What one needs is an educated public. The y need to be sufficiently DNA-lit erate to appraise the advantages and disadvantages of gene therapy. The more people involve d i n th e decision-makin g processe s th e better . Decision s should not be confined to a small group of experts, be they scientists or politicians, philosophers o r doctors. This neither condemn s nor supports gene therapy. Understandably, when it comes to genetic manipulation o f reproductive cells, religious bodies have a rather more disapproving point of view, as exemplified by the Catholic Church, which i n its official polic y statement in 199 2 reflects it s own but als o many othe r people's , mis giving:

The Lord s of Natur e j

It is immoral to produce human embryo s destined t o be exploited as though they wer e disposabl e biologica l matter . Certai n attempt s a t engineerin g of chromosomatic or genetic matter are not therapeutic but ar e intended for the production o f selecte d huma n being s accordin g t o se x o r othe r pre-estab lished criteria . Thi s engineerin g goe s agains t th e persona l dignit y o f th e human being and his unique, unrepeatable identity. For religious fundamentalists the answer is easy: one doesn't mess with God's creations. For the rest of us there is a real problem. Understanding the technique s o f reproductive cel l gen e therapy is less important than understandin g the principles : we ar e talking abou t introducing foreign genes into the DNA of the reproductive cells of a potential parent who has a defec tive gene. The object is to avoid an inherited diseas e in the patient's offspring. One can foresee the day when i t will be possible to take a sample of sperm from a man, remove a defective gene, and replace it with a normal gene. The sample could then be used to fertilize hi s partner' s eggs. Once again, I can see no ethica l objection to what would onc e have been regarded as a miracle. On the fac e o f it, only medical good could com e of such a manipulation. O f course it could go wrong, but s o can any medical procedure. So why d o the officia l bodie s object, and a lot of other people worry? On the purely emotional plane, there is perhaps a feeling that we are interfering with nature at the deepest level. Another predictable fear arise s from th e Frankenstein scenario : somewhere in a cellar the crooked (mad?) scientists, in the service of th e Leader , are producin g subservient , merciles s monsters . Bu t fo r this , on e doesn't nee d a laboratory. Hitler produce d th e SS ; Pol Po t produce d th e Khmer Rouge; Dr. Mengele an d th e Japanes e performed medical experiment s o n huma n beings. Those who advis e caution in the are a of genetic engineering see such horrendous episodes as supplying them with legitimate backing, but on these grounds one would have to ban surgery, injections, and many of the accepted techniques of medicine. It i s my belief that thos e who fea r geneti c engineering have fa r more reason to be perturbe d b y the socia l doctrine s o f the kin d promulgate d by the nineteenth century geneticis t Franci s Gallo n o r th e racia l theorie s embrace d b y twentiethcentury fascist regimes and their admirers. There is no need for genetic engineering if a government, or indeed a n individual, wants to treat human beings like laboratory animals.1 Quite apart from ethical problems, there are biological dangers inherent i n gene transfer. Those involved in genetic engineering are aware of them. In research institutes using recombinant DNA techniques, part of the work is carried out in laboratories that resembl e inverted steril e rooms ; nothing mus t be allowed to leave th e room unless i t is monitored. The fear i s that genetically engineered bacteria could have unpredictable effect s i f they escaped and subsequentl y multiplied. Thi s i s a far more realistic concern than the cloned-superman fantasy. It is not that the bacteria could be pathogenic, although they might, but rather that they could have un1 It will be interesting to see the long-term results of the use, in the United States, of a sperm bank confined to donors who are prominent scientists and intellectuals. Personally, I would prefer an average child of my own to an artificially inseminated child of a genius. But maybe I am revealing a vein of sentimentality or macho possessiveness.

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predictable effects o n the loca l ecological balance. Man has upset this balance before, by introducing foreign specie s into an ecosystem. The biological consequence s o f genetic manipulation ar e no t th e onl y are a of controversy associate d wit h th e huma n genome . Th e mos t controversia l subjec t has been IQ , but a growing area of public concer n i s genetic testing. We glance at both. Genes and Society I: Time for the Emperor to Get Dressed?

There used to be many Jewish boxers. My father reeled out their names, going back to the eighteenth century : Samuel Elias, known as Dutch Sam, the originator of the uppercut; th e Sephard i Je w Danie l Mendoza , th e firs t know n scientifi c boxer. 2 Closer in time to me was the Lowe r East Side boy Benny Leonard, who retired i n 1925, afte r eigh t brilliant year s as undefeated lightweight champio n o f the world . When I was four , Ma x Baer held th e heavyweigh t championship o f the world. My father explained: "Jews are good at boxing, it's in our blood." Today there is hardly one prominent Jewish boxer. Despite m y father' s claim , boxin g abilit y i s almos t certainl y no t inherited . A more loaded question i s whether IQ is inherited and , if so, whether som e races are less intelligent an d are doomed to remain so. Are there genes for intelligence—and where can we get some? Will we one day demand somatic or reproductive-cell gene transfer to improve our, or our children's intelligence? Alan Turing, a genius who dealt with the general theory of computing, said that we were programmed by our genes. It is doubtful whethe r he believed that the environment ha d no place in controlling our abilities, both mental and physical, bu t this i s what man y IQ practitioners claim : that I Q is independent, o r nearly inde pendent, of the environment. Only the genes count. Is the averag e IQ of the Scot s higher than tha t o f the English ? It appears to be, from the published data . What does the result mean? A logical positivist would say that it proves that Scots obtain higher scores on IQ tests than Englishmen. Period. A Scot woul d b e incline d t o sa y tha t i t prove s tha t Scot s ar e mor e intelligent , t o which an Englishman might reply that IQ tests only test certain kind s o f abilities, and ar e no more indicative of general intelligence than the ability to do crossword puzzles. So far the argumen t ha s been only slightly barbed, but no w translate th e whol e scenario to whites versus black s an d yo u en d u p wit h campu s riot s an d visitin g speakers being shoute d down . Consider William Shockley , who share d th e 195 6 Nobel Prize for research into semiconductors an d discoverin g the transistor effect . Shockley became obsessed with what he saw as the threat to the average IQ due to the higher birthrate amon g what he declare d were low-IQ people. His spoken and written statement s quickl y develope d strongl y racia l overtones . Thankfully , th e vast majority o f the scientifi c communit y repudiated hi s views, emphasizing that his excellence as a physicist len t no weight to his genetic ramblings, but Shockley remained convinced that the Negro, as blacks were called in his day, was less intel2 Mendoza's lodgings can still be seen opposite Bethnal Green underground station, in East London. A natural middleweight, he was barefist heavyweight champion of England in the 1780s and gave boxing lessons to gentlemen. He wrote the first modern textbook on boxing, The Art of Boxing (1789).

The Lord s of Natur e I

ligent than th e whit e man. Thi s is not an argumen t that I want to get pulled into here, but there are some points that should be made. In a world in which history has resulted in the vast majority o f blacks being economically an d educationally underprivileged, it is difficult t o believe that the standard IQ tests, devised by a white middle-class society , can be applied equitably to the averag e black community . (Ther e is a t leas t on e test , designe d b y blacks , i n which blacks score d better than whites. ) Bu t there is a prior question. What does the IQ test measure anyway? Is it really testing a genetically controlled characteristic, and if so, what is that characteristic? When I was a studen t a t Universit y College London, rny firs t girlfrien d wa s a psychology student, who put me through an IQ test. My score was quite high, and I asked what the number meant. "That you're the kind of person who does well at IQ tests." It was a glib joke, but I think it was near the mark. Intelligence tests originated in the work of the French psychologist Alfred Bine t in 1905 . H e was attemptin g t o fin d a method o f predicting whic h childre n wer e most likely to fail in grammar school. H e and hi s colleague s found tha t i f the tests were based on the kinds of problems the children face d a t school, they gave a good prediction of the children's performanc e in school. Truly amazing. The obsession with racial difference s i n intelligence goes back at least as far as Darwin's cousi n Si r Franci s Galto n (1822-1911) , th e creato r o f eugenics . Convinced tha t intelligenc e wa s relate d t o th e achievemen t o f eminence, Galto n believed that the ancient Greeks had a much higher intelligence than present-day Europeans. O n th e sam e basis , becaus e i n hi s da y ther e wer e mor e eminen t Englishmen than Americans, he concluded that the Americans were mentally infe rior. Galton, incidentally, wrote a book called Hereditary Genius (1869), in whic h he attempte d t o appl y th e theor y o f evolutio n t o man . Darwi n ha d effectivel y avoided this step, but, perhaps encouraged by Galton's book, he published The Descent of Man in 1871 . The high priest of IQ in the early decades of the twentieth century was an American, Lewis Terman. Something of the mind-set of this obnoxious man can be gathered fro m hi s statemen t that the highe r birthrat e o f southern Italians a s compared with Harvar d graduate s "threatens th e ver y existenc e o f civilization." H e was a member o f the Huma n Bettermen t Foundation , whic h recommende d wholesal e sterilization i n California. His colleague Henry Goddard hung around Ellis Island, testing arriving immigrants. His results showe d tha t 87 % o f the Russians , 83% of the Jews , 80% o f the Hungarian s and 79 % o f the Italian s wer e "feeble-minded" ! (And 100% o f the testers? ) During th e 1920s , the suppose d irrelevanc e o f environment wa s show n t o b e suspect, to put i t mildly. In 1925, William Bagley discomforted the racist school of IQ by showing that in those areas where children staye d at school longer, the average I Q was higher . Wors e still, white s i n som e souther n state s of America had a lower average IQ than blacks in some northern states . In order to answer the growing criticis m tha t test s wer e ethnicall y biased, attempt s wer e mad e t o construc t "culture-fair" tests , a peculiar developmen t i f IQ, as many of its practitioners ha d stated, is purely genetically controlled. But is it? In his landmark book The Science and Politics ofl.Q. (1974) , Leon Kamin writes, "There exist no data which should lead a prudent man to accept the hypothesis that IQ test scores are in any degree heritable." You may feel that this is overstating the

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case for the environment , and Kamin himself, at the en d o f his book states, "To assert that there is no genetic determination o f IQ would be a strong, and scientifically meaningless statement," and he puts the burden of proof upon those who wish to prove otherwise. Kamin states: "That burden is not lessened by the repeated assertions of the testers over the past 7 0 years." Little has happened since Kamin wrote those words to lessen that burden. But what doe s IQ measure anyway? Intelligence is implicitly defined, fo r those who believe in IQ, by the IQ test. By calling thes e test s "intelligence " tests , th e practitioner s o f IQ tests hav e trie d t o convince us for years that that is what they are measuring. But it surely cannot be that somethin g as complex as what mos t (intelligent! ) people cal l "intelligence, " can be measured with a single number. In what meaningful sense is someone with an IQ of 134 superior to someone with an IQof 125? Oh, sure, I forgot—one of them is better at IQ tests. Worse still , the basi c premise o f IQ tests i s that they ar e measuring somethin g that is independent of learning. If it were, there might be a little more justification for supposin g it to be genetically controlled, but surel y what we normally think of as intelligence i s affected b y the stoc k of knowledge tha t we have. What we talk of as intelligence is in fac t a function of an inextricable combination of our brain circuits and our learned knowledge. And our circuits may be affected b y the learning process. I do not believe that IQ tests measure anything quantitatively meaningful , except perhaps that very low scores almost certainly indicat e gross mental handi cap, but that would be obvious without the intervention of "science." I am far from alone in the feelin g that, as in the cas e of psychoanalysis, the empero r shoul d get dressed. We have been led astray by the IQ gurus. The dangers of taking IQ too seriously are many. One can certainly sympathize with Noam Chomsky's opinion that there i s no decen t reason for attempting to fin d I Q differences betwee n differen t races. Let's try a different track . Are IQ test results a n indicator o f creativity? In 1953 , Ann Ro e measure d th e IQ s o f sixty-fou r prominen t scientists . Som e ha d hig h scores, but fo r others "none o f the tes t material would give the slightes t clu e tha t the subjec t was a scientist o f renown." Simila r studie s on the connection between IQ and creative achievement for a variety of professions in the humanities an d sciences showed no correlation excep t among mathematicians, and this only weakly. The kind of problem-solving abilities that are tested by IQ are just not the kind that are relevant to most human activities. Common experience shows us that there are people with high IQs, and possibl y impressive academi c records, who ar e highly unimpressive when it comes to almost anything outside their professional sphere. The field is wide open. David Perkins, at Harvard, has suggested, on the basis of studies on twins, that environmental effect s ar e responsible for up to half of the observed variation in human IQ scores. Consistent with this viewpoint is the fact that the average IQ of a group of schoolchildren was raised by several points by as little as one year's special teaching. The same children also performed far better than a control group on more general tests of ability than the IQ test. So what doe s IQ measure? Nothing very defined , an d excep t perhaps fo r very high and very low scores, there appears to be no quantitative connectio n between IQ scores and what most people understand by intelligence. I have the feeling tha t the "inheritance o f IQ" will soon be seen to be, if not a meaningless question, a very uninteresting one.

The Lords of Natur e |

Genes and Society II: Genetic Screening

I was a t on e tim e the chairma n o f a committee for encouraging higher educatio n among the Druz e Arabs in Israel. On e day a prominent shei k showed me a photograph o f his family . Ther e appeare d to he n o femal e members , although hi s chil dren presumably had a mother and I knew that he had daughters. It was sons tha t mattered. In India many newl y born femal e childre n ar e murdered. Shoul d fami lies preferrin g a son have the right to demand abortion s if an embry o is identified as female? The preference for male babies is the most obvious of a whole range of selective options that parents have . Thu s a couple might decid e to abandon a mentally defective chil d o r a child with severe motor disabilities. The advent of molecular biology has now brought us to the stage where such choices ca n be based on a genetic analysis of an embryo, or its prospective parents. This is one of an ever-widening range o f closely related problem s o f choice tha t aris e directly fro m th e abilit y t o identify genes in embryos and adults. It i s no w a common laboratory practice t o isolat e DN A from a n organis m an d subject it to analysis, in order to detect the presence of specific genes . This kind of work has grea t potential for the improvemen t o f human an d anima l health, but i t also generates some very tricky legal and ethical problems. DNA analysis carrie d out on an embryo might reveal that the child-to-be would suffer fro m a physical o r mental disability. I s abortion justified i f that disabilit y i s of a n extremel y seriou s nature , threatenin g th e lif e o r th e qualit y o f lif e o f th e child? If so, where would you draw the line? There is a research group that claim s that shyness is genetically controlled. Another researcher believes he has found a gene that i s responsible fo r baldness. Sill y examples , but wha t abou t diabetes or a tendency to develop Alzheimer's disease? Picture the da y when DN A analysis i s obligatory before yo u ge t accepted for a job. Improbable? Several American companies have already started genetic screening o f thei r employees . You r analysi s reveal s tha t yo u hav e a n above-norma l chance o f getting cancer or Parkinson's disease. Will you ever get employment? Or life insurance ? Insurance companie s ar e considerin g demandin g a DNA scan before insuranc e coverag e is granted . Supposin g you r girlfrien d o r boyfriend find s out tha t your DNA is suspect ; will he o r she reconsider the wisdo m o f marriage? Should you r DNA be legally your business an d n o one else's? Is this, as I feel it is, eugenics creepin g through the back door? These are issues tha t all of us should be aware of, and the y will become increasingly pressing as the Huma n Genom e Project nears completion. Although the complet e base sequence may well take many years to complete—unless improved techniques become available—the identifica tion o f all th e genes will require fa r less time . W e ca n fin d ou t what a gene is responsible for, and its location, without knowing its complete base sequence. The ability t o tell a couple tha t they both carr y the gene for a fatal diseas e is, it would see m to me, a legitimate too l in a doctor's black bag, but i f the practic e becomes widespread i t should be accompanied by specialized counselin g service s to help those who receive bad news. Are we approaching the time when, as one commercial gen e sequence r ha s suggested , w e ar e al l goin g t o hav e ou r persona l genome o n a compact disc i n th e famil y doctor' s records , or on a magnetic card , along with our credit cards? Brave New World?

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The Human Genome

The Human Genome Project i s a loosely coordinated attempt , heing conducted in nearly fort y countries , to completely sequence the 6 billion o r so bases i n huma n DNA, so that the codo n sequence of every one of the approximatel y 100,00 0 genes will be known, as well as the order of bases in the introns. It is a huge task; there are international meeting s on one chromosome, th e investigator s comparin g progress on the elucidation o f the spatial ordering of millions o f bases. Undreamed of details of our makeup are being revealed. Fo r example, preliminary estimate s sugges t that at least 550 different gene s control the chemica l and physica l structure o f the eye. The red blood cell, one of the simples t cell s in the body is associated with onl y 8 genes; the white blood cell—far more complex in form and function—is represent ed by nearly 220 0 genes, the salivar y gland by 17, the prostat e by about 1200 , the ovary by some 500, the testis by over 1200 and the liver by nearly 2100. The brain is the wor k of close to 320 0 genes. These figures will probably be subject to revisio n as research continues. The potential benefit s o f a complete analysis o f the gen e sequence an d bas e sequence of the human genome could be enormous. It is almost certain that improved techniques wil l eventuall y allo w reliabl e pinpoin t "surgery " on a patient's repro ductive-cell DNA, allowing the almost routine deletion of faulty genes and their replacement by their correctl y functioning versions. Whe n on e reflects tha t a defec t in a single gene may be the caus e o f a life-threatening disease an d tha t ove r 4000 single-gene diseases have been identified, it is clear that there is a rich fiel d for the alleviation o f human suffering . Knowledge of the human genome will pu t increasingl y powerfu l weapon s int o the hand s o f the practitioner s o f gene therapy—and int o th e hand s o f those wh o will scree n people genetically for the governmen t and fo r private companies. Th e dangers of this final invasion o f biological privacy have prompted th e draftin g o f a Genetic Privacy Act by an American professor, and a number o f states in the United States hav e alread y passe d law s partiall y aime d a t preventin g officia l bodie s o r commercial companies fro m making use o f "private" genetic information. Molecular biology has raised some strange legal and ethica l questions—includ ing the patenting of animals. Patenting Animals

At Cold Spring Harbor Laboratory in 1982 , there was a meeting of patent lawyer s and biologists to discuss "Th e Patenting of Life Forms, " specifically , the patentin g of geneticall y engineere d organisms . Th e firs t applicatio n fo r such a paten t wa s filed with the U.S . Patent and Trademar k Office o n 7 June 1971, i n respect of a microorganism culture d b y Anand a Chakrabaty . Th e patent , U.S . Paten t No . 4,259,444, was assigned o n 31 March 1981. I n April 198 8 a mouse implanted with a huma n gen e causin g cancer—th e "Harvar d mouse"—wa s th e firs t anima l t o be patented in the United States. Many plants have been patented, for example, a cotton plant genetically engineered to resist certain herbicides . Should i t be possible to patent animals ? A number o f companies are attempting to incorporate human DN A into goats , cows , pigs, and mice . Th e objective s vary, from overcomin g th e rejectio n o f th e huma n bod y t o organ s transplante d fro m

The Lords of Natur e |

other animals, to inducing human genetic disease in animals so as to be able to test drugs on them. There are ethical an d lega l issues her e that become more complex in the case of gene implantation i n humans. If I am implanted with a gene that guarantees that my son will be a musical genius, can the medical team who did it patent me or him? The question i s absurd, but is it any more absurd than the wish o f the American team that is working on the human genome to patent its findings and sell them? Incidentally, a French team working on the same problem has declared that its findings belong to humanity, a n interesting differenc e i n outlook . An acquaintance of mine in the United States , who headed a company that put a great deal of work into the partia l mappin g o f the huma n genome , once stated , "We have fifty four markers on chromosome 7 alone. We have mapped it in a way no chromosome has ever been mapped. We really own chromosome 7." He didn't mean it literally, but he clearly feels that an investment of several million, dollars in research was not made s o that he coul d freel y distribut e informatio n to one an d all . Th e company wishes to develop diagnostic tests for a variety of undesirable human genes. Is that any differen t fro m a dru g compan y patentin g it s findings ? Hi s compan y i s no t unique; the techniques ar e now fairly common . What are the legal and ethica l implications? Once again, HMS should be aware of what is being done and what it implies, both medically an d ethically . Whe n James Watson was put i n charg e of the American Human Genome Project he insiste d tha t 3 % of the budget should be set aside to finance the investigation of ethical problems, a praiseworthy demand that has borne little fruit . The Future The discover y of the genetic code and th e construction of quantu m mechanics ar e the most fateful event s in the history of twentieth-century science . In the practica l world, quantum mechanics has given birth t o the information revolution, through such device s a s the transistor , th e microchip , an d th e semiconducto r laser . The twenty-first century may be the century of the genome. It is impossible to say where genetic engineering and genetic analysis will have taken us by the en d o f the next coupl e of decades. That it will pose more ethical problems is almost certain. For the science fiction fa n one question, asked by the molecular biologist Lederberg, hovers in the background: "What stops us from Etiaking supermen?" To which he supplies the answer: "The main thing that stops us is that we don't know the biochemistry of the object that we are trying to produce." The question as to whether we can create supermen is a sensational way of asking a more prosaic question: Can we dramatically improve the mental and physical characteristics o f ourselves and our children by genetic manipulation? The answer is that in principle the means are, or one day might be, available. On which disquieting note I pass the discussion ove r to you. Molecular biology, particularly its genetic aspects, has laid a rational infrastruc ture fo r Darwinian evolution an d becom e an indispensabl e par t o f biological an d medical science. The discovery of the doubl e helix and the breaking of the genetic code hav e fille d i n a ga p i n th e hierarch y o f the sciences . Th e practica l consequences may play a major par t in shapin g everyday life i n the next century, a century in which, if we survive, we will increasingly manipulate the biological world, hopefully fo r our own good.

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It woul d b e misleadin g t o sugges t tha t a detaile d knowledg e o f th e huma n genome wil l rapidl y lea d t o spectacula r advance s i n th e treatmen t o f genetically controlled diseases . Th e identificatio n o f the locatio n an d natur e o f the norma l gene responsibl e fo r a give n biologica l characteristi c doe s no t necessaril y mea n that we can easily counter th e effec t o f a faulty gene. The potential is there, but u p to now the medica l benefits o f the analysi s o f the genom e have been scant . Nevertheless, let's end on a hopeful note . While I am writing this, a fourteen year-old boy is dying in a London hospital because no dono r has bee n foun d fo r a heart trans plant operation. In another part of the world, scientists ar e rearing genetically engineered pigs with the object of producing internal organ s that will not be rejected by the huma n body . Whether this projec t wil l b e successfu l remains , a t th e tim e of writing, to be seen. If the approac h succeeds , it could remove the great obstacle to widespread transplant operations : the difficulty o f obtaining sufficient donors . The thought o f carrying a pig's heart in you r chest migh t worry a Romantic poet or an antivivisectionist—but not the parents of a sick child .

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Life: The Molecular Battl e "Dissolution, putrefaction," said Hans Castorp. "They are the sam e thing as combustion; combustion with oxygen—am I right?" "To a T. Oxidation." "And life?" "Oxidation too..." —Thomas Mann, The Magic Mountain

In the last 350 years, the formulation of a small number of unifying concepts has al lowed us to rationalize much of what we know of the living world. We have already seen examples, in Darwinian evolution , Mendelian genetics, and the genetic code. Other major concepts include the eighteenth-century system of classification of living forms an d th e nineteenth-centur y concept s o f the cel l an d th e ger m theory of disease. Th e confluenc e o f biology and chemistr y i n th e twentiet h centur y ha s brought a rich harves t and , whil e w e ca n hardl y b e sai d t o understan d life , ou r knowledge of the workings and structure of cells has become increasingly detailed . Life is a continual struggl e at all levels. Darwinian evolution is predicated on the competition between organisms. Physiology, biochemistry, and molecular biology have show n tha t ther e i s a continual molecular struggl e within eac h organism , a struggle agains t dissolution , a struggl e t o maintai n a constan t interna l environ ment, and a struggle to negate the deleterious consequences of invasion by both living and non-livin g intruders . The organism' s abilit y to surviv e thes e battle s is based largel y on the hug e variety of shapes tha t ca n be adopted b y protein molecules. Shape is the key to most of the cell's activities . But what i s life? At what leve l of complexity doe s it begin? Certainly not at the elementary particle level , or the atomi c level , but i t was once supposed t o start at the level of the single molecule. What Is Life?

At one time, all known objects were very clearly either dead (e.g., the Pyramids) or alive (e.g., archaeologists). Both Hippocrates and Aristotle stated that an innate heat, originating in the heart, distinguished livin g organisms from dead matter. The sharp line separating dead fro m livin g was reinforced, i n the eighteenth and early nineteenth centuries, by advances in chemistry that pointed to the conclusion tha t living matter was composed of special kinds o f molecules. Substance s were isolated from living material that were never found in the clearly inanimate world. A classic case was urea, separated from urine. It was believed that such substances could not be produced from any material derived fro m nonliving matter . Thus carbon dioxide (dead) could be obtained by heating chal k (dead), but there was no known way of making urea fro m inorgani c (alias : dead) substances. An d that was because living

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material is fundamentally different fro m nonliving, o r so the story went. Living matter possessed a vital force. S o organic chemistry was born, the chemistr y of molecules that could supposedly be made only by living organisms. The cut between the living and nonlivin g world was firml y fixe d a t the molecular level, ergo life ha d been created separately from the creation of the inanimate world. And then, in 1828, a German chemist, Friedrich Wohler (1800-1882), attempte d to mak e a n inorgani c substance , ammoniu m cyanate , by evaporatin g a solutio n containing ammoniu m an d cyanat e ions , both also inorgani c substances . H e kept on heating afte r th e crystal s appeared and isolate d a white soli d tha t o n analysi s turned ou t to be not the "dead" substance , ammonium cyanate , but the "live" molecule, urea. Wb'hler hesitate d t o publish , fo r two reasons : h e didn' t quit e believ e what h e had done , an d moreove r it looke d a s thoug h h e wa s guilt y o f treachery. He ha d been a student o f Berzelius, the originato r of the vitalis t theory that organi c molecules coul d b e made onl y b y livin g organisms. 1 Wohler's discover y shoul d hav e put the vitalist theory down for a long count. An organic molecule had been created from inorgani c molecules. But there was not a lot of attention paid to his fea t a t the time . What should hav e been th e fina l decisiv e knockou t came in 184 5 when Adolph Kolb e (1818-1884) , wh o introduce d th e wor d synthesis int o chemistry , synthesized aceti c aci d fro m carbo n disulfid e (CS 2). Previously , aceti c acid , th e basis of vinegar, had bee n universally produced by fermentation of organic matter. One las t effor t t o conserv e th e uniquenes s o f "livin g molecules " came , i n 1898 , from a certain Dr. Japp. Build a molecule. Let it look at itself in a mirror. For very many molecules, what they see is another molecule, looking very like them, but differing fro m them in the way that your left hand differ s fro m your right hand. When such molecules are synthesized in the laboratory , they usually appea r as a mixture o f the two mirror images—like gloves, or shoes, coming off a production lin e in pairs. Thi s i s not normally true of molecules synthesized by cells. The cell manufactures only one of the two molecula r forms—glove s fo r your left han d only. Japp claimed tha t livin g organisms were the only systems that coul d produce optically.active molecules (i.e., one glove without th e other) . He was proved wrong in 1917 , whe n asymmetrical syntheses wer e first carried out in the lab. There are no molecules that man has not made, or cannot potentially make, from inorganic precursors. Today th e ter m organic chemistry i s misleadin g sinc e i t mean s nothin g mor e than th e chemistr y o f molecules containin g carbo n atoms . No t all organi c molecules are associated with living material. Thus benzene is an organic molecule but is not normall y foun d i n livin g cells. Ou r conclusio n i s that at the level of molecules, living and nonliving matter cannot be differentiated. Like Descartes, most scientist s believ e tha t livin g matter obey s the establishe d laws o f chemistry an d physics. 2 Thomas Huxley said it : "I can find n o intelligibl e ground for refusing t o say that the propertie s of protoplasm result from th e natur e and dispositio n of its molecules." Life is a demonstration of the degre e of complex1 In his letter to Berzelius, Wohler wrote, "I can no longer, as it were, hold hack my chemica l urine; and I have to let out that I can make urea without needin g a kidney, whether of man or dog: the ammonium sal t of cyanic acid is urea." 2 It was because of this belief that Descartes thought he could find a way to hold back aging.

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ity and organization that can be obtained from molecules , at which poin t the vitalists dro p back to their fina l defensiv e line an d desperatel y shout , "Yes , but wha t about thought ? Tha t separate s u s fro m stones , an d ther e i s n o bridgin g that ga p with chemistry an d physics." I' m going to sidestep that one. All of which leave s us withou t a definition of life an d fail s t o answer the ques tion: A t wha t leve l o f complexity ca n a syste m sai d t o b e living ? Th e mistake n chemical differentiation between living and dead molecules has been removed, but at higher level s of organization there is clearly a difference between a spanner an d a Spaniard. 3 What if we move one level u p from molecules an d instea d conside r viruses? A drawing of the T4 virus is shown in Figure 26.1. It looks more like a space capsule than a pussycat. It has si x spidery, jointed legs. Its head, which contain s th e virus's DNA , carries a long, hollow shaft. T 4 is a bacteriophage; it attacks bacteria, landing on them and standing on its legs. Next it squats down and drives the end of the shaf t throug h th e bacterial cel l wall. I t injects its DNA into the bacteria. As in science fictio n horro r movies, this DNA takes over the cell , directin g th e produc tion o f alien RN A molecules an d protein s fro m th e molecules i n the cell . With its DNA an d th e new RNA , the cel l synthesize s enzyme s that attac k and destro y the bacterial DNA. The bacteria have now been converted into factories for the production o f viruses. I s a virus alive ? It can certainl y reproduce , i n it s ow n perverte d way. Is this th e leve l at which lif e begins? Are we psychologically resistant t o the idea that a mechanical-looking objec t is alive? Let us resolve not to be worried by vague borders, and adopt the attitude of those working in the fiel d o f fuzzy logic : there are questions t o which th e answe r i s neither yes nor no. We will take a simple approach , asking what commonl y observed characteristics differentiat e undeniabl y livin g organisms from the nonliving world. The Signs of Life If we take a holistic approach , there ar e any number o f properties o f the whol e organism tha t ca n be take n to be indicativ e o f life, bu t thre e see m to be absolutel y universal:

Figure 26.1. Atypica l virus.

3

With acknowledgments to John Lennon's A Spaniard in the Works.

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• Th e need to take in a source of energy to maintain th e organism's integrity • Th e ability to reproduce • Th e ability to respond to stimul i One can quibble abou t all three. A starving man can survive for some time with no intake o f energy. However, he i s doin g it a t the expens e o f his interna l source s of energy, molecularly autocannibalizing himself. A castrated ma n ha s n o abilit y t o reproduce, but h e belongs to a living species. An d a stone (certainl y a pet stone ) can respond to a stimulus—kick it and it moves, heat it and it cracks. However, it is difficult t o think of an unquestionably nonliving object that displays all the preceding characteristics . Th e nee d fo r energ y i s perhap s mor e fundamenta l tha n th e other criteria, for without energ y intake the organism will, after a short time, not respond to stimuli or reproduce. The Source of Energ y Without foo d al l organisms di e an d disintegrate , breaking down t o simple r mole cules, most of which finall y combine with the oxygen in the air. Plants take in energy directly from the Sun and also absorb air, water, and salts. They use the sunlight to synthesiz e sugar s and othe r molecules . On e of the firs t step s i n this proces s i s the breakup of a water molecule, giving a hydrogen atom that attack s carbon diox ide and thus starts the long chain o f chemical reactions leading to glucose. Deprive plants o f light for a long period, and thei r delicat e and comple x structur e disinte grates. Animals canno t directly utilize the Sun's energy , and many animals rel y on meat or fish as their primar y source of energy, but ultimately the sourc e of all fles h is plant material, so that animal s indirectly use the Sun' s energy . The average person in Western society may during his lif e ea t 8 complete cow s and aroun d abou t 35 sheep and 75 0 chickens, but thes e animals live by eating plant material . Because we ultimately depend on plant lif e for all our food, we also depend en tirely o n th e Su n fo r our energ y intake . Photosynthesis maintains all life on this planet, except fo r a few idiosyncratic microorganism s wit h exoti c energy sources. And whe n you burn fossi l fuels , suc h as coal or oil, you ar e releasing the impris oned prehistoric heat of the Sun . Life Is Cellular At wha t leve l o f organization , betwee n quar k an d queen , doe s lif e appear ? Ar e there any living molecules? We saw in Chapter 22 that RNA can reproduce itself i n a test tube, but i t needs a living creatur e (man) to put th e right molecules into th e system a t the righ t time. Thi s i s not characteristi c o f the reproductio n o f animals and plants. And a molecule of RNA does not need energy to maintain it s stability. It would seem that to ascend to the level of life, we need more than a molecule, however wondrous ; w e nee d a collectio n o f differen t molecules , an d i t ha s becom e clear ove r the pas t centur y that w e need a highly organize d system o f molecules. How highly? The least complex living entities we know, down there among the amoeba, contain hug e number s o f molecules coexistin g i n a flexibl e bu t mechanicall y stabl e package—the cell. Cell s com e i n a variet y o f shapes , a fe w wit h well-define d geometries, lik e th e re d bloo d cells , bu t mostl y roughl y spherica l o r ellipsoidal. Some highl y specialize d cells , lik e nerv e cell s o r sperm , hav e on e o r more thin ,

Life: The Molecular Battle |

fiberlike extensions . All living systems are composed of one o r more cells. A bacterium is single-celled; a human being contains something like 10 trillion cells. Repeating a n earlie r conclusion : th e fac t tha t th e content s o f the cel l includ e ver y large (highl y improbable) molecules, and tha t the cel l is a highly ordered (highl y improbable) structure, implies tha t living matter is in a state of comparatively low entropy as compared with the disorganize d mess of small molecules into which i t disintegrates when it dies. Summarizing the facts , we take as our definition of a living form: A low-entropy, dissipative system of molecules, organized into cells, responding to stimuli and capable of reproduction .

This reads like an interdepartmental memo, not a description of a living organism, s o let's pu t som e flesh o n it. Living forms, an d thei r cells , from th e simples t to the mos t complex, share a number o f characteristics, among which are the following: « Cell s arise by the divisio n o f existing cells. • Cell s differ widel y in detailed appearance, depending on their function , bu t all have a membrane around them and a variety of interna l "organelles" that are usually foun d t o hav e identica l o r simila r function s t o thos e foun d i n most other organisms. • All living cells contain water as an essential component. • Living material contains twenty or so of the chemical elements, of whic h carbon, hydrogen, oxygen, nitrogen, phosphorus, and sulfur ar e numerically th e most predominant. The first fou r in the list make up abou t 99% of all livin g matter. • Al l living material, from the amoeba upward, is composed primarily of about twenty amino acids, five heterocycli c nitrogenous bases (Figur e 24.la), a selection o f lipids , an d som e sugars . Amin o acid s ar e th e basic unit s fro m which protein s ar e constructed. The nitrogenous bases are essential components of the nucleic acids, DNA and RNA. Lipids include what we commonly call fats , ari d als o th e phospholipid s tha t ar e basic component s o f al l cel l membranes. Simple sugars, like glucose, are the basi c units o f carbohydrate storage supermolecules like starch and glycogen. • Th e immediate source of energy utilized by the cell is adenosine triphosphate (ATP). Thi s molecul e appear s t o b e ubiquitous , havin g bee n identifie d i n every kind of living organism. What Is a Cell? A cell is an organized, dissipative syste m of molecules, often capabl e of reproduction. It is possible to take small bits of tissue from plants arid animals, and even single cells, and maintain them in a suitable culture medium, during which time they maintain thei r structure , respond to stimuli, absorb sources of energy and produce energy, an d i n man y case s divide . Ou r definitio n o f life say s that they ar e alive . When they lose their structural integrity and stop importing and exporting energy, we say that they are dead. In practical terms it looks as though the unit of life is the cell.

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The Cell as a Black Box

There is a continuous flo w of matter into and ou t of living cells. Cells die without a supply of matter of the right kind, although som e spores can survive for years in a state o f dehydration an d the n com e to life whe n wate r i s supplied t o them. Suc h systems are analogous to food i n a deep-freeze—all chemica l processe s have been halted. Nevertheless, the living cell needs food, and one way of looking at the cell is as a chemical converter , a unit that transform s incoming molecule s int o material products. Many of the products are needed to replace worn-out structura l components, but in multicellular organisms some products, such as adrenaline o r the sex hormones, are produced in specialized cells and exported to other cells. The waste products of the cell's chemical activity include carbon dioxide, water, and a variety of othe r molecule s tha t w e excrete . The norma l intak e o f the bod y cell s include s oxygen, amin o acids , glucose , lipids, vitamins , certai n meta l ions , an d trace s of other substances. Some of these are not essential, in that the body can manufacture them from other molecules. Thus the amino acid glycine can be manufactured from other amino acids, but tryptophan can't . Cells are organized. They contain distinct structures, but the molecules of which these are composed are continually breaking down. The structures are maintaine d by the synthesi s o f new molecules . This i s what Thoma s Huxle y meant whe n h e said that "livin g protoplasm . .. is always dying , and, strang e as the paradox may sound, could not live unless it died." Synthesis is part of life's struggle to maintain itself. Th e red blood cell has no nucleus an d no DNA, so that it cannot synthesiz e proteins. In consequence, its lifetime is quite short, typically about 120 days. Moreover, i n th e absenc e o f DNA it canno t reproduce, which explain s wh y th e bod y manufactures abou t 10 0 billion re d bloo d cell s ever y da y t o maintai n th e tota l number that flow through its 60,000 or so miles of blood vessels. Cells vary in their size, shape, contents, and function . Muscl e cells do not look like, or function like , brain cells. Most cells are too small to be seen with the naked eye. Conventional wisdo m proclaims that the reason for this is that materials ente r the cell at its border and make their way across the cell by diffusion, lik e the petro l vapor in Chapter 18. This is a very slow process on the macroscopic scale, so that a cell large enough to be visible to the unaided ey e would be too large for material to find it s way across the cell in a reasonable time. In some unicellular animals there appear to be ways of pushing materia l aroun d th e cel l s o that ther e is a little les s limitation o n thei r size . The larges t cells are , in general , eggs, but the y contai n a built-in suppl y o f food. Conventiona l wisdom abou t the siz e of bacteria was challenged by the discovery , in 1993, of Epulopiscium fishelsoni, a bacterium living i n the intestin e o f th e brow n sturgeo n o f the Re d Sea . Thi s microscopi c monster , shaped like a baguette, is a twenty-fifth o f an inch long, a million time s more massive than the best-known bacterium, E. coli, and visible to the naked eye. Muscle cells ar e long and thin, as suits their function , whic h is to contract in a certain direction . Re d blood cells have a large ratio of surface to volume, which is also consistent with their function , whic h is to absorb oxygen rapidly in the capillaries o f the lung s an d giv e it u p rapidl y withi n th e res t o f the body . Some cell s have small threadlike projection s that can be waved so as to propel the cell. Plant cells ofte n hav e specialized organelle s containing pigments that pick up th e radiant energ y of the Sun . Th e dominant exampl e i s the chloroplast , whic h contains

Life: The Molecular Battl e |

chlorophyll. The catalogue of cell types is long, hut i n spite of the great diversity of structures an d functions, certai n feature s are common to the structure of almost all known cells . Cell Components The Cell Membrane In 1855, Karl Nageli showed tha t pigments penetrated damaged cells far faster tha n undamaged cells. He concluded tha t there was what he called a plasma membrane around th e cell , a suggestio n confirme d in 189 7 b y Wilhel m Pfeffer . Thi s mem brane needs to be stable enough to prevent the cel l content s fro m escapin g easily, yet permeabl e enoug h t o allo w foo d materials , oxygen , an d othe r substance s t o come in, an d th e product s o f the cel l to com e out. Thu s th e cell s o f the pancrea s need t o inges t startin g material s i n orde r t o synthesiz e insulin , an d th e insuli n must be able to escape to perform it s function in the body. Cell membranes are highly comple x structures. Different type s of cells have different type s of membranes; a nerve cell has a different membran e fro m a liver cell, because the cells perform differen t function s and part of their functioning depends on th e structur e o f their membranes . Al l cel l membrane s ar e made u p o f several types of molecule, but nearl y al l membranes have something in common: they are based on a family o f long, flexible molecules with heads containin g a phosphoru s atom and usually carrying an electric charge. It is the phospholipid molecule s that give th e membran e it s mechanica l stabilit y an d it s flexibility . Thes e molecule s cling to each other, strongly enough to maintain th e integrity o f the membrane hut not strongl y enough to prevent distortio n o f the membrane , such as you will see if you examin e the shap e o f an amoeba under th e microscope. Many molecules tha t cannot penetrat e th e phospholipi d membran e gel : in an d ou t o f the cel l throug h specialized channel s o r ar e ferrie d acros s by tailor-mad e "boats. " Bot h channel s and boats are inherent component s of the membrane, and the nature of their structure and functioning is an area of very active research. Nerve cell s hav e long extension s alon g which electrica l impulse s pass . Thes e impulses ar e generated by a complex mechanism that involves the passage of sodium an d potassiu m ion s fro m on e sid e o f the membran e t o the other . Specialize d channels fo r this "io n transport " hav e bee n identified . The y com e with "gates, " which ar e able to close under certai n circumstances . The membrane s o f al l cell s contai n protei n molecules , ofte n wit h attache d sugar-type molecules . On e o f th e commones t role s o f thes e component s o f th e membrane is to act as receptors for specific molecule s tha t arrive from othe r parts of the organism , or are parts of the externa l surface of invaders such as bacteria, Receptors have shape s tha t ar e complementary (loc k an d key ) to on e specific molecule or a small group of molecules of related structure . Thes e receptors are essential to the functioning of most cells, particularly because one of the ways in which a rnulticeHular organis m controls its overal l functionin g is to sen d message s from one part o f the organis m t o another. Som e of these message s are electrical, via th e nervous system, but very many are chemical. Substance s are produced i n one peirt of th e bod y an d trave l t o othe r locations , wher e the y trigge r specifi c responses. How does the messenge r know which cells to go to? Why don't al l the cell s on its journey allow i t to enter ? The answer i s the presenc e of specific receptors on th e

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target cells . Onl y on e lock suits th e key . This them e wil l recu r frequentl y i n this chapter. The Nucleus: The High Command The nucleu s i s a distinct entity , ofte n roughl y spherical o r ellipsoidal, havin g it s own membrane and containin g the cell' s DNA. In some primitive cell s there is no nucleus and the genetic material floats fre e i n the cell. Cells with nuclei are termed eukaryotic cells , i n distinctio n t o prokaryotic cells . Eukaryote s encompas s th e whole of the living world except bacteria, blue-green algae, and a few other simple organisms. The first sign s that we have of eukaryotic cells are from abou t 1.2 to 1.4 billion years ago, compared with th e estimate d emergenc e of life abou t 3. 5 billion years ago. The Mitochondria: The Oil Well The cell synthesize s comple x molecules lik e proteins fro m relativel y smal l molecules like amino acids. In Chapter 24 we saw how DN A and RN A provide the surfaces o n which protein s ar e assembled. Howeve r a production lin e i s not enough; there has to be an input o f energy.4 In all known cells the immediately mobilizabl e source of energy used by the cell is adenosine triphosphate (ATP) . This molecule is made i n specialize d organelles , smal l structure s withi n th e cel l know n a s mitochondria. It is the breakdow n of the AT P molecule (by the los s of a phosphate group) that provides the energ y for a wide variety of the cell' s activities . Th e number o f mitochondria in a cell is thus related to its energy requirements. Muscle cells need large amounts of energy when the y contract, and the y get this from th e cellula r stoc k of ATP. Onc e this i s broken down , i t has t o be replaced, and thi s ca n be don e more speedily the greater number of mitochondria tha t ar e present. In the muscles tha t drive the wings of insects or hummingbirds, there can be up to 1 million mitochondria in each cell. The mechanisms by which AT P is synthesized and the way in which it s energy is utilized by the cell are well understood but are too specialized to go into here. An average cell, on an average day, synthesizes about \ millio n molecule s of ATP per second, to replace those that break down to supply energy. Problems

Development All of us star t our lives as single cells . Most adult organism s contain millions, bil lions, or trillions of cells, but a multicelled organism is not just a large collection of single cells, living independent lives . A healthy livin g organism is akin to a wellcoordinated army, not to a disorganized rabble. This fac t present s u s with a series of relate d problem s that ar e a t th e cuttin g edge of biological research. Tw o are of central importance: How does a single cell know how to develop into a coordinated mass of cells having different structure s and functions? An d how is a multicellula r organism coordinated? 4 For the chemist, strictly speaking, I should be talking about free energy here, but this would unnecessarily complicate the general lines of the argument.

Life: The Molecular Battle |

The fertilized human egg , during its first few divisions, appear s to be a cluster of identical cells , but soo n th e roughl y spherica l shap e distort s an d differentiatio n sets in. Primitive structures can be seen that develop into the organs of the baby-tobe. These structures contai n cells that are typical of that structure. Ho w do a small cluster o f identical cell s "know " ho w t o develo p alon g differen t structura l an d functional paths ? The developing human cel l contains, in its DNA, the potential to become any of the over 200 types of cell in the formed adult . Every cell starts with identical DNA, yet at some stage different gene s are turned o n o r off in differen t cells . One o f our great area s o f ignorance is th e natur e o f this differentiation—ho w i t i s triggered; how a set of cells become s a distinct , functionin g organ ; how a set of organs becomes a coordinated, functioning organism. We know that in certain cases, at an early stage of development, if we remove a part o f the embry o that i s clearl y destine d t o become a certain orga n and graf t i t onto another location on the embryo, it will "choose" to develop like the cells iri its new surroundings. I s the effect o f the new environment due to the passage of chemicals passe d int o th e intrude r cell s fro m thei r ne w environment ? Presumably th e role of such messengers would be to turn off certain genes and turn on others in the transplanted cells . Ar e receptors on the cel l surface s involved ? And why doesn' t the intruding tissu e chang e the directio n o f the cell s in its new environment ? I s it outvoted? We have no coherent understanding o f the proces s of development, but i t looks as though a modest breakthrough has been made in identifying the nature of the genetic control of development. A group of genes, the so-called Hox genes, have been found, which ca n apparently "switc h on " cells to their destiny. All the cells in the embryo have th e sam e set of Hox genes, but, by an a s yet unknown process , only certain Hox genes are active in a given location. Thus the cells at one end of the embryo will develop into the head of the organism because the relevant Hox genes are the onl y ones working. In the cell s farther back, another group of Hox genes turns on and directs the development of the cells into the organs appropriate to that location. A t the time of writing, the mechanism by which differen t group s of genes are turned o n i s no t known , althoug h ther e ha s bee n som e speculatio n tha t varyin g concentrations o f certain molecule s in differen t part s o f the embry o ar e responsible. Thus in the fruit fl y (Drosophila) egg, it has been shown that a chemical, acting at one end of the dividin g egg , induces the cell s at that end to switch on the genes that lead to development o f the head. The story is complicated, but i t is slowly unfolding. Control

The variet y o f chemical reaction s occurrin g i n cell s i s enormous . Al l these reactions have to be coordinated in the cell and between cells, otherwise the organism would self-destruct. Control over the organism's internal environment is part of the struggle to maintain life. We hav e mor e o r les s consciou s contro l ove r some o f our bodil y movements , through the passage of electrical impulses fro m th e brain t o our muscles, although some muscles , suc h a s those o f the heart , ar e outsid e ou r consciou s control . We have no conscious contro l ove r the reactions in our cells. The extraordinary thing is that within eac h cell, and within the complete organism , the multitude of reac-

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tions and messages is evidently under overall control. Thus under normal circumstances the amoun t of each o f the thousand s o f molecules in th e cel l remains ap proximately constant . I f an exces s of, say, an amin o acid i s added t o the cell , th e speed of certain reactions increases and others slow down, the net result being that in a short time the cell restores itself automatically to its normal state, the concentration of the amino acid returning to its normal level. Without this and other intraand intercellula r contro l mechanisms, th e vas t collectio n o f cells tha t constitut e the animal body would be wildly unstable. The problem of control is intimately connected with the mechanisms o f communication withi n th e body , which i n tur n depen d heavil y o n the shape o f certain molecules. Enzymes provide a good example. Turning Enzymes On and Of f Enzymes are the chemica l catalyst s of the livin g cell. Withou t them th e reactions within th e cel l could tak e place but woul d b e very much slower , sometimes by a factor o f a million o r more. Life could not continue under these circumstances. But it i s no t enoug h tha t hundred s o f these catalyst s ar e foun d withi n th e cell ; the y must be controlled. Thus there are enzymes that are responsible for the contraction of muscle cell; how do they know when to act and when not? Why don't they act all the time if they are sitting there? The answers to these and thousands o f other control problems lie in the beautiful rang e of ways in which enzyme s respond to other molecules. Enzymes are all very large protein molecules, but only small areas on their surfaces are responsible for catalyzing the reaction between other molecules. Thus there are enzymes, the lipases, that speed up the rate at which wate r molecules attack and break open the fats that we eat. On the surfac e o f these enzymes there are specialized regions that are so shaped as to accept lipid molecules. These active sites are the wrong shape to fit almost any other type of molecule with which they come in contact. When a lipid molecul e sit s o n such a site, it is subtly affecte d b y its surrounding s so that one of its chemical bonds is weakened. This is the origin of the enhanced rate of reaction with water, a reaction that could go at a barely perceptible rate if the enzyme were not present. A molecule whose reactions are speeded up by sitting on the active site of an enzyme is termed the enzyme's substrate. An enzyme may have only one naturally occurring molecule as a substrate or it may act on a number o f structurally related molecules. We can ofte n find , o r design, a small molecule that wil l fi t the activ e site of an enzyme. Suc h a molecule interferes with th e actio n o f the enzyme ; it block s th e parking space, or, if you like, it puts a strange key in the lock. Such inhibitors might come from inside the cel l o r from another place in the body, or they might be ingested by the body. The strength with which inhibitors bind to an active site varies. A catastrophi c extrem e is when a n inhibito r sit s o n an activ e sit e an d refuse s t o leave. Th e molecule s o f certain nerv e gases bind fiercel y t o th e activ e site o f enzymes connected with the transmission of nervous impulses, thus causing paralysis and death . Inhibition provide s on e o f the body' s standar d method s o f controlling the con centrations of molecules in the cell . Often this control involves a feedback mecha nism. A simple exampl e occurs in th e cas e of the synthesi s o f certain molecules . Suppose that a certain amino acid is synthesized by a chain of reactions, each cat-

Life: The Molecular Battle |

alyzed by an enzyme. The cell is supposed to have an ample stock of starting material and the synthesis proceeds , but a t a certain stag e it is advisable to tell the system to stop—to turn off the production line. The way that this is done could be that one of the enzymes in the production line has an active site that is a good fit to the final product, the amino acid. As the concentration of the amino acid rises, some of it binds to this enzyme, blocking its active site. When all the enzyme molecules are blocked by the rising tide of amino acid, the enzyme ceases to operate. Production stops. If the amin o acid concentratio n subsequently drops , for any reason whatsoever, some of the amin o aci d molecule s that are acting as inhibitors leav e the en zyme, which can then start operating again, setting the production line rolling once more. Thus i s the level of the amino acid concentration maintained b y a feedback mechanism. The process depends on the fact that the amino acid is weakly bound to the enzyme. If it were too strongly bound, it would sit more or less permanently on the active site of the enzyme and permanently destroy the production line.5 Enzymes can be switched off , but they can also be switched on. There are many ways of doing this, most of which depend on the fact that an enzyme is a large, flexible molecule that can change its shape. Here is an example. The 1966 World Cup The contraction of muscle cell s is a complex process that depend s heavily on enzymes that act on certain components of the cell. We would have permanently contracted muscle s i f these enzyme s acte d al l th e time , an d s o they normall y hav e shapes (conformations ) tha t are inactive . Whe n I was watchin g the 196 6 socce r World Cup , my brain sen t electrica l impulse s t o th e oute r surfac e o f my muscle cells. Eac h impulse resulte d i n th e openin g of a channel i n th e membran e o f my muscle cells, a channel that allows calcium ions to pass. Now normally the concentration o f calcium insid e th e cel l is about 10,00 0 times les s than i t is outside the cell. When the channel opened in the membrane of my muscle cells, the excess calcium started to flow in. Inside the cell, it sat on two molecules called troponin and calmodulin. These are effectors, molecule s capable of switching on one specific enzyme or a small group of enzymes, but the y themselves ar e impotent withou t th e calcium ion sitting on them. When the calcium ion sat on, say, troponin in my muscle cells, it changed the molecule's conformation so that it fitted onto a site situate d ori one o f the enzyme s that is responsible fo r the contractio n o f my muscl e cells . The effecto r change d the conformation of the enzym e so that it became active. My muscle cell s contracted , and I clenched m y fists . I als o shouted , "Goal!! " whe n Geoff Hurs t scored his first goal. When the electrical impulse stopped, the channe l in the cel l membrane closed and the exces s calcium i n the cel l was pumped out . The effector s los t their calcium, and wit h i t their shape, fin d fel l of f the enzymes . The activ e site s o f the enzyme s resume d thei r distorte d shapes , th e enzyme s no longer affected th e cell, and my fists relaxed—for a moment. There ar e man y variations o n thi s game o f enzymic control , an d th e cel l ha s some pretty fancy way s of controlling th e activit y o f its enzyme s and thereb y th e concentration of the products that it produces or the material that it absorbs. All is 5

Notice also that the feedback mechanism creates a nonlinear process; the rate of amino acid production is not proportional to the amount of starting material. Many of the processes within the cell are nonlinear, and this fact suggests that it may be profitable to examine them by the methods of chaos theory.

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entirely explicabl e i n term s o f well-known chemica l principles . Thi s i s tru e o f every bodily function discovere d in living organisms. The Communications Network The best-know n communication s syste m i n th e bod y i s th e nervou s system , a branching syste m o f fibers tha t spread s ou t fro m th e brai n an d th e spina l chord . The number o f nerve cells, neurons, i n the brai n is about 10 0 billion, an d eac h is linked to at least one other neuron an d sometime s to as many as several hundred. Electrical impulse s flo w alon g the membrane s tha t cove r the fibrou s extensions , the axons, that radiate fro m the central body of the neuron. At first sight the system looks as if it depends entirely o n the passag e of electrical currents. However , most axons are not very long, and what might appear to be a continuous nerve fiber consists o f chains o f neurons wit h th e tip s o f their axon s touchin g th e surfac e o f the next neuron in the chain—a bit like a daisy chain. Currents are incapable of passing between adjoinin g axons. 6 Th e tin y ga p between th e nearl y touchin g neuron s i s termed the synapse, an d i t is a very poor conductor of electricity. The mechanis m by which the current is maintained fro m axon to axon is chemical. The arrival of an electrical impulse at the tip of an axon stimulates the release of a chemical messenger, a neurotransmitter, which i s a molecule that diffuse s acros s the synapti c gap. When it reaches the othe r sid e i t is adsorbed o n special receptors , situated o n the outer surface o f the secon d neuron's membrane, and s o shaped a s to fit the neurotransmitter molecule . (Fo r the thousandt h tim e we see the significanc e of molecular shape.) Once absorbed, the neurotransmitte r result s i n the formatio n o f a new electrical pulse, which passes along the axon of the second neuron, an d so on. The neurotransmitter doe s not surviv e very long afte r i t has been released . If it did , i t would carry on stimulating the second neuron, and even in the absence of a stimulus from th e firs t neuron, currents would never cease, which coul d mean that long after someon e ha d stuc k a pi n i n you r finger , yo u woul d kee p feelin g th e poin t going in. Thus, a common neurotransmitter, acetylcholine , i s destroyed, by a purpose-built enzyme, within two thousandths o f a second after secretion . There are a wide variet y o f neurotransmitters, the best-known being dopamine , which acts i n the synapse s o f one part of the brain, and acetylcholine , which act s in some of the synapses o f the autonomic nervous system, tha t par t o f the nervou s syste m tha t controls our internal workings and over which we have no conscious control. The venom o f some snake s contains substances tha t fi t into those receptor s o n muscle cells which adjoi n the tips of nerve axons. A bite from suc h a snake can result in paralysis, which ca n be reversed by a similar substance to that in the venom, one whic h i s shape d s o that i t ca n compet e fo r the sam e recepto r bu t i s no t s o strongly bound that it cannot fall of f afterward. Molecular Messengers The nervous syste m is only one of the tw o main type s o f internal communicatio n system use d b y th e body . We also use a very wid e rang e o f chemicals tha t carr y messages to specifi c organ s or cells. Neurotransmitters d o this over the extremel y small distances between adjacen t axo n tips. 6 The truth is that these are not conventional currents, that is, movements of charge along the nerve. This is not important for our present tale.

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The huma n bod y contain s a numbe r o f endocrine glands, an d othe r organs , which can secret e hormones. Hormone s are a major mean s o f communication between th e organ s o f the body . Among the better-know n endocrin e gland s ar e th e pancreas, the ovary, the testes, the digestiv e system, the thyroid gland, and the pituitary gland. The pancreas, for example, produces insulin and glucagon, which, as already mentioned, control glucose levels in the blood. Hormones are released in response to specific or general stimuli. Thus the secretion of the hormone prolactin, which stimulate s milk production, is the result o f a specific messag e to the anterio r pituitar y gland . On the othe r hand , epinephrin e (better know n a s adrenaline) , which i s produce d b y th e adrena l medulla , raise s both the heartbeat and the concentration o f glucose in the blood, and can be secreted i n response to a variety of stimuli, includin g fear , th e new boy on the block , or listening t o the muscle-tensing , driving syncopatio n i n Beethoven' s Seventh . Al l hormones ac t initially b y being recognized and adsorbe d by specialize d recepto r sites. Th e biologists tal k o f target cells. Thus, a cell that ha s n o receptors for thyrotropic hormone will be completely blind t o this molecule, which i s produced in the pituitary and acts on the cells of the thyroid gland. Sometimes th e recepto r is within th e cell , not o n its surface . Th e steroid-typ e hormones, those related to cholesterol, can usually move straight through the outer membrane of the cell and find their receptor site either in or near the nucleus of the cell, influencing the working of the cell' s DNA. Other hormones, for example, proteinlike molecules, cannot penetrate the membrane of the cell , and their receptors are o n the surface . I f such hormone s are to affec t th e interna l workin g of the cell , they must presumabl y do more than si t on the doorstep . One way in which externally adsorbed substance s can act is exemplified by the neurotransmitters, which, when the y ar e adsorbe d b y thei r receptors , induc e neighborin g io n channel s t o open so that ions can flow across the cell membrane. It is this flow of ions that produces electric currents i n nerve cell membranes. Another mechanism for externally adsorbed molecules to influence the cell involves the presenc e of a protein molecule, sometime s calle d a G-protein , whic h sit s i n th e membrane , nex t t o th e receptor. Adsorption of the hormone by the receptor changes the latter's conforma tion, which i n turn affect s th e G-protein. This protein i s situated so that part of its surface i s in contac t with the contents o f the cell, and changes i n its conformatio n can trigge r enzymes tha t ar e situate d nex t t o it , i n th e interio r o f the membrane . Thus is a series o f reactions initiated, whic h on e hopes will be of benefit to the organism. We are only just beginning to understand the remarkable control mechanisms of the cel l an d o f the whol e organism . Th e focu s repeatedl y return s t o th e rol e of shape. Defense Matters It is not enough for the organism to control its internal environment when times are good. It has to be able to defend itself when times are tough. Living organisms have a whole range of weapons with which t o fight invaders. I concentrate on human defense . There are some simple protective systems, capable of repelling microorganisms before they reach our internal systems , although there are bacteria livin g i n ou r digestiv e systems, with which w e ar e happy t o coexist. The skin provides a mechanical barrier to microorganisms, which ar e also discour-

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aged by a variety o f secretions, bu t thes e ar e certainly no t enough . Evolution ha s provided us with an immune system, a collective term for a highly complex, amazingly versatile collectio n o f cells and protein s tha t do battle wit h those invaders , dead or alive, that penetrate our outer defenses. AH the mechanisms of the immune system depend on shape recognition. Phagocytes

The basis o f the immun e syste m is a set of cells, all of which ar e manufactured i n the bone marrow. Some of these cells, the phagocytes, literall y ea t invading bacteria, engulfin g them . Phagocytes , whic h accoun t fo r ove r hal f th e blood' s whit e cells, circulate throughou t the body's tissues. Ove r 100 billion ar e produced daily by th e bon e marrow , so that i n case s wher e th e bon e marro w i s dysfunctiona l a vital part of the body's defenses is absent or weakened. How d o phagocytes know whic h cell s to attack ? Why don't the y ea t red blood cells? By now you know that shape is the answer. Bacterial cell walls contain a variety of "markers," molecules that fit into receptors on the cell surface of the phagocyte and trigger its activities. The fact that animal phagocytes carry such receptors is clearly the result o f a long evolutionary process. The phagocytes are backed up by a group of protein molecules in the blood, collectively known a s complement. The y have several modes of action, one of which is to attach themselves to alien microorganisms, thus providing markers for phagocytes to recognize. Complement molecules ca n also attach themselve s t o large invaders, such as parasitic worms. These organisms are much too large to be engulfed by phagocytes, but onc e the complement has labeled them with a marker, they are recognized b y a grou p o f specialize d cells , th e mas t cells, basophils, an d eosinophils. The last named can now bind to the invader and destroy it by a variety of mechanisms , includin g th e us e o f an enzym e t o che w u p th e invader' s bod y wall. Mast cells and basophils d o not challenge invaders head-on. One of the ways in which they act is by releasing molecules that help the body's tissues to fight invasion. A well-known example of such a molecule is histamine, which widens th e capillaries i n th e neighborhoo d o f the invasio n bridgehead , resulting i n wha t i s known as inflammation, a phenomenon tha t provides a better blood supply to the invasion point . Lymphocytes Apart fro m th e syste m o f blood vessels , vertebrate s hav e a lymphatic system, a branched networ k o f tubes tha t carrie s a practically colorles s liquid , th e lymph . This liquid, which is found in the tissues o f the body, has its origin in the serum of the blood that filter s throug h the walls of the capillaries , an d ou t of the blood vessels. The lymphatic syste m provides a means of channeling th e liquid bac k to th e bloodstream. Part of the system is a series of lymph nodes, clumps of tissue through which the lymph flow s an d which, whe n swollen , you can often detec t under th e skin. The lymph nodes are one of the main location s for lymphocytes, a collective noun fo r a group of three kind s o f cells, the B cells, the T cells, an d a third group that contains so-calle d natural kille r (NK ) cells . The important thin g abou t B cells is that they produce antibodies. The antibody defense mechanism shows the principle of shape recognition at its most powerful. The B cell produces receptor molecules tha t sit on its surface. Now

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these receptors, known as immunoglobulins, are essentially chains o f amino acids (polypeptides), and their synthesis is controlled by the genes of the cell. Evolution has ensured that B cells have a variety of genetic makeups, which means that there is a tremendous range of receptors on the surfac e of the body's B cells. Receptors for what? For almost anything! In contrast, phagocytes are limited; they have a number of receptors tha t fit markers o n most bacteria, bu t they canno t cop e with invader s which d o not have markers that suit the phagocytes' range of receptors. The B cells have so many types of receptor that on e o f them is almost certai n to fit onto some region of the invader, be it molecule or virus. An invader that binds to a receptor is known as an antigen—think of this as short for ant/body generator. Once an antigen is recognized by a B cell, a flurry o f activity results (Figur e 26.2). The cell divide s into plasma cells, which are just production line s for more of the successful receptors, the immunoglobulins , o n the origina l B cell. Th e plasma cells produc e very large numbers of the receptors, which ar e released into the lymph and at this stage are renamed. They are the famous antibodies, which by hanging on to the invaders either rende r the m inactiv e o r provid e markers fo r the receptor s of complement (see above) which allows phagocytes to recognize the join t complement-microorganism complex. The tremendous versatility o f the B cells is both an advantag e and a disadvantage. In the Pari s flea marke t there used t o be a stall that had boxe s full o f keys. If you had lost the key to a lock, you could bring the lock with you and spend an hour or two rummagin g through the boxe s hopin g t o find a replacement. The chance s were that you would fin d somethin g because there was such an enormous choice. This is what happens with a n invading antigen—molecule or virus—but the problem is that there is usually only a very small number of B cells that carry a suitable antibody. Th e other keys are useless. It is true that as soon as the antige n binds t o the correct : B cells they start turning out antibodies, but they cannot always do this fast enoug h to cope with a massive invasion. The versatility of the B cells com.es at the expense of their overall effectiveness . One way that man has found to help the B cells is by vaccination. This depends on the fact that even when a harmful microorganism has been "killed" by, say, heat treatment, its surface may still carry unaffected antigens . These can induce the formation of large amounts of antibody when they meet the right B cell. The antibodies remain in the body and, until their numbers decreas e drastically by the normal wear and tear of life, they are ready to immediately attack the active form of the microorganism if it appears. There are people who regard this procedure as an offens e to God.

Figure 26.2. B cells react with a suitable antigen to produc e plasma cells, which act as factories for th e production o f antibodies.

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HIV

There are other types of lymphocytes, some of them involved in the division o f the B cell into plasma cell s once it recognizes a specific invader (Figure 26.3). Tc cells attack and destro y body cells that have been invade d b y viruses, thus preventin g the viru s fro m reproducin g itself. Bot h B cells an d T c cells, which are in the fore front o f the body' s defenses, are stimulated b y othe r cells, th e T h ( T helper) cells , and inhibited by Ts cells. The HIV virus has found the Achilles' heel of the immune system. It attacks the Th cells and gradually stops them fro m helping the B and Tc cells, preventing the forme r fro m producin g antibodies and the latte r from attacking virus-infected cells. I have only touched on some of the aspect s of the body's defense s against invasion. The immune syste m is responsible for the rejection of molecules or cells tha t differ fro m those it meets in the healthy body. The downside of this ability is manifested b y th e phenomeno n o f rejection, whic h i s a major proble m i n orga n transplants an d ca n b e countere d t o som e exten t b y usin g drugs , th e bes t know n of which is cyclosporin, to suppress the immune system. The markers which eac h of us has o n our own body cells are, of course, genetically determined. Si x genes control the synthesi s o f markers, and they lie close to each other on chromosome 6. These genes exist in over a hundred mutations , an d different peopl e have differen t combination s o f these variants. Th e chanc e o f two strangers having the sam e set of mutants, and therefor e the sam e set of markers on their cells, is tiny. Thus the immune system of one person will "see" foreign, unfa miliar markers on the cells of a transplanted orga n and will produce antibodies to these cells , resultin g i n thei r destructio n o r interferin g wit h thei r functioning . That's rejection. However, because the genes are close to each other on the chromosome, they are generally inherited a s a complete group, rarely being broken up by crossing-over (see Chapter 21) in passing from parents to offspring. Thi s means that the inheritanc e o f these genes is fairl y straightforwar d and a child ha s a roughly one-in-four chance of having the same six genes as its brother or sister. This is why

Figure 26.3. (a ) Tc cells attack normal cells that have been invaded by viruses, (b) Both B cells and Tc cells are stimulated by the Th cells, but the HI V virus attacks Th cells.

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transplants betwee n matchin g sibling s ar e ofte n mor e successfu l tha n betwee n strangers, or between siblings who have a different se t of genes. Life Is Inseparable from Defense The elucidatio n o f the natur e o f the defens e mechanism s o f the livin g cel l and of the whol e organis m i s on e of the key s to combatin g some of the crueles t disease s plaguing man—and beast. I have limited the discussio n here to a cursory glance at some centra l subjects. In discussing lif e I have avoided whole areas , preferring t o illustrate som e o f the genera l characteristics o f the cel l an d o f living material. I n particular I wished t o convey the central importance of molecular shape in the normal functioning and the defens e of the body. Life or Death Why do cells die? Why shouldn't a cell live forever ? One of the most surprising findings, which cam e early in the history of embryology, wa s that the development of the embryo is accompanied by the apparently natural death of many of its cells. One can see why this could happe n in, for example, the developmen t o f the foot , where one mechanism fo r the formatio n of toes from a simple block of dividing cell s would be for cells situated between the future toes to die, leaving "bays." Subsequently , i t was found tha t in many developing eggs, cell division wa s invariabl y accompanie d by a selectiv e patter n o f cell death . Reproducible phenomen a hav e a reason, an d i n cell s i t i s natural t o ask if cell death is gene-controlled. The idea arose that there might be a "death gene" in normal cells. Such a gene has been found in a wormlike creature, about 1 millimeter long , called Caenorhabditus elegans. This organism has a gene known a s ced 3, which appears to dictat e the suicid e o f the cell . In mutant organism s i n whic h ced 3 is inactive , cells seem to be immortal. There are many questions to be asked, the first o f which is: why do we need a death gene? The answer that springs to mind i s that in the absence of such a gene, there would be nothing to stop cells from dividin g and prolif erating indefinitely, as they try to do in cancerous tumors. But if there is a gene that programs cell suicide, how do we stay alive? A gene dubbed ced-9 has been found i n C. elegans, and i f ced-3 is a death gene, then ced-9 can be termed a life gene. When we examine mutant cell s in which ced9 is inactive, we find that they quickly die. At about the same time as this work was going on, it was found that there is a gene in humans, name d bcl-2, that appears to do the same job as ced-9. This research raises a multitude o f important questions. Is there a genetic clock that determine s ou r lifetimes? What is the role of these genes in cancer ? In aging? There i s a long way t o go , but w e hav e th e firs t sign s o f a genetically controlle d mechanism tha t decide s whether cell s shoul d liv e or die. That this mechanis m i s far from simple is suggested by the findin g that the longevit y of cells is apparently dependent o n whether o r not a specific cell i s adjoine d by neighbors. I n health y pieces of cell tissue, the cells can be induced t o commit suicid e by simply separating the m fro m on e another . What kin d o f communication i s ther e betwee n cell s that counteracts th e deat h gene? We know that these two genes are not th e end of the life-death story. There is a gene, p53, which seem s to be able to detect damage to the cell, specif-

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ically to its DNA. There are repair mechanisms within the cel l that are often capable o f repairing minor damage to DNA. It seems as if p53 prevent s cell s with damaged DN A from dividin g and producin g more defective cells. It lifts thi s sanctio n once th e cel l i s repaired . However , in ove r three-quarters o f the case s of huma n cancer in which it has been investigated, the p53 gene has been found to be mutated and therefore not operational . Defective cell s can multiply. The implications of findings of this sort for the treatment of disease are revolutionary. Cancer cells have seemingly lost the knac k of dying, and mos t conventional methods o f therapy ar e based on destroying tumor cells. Maybe we should be attacking these cells at a subtler level, inducing them to commit suicide or preventing them from proliferating. The mystery of life is also the mystery of death. (No , Goethe didn't say that.) Understanding the workings of the simplest livin g one-celled organism , let alone the coordinated activities of the billions o r trillions of cells in vertebrates, is still one of the great scientific challenges. Livin g matter, and living organisms, make the most complex human-built system s look clumsy and primitive . Bu t the compute r boys are coming. The Day of the Golem Today, Capek's robots,7 the Golem, 8 and Frankenstein's monster are conceivably attainable artifacts, at least in the dream s of scientists working in the area of artificial life. A t the simples t leve l robots move around th e laborator y floor, avoidin g some objects, approachin g others, hopefull y manipulating object s that the y "like " an d possibly assemblin g them . Thes e task s requir e sensin g capabilitie s bu t als o a "brain" designe d to manipulate the incoming signals and generate an "intelligent" response to them. For nonliving systems only the computer can fulfil suc h a task at or above any but the most trivial level. Since computers are getting more powerful, and programmin g more subtle, the performanc e level o f robots is rising; although they are hardly threatening at this stage, the future seem s almost open-ended. A somewhat differen t activit y in th e artificia l life fiel d i s typified by computer programs that give ever-changing and apparently random patterns on the computer screen. The hope is that occasionall y the pattern will clearly become nonrandom, performing wha t appea r t o be simpl e tricks , like constructin g a serie s o f regular steps crossin g th e scree n o r endlessl y reproducin g som e featur e o f the pattern . With time, and increasing computer power, the programs have become more complex and pattern s hav e appeared that are complex enough to suggest (with a bit of goodwill) that they could only be the product of a living brain. The researchers fee l justified i n callin g their subjec t artificial life. A closely related subjec t is artificial intelligence, which has tended to concentrate on the construction of computer programs that are dedicated to the solution of a narrow range of problems. One has t o b e very carefu l wit h language here. Ther e i s no mor e in a program than has been put int o it, and no more can be got out of it. The fact that unexpected order emerges from a program is merely an indication tha t the human brai n i s not always capabl e of predicting all the consequence s of a long serie s of operations . 7

The play R.U.R. (1920) described robots constructed from man-made protoplasm. The Golem, who was the subject of Jewish folklore, was a computer-like perfect servant. He was given written instructions, usually put into his mouth. His main fault was that he took his orders completely literally. 8

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The achievements o f these programs are indeed sometime s surprising , but hardl y staggering. And they are all products of the human brain. There is no doubt that the programs will produce mor e and more surprising behavior , an d if this book were being writte n i n 50 0 years' time , it s content s migh t b e chose n b y OMNIWRITE , who (who? ) would also edit it, while a titanium alloy AUTHORSOOTHESS would bring me a whisky and stroke my noble brow. It would be foolish to attempt to predict how far these experiments will take us. Some practitioners see the present a s the er a in which artificia l life originate d in a warm pool, but this time a pool of program writers. They foresee two species on the Earth, Homo sapiens an d Homo even more sapiens. There will be soft living matter and hard living matter. Whether we will get that far no one knows, but it would be rash to suppose that in 5000 years' time there will not be entities with a large range of capabilities, including possibly the ability to reproduce by building new entitie s and t o improve their ow n programs using the techniques a t present being investigated b y th e artificia l intelligenc e experts . I s this wha t w e reall y want t o do ? I admit that a large part of my objection to such a course is based on irrational dislik e of the idea of humanoids, and on a rational fear that such humanoids would reach a stage at which the y were a threat to the existenc e of soft life . I t would, to my taste, be a nightmare worl d i n whic h ther e wa s n o on e lef t t o fee l a pai n i n he r ches t when she read George Seferis's lines: Man frays easil y in wars; man i s soft, a sheaf of grass, lips and fingers that hunger for a white breast eyes that half-close in the radiance of day . . . From The Last Stop (translated by Edmund Keeley and Philip Sherrard) But perhaps, God help us, there will be soft humanoids . A Designing Hand?

The shee r complexit y o f life, th e astonishin g wa y i n whic h livin g organism s ar e adapted to their environment, the emergenc e of life itself , the fac t tha t i t is almost incredible that the universe should have developed so as to allow the formation of living matter—all this has led many thinkers t o suppose that the emergence of life and o f man an d woma n canno t hav e been accidental. Thi s is an old argument , famously presented in 1802 by the theologian William Paley (1743-1805) i n his tale of a man finding a watch. Such an intricate construction, reasoned Paley, could not conceivably have come about by chance; the watch must have been the result of a designing hand. This i s true but irrelevant . Watches are indeed designe d by an intelligent being, but man is not; he evolved, and the obvious counter to Paley is that machines canno t reproduc e an d evolve . Living form s can , and thi s i s what the y did. Evolution disposes of teleology. Paley is always quoted in this context, but his thesis was far more vigorously pressed by the eighth earl of Bridgewater, who in his will lef t £800 0 to finance a project i n which eigh t authors woul d write text s illus-

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trating "the Power, Wisdom, and Goodness of God" as manifested in the desig n apparent i n th e animat e an d inanimat e world. Eigh t volumes wer e duly published , the last in 1836 . There is perhaps mor e to the desig n hypothesis tha n Paley' s naiv e analogy , because it has been revive d i n a rather differen t for m by a number o f modern physi cists, in general thos e with an interest in cosmology, which is not surprising since an important par t o f the new evidenc e that the y marshal i n support o f their thesi s comes from a consideration o f the developmen t o f the universe , i n particula r th e synthesis o f the chemica l elements . W e will glanc e at thei r idea s i n Chapte r 35, where we look at the creation of the universe . A somewhat different are a of controversy is the relevance of biology to morality, a question with very long roots indeed, one of which i s Aristotle's belief that every organ in a living organism is created by divine interventio n an d is specifically designed t o fulfi l a definit e function, acting i n cooperatio n with ever y other organ . This i s a teleological doctrine—th e assumptio n tha t activitie s an d structure s ar e adapted to a predetermined end . Clearly, teleology has much i n common with the design hypothesis. Both Aristotle and William Paley would sa y that the gods knew that they wanted you to see, so they designed eyes. Teleology can, and has been, extended to suppose that man is designed not only so as to function biologically in a certain way but als o to function ethicall y in a manner related to his biological nature. Thi s i s differen t fro m th e attempt s t o appl y evolutio n t o ethic s tha t w e ra n across in Chapte r 25 . Here it i s the desig n and existenc e o f the singl e individua l that ar e suppose d t o hav e ethica l implications , quit e independentl y o f the exis tence of evolution. It is surprising how persistent this belief is. It is possible that som e readers will sens e a connection between biolog y an d ethics. It's a good topic for a warm summer evening , on a flower-covered balcony.

27 The Origin of Life? Take Your Choice To believe that physical and chemical forces could by themselves bring about an organism is not merel y mistaken but, as already remarked, stupid. —Schopenhauer, Parerga und Paralipomena

I do not kno w the origi n of life. Thos e o f us wh o hold , lik e I do, that lif e emerge d spontaneously fro m inanimat e matte r are , we mus t admit , a t a distinctl y embar rassing disadvantage: we have not yet come up with a convincing mechanis m for abiogenesis. In his presidential address to the 1871 meeting of the British Association for the Advancemen t of Science, Lord Kelvin stated, "Dea d matter cannot become living withou t comin g unde r th e influenc e o f matter previousl y alive . Thi s seems to be a s sure a teaching o f science as the la w o f gravitation." If he i s right, which I doubt, then life must have been present in the universe for all past time. Either tha t o r we mus t tur n t o the finge r o f God in th e Sistin e Chapel , and indeed , after reading this chapter you may well conclude that that is our only hope. During the nineteenth century , abiogenesis was given a boost by the successfu l synthesis of organic molecule s from inorgani c precursors, but the fact that we can synthesize amin o acid s an d nuclei c acid s fro m inorgani c startin g material s doe s not explain ho w lif e started . We are intelligent beings who can purposefully brin g together chosen chemicals unde r carefull y controlle d conditions. Thi s i s very different from accounting for the spontaneous formatio n of living systems in an inanimate world empt y o f all intelligence. An d w e hav e com e nowhere nea r creating life in the laboratory. There have always been those who have held tha t life is a property that canno t possibly arise out of inanimate matter, not because they can't conceive of the chemical pathway but because it offends thei r view of the universe. This is the "Life-is sornething-special" schoo l o f thought, fo r whom th e uniquenes s o f life i s threat ened by mean little scientist s in scruff y la b coats trying to prove that a proto-Bach originated in a mixture of gases that was struck by lightning: Science! . . . Why preyest thou thus upon the poet's heart. Vulture, whose wings are dull realities. Edgar Allen Poe, "To Science" Those who prey upon the poet's heart know that, in tackling the problem of the origin of life, there are two basic, and interdependent, question s that have to be answered: 1. Living system s ar e base d o n extremel y larg e and comple x carbon-containing ,

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molecules. A s Si r James Jeans remarked, "Lif e exist s i n th e univers e onl y because the carbon atom possesses certain exceptional properties." In contrast, the nonliving worl d fro m whic h lif e i s presume d t o hav e arise n i s compose d o f small, ver y simpl e molecules—excep t fo r silicates, whic h ca n for m enormou s chains of atoms but ar e not a basis for life. How did the large, complex, carboncontaining molecules of life originate in the first place? 2, Livin g system s ar e ver y highl y organized . Th e livin g cel l i s a ver y spatiall y structured entity , operatin g through a sophisticate d syste m o f catalysis, trans port, and feedbac k mechanisms. I t is a highly improbable structure , or , in othe r words, it has low entropy . How did the molecules of life get organized? One can believe that a complex system like the living cell is capable of manufacturing large , complex molecule s fro m small , simpl e precursors , bu t th e origina l manufacturing mechanis m ha s t o com e fro m somewhere . Factorie s makin g CD players d o not assembl e themselves . Believer s in abiogenesi s ar e forced t o accept that life is a self-organized invention. To construct an y convincin g theor y o f abiogenesis, we mus t tak e into accoun t the condition o f the Earth about 4 billion years ago. The Violent Childhood of the Earth The Eart h i s abou t 4. 5 billion year s old . Fossi l remain s o f microorganisms hav e been foun d dating back about 3.5 billion years . Water is essential fo r life, an d th e Earth wa s certainl y coo l enoug h fo r ocean s t o exis t a t tha t time , althoug h the y could have been warmer than they are now. We can get some hint of conditions o n the young Earth by looking at the Moon. The Moon has been aroun d fo r about th e same time as the Earth. Because of the lack of water, or a significant atmosphere, it s surface ha s not been shape d an d smoothed in the way that the Earth's has. Tha t is why the craters on the Moon's surface, created by meteorites, asteroids, and assorted interplanetar y debris , hav e remaine d largel y unchanged fro m th e tim e o f impact. The wealth o f craters on the Moo n gives us good reason to suppose tha t th e Earth, too, suffered fro m regular and massive cosmic bombardment. Afte r the emergence o f life, giganti c collision s coul d hav e wipe d i t out , ove r most o r al l o f the Earth. Thus it has been estimated that the arrival, probably in the Caribbean area, of an asteroid measuring about 6 to 7 miles acros s might have resulted in the destruc tion of the dinosaur s and th e eliminatio n o f over half the living creatures o n Earth about 65 million year s ago. It is possible that there was a shower of objects around this time. Very large falling objects could have generated enough heat on landing to boil the oceans, and i f an object fell o n land, huge clouds of dust could obscure the Sun fo r long enough to threate n th e continuanc e o f plant life . Ther e i s evidence , from fossil remains, that there have been at least four periods in the last half billion years i n whic h u p t o 80 % o f marin e specie s hav e bee n wipe d ou t b y climati c changes, by changes in se a level, and b y periods o f enormous volcanic activity. In fact, about 250 million years ago it looks as though cataclysmic volcanic eruption s in Siberi a eliminate d al l but abou t 5 % o f the livin g forms , plan t an d animal , o n Earth. The belief is that Siberia was effectively drowne d i n lava and that monstrous dust clouds hid th e Sun . Th e resulting changes in climate initiated a n ice age and global downpours o f acid rain.

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I have se t this violent scen e at the outse t t o underline th e force s range d against the survival o f life onc e it did emerge . How on Earth (sorry) did a fragile scattering of lif e maintai n it s hold , whateve r it s origin ? Or was i t wiped ou t severa l times? And di d i t arriv e her e severa l times ? Ove r 20,00 0 meteorites a yea r arriv e here , most of them not much larger than an egg. Do some carry living material? The "They-Came-from-Outer-Space" Hypothesis The supposition tha t lif e cam e from spac e answers the question Wher e did lif e o n Earth come from? but not the question Where did life come from? Comets and asteroid s usuall y contai n organi c matter, and som e scientists hav e said thi s i s ho w lif e reache d Earth . One problem i s tha t th e collisio n betwee n a large objec t an d the Earth would easil y generate enough heat (microscopi c kinetic energy) to incinerate an y organic material in the projectile to carbon, carbon dioxide, oxides of nitrogen, and othe r small inorganic molecules. A variation of the life-from-space theor y envisages the arrival of complete organisms fro m space , which i s 1950 s B-fil m territory . A prominen t advocat e o f this view was the English astronomer Fred Hoyle, who has suggested that many human ailments, includin g cance r an d AIDS , originate d i n "space-bacteria. " Th e boo k Lifecloud (1978) , by Hoyle and his collaborato r Chandra Wickramasinghe, was described by the biologist Lynn Margulis as "wanton, amusing , promiscuous fiction." It was also not entirely original ; the Swedish chemist Svant e Arrhenius had, about eighty year s previously , als o propose d tha t lif e ha d arrive d here i n spore s pro pelled through space by the pressur e o f light.1 Considering the abilit y of spores to survive in adverse conditions fo r many years, and to germinate in favorable conditions, on e canno t swee p asid e thes e ideas , but ther e i s no t eve n on e supportin g piece o f evidence. Conclusion: firs t theory—ver y shaky , and ver y unsatisfactory , since it does not explain the origi n of life. Next in line, but basically the same as the meteorite theory, is the ID P hypothesis, designe d t o provide a source of large organic molecules that would be a construction ki t for life. Thi s focuses o n interplanetary Dust Particles, which are supposed t o be , an d coul d wel l be , continuall y settlin g o n Earth . Sinc e the y ar e presumed to be small, with diameters considerably less than a millimeter, they will float gentl y through th e atmosphere , bringin g with them no t lif e bu t comple x organic matter. The heat create d by their impac t o n landing would b e negligible . If such particles are still snowing down on us, then those that have fallen on the icedover areas, such as the regions around the poles, must be trapped in the ice, which, if melted , shoul d revea l th e presenc e o f organic material. Th e experiment s hav e been done . Th e result s ar e no t encouraging ; trace s o f organic matte r hav e bee n found, but negligible amounts of amino acids, and a cynic might challenge their extraterritorial origin. Between 197 7 and 1981 , Hoyl e and Wickramasingh e came out with a series of strange articles o n the composition of interstellar dus t clouds. These papers could not be ignored because of Hoyle's prestige (as an astrophysicist, not a biologist), but they have tarnished hi s image forever. First, the authors kept changing their minds 1 Light does have a pressure. Maxwell proved this theoretically, and it has since been demonstrated experimentally.

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about the chemical s that they claim to have identifie d in interstellar dus t clouds ; second, their scienc e i s unacceptable. Wha t they di d was to examine th e infrared (IR) light comin g from these clouds. We have seen that the radiation emitte d o r absorbed b y differen t material s ca n b e use d fo r identificatio n purposes . However , convincing identification depend s absolutel y on the presenc e o f well-defined frequencies in the spectru m (se e Figure 15.6). This i s very far from th e cas e in the IR spectra of dust clouds. The gross uncertainty of the authors' methods is tellingly illustrated b y th e histor y o f their publications . The y starte d of f by "identifying " graphite an d silicate s i n th e cosmi c dust , bu t abou t fiv e year s later they change d their minds , no w "identifying " a n organi c polymer (se e Chapter 13 ) called poly oxymethylene, a molecul e tha t ha s n o biologica l significance . This wa s no t th e end; two years later they claimed that they had identified a mixture o f eighteen different organic polymers. Within about a year they had identified a different suspec t altogether. This tim e it was cellulos e that had bee n see n at the sit e of the crime . I won't go into too much detail , but their compariso n of the dus t spectrum an d tha t of cellulose was, how shal l I put it—imaginative . Incredibly, this was still no t th e end o f the shameles s pseudoscience . On e bright mornin g the author s wok e up t o the realization that the dust spectrum was really (wait for it, folks) that of a mixture of bacteria and algae that had gone through a process of freeze-drying in space! One almost regret s tha t th e serie s o f papers di d no t continue , finall y identifyin g th e spectrum as belonging to a mixture of Maxwell House and freeze-drie d ET. In any case, th e theor y suffer s fro m al l "they-came-from-outer-space " theories : eve n i f true, it doesn't explain ho w organi c material (carbon-containin g molecules) or life originated "out there." Let's get back to this planet . Terrestrial Abiogenesis

Creative Lightning In 192 4 the Russian scientist Aleksandr Oparin made the firs t clea r statement o f a modern theory of abiogenesis. Oparin claimed that Engels had influenced his theory, and he was one of the few Soviet biologists who sided publicly and vociferously with th e charlata n Lysenk o (see Chapte r 23). 2 Opari n propose d tha t whe n lif e emerged i t wa s o n a n Eart h wit h a very differen t atmospher e fro m today's . Th e "air" then was composed mainly o f hydrogen, methane (CHJ , ammonia, and water vapor. There wa s n o oxygen . Under the influenc e o f the Sun' s light , of lightning, and o f hea t fro m volcani c eruptions , thes e gase s reacte d t o giv e organi c com pounds. The source of carbon was obviously the methane . Over a period to be measured in hundreds of millions o f years, the concentratio n of thos e organi c molecule s tha t ende d u p i n th e ocean s increase d enormously . Those tha t fel l o n Eart h di d no t interes t Opari n sinc e th e emergenc e o f life , a s everyone agrees , needs a n aqueou s environment . Th e next stag e is a huge hand wave: "Life developed from this marine solutio n o f molecules." A very similar theor y was advanced in 192 8 by the English scientist J . B. S. Haldane, wh o wa s unawar e o f Oparin's work . Both Oparin an d Haldan e based thei r 2 He was also a fan of Olga Lepeshinskaia, who wa s awarded the Stali n Prize for 1950, for supposedly generating living cells from solutions containing egg white, among other things. She branded Pasteur as a reactionary and an idealist, presumably because he had denied the existence of spontaneous generation. She should have collaborated with Hoyle.

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hypotheses o n the propositio n that th e atmospher e tha t prevaile d whe n lif e firs t emerged was effectively fre e o f oxygen. Earth is the only planet in the solar system with a significan t percentage o f oxygen in it s atmosphere , hut i t i s suppose d b y some scientists that the source of that oxygen is almost entirely du e to the process of photosynthesis i n plants. In this process the green leaf uses sunlight to build sugars from water and carbo n dioxide. One o f the product s of photosynthesis i s oxygen. If photosynthesis is the sole origin of atmospheric oxygen, then there could indeed have been no oxygen in the atmosphere of the pre-life Earth, since there were no plants. The Oparin-Haldan e hypothesis remaine d o n paper unti l 1953 , whe n Stanle y Miller, working with the eminen t chemist Harold Urey at the Universit y of Chicago, performed an experimental test of the theory. The idea was simple: to attempt to produce organic molecules by taking a mixture o f small molecules and subjectin g them to conditions presumed to simulate those on Earth, 4 billion years ago. They guessed at the composition of the Earth's atmosphere, as it was before life emerged. Into a flask the y put water , hydrogen gas, ammonia, and methan e (CH 4). Water is not controversial . The othe r gase s have th e virtu e o f being simple , an d although methane i s technically a n organi c molecule, it i s certainl y some way, in term s of chemistry, from say amino acids. Ammonia is there to provide a source of nitrogen, essential for amino acids. Then they added lightning, or at least its equivalent, electric sparks, which the y passed throug h the mixtur e o f gases and water vapor. The flask was heated, stirred, and sparked for several days, during which time the contents turne d int o a reddish brow n mess . Th e experimen t wa s carrie d ou t man y times, with differing percentages of the reactant molecules and different intensitie s of electrical discharge. The results ca n be summed u p simply: the methane disap peared from the gas , and th e mai n produc t o f the reactio n was tar , which i s th e name that organi c chemists giv e to a thick dark , gluey organic residue that sometimes appears in reactions between organi c molecules. Analysis of the residue i n Miller and Urey's flask showed the presence of about a dozen smallish organic molecules plus trace s o f many othe r substances . O f the majo r products , two wer e of special interest , the amin o acids glycine and alanine. These are two of the twenty amino acids occurring in the proteins of living organisms.3 This looke d lik e a stupendou s breakthrough , especially a s othe r mixture s of simple gases produced additional biologically important molecules such as sugars. Furthermore, Sidne y Fo x showe d tha t i f a solutio n o f amino acid s i s repeatedl y heated, dried, and redissolved—a cycle that could happen in nature—small, roughly spherical clumps o f proteins begin to be formed. The Miller experiment i s the most quoted work in the field . N o one had previ ously com e anywhere near producing such biologically vital molecules a s amino acids fro m simpl e molecules , i n condition s tha t migh t conceivabl y hav e ap proached thos e o f 4 billion year s ago. 4 Som e scientists though t the searc h for the origin of life ha d almos t ended. Nucleotides, needed fo r the synthesi s o f RNA and 3 To simulate the effec t o f sunshine, some mixtures wer e bathed i n ultraviolet light. They also yielded organic molecules. 4 A competent organic chemist ca n synthesize amino acids from simpl e molecules, but she will be using suitable apparatus, an d many othe r molecules or inorganic compounds, som e of which act as catalysts. These were not the conditions prevailin g 4 billion years ago.

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DNA, would probably turn out to be obtainable under similar conditions, and then all that was necessary was to fill i n the steps leading from th e arnino acid mixtur e to the first primitive cell. No one thought this would be easy, but the Miller experiment appeared to have broken down the main gate of the castle. Perhaps, after all , life started in this way, in what Darwin called "a warm little pond." So what is the bad news? There is plenty. The simplest criticism of the Miller experiment is that it does not account for the production o f nucleotides, th e essentia l component s o f RNA and DNA . Life de pends on nucleotides; without DNA (or RNA) the cell as we know it could neither synthesize its components nor reproduce. Now all nucleotides contain phosphoru s atoms, and it is certain that inorgani c phosphorus compound s existed "i n the beginning"—we know that from geological studies. Nevertheless, it has not been possible t o produc e nucleotide s i n a Miller-typ e experiment . On e wa y aroun d thi s problem is to suppose that when lif e started it was based only on proteins. We will return to this hypothesis shortly . Another serious criticism of the Miller experiment concerns the role of methane. Miller and Ure y chose methane for two reasons. First, they needed a source of carbon atoms; otherwise, no life . Second , they wanted wha t chemists cal l a reducing atmosphere. Without getting technical, you can appreciate that doing the opposite, using an oxidizing atmosphere, woul d be doomed to failure. Thu s supposin g you added oxyge n to the mixture to be sparked. Sparking and heating would result in burning th e othe r components , wher e possible . Th e hydroge n would en d u p a s water, the ammoni a as a mixture of water and oxide s of nitrogen. In general the reaction between oxyge n and smal l organic molecules gives smaller inorganic molecules such as water and carbon dioxide . There is no building up of more complex molecules like amino acids. That is why Miller and Urey chose to exclude oxygen. But did the atmosphere of the Earth ever contain large amounts of methane? It i s tru e tha t methan e i s on e o f th e component s o f "natura l gas, " whic h i s trapped in huge underground cavitie s in som e parts o f the world and i s used a s a fuel. Bu t this methane is produced by the effec t o f millions of years of pressure an d heat actin g on prehistori c plant material . There ha d t o be lif e befor e thi s natura l methane could be formed. Coul d there nevertheles s have been methane i n the atmosphere of the earl y Earth, before life ? We can get hints by looking at other planets in th e sola r system . Mars , an d eve n mor e Venus, are not drasticall y differen t from th e primordial Earth. Their atmosphere s ar e very rich in carbon dioxide, no t methane. This is a problem. Since Miller's firs t experiments , there ha s bee n a change o f opinion abou t th e early Earth's atmosphere. One thing is certain: it could no t have contained signifi cant amounts of both hydrogen and oxygen. The first flas h of lightning would have initiated th e mother of all explosions. There is at present no evidenc e that the atmosphere was reducing (methane and hydrogen), and the prevalent opinion a t the moment i s that th e Earth' s atmosphere, at the tim e that lif e emerged , was mainl y carbon dioxid e and nitrogen , with smal l amount s o f hydrogen. In the absenc e of methane, Miller-type experiment s with carbo n dioxide, hydrogen, ammonia , an d water produce only the amino acid glycine, in very small amounts. It is possible to get other arnino acids if the ratio of hydrogen to carbon dioxide is greater than one, but as Miller himself admits, it is highly unlikely that there was enough hydrogen in the atmosphere of the Earth to maintain such a ratio. The gravitational pull of the

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Earth o n hydroge n molecule s i s rathe r weak , an d the y als o trave l ver y fas t (se e Chapter 1), and thus tend to escape from the atmosphere. There are other doubts about the Miller approach. One criticism, which could be aimed at almost any theory of abiogenesis, is that even if a mixture of amino acids were produced, it would not be particularly stable. Among the processes tending to destroy the "primitive soup" is adsorption of organic molecules on rocks, although there are of course those who woul d see this a s part of a. new theory , in which lif e forms o n the surfac e o f underwater minerals. W e will loo k a t two theorie s of this kind shortly. An interestin g aspec t of Miller's experiment s i s the relativ e amount s of amino acids that he obtained. An average over many experiments shows ratios of different amino acids that are not too different from those obtained by the analysis of the organic matter found i n som e carbon-containing meteorites. Th e similarity strongly suggests that there have been natural Miller-type experiments in space. If this is so, and if (bi g if) lif e starte d b y Miller' s mechanism , th e obviou s conclusion i s tha t there i s a reasonable chance tha t lif e starte d elsewher e i n th e universe . I t would still have to be water-based, to be life o f the kind that we know. In 1996, evidence was presented that strongl y suggests that there ar e fossil microorganism s in rocks recovered from Mars. The Haldane-Oparin-Mille r hypothesis i s out o f fashion. Of the fort y o r so simple molecules that would be needed to form a primitive cell, the experiment produces two. It is worth bearing in mind that glycine contains only ten atoms and alanine, thirteen. The simplest nucleotide contains thirty atoms. The probability that a give n larg e molecul e wil l b e produce d b y chanc e fro m smal l molecules , b y sparks, falls drastically as the molecular size increases. It ha s t o b e realize d tha t eve n i f heat, radiation , an d lightning , o n th e youn g Earth, had produced all the amino acids and nucleotides needed fo r present form s of life, the ga p between an aqueous solution of these molecules and a living cell is stupendous. It's a question o f organization: in the absence of a guiding intelligence, how di d th e component s ge t together? Even with a guiding intelligence, present day scientists are not doing very well. For the moment, let's show the Miller experiment to the side door and see who is next in line in the waiting room. The Call of the Depths In the 1970s , exploration of the sea bottom revealed that there were tiny volcanoes blasting molten matter into the ocean bed. These hydrothermal vents can heat the water to well over 100°C, and there are scientists wh o believe that life began in this saunalike atmosphere . It' s hot dow n there , but ther e ar e bacteria tha t liv e in ho t springs in near-boiling water and there are many microorganisms that have adapted to the eerie environment nea r the vents, using sulfur-containing molecule s as a source o f energy. How coul d life star t down there? Well, if you tak e a solution of simple molecules , put the m i n th e scientifi c equivalent o f a pressure cooker , and leave them to cook, you can produce an impressive yield of amino acids. What simple molecules ? Ah, there' s th e rub . Thos e use d b y th e experimenter s include d formaldehyde, cyanid e ions, and carbon dioxide. No one will quarrel over the carboii dioxide , bu t th e othe r tw o molecule s hav e bee n handpicked , wit h malic e aforethought. They are both very chemically reactive, and it is understandable that cyanide was chosen sinc e it contains both carbon and nitrogen. Is there goo d rea-

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son to suppos e that cyanid e an d formaldehyd e are , or were, that commo n dow n there, or indeed anywher e excep t in chemica l suppl y companies ? Not at present. And where are the nucleotides? This is an aquatic variation o f the Oparin-Haldan e hypothesis, and i t suffer s fro m on e o f the majo r defect s o f the Mille r experiment : the startin g molecules have been chose n with littl e o r no evidence that the y wer e really present in nature. Next theory, please. Convenient Surfaces There are at least two theories based on the premise that certain inorganic minerals have surface s which , becaus e of their shape , are capabl e o f acting a s catalysts for the formatio n of key biological molecules. The appropriate small molecules, drift ing randomly through the primeval soup, are trapped when they strike the particular part of the surface that fits them. During the time that they are immobilized, another type of molecule may chance on the trapped species and link up with it. The surface ease s the linkup process by holding the reactants i n suitable position s an d inducing shift s o f their electro n cloud s that facilitat e th e formatio n o f new bonds . The ne w molecul e the n sit s aroun d waitin g fo r the nex t component . Ther e ar e many example s o f solids actin g as catalysts for synthetic chemica l reactions , an d their actio n clearl y depend s o n on e o r more o f the reactin g molecule s bein g ad sorbed o n th e surfac e o f the solid . Of course the geometr y of the surfaces , o n th e atomic scale, is crucial to the biogenesis story, as it is for any solid-state catalyst. One variation o f the theor y has bee n presente d by the Glasgow-base d scientis t Graham Cairns-Smith. The materials h e focuse s o n are clays, which you may say haven't go t a well-defined surface, but at the microscopic level they have a definite and regularl y repeating structure because they ar e silicates o f the kin d illustrate d in Figur e 13.6. Cairns-Smit h envisages the chanc e production o f a huge variety of surfaces, som e of which are so shaped a s to act as templates for vital organic molecules. I will not go into detail, but the theory is certainly ingenious, original, and no less convincing than th e othe r theories. Unfortunately , i t is also no more convinc ing. And it will take a hell of a job to prove. Another theorizer, Gunther Wachtershauer, a patent lawye r with a doctoral degree in organic chemistry, also suggests that inorganic crystals were the substratu m on which lif e developed. He favors a substance known as iron pyrites, a compound of iron and sulfu r tha t forms beautiful iridescen t crystal s that gave rise to the common name "fool's gold." It has an advantage over clays in that it is naturally reduc ing, being prepared to give up electron s to the right acceptors and thus play an active part in the reactions presumed t o occur on its surface. Wachtershauer suggests that nucleotide s coul d form o n such a surface, an d tha t th e firs t for m o f life migh t have been a grain of pyrites surrounded by a membrane. Stanley Miller refers to the pyrites theory as "paper chemistry. " H e has a point. The fac t i s that neither of the proposer s of the cla y and pyrite s theories hav e gone into the laboratory one morning with a mixture of clay and some really simple molecules, and come out sometime later with a complex organic molecule. Thu s it has been possibl e to build polypeptide s from amin o acids in the presence o f clay, but the process also needed the helping hand o f a molecule called adenosin e 5'-phos phate, a molecule tha t i s extremel y unlikel y to have bee n aroun d 4 billion year s ago. An d th e rea l proble m remains : eve n i f there wer e polypeptides , it' s a hug e jump to get to a living, reproducing cell.

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Which Came First? Where are we? Amino acids have emerge d fro m Miller-typ e experiments, but no t nucleotides. Thi s brings us up agains t a fundamental problem. We have see n tha t DNA is responsible fo r the replicatio n o f the cell . If a primitive cell contained only proteins, it would have no future. Protein s cannot replicate themselves. Such a cell would eventually age and die without progeny. We are not aware of immortal cells. On the other hand, imagine a primitive cell with only nucleotides. We know that DNA can direc t duplicatio n o f the cell , initially b y duplicating itself . But that duplication needs certain enzymes, an d in a cell with no proteins, DNA could not duplicate—remember that all enzymes are proteins. Neithe r could suc h a cell direct the synthesi s o f proteins—a process that itsel f requires enzyme s (see Chapter 24). In any case, it is rather difficult to see how such an enzymeless cell would carry out the thousand s o f functions that are typical o f a living cel l an d whic h depen d ab solutely on the presence of enzymes. We see that nucleotides (DN A and RNA) and proteins ar e an interdependent system as far as the replication o f cells is concerned, and without replication the glorious and miraculous assembl y of the first living cells would have led nowhere. Lif e would occasionall y spring up here and there only to die every time, in sterile loneliness. Like the twinkling o f glowworms in the dark . It stretche s eve n th e credulit y o f a materialistic : abiogenesis fanati c t o believe that protein s an d nucleotide s persistentl y emerge d simultaneously , an d a t th e same poin t i n space , fro m th e primeva l soup . W e are i n troubl e enoug h withou t adding event s o f an astronomica l improbability.5 And i f simultaneity i s not feasi ble, whic h cam e first ? Nucleotides o r proteins? And ho w di d th e primitiv e life form survive if it was deprived o f either o f them? Glimmers of Hope The Naked Gene It was accepted for many years that there was a clear division of labor between proteins and nucleic acid : proteins were the catalysts of the living cell but could not be replicated without DNA, while DN A did no t appea r to act as a catalyst but coul d replicate with the help of proteins (enzymes). I n other words, there were two complementary systems—genes and enzymes, both dependent o n the other if they were to maintain th e living process but neither abl e to do the work of the other. New avenues o f thought hav e been opene d up b y the remarkable work of Sidney Altaia n and Thomas Cech, which earned them the Nobel Prize for chemistry in 1989. They showed tha t under the right circumstances RNA can act as a catalyst, thus possibly dispensing, at least initially, wit h th e need fo r a protein in a primitive lif e system . In other words, they opened up th e possibility that only one type of molecule was necessary for the creation of life. The y showed that RNA had propertie s that were reminiscent of those of enzymes. A second advance, in the laboratory of Leslie Orgel in the Sal k Institute i n California, wa s th e demonstratio n that , i n a solutio n containin g othe r simpl e mole 5

Of course you could sa y that the primeval oceans were so stuffed wit h amino acids that anywhere that nucleotides appeare d they landed in the middle of amino acids. No one has suggested this up to now, but it would require staggering amounts of carbon.

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cules, mononucleotides (th e units fro m whic h nuclei c acid s ar e constructed , se e Chapter 24 ) can be induce d t o replicate themselves without th e hel p o f proteins. Furthermore, we know from Spiegelman's work (se e Chapter 22) that RNA , in th e right circumstances , can evolve . Sinc e amin o acid s migh t conceivabl y hav e bee n produced in the "soup, " RN A may have evolved into a form capabl e o f interacting intelligently with them, starting the trail to polypeptide synthesis. Once again, much i s paper chemistry, but nevertheless , all this i s very suggestive, since it opens the way for a theory of the origin of life based on RNA, or at least on a self-replicating molecule, needing no protei n t o help i t i n tha t process . The suggestion is that life began not with a primitive cell but with a structure more akin to a gene, and tha t th e gen e evolved a structure t o look afte r itself—tha t structur e being the cell. Those who have read Richard Dawkins's provocative book The Selfish Gene (1976 ) will be strongl y reminded o f his pictur e o f the gen e ensuring it s survival by "living" within the body of its host. If RNA did appear at an early stage, and we take into account its catalytic activity, then ther e migh t hav e bee n fa r more comple x behavio r i n th e primeva l sou p than had, until recently, been envisaged . We need that complexit y in order to produce eve n the simples t entit y that display s the characteristic s tha t we deman d of life: the ability to reproduce and th e need to take in and produc e energy. RNA can carry information and coul d conceivabl y replicate withou t th e need fo r enzymes. The "nucleotides first" advocates have been the first to admit that a massive stum bling block stand s i n thei r path : th e synthesi s o f RNA by chance i s a highly im probable process, and as yet no one has presented a mechanism b y which it might have occurred . It's tough enoug h doin g it in the laboratory , and n o on e has com e anywhere near producing RNA by mixing simple molecules and subjecting them to the imagined condition s prevailing when the Earth was young. Even when you do have RNA, the proces s of self-replication in the laborator y is not a t all straightfor ward, an d i t require s considerabl e interventio n o n th e par t o f the experimenter . The RNA trail is fascinating for the light it has thrown on the behavior of this molecule, but we are still a long way from explaining it s genesis, let alone that of life. The Naked Protein In complet e contrast to the previou s scenario, i n which RN A is the onl y comple x molecule needed to originate life, there have been suggestions that life started with self-replicating proteins : it is the proteins that are the only type of molecule needed to fil l th e role s of both replicator s an d catalysts . Thi s avoid s th e difficult y o f explaining the simultaneous abiogenesi s of the nucleotides, which are far more complicated molecules. The late arrival of the nucleotides o n the scene would then herald a whole ne w level of sophistication i n the cell's abilit y to evolve, which coul d account fo r the fac t tha t afte r th e appearanc e o f single-cell organism s abou t 3 to 4 billion years ago, evolution seemed to stand still for a couple of billion years before multicellular organism s appeared. 6 It is not beyond th e bounds o f possibility tha t under the right circumstances a protein coul d be self-replicating. There is nothing in the laws of physics or chemistry that forbids this. It could be objected that all the 6

It appears to me that another explanation of the huge stretch of time for which unicellula r organisms failed to evolve is that bombardment by meteorites, comets, asteroids, and othe r interplanetary junk could have wiped out life several times in the first couple of billion years after it s first appearance.

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proteins that have complex function s i n the cel l (e.g. , enzymes) are composed of a dozen or more (up to twenty) different amm o acids, and that it is highly improbable that such a range was available in the "soup." This is not an insurmountable objection. We know that the shape o f enzyme molecules plays a central role in thei r functioning, an d i t is possible tha t a small number o f amino acids would be suffi cient to confer the required flexibility of shape, and therefore function, i n building primitive proteins . In this case, Miller's two amino acids (glycine and alanine ) are more significant than we supposed . Agai n I must sin g th e part y pooper's refrain , "This is paper chemistry." It is; the experiments are waiting to be done. The Birth of the Cell? Life exist s i n unit s enclose d by a sack—th e cel l membrane . Suc h a n enveloping structure is needed to maintain the physical integrit y of the cell, as well as to perform othe r vita l functions . A universa l componen t o f all cel l membrane s i s th e phospholipid molecule. If you tak e a dollop o f most types o f phospholipid, put i t in a nearl y neutra l aqueou s solution , an d the n gentl y agitat e th e solution , th e greasy lump wil l brea k up an d it ca n be shown that th e liberate d molecule s will spontaneously aggregat e int o closed , microscopic , approximatel y spherica l en velopes—or vesicles, as they are called in the jargon of the lab. It is not beyond the bounds o f reasonable possibility that phospholipids could be formed i n the soup . The problem is that no one has done this in Miller-type experiments. Another class of molecules that form roughly spherical, closed structures in water are detergents, which ar e considerabl y simple r tha n phospholipids . Th e tendenc y o f the greasy ends o f detergent molecules t o clum p together and avoi d water results i n th e formation o f closed structures having their greasy side facing inward . Th e structure s formed b y detergen t molecules are far less stabl e than those forme d b y phospho lipids, but if we are doing paper chemistry, then they could form a cell-like capsule in which the firs t simpl e cell developed. I'm not at all sure that I believe that, but some do. It is significant for all theories concerning the origin of life that the phenomeno n of self-organization , as exemplifie d by phospholipi d an d detergen t molecules, i s now a hot subjec t in chemistry. I f you want to follow this fascinating trail, look for "supramolecular chemistry" in the scientific literature. Back to Miracles?

None of the present theories of the origi n of life is strongly favored by the scientific community. In fact, I would no t blame you if , by this stage, doubt is creeping into your mind, or is perhaps already firmly installed in the throne room. Francis Crick has written, "The origin of life appears to be almost a miracle, so many are the conditions which would have had t o be satisfie d to get it going." The finge r o f God is certainly a tempting way out. The probability of a crowd of small molecules form ing the needed large molecules to start the long, complex path to a single cell seems to be almost zero. Going back to our 200 dollars' worth of chemicals again: no one would deny that attempting to creat e Ki m Bassinger/Mel Gibso n by heatin g an d shakin g the mix ture, although worth trying, might take forever. Bu t that doesn't prove that lif e ha s

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supernatural origins . Up to now, in attempting to prove that it hasn't, we've probably just made the wrong starting assumptions. Th e problem is that we don't kno w what the right ones are. One thing is absolutely certain: we get no help from spontaneou s generation , the emergence of completely formed complex organisms from inanimate material. Thi s nonexistent phenomenon ha d a long history and should hav e dropped dea d whe n Pasteur showed tha t a broth that ha d bee n boiled an d the n lef t i n a sterile atmos phere did not show signs of bacterial growth for many days. 7 The little museum i n the Institut Pasteur in Paris has some of the vessels in which Pasteur seale d boiled broth. They were, when I last saw them, apparently free o f all bacteria. Later experiments of this kind purported to show that othe r nonliving system s could generate life. Probably the last serious attempt was by H. C. Bastian, who i n 187 2 described his result s i n hi s hug e book The Beginnings of Life. Hi s experiment s resemble d those o f Pasteur. He placed infusions of hay an d a variety of other organi c material in hermetically sealed flask s an d boiled the m for many hours, long enough for all life to have been destroyed—in his opinion. Th e flasks were sealed and lef t to cool at room temperature, and within a day or two it was obvious that there was bacterial growth . The experiment s wer e repeate d b y John Tyndall . By meticulously ex cluding bacteria, Tyndall showe d tha t th e content s o f the flask s remaine d sterile , stone-dead. Spontaneous generation has not reared its head again. Paradoxically, Tyndall would hav e wished i t otherwise. H e was a notorious agnostic, som e sai d atheist , an d i n genera l i t wa s scientist s o f his opinion s wh o looked to spontaneous generation, or abiogenesis, as a phenomenon tha t supporte d their inclination t o dispense with the need for supernatural intervention . Tyndall' s famous presidentia l addres s to the 187 4 meeting of the Britis h Association for the Advancement of Science, i n fact , containe d a defense of the continuit y o f nature, the inseparability o f the inanimate and the animate. Thi s was too controversial for his time, and the address was to create a public furor. 8 I t is ironic that the very scientist who needed spontaneous generation to dispense with miracles should be the one to finally kill it. Self-Organization

The basic problem facin g anyon e who i s looking for the origi n o f life i s to account for th e formatio n o f a complex , very highly organized, self-sustaining and selfreplicating system out of a mixture o f chemicals that, certainly i n the earl y days of the soup , displaye d none of these characteristics . A s Jacques Monod, the eminen t French biologist wrote in Le Hasard et la necessite (1970), "The univers e was no t 7

Of course, in a way, abiogenesis is spontaneous generation, if by that phrase we mean the appearance of life fro m nonlife . However, the proponents of spontaneous generation were talking about the appearance of fully formed living forms, anything from mice down to maggots and bacteria, not the gradual evolution of living matter from simpl e molecules over a long period of time. 8 Most Victorians could not understand that the man they saw as a deluded materialist, could, in his address say: "The world embraces not only a Newton, but a Shakespeare—not only a Boyle, but a Raphael—not only a Kant, but a Beethoven—not only a Darwin, but a Carlyle. . . . They are not opposed, but supplementary—not mutually exclusive, but reconcilable." He sounds sympathetic.

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pregnant with life nor the biosphere wit h man. Our number cam e up in the Monte Carlo game." We aske d tw o question s nea r th e beginnin g o f this chapter , bu t w e hav e dis cussed only on e of them: the origi n of the molecule s o f life. W e found no convincing answers . Regardin g the secon d question—th e productio n o f a stabl e syste m with lower entropy (les s probability) tha n its normal equilibrium state—is not only possible, it has been observed (see Chapter 18). In considering the possibility that a system can spontaneously organize (move to lower entropy) , let us remind ourselve s onc e more that the secon d law of thermodynamics onl y say s tha t th e entrop y o f an isolated syste m increase s du e t o an y changes. (A n isolated syste m is one in which neither matter nor energ y can cross its borders.) There i s nothing i n the law that say s that entrop y cannot decreas e or hold steady for a system in which either energy, or matter and energy, can cross its borders. Such a system is the living cell . This dispensation , grante d t o closed o r open systems , t o maintain o r decrease their entrop y completely changes the rules of the game. It removes one of the great conceptual barriers that at one time threatened t o overthrow any theory of abiogenesis, namely , th e mistake n "principle " tha t system s coul d no t los e entrop y an d move from comparativ e disorder to comparative order. But how coul d primitive cell s maintain a highly organized (low-entropy) state, even if they somehow achieve such a state? How Long Can We Keep the Fir e Alive? Life versus Entropy In th e nonlivin g worl d i t i s almos t universa l t o fin d tha t natura l chemica l an d physical processe s ar e accompanie d b y a n increase i n entropy , that is , a los s of order. There are no systems more ordered than the living cel l and its components. We expec t matte r tha t i s i n a highly organize d form , suc h a s an enzyme , a DNA molecule, o r a living cell , to be unstable wit h respect to breaking up int o smalle r components. That' s the way the universe goes. Living systems continually underg o chemical an d physical change . Why do they not invariably disintegrat e into small er, more probable, molecules, thereby increasing the entropy of the cosmos, in obedience to the second law? They do. When a living organism dies it decomposes, which just means that the fantastically comple x molecule s o f which it i s made break dow n int o fa r simpler components. The spontaneous proces s of decomposition goe s the way that the second law predicts: the complex, highly ordered syste m breaks up into a highly dis ordered mess . Th e structur e o f the cel l collapse s (become s disordered) , an d th e large, entropy-poor (highl y organized) molecules tha t i t contains disintegrat e int o small, entropy-ric h molecules , destroyin g th e miraculou s orde r an d leavin g th e fragments o f the cel l to wander abou t in a disordered manner . Th e entrop y (alias disorder, alias probability) o f the universe increases . This happens spontaneously , as the second la w predicts. Th e problem is that while i t is alive an organism maintains its highly ordered, low-entropy state. It fights the second law. Living matter would much rather be dead. Living matter is a curiosity. Rephrasing our question, we ask: Granted that life exists, how can a living organism be at low-entropy equilibrium (and they

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The answer is contained in our previous consideration of systems at dynamic equi librium. Livin g forms are in dynamic equilibrium, like the heated tube of helium i n Chapter 18. The tube was kept far from its normal equilibrium stat e by a flow of energy through th e system . Ho w does the body maintain th e comple x structura l in tegrity of its cells and o f the molecules within th e cells , i n the fac e o f the destruc tive influence of the spontaneou s tendency to raise its entropy by decomposing? It eats. Withou t foo d inpu t w e di e an d the n drif t rapidl y awa y fro m equilibrium . What is the nature of this ingested material? Plants take in very simple, high-entropy molecules such as water, carbon diox ide, and nitrogen-containing salts, and fro m thes e build up complex , low-entropy molecules, especially carbohydrates. They manage to produce low-entropy molecules fro m high-entrop y precursor s because the buildin g u p proces s i s drive n by the energ y in th e Sun' s light. 9 Plants are largely synthesized from high-entropy molecules. Animals, on the othe r hand, canno t live on carbon dioxide, water, an d salts. We eat plant and animal material that ha s large, low-entropy molecule s i n it. These molecules, in the end , are derived from photosynthesis , th e great creator of order o n this planet . Thu s animal s tak e i n relatively comple x molecules throug h their intestina l membranes—molecule s suc h a s amino acids an d simpl e sugars — and build the m u p int o eve n more complex materials, such a s proteins. Animal s are highly ordered systems that, in contrast to most plants, ar e largely synthesized from highly ordered (low-entropy) molecules. I n our bodies we continually synthe size comple x molecules t o replac e thos e tha t naturall y brea k down , an d w e ar e helped i n this struggle against entrop y increase by taking in comparatively highly organized, low-entrop y molecules . Thu s w e ca n loo k at the stabl e equilibriu m o f living matte r a s a dynami c stat e i n whic h low-entrop y living matte r i s defende d against the irreversibl e march to higher entrop y by means o f an intake o f suitable material. We are removing low entropy from the external world and using it to keep down our own. It might be thought tha t we could directl y utiliz e very large low-entropy molecules in our food, such as DNA and proteins. This is not what we do, and cannibal ism does not replace the cannibal's DNA and enzymes with those of his victim. We do tak e i n ver y larg e molecules, but w e partiall y brea k the m dow n int o smalle r components, such as amino acids and simple sugars, which are still comparatively low-entropy molecules, and use these to build up ou r own cell constituents . Th e Austrian physicist Erwin Schrodinger (1887-1961) said that living organisms were eating low entropy from thei r surroundings to maintain their ow n entropy at a low level. Of course this is not the only role of food; we need various elements to maintain ou r health, an d w e also need a source of energy. Note that th e metabolis m of food i n ou r cell s result s i n th e formatio n o f heat, whic h w e giv e u p t o ou r sur roundings. Heat is the form of energy with the greatest entropy (due to the disorde r of the moving molecules), so we are taking in a source of low entropy and exporting 9 This energy is in a highly available form ; it induces photosynthesis whatever the temperature of the plant. I t is not a degraded for m o f energy like heat, and in fact there i s justification for saying that it is in a state of low entropy .

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high entropy . That's ho w w e figh t th e battle against our own natural tendenc y to drift t o higher entropy. Postscript

The enigma of the origi n of life is fascinating and o f little practical significance, As far as solving the problem is concerned, we may in the end have to be satisfied wit h a small selection of credible possibilities . To those who see no way out but divine intervention, I would point out that you are asking more from scientist s tha n yo u hav e a reasonable right to expect at this stage. You are asking them to account for the creation of the most highly organized mechanisms i n th e universe , i n term s o f a world tha t vanishe d nearl y 4 billio n years ago, leaving very little indication o f what it was like except in rather general terms. The journey between Mendel and the genetic code would hav e seeme d utterly impossibl e t o a n early-nineteenth-centur y scientist ; the y didn' t eve n know the structure of atoms. But we made it. I had on e long conversation with J. B. S. Haldane, which started off with politics and ended up with science. When I questioned him about evolution, one of his remarks sparked my interest, and sent me to the library that evening: "Evolution's not the problem. Life is." Then he said, "Oparin and I once had an idea about that, but we'll never know the real answer." An Apology

Much ha s bee n lef t unsaid . I have limite d mysel f to pointin g ou t a fe w centra l themes in the scientist' s way of dealing with livin g organisms. The biological sciences are far larger in scope, and far richer i n detailed knowledge, than I have suggested. But we are also vastly ignorant, especially o f two related areas: consciousness and the interactio n of mind an d body. I promised i n the introduction t o keep away from consciousness , and I will keep my promise. Regarding mind an d body I will also pass. There are those who state firmly that what we call the mind is merely a manifestation of the body. This may well be true, but I'm not going to be drawn in o n that one . An d i f you think tha t th e natur e o f the min d i s elusive, just wait until we get to the next chapter.

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vii The Dissolution of Reality? Mount then, my thoughts, here is for thee no dwelling Since Truth and Falsehood live like twins together. Believe not sense , eyes, ears, touch, taste, or smelting. —John Dowland, "Tell Me, True Love"

The twentieth century has seen a second scientific revolution that boasts two of the most powerful conceptions of the human mind—the general theory of relativity and the quantum theory. One has changed our image of space and time, and has shown us that matter and energy are two names for the same shadowy entity; the other has allowed us to understand and predict the nature of matter and radiation with a degree of detail that would have seemed miraculous to the scientists of previous centuries. It has also put in question our ability to grasp reality.

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28 The Inexplicable Quantum I think I can safely say that nobody understands quantum mechanics. —Richard Feynman

The quantum theory is not explicable in commonsense terms. Its axioms, and some of its predictions, go against all our built-in preconceptions as to the nature of reality. In the 1930 s Niels Bohr, one of the theory's fathers, was reported to have said that if you weren't confused by quantum mechanics you didn't really understand it. Perhaps the most powerfu l theor y that scienc e has constructe d grew out of the need to explai n aspect s of nature that were utterly inexplicabl e i n term s o f Newton's mechanics an d Maxwell's laws. It is, for example, impossible to say much of importance concerning the behavior of nuclei, atoms, and molecules without using quantum theory. When Leibniz read Descartes's method of stripping away all doubtful beliefs an d then building up a true philosophy , he mocked its generality. The method boiled down, he said , to "take what you need and d o what yo u should, an d you will get what you want." This could better be said of the way that quantum mechanics is almost universally used. We put in some physical facts, follow the rules for obtaining the needed results, and almost always get what we want. The comparison between the theoretical results and experiment is rarely disappointing. It can be said of quantum mechanics that we are thankful, impressed, but, in the still of the night, profoundly uneasy, because the quantum theory presents us with paradoxes more puzzling than the questions that it solves. Einstein always saw the quantum theor y a s imperfect and transitory . One can understand hi s discomfort . Quantum mechanics implies tha t to many of the questions that we ask of physical systems we will, in principle, only obtain answers couched in the language of probability. We will never be abl e to say , "If you d o this to a molecule, then tha t wil l happen," but only, "If you do this, there is such and such a probability of that happening." Som e physicist s believ e tha t ther e wil l b e som e nontrivia l change s i n quantum theor y before ver y long. Others claim tha t an y major chang e is impossible; the theory as it stands is just too successful to stand much alteration . We will go back to the beginning of the century, when the great breakthrough occurred, and see why and how it happened. If at the end you find the theory unsatisfactory, you are in excellent company, but you might bear in mind Bohr's reproof of Einstein: we must not tell God how to run the world. The Grainy Texture of Nature As a child yo u probably swung on a swing at some time, perhaps pushed by on e of you r parents . I f he o r sh e pushe d steadily , you swun g backwar d an d forwar d

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repeatedly, throug h th e sam e arc . M y fathe r use d t o d o thi s fo r me, unti l I wa s banned from that park for shooting arrows at people. (I was dumbfounded—th e arrows were blunt.) We will cal l the child an d the swing, together, an oscillator. My father coul d contro l th e height I reached at the en d o f the ar c by altering the forc e with whic h he pushed me . This means that he was controlling the total energy of the oscillator. The higher the end o f the arc, the greater my potential energ y at that point—or, if you like, the more work my father had t o do to get me there. At the extreme of the arc I was stationary, and all my energy was potential energy (see Chapter 17). Suppose that at the extrem e point o f one particular ar c I had a total energy of exactly 600 joules. Could I be given an energ y of 599 joules? Obviously yes. All that woul d b e necessary would b e for my father t o push me a little less forcefully , so that I rose a little less higher at the end of the arc. Could he have given me an energy of 599.9 joules? Of course. And o f 599.9683885214 joules? In principle yes, although th e accurac y of the measurement s neede d t o verify suc h a n energ y would test the experimenter. Common sense says that if the oscillator can be given two differen t energies , say zero (don't push the swing ) and 60 0 joules, we can in principle giv e it any energy between 0 and 600. In the same way, common sense says that if a car can travel at a maximum spee d of 120mph, then i t can travel at any speed between zer o and 120 mph, and thus it can have any predetermined kineti c energy up t o the maximum, value. Until December 1900, it was universally believed that we could choos e the energy o f an oscillato r t o b e an y valu e tha t w e wished , betwee n zer o an d som e physically determined maximum. I t would have been said that the allowable energies of an oscillator formed a continuum. There ar e a number o f basic quantitie s beside s energ y that appea r t o have this kind o f continuity. Lengt h is the simplest . W e intuitively believ e that w e can , i n principle, separat e two bodies by any distance that we choose. Similarly, common sense—that most insidious o f brainwashers—tells us that time is continuous . Freud's Psychopathology of Everyday Life appeare d in 1900 , opening a new er a in th e wa y tha t peopl e thought about their interna l world . It is doubtfu l i f any of those who took voluble sides with or against Freud realized that a paper publishe d by a Germa n physicist o n 1 4 December o f that sam e yea r wa s t o creat e a n eve n more thorough revision of the way we see the external world. Max Planck's suggestion seemed innocuous enough ; it was that the total energy of a collection of oscillators ca n assum e onl y discrete values. 1 I t i s a s thoug h Planc k (1858—1947 ) ha d said tha t in th e playground in the park , the total energy of all the childre n o n the several swings coul d onl y have certain discret e values, jus t as the tota l number of swings can be only an integral number . A collection of oscillators sound s a bit remote from daily life, but it isn't. As we saw in Chapter 16, the atoms and molecule s of an y soli d body , fo r example, ar e ceaselessly , and unstoppably , vibrating . You, and muc h o f your surroundings , ar e collections o f oscillators. Planc k was sayin g that the energy of such systems of oscillators comes in little packets, quanta. If you have 3 7 quanta you can't go up to 37 and a half, the next stop is 38. a

For the scientific reader it should he pointed out that, contrary to the impression left by most textbooks, Planck did not originally equate the energy of a single resonator with an integral multiple of/iv, although he did repeatedly writes expressions like U(N)=Pj!!V with P an integer, where U(N) is the total energy of the N resonators.

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Planck had a reason for plucking his highl y curiou s assumptio n ou t o f the air . He was tryin g to explai n Figur e 15.8b . Was it possible to predict what fractio n of the total radiant energ y of a blackbody was associated with a particular frequency ? Planck's solutio n fitte d th e fact s exactly . As others had don e before him , he mod eled th e blackbod y as a collection o f oscillators givin g off radiation. Th e novelty that he introduced int o the calculation s was his assumption o f the discreteness of the total energy of the oscillators. It worked: if you gave him the temperature of the heated body, he could predict accurately what fraction o f the total energy of the radiation would be associated with any particular range of frequencies. Thi s success did no t necessaril y validat e Planck' s assumption , bu t i t certainl y mad e peopl e think. If it was true, what could it mean—that a system could have only certain values for its total energy? It was lik e saying that the sum of the height s of a group of people could be only an exact number of inches. As though my daughter and I together coul d tota l 13 4 inches i n heigh t bu t no t 134.5 . Th e nex t allowe d figur e would be 135 . This i s obviously not true , so why shoul d th e energ y of oscillators behave in this strange way? Planck said of his epoch-making assumption: "It was an act of desperation. . .. I had to obtain a positive result under any circumstances and at whatever cost." The justification wa s that it worked, it solve d the black body problem. 2 But , although he told his so n that he thought he had don e somethin g as important as Newton's work, much later, in 1922, he said that the quantum had called forth " a break with classical physics far more radical than I had initiall y dreamt of." Planck was worried. For at least a decade he struggle d t o find a way o f solving the blackbody problem without assuming "quantizatio n o f energy." He was tied to the past. One can understand his reservations; no one had ever dreamed that energy was anything but a continuous entity , to be poured ou t like water, not counted like sheep. Enter Einstein Einstein realized that Planck's hypothesis coul d be taken to imply that the individual oscillators that appea r i n nature , say vibrating atom s o r molecules, ar e eac h characterized by a certain discontinuou s se t of energies. They can vibrate more or less violently, but they cannot have any arbitrary energy. Their energies can be increased only in finit e steps , by packets of energy, quanta, just as American money cannot be counte d out i n unit s les s than cents . Th e energ y of a packet would b e proportional to the frequenc y o f the oscillator. If something vibrated very fast, then its quanta would be larger than that of a slower oscillcltor . The oscillator ca n only have a total vibrational energ y equal to an integral number of quanta. The amount of money you have in your pocket cannot be twenty-three and a half cents. The siz e of the packe t of energy, the energeti c cen t whic h w e cal l a quantum, was formally given by:

e=h v where e is the energ y of the quantum , v is the natura l frequenc y o f the oscillator, 2

In fact Planck made another revolutionary assumption in his paper, but it is not amenable to simple explanation. If there are any specialists reading this: Planck anticipated Bose-Einstein statistics.

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and h is the famou s Planck's constant. Th e value o f e is thus proportiona l t o th e natural vibration frequency o f the oscillator. Push a swing and le t it go. It has a natural frequency at which i t oscillates. Thi s is the frequency that we put into the preceding equation. Tuning forks have natura l frequencies, an d s o do atoms and molecules, although you can't se e or hear them . The equation says that i f any oscillato r has a certain natura l frequency , v , then i t can only have an amount of energy that i s equal to one, two, three, o r more quanta—packets of energy—each packet equal to h times the frequency of the oscillator . For the swing in the park, the size of each quantum, in round numbers, is about 3 x 10" 34 joule, as can be seen from the footnote, 3 where it is also shown that to add one quantum of energy, my father would have had to increase my height a t the en d of each arc by about 10" 36 meters. The difference s i n both energy and height ar e far too minut e t o be detecte d b y present-da y techniques . Wha t thi s say s i s tha t th e packets o f energy of the swin g ar e so incredibly smal l tha t t o al l intents an d pur poses the energ y of the swin g i s a continuum. I t is as though you were climbing a staircase in which th e height of each step was a billionth o f an inch. It would look and feel like a continuous slope . So what d o I need quant a fo r if they ar e s o smal l tha t I can't detec t them ? It' s rather lik e the post—Worl d War I German mark. Money only came in multiples of marks, but one mark was so worthless that it had no practical significance. In 1900 the only use for quanta seemed to be in the solution of the blackbody problem. But not fo r long. The Photoelectric Effect: Bullets of Light ? The idea of energy "quantization" wa s not greeted with wil d acclaim . Why couldn't an oscillator have any energy that it wanted to? Einstein, never afraid of the dark, or the light, pressed on. What Planck had don e was to suppose that the blackbody oscillators, the atoms in the walls o f the cavity, gave u p o r accepted energ y only i n finit e packets—quanta . Thi s doe s no t reall y mean tha t energ y i s quantized . Einstei n likene d i t t o servin g bee r i n tankards , which didn' t impl y tha t bee r existed onl y i n tankar d quantities . Einstei n wen t much furthe r tha n Planck . H e quantized light . H e was sayin g that bee r did exis t only in units of a tankard. Next, he ran a bulldozer through on e of science's mos t sacred beliefs, declarin g light to be composed not o f waves but o f discrete packets, tiny immateria l pellets , eac h carryin g on e quantu m o f energy. By doin g this h e solved anothe r outstandin g problem : the photoelectri c effect . H e wo n himsel f a Nobel Prize. The explanation of the photoelectric effec t is a turning point in science. It is the counterpoint t o Young' s two-sli t experiment . On e ma n showe d tha t ligh t wa s 3 Let's see how this applies to the swing. The frequency, v, of the swing can he taken to be ahout one cycle (trip back and forth ) i n 2 seconds, or 0.5 cycles per second. The value of h is 6.6 x 10" 34 joule seconds. So the size of the packets of allowable energy, the quanta, that can be given to the swing is £ = hv = 6.6 x 10~ 34 x 0.5 joule or ~ 3.3 x 10" 34 joule. This is a tiny quantity. To see ho w small, suppose that my father wishes me to have more vibrational energy and that he wants to increase my energy by one quantum, the minimum allowable increment. To do this, he has to do the same amount of work. That means increasing my height at the en d of the arc. The work done in increasing my height is mgH, where H is the extra height by which I am raised (se e Chapter 17) . If my mass was 30 kilo, mgH~ 300H . The value of H that makes this equal to the energy of one quantum is 1.1 x 10"36 meters.

The Inexplicabl e Quantum |

wavelike, th e othe r tha t i t wa s particlelike . Einstein' s articl e effectivel y create d quantum mechanics. 4 He published hi s idea s i n 1905 , i n the Annalen der Physik. In the same year and in the same journal, he published tw o papers on special relativity, which opene d a new era in physics, and a paper on Brownian motion, whic h alone would have made his name. There has never been such a concentrated exhibition o f genius since 1666 , the yea r (and a half) i n which Newton formulated for himself, but di d no t ye t publish, th e la w of universal gravitation , the law s o f motion, and the element s of the calculus—apar t fro m splittin g ligh t with a prism. He was twenty-four. Einstein was twenty-six. In 1887 , Hert z foun d tha t whe n h e create d a voltag e differenc e betwee n tw o metal plates he could make sparks jump between them. When he gradually separated the plates, he reached a distance at which sparks no longer appeared; we would say tha t electron s wer e n o longe r jumping from on e plat e t o th e other . However , when h e turne d o n an electri c ar c lamp nea r the plates , th e light , shining o n the surfaces, brought back the sparks . The following year Hallwachs showed that if tin uncharged meta l surfac e wa s illuminate d wit h U V ligh t i t becam e positivel y charged. The explanation o f these observations had t o wait until J. J. Thomson discovered th e electron . I t was Thomso n wh o correctl y surmised tha t U V light wa s ejecting the negatively charged electrons from th e metal surface an d leavin g an excess of positive charge. It was these electron s that were jumping across the gap between th e UV-irradiate d plate s i n Hertz's lab. This i s the photoelectri c effect , th e basis o f most device s that ope n door s o r operat e toilet flushe s when yo u break a light beam. So far so good, nothing particularl y revolutionary. But in 1902 , Philipp Lenard (1862-1947), a racist5 Nobel Prize winner, studied th e effec t o f varying the intensi ty and frequency o f the UV light falling on the metal. If the intensity of the light was increased, th e numbe r o f electrons pe r secon d leaving the surfac e increase d but, completely unexpectedly, the y stil l ha d th e sam e velocity. Why didn't a more intense bea m give the electron s a bigger kick? A larger wave i n th e ocea n certainl y creates more havoc because it carrie s mor e energy . The peculia r aspect of the experiments was that the velocity at which the electrons left th e surfac e did increase when the frequency o f the UV light increased . It is worth looking closely at Einstein's controversial explanation o f all this. Einstein proposed that light was not continuous but consisted of packets, light quanta, each having a fixed energy , completely determined by the frequency o f the light. A beam of light behaved lik e a stream of bullets, no t a wave. Moreover, he proposed that the energy of each of these packets, which are now called photons, is given by h times the frequency of the light, E=hv, just like the packets of energy that characterized Planck's oscillators. Thus UV light having a frequency o f 1016 Hz consists of a stream of photons eac h having 10 0 times the energ y of photons o f IR light having 4

Other scientists developed quantum mechanics into a form that Einstein could not accept. Hie acknowledged that the theory was a valid practical tool for accurately predicting the behavior of light and matter, but he could not accept a central axiom of quantum mechanics, namely, that the outcome of any given measurement could be stated only as a probability, not a certainty. We will come back to this matter in the next chapter. 5 Lenard, whom we will meet again, published a treatise called Deutsche Physik as an antidote to "Jewish science." He once remarked, "Science, like every other human product, is racial and conditioned by blood."

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a frequency o f 1014 Hz, which i s why U V light can cause skin cancer and I R can't. Both photons travel at the same speed, the speed of light. Increasing the intensity of a light source increases the rate (but not the speed ) at which photons leave the source. If their frequency has not been changed, neither has the energy of the indi vidual photons. A mechanical analogy is that firing a pistol faster doe s not change the velocity, and therefore the kinetic energy, at which the individual bullets leave the muzzle, it merely changes the rate at which bullets strike the target. What are photons? In a letter that he wrote in 1951 , Einstein admitted : "All the fifty year s of brooding have not brought me any nearer to an answer to the question, 'What are light quanta?' " Newton must hav e been smiling , fo r he ha d state d tha t light was a stream of "corpuscles. " Einstein used the idea of photons to quantitatively explain the photoelectric effect. The electrons in a metal are obviously held to the metal by some force; otherwise they would leave spontaneously. Picture such an electron in a beam of light as being bombarded by a strea m of light bullets . I f the blow s ar e too weak the elec trons will not be pushed away from th e metal, no matter how intense the stream of bullets. If you can't throw a ball hard enough to dislodge a coconut, it doesn't matter i f you increas e the rat e at which yo u are throwing balls. Th e only way to dislodge th e coconut s is t o throw th e ball s harder , t o increas e thei r kineti c energy. This is how Einstein sa w things, and he declare d the energy of a photon to be determined by the frequency o f the light , through the relationship E = hv, not by the intensity o f the ligh t beam, which only determines the number of photons hittin g the target in a given time. The higher the frequency th e more energetic the photon. If the frequency o f the light is too low, the energ y of the photon will not be enough to eject the electron . Increasing the intensit y (th e rate of impact) of low-frequency light will leave the electrons in the metal unimpressed. However, as the energy (fre quency) o f the photon s i s raised, the electron s will fee l harde r an d harde r blow s until at some value of the energy (that is, at some value of the frequency of the light) the electron s will be knocked free becaus e they ar e struck by photons with suffi cient energy to dislodge them. This is exactly what is observed: below a certain fre quency, which i s characteristi c of each metal , no electron s are ejected , n o matter how intense the light. In 190 1 Planc k obtaine d a value of 6.55 x 10~ 34 joule.second for his ow n con stant. In 1916 Robert Millikan analyzed his experiments on the photoelectric effect , using Einstein's theory, and found a value of 6.57 x 10" 34 joule.second. Despite the apparent verification of Einstein's ideas, Millikan, in 1915, commented: "Einstein's photoelectric equation . .. appears in every case to predict exactly the observed results. . . . Yet the semicorpuscular theory by which Einstein arrived at his equatio n seems at present wholly untenable." In other words, whatever happened to waves? Lord Rutherford was equally puzzled: "There is at present no physical explanatio n possible o f this remarkabl e connectio n between energ y and frequency. " H e stil l thought in terms of waves. The energy of a wave is associated with its amplitude, that is, with its intensity. Bigger waves carried more energy. This is why Rutherford expected that if the intensity o f a light beam was increased there was more chance that it would blast electrons out o f the meta l surface. But , as we said, i f you can' t throw the balls hard enough , you won't knoc k off the coconuts, no matter at what rate you throw them. For over a decade Einstein was practically alone in believing in light quanta —

The Inexplicabl e Quantum |

photons. Just a s Thomas Young had bee n ridicule d whe n h e declare d ligh t t o be wavelike, so Einstein was now smiled upon pityingly when he declared light to be corpuscle-like. The wheel had turned ful l circle. Today no physicist denie s the existence of photons. They can be detected. When light shines on a screen covered with a suitable scintillator, the screen shines. I f the intensity o f the light is reduced, the intensit y o f light from th e scree n falls with it , but a t a certai n stage , when th e ligh t i s ver y weak , th e scree n cease s t o radiat e equally fro m al l part s o f its surface . Spot s o f light begi n t o flicke r agains t a dark background. These are the places that photons are striking. Similarly, photoelectric cells, which respond to radiation by producing an electric current, will give an apparently continuou s outpu t o f current i n a strong light, but whe n the light i s very weak, th e stead y curren t begins to falte r an d finall y become s a random serie s of pulses. Photons are at work. Light has to be very weak for these phenomen a t o be detected, as you ca n se e from the fac t tha t a n averag e 100-watt lightbulb give s off about 3 x 10 20 photons ever y second, a photonic Catling gun giving a steady rain, rather than the isolated shots of a Wyatt Earp. A New View of Nature Planck's concep t o f quantization, Einstein' s photon , an d th e explanatio n o f th e photoelectric effect pu t a heretical question mark next to both Maxwell's wave theory and the belief that energy could be reeled out like curtain material and cut into any length that the customer required. During th e quarte r o f a centur y followin g Planck' s inspire d guess , i t became clear that when we move down to the scale of the atom, nature behaves in ways not explicable i n term s o f th e classica l law s tha t gover n Newton' s an d Maxwell' s world. Classical physics was not demolished; it was shown to have very deep limitations. We are going to tell two quantu m stories . One will be about the atom , because that is the basis of our life o n Earth. The quantum theory accounts completely for the behavior of atoms and molecules. Our other story will be about quantum mechanics itself. The firs t stor y is an attempt t o convince you that quantum mechanic s works and i s useful. Th e second story is far stranger, it is the scientific equivalent of a psychedelic "trip. " The Atom The discover y of the electron an d th e nucleu s lef t classica l physic s i n a n embarrassing situation: how did you put them together to make an atom? Rutherford ha d shown tha t th e ato m was much bigge r than th e nucleus , whic h implie d tha t th e electron was careering around in the nuclear sky. How did it resist the attraction of the nucleus? Why didn't it "fall to Earth"? Easy. It rushes around in a circle, like the Earth roimd th e Sun , whic h woul d hav e solve d the proble m had Maxwel l neve r lived. His equations predict that an electron behaving like a planet to the nucleus' s sun should , becaus e o f its motion , emit electromagneti c waves. For the classica l picture of the atom this emission of radiation has a suicidal consequence: since the emitted waves contain energy and it must come from somewhere, it can only come by a continuous depletio n o f the electron' s kineti c energy . The electron wil l slow

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down, and as it does so it will spiral inward, ending up by crash-landing on the nucleus. It obviously doesn't do this. In 1913 Niel s Bohr invented a new theor y of the atom. He used one of the great principles o f science: if the theory denies the fact , rejec t the theory. Future histori ans ma y wel l as k why thi s principl e seem s t o be s o neglected i n othe r area s of human life . The firs t principl e o f Bohr's ato m wa s tha t a n electro n doe s mov e i n a stabl e path, circuiting the nucleus, rather as a moon circles its planet. His second assump tion wa s that, i n contradictio n t o classical physics , a n electro n movin g around a nucleus does not radiate waves and lose energy. Question: Why not? Answer: Don't know; but, like Planck, let's kee p going and se e what turn s up. The third assump tion concern s what i s known a s the angular momentum of the electron . This i s a simple concept. For a particle of mass m, going around in a circle of radius r, with a velocity of v, the angular momentum is just mvr. Now in the sensible, stai d worl d of classical physics, for a given body at the en d o f a given string, say the iro n bal l whirling aroun d a hammer thrower' s head , the onl y way to alter the angula r momentum is to change v, the velocity, and obviously v can be given any value that is desired. In short, in the classical world, angular momentum, like energy or length or time, is a continuous entity ; it can have any value under the Sun. You can guess what Bohr did. He quantized angular momentum, declaring tha t it could exist only in multiples of a certain basic unit. Bohr considered the hydrogen atom, which ha s only one electron. The electron, said Bohr, could circle around the nucleus, provided that it had an integral numbe r of packets of angular momentum. Th e result o f this limitatio n i s that ther e are restrictions on the energy of the electron, so that the electron in the atom was allowed to have only certain discret e energie s (Figure 28.la). This restriction o n the energy of the electron was accompanied b y a restriction o n the paths that were allowed to an electron . I t could no t choos e an y pat h i t liked , a s the Eart h ca n i n Newton' s world. Bohr thus envisaged an atom in which th e electro n had a limited choice of paths around the nucleus, and in any given path the electron had an energy associated with that path. An electron could not choose a path, or an energy, other than one of those allowed. I n this, i t differ s radicall y from th e planet s i n th e sola r system. In Newton's world the paths of the planets are completely arbitrary, fixed onl y by an accident o f birth—the way i n which the origina l disk o f matter tha t forme d the sola r syste m broke up. Ther e ar e a n infinit e numbe r o f possible path s fo r the Earth to travel around the Sun , and they form a continuum i n the sens e that I can

Figure 28.1a. Th e atom that Niels Bohr made. The circles represent some of the only possible paths allowed to the electron.

The Inexplicable Quantum

find a path with any particular energy that I choose. Bohr's electron was riding on a carousel with an infinite number o f circles of horses, but these circles were associated wit h a discret e scal e o f energies. A n electro n could si t i n an y circl e that i t liked, but no t between th e circles , an d eac h circl e had a differen t energy . Bohr's conception o f a nucleus surrounde d b y electrons , each i n on e o f a set of allowed paths, or orbits, is the model behind th e conventional but highly misleading drawing of an atom (Figure 28.la). Each of Bohr's orbits had a different distanc e from th e nucleus. An electron that had a path farther fro m th e nucleus would be easier to remove from th e atom than one nearer the nucleus , because th e electrostati c attraction between nucleu s an d electron falls off with distance. In the normal hydrogen atom the electron would try to get as near to the nucleus as it could, because of their mutual electrostatic attraction. It would therefore normally occupy the nearest allowed orbit, which is usually called the lowest orbit, because it has the lowest energy. You have to do work to "lift" it into an orbit that is farther fro m the nucleus. You would be fighting the pull of th e nucleus , just as it takes work to lif t a boulder highe r abov e the Earth . This work, in moving between any two orbits, was one of the things that could be calculated from Bohr' s theory. We can thus calculate the energy difference betwee n two orbits. This allowed a connection t o be made between Bohr's invisible, somewhat peculiar, and definitely hypothetical atom and the real world. Suppose, for some reason, that a n electro n found itsel f in on e o f the highe r orbits. Its natural tendency, due to the attraction of the nucleus, would be to fall int o a lower orbit. In doing so it would lose energy, like Joule's weight falling and giving up energy to the water. Where would this energy appear? Bohr turne d t o Einstein' s concep t o f photons. Th e energ y would appea r a s a photon, a "particle" o f radiation, having an energy equal to that which the electron had lost. But Bohr could calculate the energy lost by the electron in "falling" from a higher to a lower orbit. It is simply equa l to the energ y difference betwee n the orbits. Now the energ y of the photo n i s connected to its frequency by Planck's relationship, E = hv. Boh r worked out the energie s of the differen t orbit s and deduce d the energies, and therefore the frequencies, o f the photons that would be emitted if the electron jumped between any two of them. He was predicting the frequencies of the light given off by a heated hydrogen atom (Figure 28.Ib).

Figure 28.1b. Tw o of the notes that the hydrogen atom sings when an electron drops from one orbit to another.

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Years before al l this, severa l diligen t researchers had observe d the light emitte d by the hydroge n ato m when i t was a t high temperatures . Man y frequencie s wer e observed, bu t ther e seeme d t o be n o patter n connectin g them. An d the n histor y amused herself. A math teacher in a Swiss girl's school, Jakob Balmer (1825-1898), who wa s obsesse d wit h numbers , wa s give n th e firs t fou r frequencie s (o r wavelengths) in the hydrogen spectrum, in response to his claim that he could find a formula to fit any fou r numbers. In 1885 he succeeded in fitting the wavelengths, A, , to a simple expression tha t was later rewritten i n the following form: where, if n is put equal to 3, 4, 5, and 6 the observed four wavelengths are obtained. In the expression, R is a constant that had to be given the value 109,702 cm"1 to make things fit. Thus if you put n = 3, the value obtained for A, is 6.56 x 10" 5 cm, and this is one of the frequencie s emitte d by heated hydrogen atoms. No one had th e faintest clue how to give a physical rationale for this infuriatingly simpl e expression . The expression that Boh r obtained theoretically, fo r his mode l of the hydrogen atom, was: which include s Balmer' s expression a s a particular case (whe n ^ = 2) and allow s the calculatio n o f lines tha t Balmer' s formul a di d no t cover. 6 Boh r calculate d R from his theory . He found a value of 109,677.656 cm"1. Whether one does or does not understand th e meaning of quantized energ y and angular momentum , whether o r not on e believes in photons , i t cannot b e denie d that Bohr's achievement was remarkable. There must surely be some truth in a theory that can accurately predict the wavelengths of scores of lines in the spectrum of an atom. This was no trivial feat . Bohr's Atom

The significance of Bohr's achievement is twofold: 1. Althoug h his theory was soon replaced by a more basic approach, he had show n that the introductio n o f quantization, coupled with th e courag e to ignore some of the hallowe d tenet s o f classical physics, opene d u p th e intimat e structur e of matter t o quantitativ e explanatio n an d prediction . Toda y th e consequence s of Bohr's breakthrough are everywhere, from solid-stat e electronic s to fiber-optics , from basi c chemistr y an d molecula r biolog y t o th e pharmaceutica l industry , from th e understandin g o f superconductivity to th e behavio r o f white dwarf s and the forces between elementary particles. 2. Bohr' s theory, by its success, showed that in attempting to explain the behavior of matter, the principl e o f quantization, a nonclassical idea , probably had t o be extended t o mos t o f the basi c propertie s o f matter, an d no t onl y t o radiation . Planck quantized the vibrational energy of oscillators, Einstein quantized radiation, an d Boh r quantize d th e angula r momentu m o f th e electron ; bu t i t ha s turned out, for example, that we also have to quantize translational energies , the kinetic energy of motion. Does this mean that a molecule in a box is allowed t o 6

For example, putting n^ = 3 and n2 = 4, a wavelength o f 1.876 x 10" 4 cm is obtained. Thi s line appears in the observed spectru m o f hydrogen atoms.

The Inexplicable Quantum |J^Z

travel only at certain discrete speeds? In principle yes, but the quanta of translational energy (the amounts by which you can increase or decrease an object's kinetic energy) are generally too small to be detectable. Let's temper our enthusiasm, and clear the ground a little: • Th e Bohr model is part of what physicists came to call the "old quantum theory." It gave the right answers to a small number of questions, but it was based on a number of seriously false assumptions . « Th e pictur e o f electron s revolving , somewhat lik e planets , i n well-define d paths is false. Thi s is not what they do at all, although they do have well-defined energies . The occasional paralle l draw n between the sola r system an d atomic structure is ill founded. The laws controlling planetary movement and the behavior of electrons are utterly different . In the years that followed the Bohr atom, more surprises were to come; matter was far curiouse r than anyon e had imagined . In the next two chapters we take a walk through the quantu m Disneyland, but her e we jum p forwar d fro m 191 3 t o today and see what practical doors quantum mechanics has opened. The Elements Revealed

The chemical properties of matter depend overwhelmingly on the properties of the electron. Quantum mechanics reveal s what electrons are doing inside atoms , metals, proteins, what hav e you. It is a straightforward mathematical exercis e to us e quantum mechanic s t o calculate the properties of the hydrogen atom—it has onl y one electron . Th e calculatio n o f the propertie s of atoms othe r tha n hydroge n i s more difficult, but suc h calculations are getting better and better and have for long been sufficien t t o allo w a very good understanding o f the wa y tha t atom s o f th e chemical elements behave. Take one example, the sodium atom. The atomic number of sodium is eleven, which means that the neutral atom has eleven proton s an d therefor e eleve n electrons . Quantu m mechanica l calculatio n shows that two of these must be quite near the nucleus o n the average. It takes a lot of (calculated) energy to pull them out of the atom. Another eight electrons are, on the average, farther from the nucleus and take less energy to dislodge. Finally, there is one electron that, again on the average , is clearly farthest from th e nucleu s ari d easiest to tak e from th e atom . We can sa y that th e electron s ar e grouped in thre e "shells," tw o in the lowest shell, eigh t in the next, and on e in the "highest " shell . We begin to understand why it is that the sodiu m atom has a tendency to lose one electron (see Chapter 13) and almost always appears as the sodium ion, having one positive charge. If you g o to the nex t ato m in th e periodi c table, magnesium, you will find that it has an atomic number of twelve and therefore has twelve electrons. These are arranged with two in the lowest shell and eight in the next, as with sodium, but there ar e two electrons in the highest shell , not one, as in sodium . When magnesium metal reacts, it almost alway s gives up two electrons, obviously those in th e highes t shell , whic h ar e th e farthes t from th e nucleus . Th e periodi c tabl e suddenly starts to make sense. Quantum mechanics has provided an explanation of the general features o f the electronic structure of all the atoms known to man. This is on e o f the pillar s supportin g moder n chemistr y an d biochemistry , an d man y areas of physics.

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When a molecule forms , ther e i s a rearrangement o f the electron s o f the con stituent atom s (see Figurel3.4a). By using the equations of quantum mechanics, we can calculate, to greater or lesser degrees of reliability, the energie s and the spatia l distribution of all the electrons, giving us a picture of the size and shape of the molecule. Thi s knowledg e allow s a rational explanatio n o f most o f the propertie s of molecules, includin g thei r willingnes s t o react with othe r molecules, an d th e expected results o f such reactions. The electronic structur e o f metals and semimetal s is of cardinal importanc e i n explaining thei r propertie s an d designing new materials and devices. The study of the quantized electroni c energ y levels in metals, an d particularly in semiconduc tors, i s a centra l par t o f the theor y o f these material s and th e explanatio n o f th e properties of transistors, semiconductor lasers, and the other sophisticated an d fascinating paraphernalia o f modern micro- and optoelectronics. There is a whole discipline called quantum electronics . The Music of Matter The ligh t given of f or absorbed by atom s and molecule s i s a mixture o f many frequencies, a mixture that is characteristic o f each atom or molecule (see Chapter 15). Bohr had show n why . Fo r atoms it is the fallin g o f electrons fro m on e orbi t to another tha t i s th e origi n o f emitted light . Similarly , whe n a n ato m absorb s ligh t i t does so because, when a photon is swallowed, an electron jumps from a lower to a higher orbit. The energy of an electron depends on which orbit it is in, and the light that it gives off, o r absorbs, when it jumps from one orbit to another has a frequency that depend s o n the differenc e i n energie s o f the tw o orbits . Now differen t atom s will o f course have differen t set s o f energies fo r their orbits , each ato m being distinctive in this respect. Consequently, each ato m will be characterized by a differ ent set of frequencies for the ligh t that it will absorb or emit, and this is in fact also true of molecules. Each atom, and each molecule, sings a different tune. Which is why, when w e examine th e light fro m th e stars, we hear familia r melodies; we can recognize the chemical elements, even though we may never even reach the nearest star. Atoms or molecules fo r which th e energ y difference betwee n certai n orbit s is of th e appropriat e magnitud e ca n emi t o r absor b visible ligh t whe n a n electro n moves from one of those orbits to another. This is the origin of color, and it is possible to calculate whether a molecule, or atom, will be colored. The Greenhouse Effect

The Earth appears to be warming up. The blame has been laid at the door of certain gases, both manufactured and natural. The basic mechanism o f the greenhouse effect is simply explained by quantum mechanics . In discussing the greenhouse effect, i t is necessary to take into account the vibrations an d rotations of molecules. A s you would expect , a molecule canno t vibrat e or rotate at any ol d frequency . Just as for a simple oscillator , like a swing or a pendulum, ther e ar e a set o f allowed vibrationa l frequencie s for each differen t mole cule and, as in the cas e of the swing , if you want to make a molecule vibrate mor e vigorously (with a greater amplitude), you have to give it a packet of energy corresponding exactl y to the differenc e i n energy of two given vibrations. Th e same applies t o rotations. A molecule canno t rotat e in an y way that i t chooses . It has cer-

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tain allowed rotational energies; the carousel cannot rotate at any speed that it feels like. I f it i s rotating at on e spee d an d jump s to anothe r highe r speed , it mus t h e given th e energ y differenc e betwee n th e tw o "rotationa l levels. " Bu t yo u kno w that—from pushin g playgroun d merry-go-rounds. Thus whe n radiatio n induce s a change i n eithe r th e vibratio n o r rotation of a molecule, the proces s involves th e taking in or giving out of photons at well-defined energies , which means well-de fined frequencies. 7 Molecules that have absorbed suitable photons will vibrate and rotate faster, an d we ca n say that they are hotter. Indeed, if we put a thermometer into a sample of a gas that i s absorbing light, we would fin d tha t the temperatur e was rising, which i s not very surprising since the molecules are absorbing energy. This is the basis of the greenhouse effect, a s we will now see. The frequency distributio n o f the Sun' s radiation, which i s a typical blackbody curve, is shown in Figure 28.2. The Earth's atmosphere is effectively transparen t to the Sun's rays, which means there are no molecules in the atmosphere that strongly absorb ligh t a t the frequencie s emitted b y the Sun . All the visibl e ligh t come s through, and so do almost all the other frequencies. This radiation warms the Earth, but it does not directly warm the atmosphere because it is not absorbed. Now since the temperature of the Earth over the centuries has not risen continuously (until recently), most of the energ y we get from th e Su n must be sent back into space. The Earth does give off radiation, but certainly not visible light, otherwise we shoul d have full daylight in the night. The distribution of frequencies given off by the Earth is also shown in Figure 28.2. The curve resembles that for a blackbody at about 0°C. The frequencies sent out are generally much lower than those in sunlight and are concentrated in the IR range. This is because the Earth is a much cooler body than the Sun. When this radiation travels upward through th e atmosphere, some of it is absorbed by molecules in the air because some of the frequencies now match the vibrational and rotational absorption frequencies of a number of gases—look at Figure 28.2. The gases involved are primarily carbon dioxide, methane, water vapor, and

Figure 28.2 Th e radiation of the Su n is hardly absorbed by the gase s in Earth's atmosphere. However , the radiatio n emitted by Earth is absorbed by a number o f molecules, at the wavelength s indicated.

'Molecules can also give out or absorb radiation when their electrons jump from on e molecular orbit to another, but this a process that is not relevant to our discussion of the greenhouse effect .

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CFCs, the last being the (now unpopular) gases in some spray canisters. The gas molecules that have absorbed energy from th e Earth's radiation will vibrate or rotate faster; they are hotter. The atmosphere warms up. That is the greenhouse effect . Th e finger o f blame is usually directed at carbon dioxide, but there is a growing danger from methane . Thi s molecule is produced in a number o f ways, including coa l mining—whic h liberate s undergroun d pocket s o f gas—garbag e dumps, ric e paddies , an d th e thoroughl y unsocia l persona l habit s o f cows . A methane molecule can trap about thirty times as much energy as a carbon dioxide molecule. The concentration of both of these molecules in the atmosphere has been growing at a rate of about 1% a year for some time. Some scientists believe that the greenhouse effect ha s been exaggerated, that atmospheric warming is small enough to be a temporary glitch within the bounds of normal statistical variation. On this issue, HMS should liste n to both sides but err on the side of pessimism. Quantum mechanics ha s been applied t o the nature o f the mos t basic particles from whic h matte r i s constructed. It has sprea d into biology, into electroni c technology, int o cosmology , into dru g design , and i s eve n being brought into discus sions on the operation of the brain. If the reader stops here, he will have come away with the impression tha t we have acquired a highly useful mean s o f systematizing the behavior of matter and a reliable predictive technique. Quantizatio n is perhaps a little strange, but you've probably heard taller stories. This impression is correct, but it doesn't tell the whole story. Quantum mechanics has force d u s t o reconsider ou r whole picture o f the universe—a t the deepes t level.

29 New Ways of Thinking I have therefore found it necessary to den y knowledge in order to mak e room for faith. —Immanuel Kant, Critique of Pure Reason

The Magic Formula The way that Bohr treated the hydrogen atom was a mixture of concepts taken fro m classical physics , mixed with Planck's idea o f quantization an d Einstein's concept of photons . Th e theor y di d no t survive ; a fa r more seriou s brea k wit h classica l physics was soon to come. Before we start, the reader should glance at the above quotation fro m Kant . The bases of quantum mechanics are not observable or derivable. At the present stage of scientific history, all that we can say is that most scientists accep t them—on faith . The most important words in the language of those who use quantum mechanics in order to deal with matter is wave function. It is a definite faux pas to ask your hostess where an electron is . You ask what its wave function s are. Every system ha s a set o f wave functions , fro m th e smalles t particle, whatever that turns out to be, to the whole universe. You do too. A wave function is a mathematical expression ; its form depends on what system you are concentrating on . The set of wave functions for an atom, a molecule, or any physical system contains everything that can be known about the system, by which I mean that i f you subject the wave functions to the right mathematical manipula tions you can find out the value of any physical property: the allowed energies of the body, its magnetic properties, its electrical properties, its color, and so on. It is wave functions that give a size and shape to our molecules-in-a-box. If this is so, it sounds as if the mystery of matter has been solved. In principle this is true, just as for macroscopic bodies traveling at speeds much less than that of light, Newton's laws, also in principle, provid e the means for predicting motion. In both cases the complexity of the system may result in practical limitations t o our predictive power. Finding the wave functions for many systems i s a computational tas k that is beyond the capabilities o f our largest computers, so we usually calculate approximate wave functions of large systems because that is the best that we can do. In fact, th e wave functions for individual atom s and molecules containing up to twenty atoms or so can be found to a very high degree of accuracy.1 The wave functions for larger systems have to be crudely approximated , but i t is surprising ho w much information can be obtained by cunning. Thu s i t is far beyond us to obtain the wave func tions for a living cell, but in dealing, say, with the molecular mechanism of human 1

Even then we have to be content with wave functions that are in numerical form—that is, they are composed of tables of numbers, or combinations of simple functions, rather than compact expressions. Our inability to find analytical solutions to problems involving the motion of more than two bodies still hounds us in the corridors of quantum theory.

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vision, it is helpful t o know details of the structure and reaction to light of the visual pigments i n the retina, and w e know enough about the wave function s o f these molecules to understand why they do what they do. At thi s stag e th e reade r ma y b e asking , "Yes , wonderful—but wha t ar e wav e functions?" Tha t questio n wil l b e sidesteppe d t o mak e wa y fo r another one : "I n practice, where do wave functions come from? " Answer: To construct wave functions we have to know: • whic h physica l particles constitute our system, • wha t their basic properties are, and • wha t forces operate between them. Thus to find the wave function for the hydrogen atom, we need to take into account the fac t tha t ther e i s on e proto n an d on e electron , eac h wit h it s ow n mas s an d charge. We also need to know that Coulomb's law (see Chapter 8) operates between the tw o particles. At this point, i f we were working in the eighteent h century , we would procee d t o use Newton' s laws o f motion to calculate th e path s o f the elec tron. We must abando n this wa y of thinking. Instead , we put th e fact s int o a n entirely ne w universa l equation , th e Schrodinger wave equation, afte r th e poetry writing Austria n physicis t Erwi n Schrodinge r (1887—1961). 2 Thi s equation , published i n 1926, generates wave functions . Schrodinger constructe d hi s equatio n intuitively . Th e equation , whic h i n it s form i s very closely related to Maxwell's equations, can be regarded as a quantum mechanical equivalen t of Newton's laws of motion, but its output is very different . The first proble m that Schrodinge r fe d into his equatio n was that o f the hydrogen atom. He obtained exactly the energies that Bohr had; in other words, he could duplicate the observed frequencies of the hydrogen spectrum. But his equation was general; it applied to any system under, over, or including the Sun, while Boh r had constructed a theory for one system—an atom with one electron. What Schrodinger said was , tell m e what elementar y particle s ther e ar e in you r system , tell m e th e forces acting on them, I'll put them in my equation and, in principle, I will give you a set of mathematical expression s (wav e functions) tha t will describ e your system completely. If I can't, it's because my calculator is too small. Although the energie s derived fo r the hydroge n atom by Bohr and Schrodinge r wer e identical , th e elec tronic "paths" obtained by Schrodinger were entirely different . The solutions to the Schrodinger equation, for an y system, always come as a set of wave functions, each of which is linked to an energy.

Each wave function can be used to give a picture of the whereabouts of the electro n when i t has one of the allowed energies. Thus for the hydrogen atom we get a series of "paths," eac h of which has a definite energy. The wave functions thu s appear to be the equivalen t o f Bohr's orbits, and s o far there doe s no t appea r t o b e suc h a startlin g contras t betwee n th e classica l an d quantum world; all that we have been asked to believe is that the energy of a system is quantized, it cannot assume an y value that it chooses. But there are basic differ 2 Although not Jewish, Schrddinge r moved to England when the Nazis started dismissing Jews and later spent many happy years in Ireland, where he was given grea t support hy Prime Minister d e Valera.

New Way s of Thinkin g |

ences between the way that quantum mechanic s claim s that electron s behave and the paths of the planets or the nice circular orbits of Bohr's atom. It is here that we begin to feel that we are drifting far away from th e classical view of the cosmos. The wave function for an electron differs fundamentall y from the classical equations that give the path of a stone. For the ston e we have expressions that link th e time with the exac t position of the stone . If we put a value of the time into the expression, we can calculate th e position an d th e velocity of the ston e at that time, and we can experimentally check our conclusions. The wave function doesn't give us a path for the electron, and we cannot predict with certainty that an electron in an atom will be at any one place in particular. We can calculate the probabilities of finding a n electro n at differen t point s i n space, but w e can sa y nothing about the electron's path between those points. The electron is not a train; it may leave one place and turn up at another, but there is no point in looking for the railroad track. The smile of the Cheshire cat may appear up on e tree, fade away , and then appear on the roof, but don't ask where it was in the meantime. So what does it mean when I wrote earlier that the hydrogen wave functions give the "whereabouts" or "paths" of the electron in the hydrogen atom? Pick one corner of the room that you are in, where three walls meet at the bottom of the room . This i s to be your zero point, to which al l measurements of position are referred. The three edges of the room sprouting from this point will be labeled x, y, and z; the vertical edge is labeled z. Now any point in the room can be labeled by thre e numbers , the value s o f x, y, an d z correspondin g to tha t point . Fo r instance, one possibl e position fo r the ti p o f your nose might be define d by x = = 2.5, y - 4 and z = 1.6 (we are using meters, and I assume that you are tall enough to have your nose at 1. 6 meters fro m th e floor) . No w take a simple mathematica l expression—a function—i n onl y two variables: xy, tha t i s x time s y. Plo t it , within th e confines o f the room. This we do by finding out the value of the function at a large number of points i n the room (Figure 29.la). All of the points will be on the floor , since z does not appear in our function. A complete map of these numbers gives the value of the functio n at all possible points o n the floor , whic h i s not particularly useful. The wav e function s fo r th e hydroge n ato m ar e mathematica l expression s i n three variables, which we can choose t o be x, y, an d z, althoug h ther e ar e other choices.3 In a n atomic o r molecular system , any three values give n to these vari-

Figure 29.1a. Value s of the function xy for a few point s in the x- y plane. 3

I have ignored a part of the wave function that deals with the so-called spin of the electron. Thi s will not concern us.

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Figure 29.1b. Th e whereabouts of an electron in an average hydrogen atom. The imaginary sphere, which is centered on the nucleus , includes the place s that account for about 99% of the probability of finding the electron. The graph shows the probability of finding the electron in a thin spherical shell centered on, and at an arbitrary distance from, the nucleus.

ables pick out a place in the ato m or molecule, just as any point on the floor of our room corresponds to definite values for x and y. Given a certain wave function, we can choose many trios of numbers an d wor k out the value of the wav e function at many points in space. In other words, we can assign a number to any point. We use one of the wave functions that Schrodinger found for the hydrogen atom. A hugely simplified impressio n o f the resultin g ma p i s show n i n Figur e 29.Ib , an d i s described more fully in the caption. We call such maps orbitals. The map is the quantum mechanical analogue of one of Bohr's orbits, but it is very different i n nature. Nothing Is Certain Max Born (1882-1970), another refugee fro m Hitler' s Germany, 4 suggested how t o interpret wave functions. Born said: Choose a very small volume in space, find the value of the wave function at a point i n that volume , square it, 5 and th e resultan t number i s proportiona l to th e probability o f the electro n being i n tha t smal l volume.6 If we were inside th e spherical orbita l in Figure 29.Ib. we would experienc e a clou d th e densit y o f which woul d b e proportiona l t o findin g th e electro n a t a given point. Suc h clouds are called atomic orbitals—not atomic orbits. No path is detectable in an orbital. Another wa y o f presenting th e probabilit y o f finding the electron in the spherical orbita l is shown i n Figure 29.1b. What Born was saying was that we can only talk in terms of probabilities of finding the electron at a certain place, and that those probabilities ar e contained in the wave function . Schrodinger neve r accepte d thi s interpretation . Lik e Einstein, h e refused t o believe that we can describe reality only in terms of probabilities. Bern's interpretation say s that you cannot describe the flight of an electron in an atom. The electron might be at a certain point an d i t might not. If the value o f the 4

The two great theories of modern physics, relativity and quantum mechanics, are largely the product of German-speaking scientists. In many of their biographies you will find the phrase "lef t Germany (or Austria) in 1933." 5 If it is a complex number, then calculate its magnitude. 6 The exact probability is equal to the magnitude of the wave function times the volume of the box. If you always choose the box to have the same volume, then the magnitude of the wave function is proportional to the probability of finding the electron in any given box.

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Figure 29.2. Som e other possibilities for the whereabouts o f an electron in the hydrogen atom . As in the previou s figure, the imaginar y surfaces enclose a "probability cloud." Each of the three orbitals is oriented at 90" to the other two .

wave functio n i n a tiny box around tha t poin t is squared an d th e answe r i s 0.18 , and at another point it is 0.09, then there is twice the chance of finding the electron at the first point. But there is absolutely no guarantee that it is there. It is not like a planet fo r which, if we know its position at a certain time, we can predict its exact position at a later time. The Schrodinge r equatio n automaticall y provide s u s wit h a n energ y fo r eac h wave function. The normal state of the hydrogen atom, the state with the lowest allowable energy , is that i n which a n electron is somewhere in the orbital i n Figure 29.Ib. We can say no more about its whereabouts. Thus normally, a hydrogen atom is best visualized a s a spherical clou d representin g the blurred imag e of the elec tron as it moves unpredictably abou t the tiny nucleus . As in the Bohr atom, the electron can be induced t o jump to other orbitals, having higher energies . Thes e orbital s ar e based o n differen t wav e functions , just as Bohr's various orbits described different trajectorie s i n the nuclear sky. A few of the higher orbital s o f the hydroge n atom , based o n th e solutio n o f the Schrodinge r equation, are shown i n Figur e 29.2 . Note that th e three hourglass-shape d orbital s have identical shapes , differing onl y in orientation. This is a hint of the role of symmetry i n shaping nature, a role that wa s fully reveale d only in the mid-twentieth century. Once we have a set of wave functions for a system, we can in principle manipu late i t mathematically t o deriv e not onl y th e differen t possibl e physica l distribu tions of the electrons but also the values of any physical property of the system that we want. Th e reliability o f our results depend s o n how accuratel y we have calculated th e wav e function , jus t as , i n th e worl d o f classical physics , a predictio n about the positio n o f a comet depends o n how accuratel y we have calculate d it s path. To summarize the quantum approac h to the structure of matter: • I n the realm of atomic and molecular quantum mechanics, the most commonly used equation is the Schrodinger wave equation. It is the quantum replacement for the classical laws of motion. • T o solve th e equatio n fo r a given syste m require s a prio r knowledg e o f th e types of particles that constitute th e system , their mas s and charge , and th e forces actin g between them. This i s no differen t from the knowledge needed

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to treat similar problems for macroscopic bodies, using classical laws . • Th e solution to the Schrodinger equatio n gives the allowed, discrete energies of the system. With each energy come one or more wave functions . • Onl y certain spatia l distribution s ar e allowed fo r electrons i n a system, an d those distributions ar e derived from the squares of the wave functions . • Ther e is no mention of a path for the electron. We are not told how i t moves. • W e ca n onl y expec t probabilitie s whe n w e as k fo r th e whereabout s o f a n electron. It i s particularly in th e las t two point s that the brea k with classica l physic s i s so striking, and has given rise to much speculation about the breakdown of the deter ministic worl d picture . Werner Heisenberg sai d that we should no t even attempt t o create a visual pic ture of the atom. Influenced by the positivistic philosopher-physicis t Mach , he believed tha t al l w e ca n kno w ar e measurables , suc h a s th e frequenc y o f spectra l lines. I n 192 5 he produced a formalism based o n measurables only . His methods, which wer e slightl y prio r to , an d apparentl y differe d radicall y from , thos e o f Schrodinger, gav e the sam e results. It was a remarkable intellectual feat , based o n an area of mathematics calle d matrix theory. Later the two approaches were show n to be completely equivalent, merely differing i n their mathematical structure . Quantum theory has revolutionized our understanding o f the interaction of matter with radiation. We can use a knowledge of the energ y levels o f atoms o r molecules to understand the absorption and emission o f radiation. W e can design lasers, light sources producing synchronized photons. Using quantum mechanics, the initial step s i n photosynthesi s an d i n visio n hav e bee n clarified . W e know exactl y why certai n substance s ar e colored and how t o design colored molecules. W e understand how radiation can sometimes change the shape of a molecule or even rupture its bonds. Quantum theor y is not earthbound . Thus the concept o f energy levels has been used, fo r example , t o giv e a n explanatio n o f the behavio r o f the star s know n a s white dwarfs an d of the nuclear processes in the Sun that give us energy. Since relativity is a universally applicable theory, it too should be taken into account in any theory of the behavior of matter, but it does not make an appearance in Schrodinger's equation . Thi s defec t wa s firs t remedie d i n 192 8 b y Pau l Adrie n Maurice Dirac (1902—1984), the English son of a Swiss father. In conformation with our approach, we will not write down Dirac's equation for an electron, but we cannot ignore one of its consequences. The solutio n of Schrodinger's equatio n gives a series of energies to go with the wave functions. Th e solution o f Dirac's equation gives pairs of energies, one positive, one negative. A lesser scientist tha n Dirac may well have been tempted to ignore, as meaningless, the negative energies that came out of his equation, but Dirac had a highly origina l mind, and the consequence that came out of his musings was that there shoul d exis t a particle, with the mass o f the electron but with a positive charge. The positro n wa s discovere d by Carl Anderson i n 1932 . Dirac shared th e 1933 Nobe l Prize wit h Schrodinger . His equatio n als o correctl y predict s tha t th e electron, and also the positron, is magnetic—that it has "spin," a property that we mentioned i n Chapter 8. The positron was the first antiparticle t o be discovered, but Dirac predicted that

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every particle that is charged has an antiparticle, with the same mass but opposite charge. The antiproton was discovered in 1955 , but the neutron, being electrically neutral, ha s n o antiparticle . W e can classif y al l thes e antiparticle s as antimatter. The justification for the label antimatter i s that, for example, a meeting between an electron an d a positro n result s i n mutua l annihilation , th e destructio n o f thei r charge an d mass , and th e formatio n of two photons . Thi s phenomeno n ha s been the basis of the fear that there might be a universe, out there somewhere, composed completely o f antimatter. I f there is , we ca n onl y pra y that ne'e r th e twai n shal l meet. Science never fossilizes, at least not in this century. Bohr's atom was soon overtaken by deeper theories; the interpretation of Dirac's ideas has been modified. And the quantum theory itself, the most fascinating theoretical framework that man has yet devised, remains a minefield of paradoxes. It is to those paradoxes that you may wish to turn next, but before we do there is one fact that deserves a short mention . The Sameness of Matter No two star s are exactly the same . No two system s o f a planet an d it s moons ar e identical. Bu t all electrons are the same . All protons ar e the same , as are all neu trons an d al l the othe r known subatomi c particles. Thus , as far as we know, every electron has exactl y the sam e mass, the sam e charge, arid the sam e magnetic moment. "The y al l loo k the sam e to me." We don't know why matte r come s in th e form o f absolutely identical particles; it is one of the great mysteries.

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30 The Land of Parado x We live in her midst and know her not. She is incessantly speaking to us , but betrays not he r secret. —Goethe

This chapte r i s an attempt to indicate th e enchantin g strangenes s of quantum mechanics. We concentrate on ideas , not mathematics . We have Richar d Feynman' s assurance that quantu m mechanics i s not the mos t understandable o f subjects, an opinion with which th e reader may well concur by the time he is halfway through the chapter. 1 Quantum theor y i s most concisel y expresse d i n th e languag e of mathematics, but since mathematics i s one of the more resistible temptations in life, I have rejected the elegan t formalism and contente d mysel f with a tiny selection o f straightforward equations. I am bolstered by Leo Szilard's well-known remark that elegance is for tailors. Einstein, to the end of his life , regarded the quantum theory as being fundamentally defective. A number of modern physicists concur. One can sympathize: quan tum mechanics ha s spawne d som e of the mos t peculiar concept s that scienc e ha s ever produced. If yo u too k quantu m mechanic s a t college , you hav e probabl y becom e blas e about some aspects of the theory that at one time were guaranteed eyebrow raisers. Maybe energy does come in little packets; so what's s o strange about that? Shouldn't w e accep t nature fo r what i t is ? After all , the discretenes s o f energy may be a strange phenomenon, bu t i t is not unbelievable. Th e firs t Europea n to see a giraff e was probably astounded. But the giraffe wa s merely unexpected; it was not incomprehensible. There are some aspects of quantum mechanics that not only defy common experience, they defy reason . Paradox One: Oh! A Life on the Ocea n Wave Prince Loui s d e Broglie (1892-1987) , a n aristocra t wh o use d hi s brain , serve d i n the Frenc h nav y a s a young man, where h e installe d th e firs t radi o o n a Frenc h ship. H e was thus doubl y suite d t o make one of the mos t startling , an d basic , advances in quantum mechanics—the suggestion that matter behaves like waves. To understand D e Broglie's ideas we need to know what momentum is . Momentum i s simpl y th e produc t o f mas s time s velocity . If , lik e th e sprinte r Linfor d Christie, your mass i s about 10 0 kilo an d yo u ar e running a t about 1 1 meters pe r •'Except for the material contained in the sections entitled "Paradox Two: Measurement" and "Paradox Four: Uncertainty," this chapter is not a preliminary to any other material in this book.

The Lan d of Paradox | second, then your momentum i s 100 x 11 = 1100 kilo.meter/sec . Momentum gives an indicatio n o f the impac t a body has whe n i t hits something . A double-decker bus has far more momentum than a bicycle traveling at the same speed. In 192 4 d e Brogli e presente d hi s doctora l thesi s t o th e examiner s o f the Sor bonne. His proposition was that if a particle had a momentum o f p, then it also had a wavelength, X , given by: = h/p

where h is Planck's constant. What he was saying was that any moving body, say a bicycle, has a wavelength. Very strange. The examining committee for de Broglie's doctorate didn't want to make fools of themselves by accepting the thesis if it was sheer rubbish. They sent a copy to Einsteirt, who gave it his stamp of approval. De Broglie was awarded his doctorate, but apparently n o on e but Einstei n too k him seriously . Afte r all , what di d i t mean to say that moving matter ha d a wavelength? Hav e you go t a wavelength whe n yo u walk along the street? Let's put i n some numbers. Linfor d Christie' s wavelength as he crossed the lin e to wi n th e 199 2 Olympi c 10 0 meters wa s give n b y A , = /i/llO O meters , which i s roughly 6 x 10" 37 meters. This is about 1 million trillion time s smaller than the radius o f the proton . It is a fairly remot e possibility tha t wave s o f this vanishingl y small wavelength will result in observable everyday phenomena. And , in any case, how do we interpret th e finding? In what sens e was Christie a wave? Forward. Take a very small body, an electron (mass = 9.1 x 10" 31kg), and accelerate i t unti l i t i s moving at a speed o f 13 million kilometer s a n hour. Thi s jus t requires a suitable voltage difference i n an evacuated container. 2 If you put thes e figures into de Broglie's equation, you find that the wavelength of such an electron is about 2 x 10" 10 meters. This is about the kind o f distance that is found between adjacent nuclei in many crystals. Enter Clinton Davisson (1881-1958) and L . H. Germer. They directed a beam of electrons onto a crystal and found that the beam behaved as though it was a ray of light striking a regularly patterned surface. Th e electron beam bounced of f the crystal in a variety of very well define d directions; in other words, it was diffracted. A bell rang . Davisso n was awar e o f the the n ne w fiel d o f X-ray crystallography . I n Chapter 1 5 you sa w that whe n X-rays , with a wavelength similar t o the distance s between nuclei i n crystals , are passed int o those crystals , they ar e diffracted . Bu t diffraction i s a wave phenomenon. Ho w could electrons , whic h ar e particles, be diffracted? Davisson realized that his electro n bea m was being diffracte d jus t as though i t were a n electromagneti c wav e havin g exactl y th e wavelengt h predicte d b y d e Broglie. The moving electrons behaved lik e a wave! He published hi s work in January 1927 . De Broglie's matter waves were real. }. }. Thomson's son , G. P. Thomson, carried ou t simila r experiments , whic h als o showe d th e wav e nature o f the electron, and he and Davisson were awarded the Nobel Prize for physics in 193 7. 3 Incidentally, you can duplicate Young's two-slit experiment (see Chapter 15) with elec2

The electrons in your TV cathode tube are moving at about 70 million km/hr. It is standard practice in freshman physics courses to mention that J. J. Thomson proved the electron to be a particle and his son showed i t to be a wave. Another Nobel Prize-winning father and son were Neils Bohr, who won his prize for his work on the (electronic ) structure of atoms,

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trons, and get interference, just as for conventional waves. It was de Broglie's thesis that set Erwin Schrodinger thinking about an equation to describ e matter. His equatio n ha s similaritie s t o the well-know n equation s fo r describing the movement of waves. The atmosphere in the scientific world of the 1920 s was a mixture of intense excitement an d complet e bewilderment. Einstei n had show n tha t th e photoelectri c effect wa s explicabl e i f ligh t wave s ar e particles ; Davisso n an d Thomso n ha d shown that a beam of electrons could behave like a light wave , as de Broglie ha d claimed. My advice to HMS is to adopt the following attitude: 1. Accept the experiments . The y cannot be questioned. The y have been repeate d for decade s in lab after lab . 2. I f someone sidles up to you in Jimmy's bar and asks you whether matter is made of waves or particles, tel l her o r him tha t i n som e experiments i t behaves lik e particles and in some it behaves like waves. 3. I f the bartender in Harry's bar asks you if light is composed of wave s or photons, tell him that it is made of photons that in their behavior often mimi c the behavior of waves. In both bars you will probably be refused furthe r alcohol . At present i t is accepted that both matter and radiation demonstrat e what has sometimes been termed duality; the y hav e propertie s associate d wit h bot h wave s an d particles . I hav e bee n careful i n phrasin g th e previou s sentence . I have not sai d that matte r consists of particles, or radiation of waves. If de Broglie's relationship is correct, it should be possible to detect wavelike behavior in other particles besides the electron. Since, according to the relationship, large bodies, like Olympic sprinters, have undetectably small wavelengths, we can only expect to easily detect waves for rather small particles. This has been done for protons, neutrons, the helium atom, and the hydrogen molecule, H2. These extraordinary findings appear to completely blur the distinction betwee n matter and radiation, between particles and waves. It usually does no harm to think of electrons, or protons, as if they are particles. Experimental evidence for the "wavelik e nature" of electrons can be taken to indicate that the movement of electrons is determined by laws that have a wavelike nature. A cork bobbing in the sea is not a wave, but it s motion shows wavelike characteristics. Th e analog y i s extremel y dangerous : i t suggest s tha t th e electro n i s "really" a particle . W e don't kno w that . I f the thumb-screw s wer e applied , mos t physicists would admit that they have no proof that the elementary particles are either particles or waves. Paradox Two: Measurement

I am going to give you a faulty analogy . Toss a coin i n th e air , so that i t revolves. This is your "system." You are now going to make an "observation" o n the coin, on the system. You are going to see whether it is "heads" or "tails." To do this you have a measuring apparatus—your hands, assiste d by your eyes. As the coi n is in fligh t and Aage Bohr, who won his in 1975 for theories of the structure of the nucleus. A unique mother and daughter pair were Madame Curie, who won the Nobel Prize in chemistry in 1911, and Irene Joliot-Curie, who won the prize in 1935.

The Land of Paradox | you trap it, so that it lies horizontally o n the back of your lower hand. Yo u look at the coi n an d not e that i t is tails. You have mad e a "measurement" o n the system . There ar e onl y tw o allowe d result s fo r a measurement—head s o r tails . "Heads " means a stat e i n whic h th e coi n i s horizontal wit h hea d upward . Whil e i t i s i n flight, th e coi n i s in general neithe r heads no r tails , since i t is rarely horizontal. If you want to define what its "state" is while it is turning, you can say that it is a continually changin g mixture of heads and tails. Thus, you can imagine the state of the coin (the system) before measurement a s being a mixture of the two states that you are able to detect by measurement. For example, when i t is vertical, you could say that it was half heads and half tails. If you "measured" it in that state, by using your apparatus (your hands), you would find a head in about 50% of the measurements . Remember, "heads" mean s that the coin is horizontal when you look at it. Now imagine that you could not see the coin while it was in flight. It is clear that you can say nothing about its state before you make a measurement. At a given time it is a mixture of the two basic states, heads an d tails , but you cannot know wha t mixture. Second , when yo u do take a measurement, you force the coi n into on e of the basic states , destroying its state just before the measurement. Thi s mean s that you are not really measuring the state of the system in the same way that you measure the lengt h o f a piece o f wood. You know that a measurement o f 2 feet mean s that the lengt h not only is 2 feet; it was 2 feet before you measured it. In the world o f small particles, what you measure is the stat e that the syste m is in after interaction with the measuring apparatus. Yo u usually destro y th e stat e that the system was in before the measurement, and in doing so you lose all hope of knowing what its state was. A system, in quantum mechanics , is usually in an unknown state before we take a measurement on it, just as the turning coin is. You can object that there are sinnple ways of knowing the stat e of the coi n at any time—high-spee d photography is the obvious answer. You are right, and yo u have found one of the fault s o f the analogy. In quantum mechanics there is rarely any way of completely characterizing a state before yo u tak e a measurement, an d takin g a measurement destroy s the previou s state, so you won't lear n about it anyway. To clarify this, let us take a famous example, which wil l be of use to us later on. Figure 30.1 will help . In Chapte r 1 5 we spok e o f polarized light , light i n whic h th e vibration s o f the electric field were in one plane. We saw that there were crystals that have a special plane (see Figure 15.5), reminiscent o f a slot, such that light polarized in that plane will pas s throug h th e crysta l whil e ligh t polarize d perpendicula r t o the plan e i s stopped. W e also sa w that ligh t polarize d i n a n intermediate plan e wil l partiall y pass through the crystal. We explained thi s by saying that we can regard such ligh t

Figure 30.1. Th e behavior of polarize d photons on meeting "slits." Photons polarized at 90° to a slit will not pass . Of those oriented at 45° half will pass, and they will emerge polarized in the plane of the slit.

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as being mad e up fro m tw o components , polarize d a t right angle s t o eac h other . Only the component in the appropriate plane passes through the crystal. Thus part of th e ligh t fail s t o penetrate, and th e intensit y o f the emergen t beam is reduced . This explanatio n i s all right for waves, but what abou t photons? Photons are indivisible. We cannot account for the reduced intensity of the light emerging from th e crystal by saying that only a part of each photon goes through. To explain th e observation s i n term s o f photons, w e suppos e tha t som e of th e photons go through and some don't (Figure 30.1). Those that do must emerge polarized in the plane of the crystal, since that is what happens to light that goes through such a crystal. The photons that fai l t o go through must end up polarize d perpen dicular to the crystal plane. The coin must be either heads or tails, no matter how it fell on your hand. The photons that interact with the crystal end up in only one of two conditions. The probability of a given photon going through the crystal is determined by the angle of the plan e of polarization. If the plan e is in the optica l plane of the crysta l the probability is one; every photon of this type goes through. If it is perpendicula r to that plane, the probability is zero (Figure 30.1). What happens when the plane of polarization of the photons is at an arbitrary angle to the polarizatio n plane (th e "slot") in the crystal? In the language of quantum mechanics we must ask this question differently: What is the wave function of the photons? We are not going to write down explicit mathematical expressions ; we don't need to. Let us call a photon polarized in the plane o f the crystal, A, and a photon polarized perpendicular t o that plane, B, and call their respective wave functions, \|/(A), and \|/fB). If the plane of polarization of the light is at 45° to the crysta l plane, we can suppose that the wave function o f the photo n i s a mixture of equal contributions fro m \|/(A ) and i|/(B) , or part heads, part tails. The wave function, *P , of a photon polarized at 45° is given by: Why 1/V 2 ? Why no t 1/2 ? Because Born sai d tha t i f you square the coefficien t o f \|/(A), you get the probability that the photon will be found in state A. The square of l/A/2 is one-half, which i s the probabilit y of finding th e photon i n stat e A after th e measurement. Similarly , the probability of finding the photon in state B is also onehalf. The sum of these probabilities is one, which it must be since the photon has to emerge as either A or B; there are no other choices. Wave functions often appear as combinations o f the above sort, where the square of the coefficient before each component gives the probability of finding the system in tha t state . Thu s fo r a differen t plan e o f polarization, I might deduc e tha t th e wave function fo r the photo n wa s 0.5\|/(A ) + 0.866vj/(B). Th e probability o f finding the emergen t photo n i n th e stat e A is (0.5) 2, which equal s 0.25 , one-quarter. Th e probability tha t th e photo n wil l emerg e i n th e B state i s (0.866) 2, which i s 0.75, three-quarters. Notice that the sum of the probabilities agai n equals unity, which it must do. The photon must either go through or not; there are no other probabilities. Notice again—becaus e i t ha s ver y far-reachin g implications—wha t happen s when a photon strike s th e crysta l (th e measuring apparatus) . Either i t fail s com pletely t o pass o r it passes i n it s entirety . The measuring apparatus forces it into one or the other of the basic components—heads o r tails. I f it come s throug h th e crystal, it will have the pure wave function, \|/(A) . Thus, if the plane of polarization is at 45° to the crysta l plane an d a certain photo n goes through, we can say that i t

The Land of Paradox | has "turned int o a photon polarized in the plane of the crystal." A physicist woul d say that its wave function collapses int o that o f a photon polarize d in the plane of the crystal . The coi n ha s been force d t o be eithe r head s o r tails. Fo r that specifi c photon, the other component of the wave function, the \|/(B) part, vanishes instantaneously. On the othe r hand, i f a photon fail s t o get through, then that must be because it s wav e functio n ha s becom e pur e \|/(B) . It s wav e functio n ha s als o col lapsed. The part containing \(/(A ) has vanished . In th e classica l picture , w e sai d tha t th e intensit y o f 45° polarized ligh t i s reduced by one-half in passing through the crystal, and we accepted intuitively tha t "half th e ligh t get s through." Wha t doe s not happe n i n th e quantu m mechanica l picture is that part of a photon goe s through. All of it does. But only half the pho tons make it. Which photons go through and which don't ? We can never know beforehand. Th e only way is to test them. Those that do , do. Those that don't, don't . But if the photons ar e all identical, what decide s that one photon goes through and another doesn't? We can say nothing about this whatsoever, a statement guaranteed to irritate Einstein, who believed that on e day we would know how to sort out the A and B photons before they pass through the crystal. Our inability to predict which photo n goe s through the crystal is, according to quantum mechanics, not a question of yet-to-be-revealed knowledge. It is not a situation parallelin g ou r pas t ignorance of the caus e o f malaria. That ignoranc e was overcome when i t was discovered tha t malaria was carried by mosquitoes and the responsible microorganis m was identified . Th e effec t wa s known , an d th e caus e was found. Einstein, and a small number of other physicists, held or hold the view that one day we will be able to know which photon will go through and which not, because there ar e undiscovered mosquitoe s i n the atomic world—they are termed "hidden variables"—whic h when uncovere d will provide the means by which we will return to a straightforward cause-and-effect explanatio n of quantum phenomena. This is definitely a minority view among physicists. Nineteenth-century scienc e deal t i n certainties . Th e behavio r o f an y syste m could in principle b e calculated on the basis of deterministic laws. This confidenc e was part of Newton's inheritance. Bu t the times were changing, and, as in the case of entropy, quantum mechanics nearly always speaks not. in certainties but in probabilities. In quantum systems , those on the atomic or molecular scale, a measurement involves a gross interference with the state of the system, revealing only its state after interaction with th e measuring apparatus. We believe that we can know only what we measure. This attitude is heavily dependent o n the great authority of Niels Bohr in th e earl y years o f the quantu m theory . A s fo r th e observe d probabilities tha t emerge fro m experiment , Bohr saw them a s the deepes t knowledge that w e could have. Some regard this as an arid view of reality, but there are no convincing signs at present that quantum theory, and in particular the probabilistic interpretatio n of the wave function, i s going to be replaced in the near future . Bohr an d Einstei n ha d a prolonged an d famou s correspondenc e o n this issue, Einstein periodically constructin g thought experiments tha t refute d Bohr' s probabilistic interpretatio n o f quantu m mechanics , an d Boh r invariabl y refutin g th e refutations. Toda y there is a feeling that, although Einstei n was probably wrong in his attemp t t o brin g complet e determinis m int o quantu m mechanics , th e fina l word on quantum mechanics ha s not been spoken .

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We sa w tha t whe n a photo n wit h a n arbitrar y plan e o f polarizatio n passe s through a suitabl e crystal , the wav e functio n o f the emergin g photon consist s o f one component onl y of the wave function o f the enterin g photon. The "collapse of the wave function" that eliminates on e part of it is a predicted consequenc e o f the measurement process. But the theorists have a problem. We hav e suggeste d tha t th e wav e functio n o f a "quantu m system " collapse s when i t interacts wit h a "measuring device." Now it is a basic axiom of quantum mechanics tha t if a quantum syste m is left undisturbed it s wave function change s with time in a completely deterministic manner. There is no question of probability jumps, or of the wave function collapsing . The coin keeps on turning until it interacts with something, an d whethe r I use quantu m mechanics o r Newton's me chanics it will behave in a completely deterministic manner. Only an observation will brea k thi s deterministi c evolutio n an d introduc e probability . Wit h ou r pho tons we have brought in a measuring device, a crystal "pair o f hands" t o collaps e our wave functions, bu t we have been criminally inconsistent . Th e measuring device is also subject t o the rules of quantum mechanics ; i t should be included i n a larger wave function tha t includes both the device and the system—the photons. If we d o this w e have a larger quantum system—-th e crysta l and th e photons—tha t will evolve deterministically and will not give a definite reading on the measure ment device : a coin cannot stop turning in midair and become heads o r tails. Thi s would mea n tha t th e tota l wav e functio n ha d collapse d an d eliminate d th e par t that corresponded to other possible readings. This, according to the axiom, cannot happen: a quantum system cannot get rid of part of its own wave function; the system has to be observed for its wave function t o collapse. There has to be a measuring device—like my hands—that is not part of the quantum world. The conclusion i s that in measuring a quantum syste m I can never collapse the wave function i f I am part of the system . The only way to get a definite reading o n my measuring device, which is part of the quantum system, is to use another, external, measuring device to collapse the enlarged wave function. This means setting a device to look at the device, which doesn't help, since now, to be consistent, I have to include th e ne w devic e in th e tota l system . Afte r all , why shouldn' t i t be governed by quantum mechanics as well? Where doe s it end? If I believe that quantum mechanics i s universally applica ble; it must appl y to everything, to the whole universe. I n other words, the whol e universe is a spinning coin. How can we ever get measurements i f a quantum system cannot, on its own, collapse its wave function ? Since devices do take measurements when I observe them, then perhaps it needs the presence of a conscious mind, which is presumably not subject to quantum mechanics. The mind i s the "pai r o f hands" that catche s th e coin . Bu t why isn't the mind par t o f the quantu m system ? One way to escap e this parado x is to say that quantum mechanics itsel f is faulty, but the problem i s that when i t has to answe r questions, it does it so well. We are in difficulties, but there is worse to come. The concept of collapsing wave functions ca n have incredible consequences. I use "incredible" i n its literal sense. Paradox Three: The Phantom Pussycat

By 192 4 scienc e ha d bee n shake n t o it s foundations . Bu t there wer e barbarian s

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Figure 30.2. A n electron in a very flat box, according to classica l and quantum mechanics. In either theory the probability of finding the electron at the symmetrically place d points A and B is the same . Quantum mechanics gives us a wave function from which we can calculate th e probability of finding the electron at any given point.

coining who woul d no t leav e one stone standin g upon another . On e of these wa s Erwin Schrodiriger . H e presente d a parado x tha t i s famou s i n th e corridor s an d mousetraps o f scienc e departments : th e parado x o f Schrodinger' s cat , which i s based on the collapse of a wave function. Let us initially tak e a simpler example of collapse so as to concentrate on the essentials . An electro n i s i n a brick-shape d bo x (Figur e 30.2). Th e wall s o f the bo x ar e opaque. Lik e al l physical system s it has a wave function , a mathematical expres sion that we can use, among other things, to estimate the probability that the electron i s a t an y give n plac e i n th e box . Logic tell s u s tha t a n imaginary partitio n placed straigh t acros s the cente r o f the bo x would divid e th e wav e function into two halves that , when squared , would look identical.4 We believe this because intuition an d experimen t tel l u s tha t th e probabilit y o f finding the electro n a t tw o symmetrically related point s ( A and B in Figure 30.2) must be identical . Thi s im plies that th e square d wav e function is similarly symmetrical , because the probabilities are related to the square of the wave function at any point. Mow slip a real, extremely thin, partition across the box. Since we cannot see inside the box, w e canno t kno w in which hal f the electro n is trapped. What is th e wave function of the electron ? Presuming that the electro n cannot be found inside the partition, the wave function must go to zero there. However, whatever the for m of the wave function, its square remains symmetrical about the partition—the wave function continue s to exist, in identical for m (whe n squared), in both halves of the box. Why identical, if the electro n can be only in one half of the box? We might expect the wave function to vanish o n the empt y side o f the box, because the probability o f finding it there i s zero arid this implie s tha t th e squar e of the wav e func tion, and thus the wave function itself, must be zero everywhere in that side of the box. We have forgotten Born. We can make no assumption abou t the whereabout s of the electro n i f we cannot detec t it . We have not yet looked inside the box. A gam 4

The two halves coul d differ i n sign, one being positive an d the other negative, but after squarin g to get probabilities thi s difference vanishes.

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bier, without a doctorate in physics, would tell you, correctly, that the probability of finding the electron in either side of the box is one half. What quantum mechanics say s is: if you believe that probabilities are given by the values of the wave function, you cannot , without knowing that the electron is definitely in one half of the box, wipe ou t the wav e function in the othe r half. T o do so would b e to unjustifi ably imply that there was no probability of finding the electro n in that side of the box. Now, we determine in which half the electron actually is. What is the wave func tion now? Whatever its shape, it is zero everywhere in the empt y side o f the box, because the probability of finding the electron there is now zero—you know that it isn't there. Before the observer observed, the wave function covere d the whole box; afterward i t was confine d to on e side. Th e wave functio n ha s collapse d int o on e side of the box—because of an act of observation. There is no need to open the bo x to observe the electron; the box could be made of glass with a cloth draped over it. If th e precedin g theor y is correc t you ar e dail y responsibl e fo r the collaps e of wave functions. Every time that an act of observation (a measurement) is made on a system that can , prior t o a n observation, give more than on e answe r t o our question, the par t of the wave function representing the answe r tha t we don' t get, collapses. You fear that Fingers Mulloy has stolen your American Express card? You don't know? First construct a wave function for your card, a combination o f that for your card when i t is in your pocket, and that for the card when it is in Mulloy's pocket. Now look . It's i n you r pocket . Th e componen t o f the wav e functio n i n Mulloy' s pocket collapses. That will do nicely. Is it necessary for the observer to be human? Couldn't I train a dog to detect electrons in boxes? Would the wave function also collapse? Let's tr y a deliberatel y provocative version o f the precedin g experiment . Construct a wooden box that can be smoothly partitioned into two identical an d separable parts. Put my cat Schwarz in the box. Now, slide the partitions in place, separate the two boxes, and sen d one to the farthest galaxy known to man. Because we don't know which box contains th e hapless Schwarz, the wave function o f the cat must be divide d equally between the two boxes. What does the wave function in each box look like? Like that for half a cat? Certainly not, for the wav e function in both boxe s must b e th e same . There i s a chanc e o f finding a completel y forme d Schwarz in either box, not a mutilated Schwarz. Now open the box on Earth. Thank God! Schwarz is in this half. This means that instantaneously the wave function on the edg e of the univers e mus t g o to zero—ther e i s no possibilit y o f the ca t being there. But how can that be? How can the information have reached the second box immediately? The fastes t mean s o f communication is light , and ligh t travel s a t a known finit e speed . I t would tak e millions o f years for the informatio n to arrive. During that time, presumably, the second wave function has not collapsed, whic h means that there is a 50% probability of finding Schwarz at the edge of the universe when I know that he is on Earth. At present there is no answer to this question. It may be that the speed of light is irrelevant, that the "connection " betwee n th e tw o boxes relies o n something else entirely. But we don't know what that something is. Schrodinger was no less cruel than I. He placed his famous feline i n a n opaque

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box in which ther e was an atom that was radioactive. Suppose the atom to have a 50% chanc e of throwing out an a-particle in the nex t fiv e minutes . Also suppose that whe n th e a-particl e doe s emerg e i t trigger s a mechanism tha t kill s th e cat. Schrodinger made it a hammer smashing a vial of cyanide. What is the wave func tion o f this legendar y beast, fiv e minute s int o th e experiment ? Well , radioactive decay is completely unpredictable. It can be discussed onl y in terms of probabilities, which means that at five minutes there is a probability of one-half that the cat is alive and a probability of one-half that it is dead. Its wave function mus t contain both these probabilities, and we can do this by constructing a wave function that is half that for a dead cat and half that for a live cat: As Schrodinger might have said, was is t dass ? The living dead ? A cat in the Twilight Zone? This wave function is certainly nothing to do with classical science. Of course we can look in the box, but then the wave function collapse s to that of a cat or that of an ex-cat. The followin g question has been asked : If the presenc e of the observer collapses the wave function, the n is not the ca t an observer? And if a cat can induc e wav e functions to collapse, what abou t mice, disgusting beetles, curi ous ants? Surely a mouse would be able to tell the differenc e betwee n a live and a dead cat. And is the presence of, say, a mouse sufficient, o r does the mouse have to know that the cat is dead or alive? Einstein was skeptical about the possibility of a mouse changin g the wave function o f the universe . Th e great Hungarian scientis t Eugene Wigner held that if a machine made a measurement, for example, by detecting in which half box an electron was, the wave function would not collapse until a conscious mind observed the machine. This brings us back to the previous section. If Wigner is right, and h e was a little cautious abou t this at a later stage , it means, for example , tha t durin g th e whol e histor y o f the univers e befor e consciou s lif e evolved, there was no means of collapsing a wave function. Thi s is a real problem. Supposing tha t th e creatio n o f life depende d o n a certain molecul e reacting wit h another molecule and that there was a 1% probability of them reacting and a 99% probability of them not reacting. In the absence of a conscious mind to collapse the wave function containin g these tw o probabilities, the creatio n of life woul d be i n the positio n o f Schrodinger's cat—neithe r her e no r there . We know that th e reaction must have taken place, so have we collapsed it retroactively? If all this sounds like lonesco or the Monty Python Show, and you don't like this idea o f collapsing wave functions, tak e a breath an d se e how th e followin g argument grabs you. Hall of Mirrors Everything we have said about collapsing wave function stem s from th e basic principle that, in quantu m mechanics , an y system is associated with a mathematical expression tha t include s within i t the possibl e result o f any measurement o n the system. If I can get either o f two possibl e answers , then tha t information must al ready be i n th e wav e function. When I observe the system , I can get only one answer. After th e observatio n the syste m must therefore be in suc h a state a s to give me the answer that I observed; the alternative answer is no longer possible, and the part of the wave function associate d with it must have disappeared. Until an obser-

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vation i s made , al l possibl e answer s remai n a possibility, whic h mean s tha t th e wave function has not collapsed. Thus the basic assumption is that a wave functio n will not collapse unless i t interacts wit h a n "outside" system. But what is an outside system? Why, in the experiments with Schwarz , don't I take myself to be part of a quantum system that includes me, the box, and the cat? And then we could not record a n observatio n (collaps e the wav e function ) unles s a n "outside " observe r observed us. Which just puts the problem one step back. Why not take the secon d observer to be part of a quantum syste m that includes . . . (There was an old lady who swallowe d a fly .. .) The logical end o f the tale is that we have to take the whole universe t o be one large quantum system . The mighty wave function include s al l possible answers to all possible questions. How can it change? How can the spinning coin stop spinning if I, the observer, am actually part of the system? There is a very strange way out. Consider the cat-in-a-bo x experiment. Ther e ar e two possible outcomes: eithe r the ca t is dead and yo u are conscious o f a dead cat, or the ca t is alive and yo u are conscious of a live cat. Note that you have two possible states of consciousness, on e associated with the dead cat, the other with the live cat. The complete wave func tion fo r the ca t and you shoul d includ e bot h you r state s o f consciousness. No w suppose that the wave function canno t collapse; there is nothing outside the quantum univers e tha t ca n "sto p i t spinning." Bu t something doe s happen—whe n we open the box, the cat is either dead or alive. And here comes the crazy solution. Because there ar e two possibilities as to what will happen, both things happen. Th e universe instantaneousl y split s int o tw o universes—on e contain s a live cat , th e other a dead cat . The wave functio n doe s not collapse ; both it s component s sur vive, eac h i n a different universe . And there is a copy of you in both universes. Why? Because before the "observation" there was a probability of having the image of a dead cat in your mind, and also a probability of having the image of a live cat in your mind. You were a part of the wave function; you can't be collapsed. In this interpretation, wave functions don' t collapse, they survive—in this case one in one universe, one in the other . One of you is looking at a live cat, while i n the other world one of you is looking at a dead cat. There is no communication between thes e tw o worlds . Th e genera l suggestio n i s that ever y time a n even t ca n occur in one of several ways, it occurs in all those ways, each possible event occurring in a different universe . Thus, in the experiment in which photons go through a crystal, every time that a photon makes a choice and emerge s from th e crystal, another world splits off in which the other choice was taken. The wave function doesn't collapse ; part o f it survive s i n eac h universe . Se e how neatl y thi s solve s th e problem o f Schwarz an d th e farthermos t galaxy ? The universe split s i n two , an d the "other " univers e contains a cat in a box in a distant galaxy. No need fo r messages traveling far faster than the speed of light. Or are you saying: "If that's a neat solution I'm a fax machine." The theory of multiple universes, firs t suggeste d in 195 7 by Hugh Everett III in his doctora l thesi s a t Princeton, i s as bizarre a s anythin g tha t th e rathe r prosai c practitioners o f spiritualism an d satanis m hav e thought up—and perhaps les s believable. Where are all these universes? Has anyone yet communicated with an y other universe? Not in my family, bu t the idea is a boon to spiritualists. I presume that I exist in a huge number of copies. I am dea d i n som e o f them, because I have man y times been i n situation s wher e

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there was a reasonable probability that I could have been killed, and my wave func tion at the time of these incidents, must have been:5 After eac h hair-raising incident, the universe split. In this universe, I made it. In the other, I was buried, perhaps along with Schwarz. It gives a whole new meaning to the expression "Let' s split. " Among the ver y fe w people wh o tak e th e many-univers e theor y seriousl y ar e those attempting to apply quantum mechanics to cosmology, the study of the largescale structure an d dynamic s o f the universe . But the theor y has not provide d an explanation o f any observation s fo r which conventiona l quantu m mechanic s ha s failed. Richard Feyriman advises us to "avoid being confused by things such as the 'reduction o f the wave packet' and similar magic," but quantiim mechanics provide s the most damning evidence that science is a marvelously effective battleshi p float ing on a deep, ever-changing sea of illusions. Paradox Four: Uncertainty Something unknown is doing we don't know what. —Sir Arthur Eddington on the uncertainty principle

Descriptions of large lumps o f matter specify thei r position an d velocities. The accuracy with whic h thes e variables ca n be measured is limited onl y by human an d technical shortcomings . I n principle w e can go on improving this accuracy to undreamed-of heights. It will help us later in this discussion if we agree that, knowing the velocity of a body, we can, provided we know it s mass, immediately wor k out its momentum, since this i s defined a s mass times velocity, m x v, or just mv. In classical physics , we believe that a body, say you or me, always possess a definite momentu m and position—how could it be otherwise? One major tenet of quantum mechanics , enshrined i n the uncertainty principle, is the proposition that a body cannot have both an accurately known position and an accuratel y know n momentum . That , in principle, w e canno t simultaneousl y measure these two things to any degree of accuracy that we choose is now accepted by the vast majority o f physicists. W e are edging into strange terrain here, but let' s press on through the trees and listen to the language of the natives as they describe the motion of an electron. The uncertaint y principl e wa s state d i n 192 7 b y Werne r Heisenber g (1901 1976), who ende d up i n charge of Hitler's effort t o build a n atomic bomb and later claimed that he wasn't reall y trying. As my grandfather remarked when my fathe r denied smoking, "I believe you, but don't do it again." Heisenberg attacke d th e mos t basic proble m i n experimenta l science—th e na ture of measurement. I f you measure any propert y of a system, say the mas s o r velocity of a particle, there is a certain error involved. The size of that error is primar5

Tbis is not the complete wave function. I should includ e a part that represents th e rest o f both universes, except me.

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ily dependent on the instrument used and the care of the observer. Suppose that we are measuring the position o f a particle along a line that we label x. We call the uncertainty i n measurin g the positio n o f the particle , Ax (delta x). Usin g the nake d eye, Ax has a minimum value of about one-fifth o f a millimeter. It is difficult t o distinguish two points separated by a smaller distance. Now suppose that we simultaneously measure the momentum alon g the same line. Again there will inevitably be an uncertainty tha t we will label Ap. Classical physics puts no theoretical limitations on our ability to reduce these uncertainties as much as is technically possible. Heisenberg thought otherwise . Th e consequence of his mathematical formula tion o f quantum mechanic s is that th e product o f the tw o uncertainties , A x times Ap, or AxAp, has a lower limit; it is proof against any attempts whatsoever to reduce it. This lower limit is h/2n, where, as usual, h is Planck's constant. If we had perfec t instruments, we could reach this limit. We could write: In general we have to write AxA p > A/271, where th e greater-tha n sign, >, indicates that the product can be larger than h/2n, due to human failings. What Heisenberg's uncertainty principl e say s is that you cannot simultaneously measure the position and momentu m o f a particle to an y degre e of accuracy that you want , n o matter how sophisticated your apparatus is. This i s a property of nature. W e take a very important example. The uncertainty principle precludes the existence of a particle that is stationary. For such a particle there can be no uncertainty in its position, a fact that can be expressed a s Ax = 0. Put thi s into (1 ) and yo u fin d tha t Ap = infinity. What does this mean? I t means that if you try to measure the momentum of this supposedly sta tionary particle it can have any momentum. For if there was a value of the momentum abov e which ther e wa s no possibility o f finding th e particle, then the uncer tainty in it s momentum would no t be infinite, i t would be finite . Bu t if there i s a chance of finding any value of the momentum, then we have the absur d situatio n that we have a stationary particle that i s moving. For to have momentum it mus t move. The conclusion is that there are no completely stationary particles, which is what I asked you to believe in Chapter 16. If you coo l down a chunk of metal, the vibration s of the atom s become less violent, but you will reach a point at which th e amplitude of the vibrations refuses t o get any smaller. You can do nothing afte r this ; you can't sto p the atom s dead. The jargon for this minimal energy is zero-point energy. Th e fac t tha t it exists, an d ha s been shown to exist experimentally, is another extraordinary achievement of scientific theory. But who in his right mind would say that it is impossible to stop something vibrating? A Different Point of View Look back a t Figur e 15. 7 an d recal l th e conclusio n tha t w e cam e t o concernin g wave packets. If you know the position of a packet fairly accurately (Figure 15.7c), then th e uncertaint y in it s position , Ax , is small . However , a strongl y localize d packet cannot be given a well-defined frequenc y becaus e the packet contains such a wid e sprea d o f frequencies. Now suppose , i n th e spiri t o f de Broglie , tha t th e packet was really a particle an d that i t had a momentum determined by its wavelength. Its wavelength is not well defined because its frequency is not well defined.

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Thus there is a big uncertainty i n its wavelength, and as follows from de Broglie's equation, a correspondingly big uncertainty, Ap, in its momentum. Ax is very small and A p is very large. Just as Heisenberg says, if one uncertainty, in this case Ax, is very small, then the other, in this case Ap, must be big. If you look at the packet in Figure 15.7b, you will see that in this case the uncertainty, Ax, in it s position is quit e large . However , sinc e it i s compose d o f waves with very similar frequencies , the uncertaint y i n its wavelength, and therefor e i n its momentum, Ap, is quite small. Again, raise your hats to Heisenberg. Heisenberg gave a practical illustration of the impossibility of measuring velocity and position , showing that measurements on a particle inevitably involve d interaction with the instrument. Fo r example, in a microscope the specime n under observation i s bombarde d b y photons . Fo r a large objec t thi s make s littl e differ ence, but on the atomic scale the photon will disturb the object, changing its position o r velocity, or both, an d thu s destroyin g any chance o f measuring both variables accurately . This ha s been describe d a s the newspape r reporte r making the news. Analysis of the experimen t gives equation (1). The probabilistic interpretation of quantum mechanics, and the added fuzzines s due t o the uncertaint y principle , hav e ha d a n appea l t o thos e searchin g fo r free will. They see an unpredictability abou t nature, a looseness that opens up the steel chain o f cause an d effect . Thi s i s a very provocative subject, bu t on e that woul d take too much room to discuss properly, for this book. Paradox Five: Nothing Up My Sleeves

The uncertainty principle's mos t remarkable trick is to produc e something out of nothing. The claim of the uncertainty principle is that it can conjure matter out of a vacuum. This is better than the ten little fishes and the five loaves of bread. To perform this miracle we use an alternative form o f the uncertainty principle . The form that we need uses energy and time: What does At mean? For our purposes, the best way to interpret the meaning is to regard it as the lifetime of a system having an uncertainty, AE, in its measured energy. A simple exampl e i s a particle tha t ha s a n infinit e lifetime , a stabl e particle. Then A f is infinite and AE is zero. In other words, the energ y can be measured exactly. Now consider a hydrogen atom in which the electro n ha s jumped from the lowest orbital, the stable state, to a higher orbital. The experimental fac t i s that the electron ver y rapidly fall s bac k again . W e can sa y that th e excited state i s very short-lived. I t i s als o a n experimenta l fac t tha t th e energ y o f suc h a stat e i s "blurred"; when we attempt to measure its energy, we find a range of values that is wider, the shorte r the lifetim e of the state . Very short-lived states have very ill-defined energies. Now, what we are asked to believe is that particles can suddenly materialize out of a vacuum. By analogy with the zero-point energy of vibration, it can be supposed that electromagnetic fields also have a kind of zero-point energy. Then we can imagine that energy is "borrowed" from the field for a fraction of a second and a particle is created. We are assuming the equivalenc e of mass and energy , demonstrated by Einstein (see Chapter 32). After a short time, the particle sinks back into the sea, but a short lifetime implies a large uncertainty in the measured energy of the particle. In

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other words, it can have a large energy. We will call such phantoms virtual particles. Notice again that the shorter-lived the particle, the smaller is At and the larger is AE. Now Einstein tells us that E = me2. This means that a particle with a lot of energy can, in many circumstances, be regarded as a particle with a lot of mass. Putting everything together, it appears as if virtual particles that ar e very heavy have very short lives. This will be of relevance to us in the next chapter. The onl y excus e fo r this far-fetche d stor y is tha t i t explain s certai n facts . Se e how you feel about it after this . Imagine a real electron sitting in the vacuum. All around it there are pairs of virtual electron s an d positron s continuall y risin g from , an d returnin g to , th e fish y deep. Th e rea l electro n wil l attrac t th e positivel y charge d virtua l positron s an d repel the virtual electrons . This means that a real electron will maintain a permanent coa t of virtual positrons around it. Most electrons in nature have such a coat; they ar e sai d t o be "dressed. " Thi s ha s a n observabl e effect . Imagin e that you ar e another electron approaching our dressed friend. You will feel the repulsion of her negative charge, but that will be slightly reduced by the attractive force du e to the coat of positively charged virtual positrons . Th e othe r electron will fee l th e sam e about you, because you too will be dressed. The normal coulombi c interactio n is thus measured betwee n dressed electrons. However, when two speeding electrons in an accelerator approach each other, they can get to distances of approach that are far smaller than those expected in the everyday world. When the distance between them is very small, they wildly throw off their coats and become "naked" electrons. This increase s th e repulsive forc e betwee n the m t o a value tha t i s larger than w e might have calculated from the coulombic repulsion at larger distances. This effec t has been observed experimentally . A ver y important virtua l particl e i s the virtua l photon . Som e peopl e envisag e the virtua l photon a s emerging from the electron , buzzing around fo r a very short time and the n bein g reabsorbed. It is as though the electro n was surrounde d b y a permanent clou d of virtual photons , being born and dyin g almost as soon as they emerge. Although virtual photons don' t last that long and generally return t o their maker, they occasionally die by interacting with another electron . This is the way that quantum mechanics sees the coulombic interaction. This is an important turning point for us, and we pause to chew things over. The idea of force at a distance, as Newton found, came under attack from a variety of scientists and philosophers. Now we have an entirely different interpretatio n of force. Electromagnetic force is pictured as the exchange of virtual photons. A variety o f analogies are used to giv e students a feeling fo r this explanatio n o f force. The standard one s involve two people skating parallel to each other and throwin g objects, back and fort h t o each other . The thrower moves backward a s he throws , for th e sam e reason that cat s move backward when the y stan d o n ice and sneeze . The catche r move s backward because o f the momentu m o f the objec t caught . Th e skaters appear to repel each other. The analogy works only for a repulsive force. An attractive force needs a rather strained analogy, usually involvin g boomerangs! This radically ne w wa y o f looking at force wil l b e employed when w e come to the elementary particles. It is a classic example of the way in which science reinterprets reality . Th e previou s picture , o f a forc e actin g throug h space , obeyin g th e coulomb law, works when we use it for most problems. Down to a distance of about 10"11 cm, th e coulom b equatio n work s perfectly , an d calculation s o f the forc e be -

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tween charge d bodie s are not relian t o n the suppositio n tha t virtua l photon s ar e bopping around. The main justification of the new picture lies in other areas, particularly in the combination of quantum mechanics, Maxwell's equations, and relativity that is primarily associated with the name of Richard Feynman and is known as QED—quantum electrodynamics. This theory gives an unbelievably accurate account o f all phenomen a involvin g th e electromagneti c force . QED' s part y piece, rolled ou t whenever it s credentials ar e under scrutiny , is the agreemen t between the calculated and experimenta l value of the g-facto r o f the electron . The meaning of the g-factor is irrelevant;6 it is the agreement between experiment and theory that is supposed to astound you (it astounds me): Experimental: 2.0023193048(8 Calculated by QED: 2.0023193048(4)

) ,

where the numbers in parenthesis ar e the uncertainties in the last figure. Ca n anyone doub t tha t al l thre e component s o f QED—Maxwell, relativity , an d quantu m mechanics—have some truth in them? My conscience drives me to add a footnote to the last sentence. The theory relies on a trick: dividing both sides of an equation by infinity. This is frowned o n in the best mathematical circles. Moreover, the theory is not drawn entirely from thin air; it is necessary to put i n the measured mas s of the electro n before yo u can get the right calculated values of other physical quantities. Do virtual particles exist? Perhaps they are just a convenient way of explaining a number of phenomena, but no more than that. Paradox Six: They Seek Him Here...

We hav e no t dare d t o choos e betwee n Newto n and Einstei n o n on e han d an d Thomas Young and Maxwel l on the other . One set of Giants spoke out for corpuscular light—Newton using intuition, Einstein showing that photons explained the photoelectric effect. O n the other hand, Young's experiment is so convincing that it is difficul t t o se e ho w ligh t ca n b e anythin g othe r tha n waves . An d the n alon g comes Maxwell with a theory tha t i s preposterously successfu l in predictin g th e speed of light and the production of all types of electromagnetic waves. And, as we asked previously, how can interference be explained by particles? Can bullets annihilate each other? Let us wander farther into the enchanted wood. Here is a very strange, eerie experiment. We are going to repeat Young's classic experiment (see Figure 15.4a), sending light through two slits and observing the resultant alternatin g dar k an d ligh t lines . W e thought w e kne w wh y th e line s ap peared: because the waves from th e two slits could constructively or destructively interfere, arrivin g in phas e o r out o f phase. Bu t how ca n w e possibly explai n th e pattern in terms of photons? We will take advantage of the availabilit y of extraordinarily sensitive detectors. We are going to use instrumentation tha t can detect one photon.7 This allows us to use extremely weak light. 6

It gives the relationship between the spin of the electron and its magnetic moment . 'Nature doesn't do too badly; there is evidence that some of the visual rods of the human ey e can be triggered to give an electrical impulse to the brain, by one photon.

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When we perfor m th e two-sli t experimen t wit h extremel y weak light , we fin d that th e detector s pick up individual hit s of the photons as they strike the secon d screen. There can be no doubt that photons are arriving, not continuous waves . You can detect the localized flashes o n the screen. It is as though rain were gently spattering the marble paving stones of a previously dry piazza. This looks good for photon fans . Bu t not for long. As the hits are recorded, they start to build u p a pattern and gradually the pattern emerges: alternate lines! Of course this is what we should have expected ; that' s wha t th e resul t o f the two-sli t experimen t alway s is . Th e problem is that now the dark lines in Young's experiment seem not to be produced by interference but simpl y by the fac t tha t photons neve r arriv e at the locations of the dar k lines. W e never record a hit a t the cente r o f the dar k stripes. Thi s mean s that darknes s doe s not com e about by photons arrivin g togethe r and annihilatin g each other. They just never arrive. Photons spreadin g ou t from a particular slit apparentl y "know " that the y mus t not travel in the directio n o f the dar k stripes. Ther e is something distinctl y weir d going on here. Imagine that you are a photon passing throug h a slit. How on earth do yo u kno w no t t o g o toward th e locatio n o f a dar k line ? Ho w doe s a raindro p avoid certai n places? Maybe it is due to some kind o f interaction betwee n th e sli t and the photon? In the scientific community there i s a well-known phrase: "One experiment to o many." We are going to risk another experiment. If a photon "knows" that it can't go to a dark line because it interacts with the slit as it goes through, then shutting the other slit shouldn't mak e any difference. Ho w can a photon possibly "know" that th e othe r sli t is closed o r open? We should ge t the interference pattern with one slit open! Try it, do one experiment too many. The interference pattern disappears. Of course it does. You wouldn't expect anything else; shining a light through a single slot should give a simple, slightly blurryedged image of the slot . No dark lines, no interferenc e pattern. Youn g could hav e told us that—the trouble is that hi s explanation i s not the one we want. H e would have sai d that interference is impossible wit h onl y one slit because the part of the wave going through one slit n o longer has anythin g to interfere with. The photon model jus t leave s us wit h a headache: a photon goin g through on e slit when th e other is closed loses the ability to avoid the dark areas. The photons just spread out over the whole (previousl y patterned) area. If you open the second slit, the patter n reappears. The path of each photon appears to be influenced by the presence o f the other slit! Since i t seems unlikely tha t a photon going through on e slit ca n "know" abou t the state of a second slit, let's try another hypothesis. Mayb e the photons fro m tw o slits cooperate in some way, while they are in flight, giving each other instructions ? Crazy? Yes, but anythin g seem s possibl e i n th e quantu m world , s o let's eliminat e that possibility. We will lower the intensity o f the light so much that on the average there is only one photon i n fligh t a t any one time. It's no use—the striped patter n builds up ! Incidentally , this experimen t als o completel y rules ou t the possibilit y that, at higher flows o f photons, there are photons arrivin g in the dark spots together but annihilating eac h other. At this stag e our position i s that the pattern is produced by single photons traveling completel y independentl y o f each other . This implie s tha t a give n photo n going through a certain sli t know s where to go and wher e no t t o go (dark or light

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stripe), without interacting with other photons. (OK , you didn't expect interaction, but th e experimen t ha d to be done). How does the photon kno w where no t to go? This is very difficult t o understand. S o difficult tha t no one has explained it. How does a photon, or an electron, know that the other slit has been closed? And why does opening the other slit ensure that an individual photo n going through a slit know s tha t i t mus t avoi d th e locatio n o f the dar k stripes ? Thes e findings , checked and rechecked, defy commo n sense and classical physics . One way out of the marsh i s to suppose that a photon simultaneously travels along several paths. I won't elaborate here, except to comment that we are in very strange country. The results of the two-slit experiments cut away at the very basis of our understanding of the way the universe is. Richard Feynman used to say that the two-sli t experiment wa s the problem i n quantu m mechanics . Som e waffling noise s hav e been made by a number o f theoreticians, bu t ther e is clearly something very basic about the stuff o f the universe that either is waiting to be revealed, as Einstein firmly believed, or is simply outside the capabilities of our brains to grasp. Paradox Seven: Do We Really Understand What's Going On?

In 1935 Einstein, with two younger men, Boris Podolsky and Nathan Rosen, wrote a paper that became so famous that it is now known simply by the initials of its authors: EPR. Until recently I frequently sa w Professor Rosen walking along the paths of the university. He was a small, courteous, soft-spoken gentleman , the last person one would have expected to cause so much trouble. Heisenberg's conclusio n tha t i t was in principle impossibl e t o simultaneousl y measure certai n pair s o f properties, for example, a particle's positio n an d it s momentum, gave Einstein no rest. He was perturbed, not so much by the supposed impossibility o f simultaneously measuring the position and the momentum o f a body to any accuracy but by the deeper statement that a body could no t simultaneousl y have a definite positio n an d a definit e momentum . What coul d suc h a statement possibly mean in the real everyday world? Einstein searched for an experiment that would demonstrat e that th e positio n an d momentu m o f a particle coul d be determined exactly, and reproducibly, and that the properties o f a system could be predicted before they were measured, thus showing that they really did exist. EPR i s a n attemp t t o sho w tha t ther e ar e experiment s tha t ca n sideste p th e Heisenberg uncertainty principle, in the particular case of position and momentum, and also allow the correct prediction of a particle's properties before measurement. The experiment was not performed by the authors; it was a thought experiment. The ide a o f EPR is simple. It relies o n the principl e o f the conservatio n o f momentum, a principle o f Newtonian mechanics tha t quantu m mechanic s doe s no t question. If a system has a certain amount of momentum and n o externa l forces ac t o n it, the tota l momentum o f the syste m remains constant , forever . Th e easiest case is a body, say a spaceship, moving through space, with no force s actin g on it. The firs t law says that its velocity remains unchanged. But if this is true, then the product of its velocity times it s mass, which is its momentum, also remains unchanged . An other example: imagine two identical piece s of chewed chewing gum, each having the same mass and the same velocity, sliding toward each other on a nonsticky surface. I n this case the velocitie s com e with a sign; if the velocit y of one piece i s v

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Figure 30.3a. Th e EPR thought experiment deals with two identica l particles with identical, but oppositely opposed , momenta .

then we must write the other one as -v, because it is in the opposite direction. Thus if the momentum of one piece is mv the momentum of the other must be -mv. This means that the sum of the momenta (+mv + -mv) is zero. When they hit eac h other, they will stic k together and bot h sto p moving. The total momentu m remain s unchanged, because no external force s acted on the system. It is still zero. Now suppos e that a n initially motionles s particl e disintegrate s int o two identical fragments tha t fl y apart, the two fragments movin g along the sam e straight lin e {Figure 30.3a) . Accordin g to Heisenberg , we canno t ge t a n exac t measurement of the positio n and momentu m o f either particle . The notoriet y o f EPR rests o n th e claim pu t forwar d i n the pape r that ther e i s a simple experimen t tha t overcome s this quantum mechanica l ban , and allows both the position and the momentum of either o f the two particles to be measured t o any degre e of experimental accuracy. We follow the argumen t of EPR. Keep in mind that we are going to measure the position and momentum of particle B . Since initiall y th e single , pre-explosion, particl e ha s n o momentum , an d there are no forces acting on it from without, the total momentum of the system (the two identical , moving fragments ) mus t remain zer o after th e disintegration . Thi s means that if one fragment has a momentum o f p, the other must have a momentum of -p in th e othe r directio n (Figur e 30.3a). Thus i f we measur e th e momentu m o f fragment A very accurately, we can immediately deduce the momentum of B, without observing it directly. This is the firs t par t of the EPR experiment, and note that we have made no direct observation on B. Now there is nothing to stop us fro m accuratel y measuring the position of B; the uncertainty principle doe s not limit th e accuracy of one measurement o n a system. Thus we can measure the position of B (directly) and it s momentum (by inference), to any degree of accuracy that we like. Heisenberg says that you can't do this. But there i s another poin t here . Heisenberg says that a particle canno t simulta neously hav e a defined momentum an d position. EP R denies this . Conside r particle B. After measuring the momentum of A, we can predict, with absolute accuracy, the momentum of B, before w e measure it. A central tenet of the conventional theo ry of quantum mechanics, associated with Born and particularl y Bohr, is the doctrine tha t yo u canno t kno w anythin g abou t a particle unti l you measur e it. Onl y when you trap the spinning coin can you say something definite. Einstein says, visa-vis EPR, "If, without in any way disturbing a system, we can predict with certainty ... th e value of a physical quantity, then there exists an element o f physical reality corresponding to this physical quantity." The particle B has a real position an d a real momentum, real because predictable, since either ca n be predicted fro m th e values measured fo r A. Again Einstein took the comrnonsens e view o f the world . There are real objects ou t there with real properties that do not depend on the observer. Heisenberg and the other founding fathers say no. Bohr was adamant. Ther e had to be a flaw i n EPR—particles did not have prop-

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Figure 303b. Th e two identicall y polarized photons both have a 50% chance of passing through their slot. The "choice" of whether a given photon does or does not might be expected to be completely independent of the behavior of the other photon. It isn't.

erties before the y were observed. There is one very unlikely way around the problem, a supposition that will save Heisenberg. We suppose that fragments that once were together are always connected , in the sens e tha t measurements on one fragment, contrary to EPR, do affect th e other . In this "spooky" scenario (the adjective is Einstein's), a measurement of momentum on fragment A would induce an uncertainty not only in the measurement of the position of the same fragment but also in that o f fragment B . Some kind o f blood brotherhood unites th e fragment s forever . Rubbish? How can it matter to one fragment what is being done to the other? It has since been shown , experimentally, tha t i t does . An d w e hav e n o ide a how . EPR doesn't work . Thought experiments , even by on e o f the tw o greatest scientists i n history, need checking experimentally. Notice that the argument of EPR depends on the assumption that measurements on on e o f the particle s cannot affec t wha t i s measured , or what happen s i n an y way, to the other particle. This sounds straightforward; wh y should there be an effect, unles s w e ar e extremel y careless? This i s calle d th e assumption of locality, and it seems so obvious as to be taken for granted in classical physics. A crucial event in the history of EPR, and of quantum mechanics in general, was the publicatio n o f a paper by John Bell in 1964 , in the journa l Physics. By simple arguments Bel l prove d that i f the tw o part s o f the system , say the tw o fragment s above, cannot affect eac h other, then it is impossible to obtain the results observed in th e actua l experiments . Th e experimenta l result s prov e tha t localit y doesn' t apply—particles A and B are "talking to each other." The firs t rea l experimen t showin g tha t th e though t experimen t o f EP R was contrary to experience was performed by Alain Aspect in 1982 . It was not exactly the EPR experiment, althoug h that has now been carried out, but an equivalent experiment o n photons. The purpose o f the experiment s wa s to show that two photons ar e i n som e way i n communicatio n with eac h other , so that measurement s made on one affect th e measurements made on the other . Instead of going through Aspect's experiment, we take a particularly simple case that illustrates the principle involved. Two photons fl y apart (Figur e 30.3b) . They both have a perpendicular plan e of polarization, and they both strike crystals with polarization planes ("slots" ) at 45° to the vertical. As we saw, such a photon has an equal probability o f going through or bein g stopped . Now , commo n sens e say s tha t thes e tw o photon s mak e their choices independently; whether one of them goes through or not can have no effec t on the choic e of the othe r one. In fact, experimen t shows that the "choice " o f one photon, whether to go through or not, is conveyed to the other proton and affects it s

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"choice." Th e incredible thin g i s that th e experimen t ca n be performed i n such a way that at the time of the measurement o n one photon the other photon i s too far away to receive a light signal before i t too undergoes a measurement. Reason says that it cannot be "told" what to do by the other particle before i t itself is measured. And ye t i t seem s to kno w wha t th e resul t o f the othe r measurement was , and t o react accordingly . The particle s no t onl y spea k t o eac h othe r bu t als o appea r t o communicate faster than light. There have been some very clever variations o f these experiments , but the y all point to two inescapable facts : • Th e photon s o r particle s involve d ar e no t "localized" ; somethin g connect s them across space. There is no reason to suppose, on the basis of the experiments, that they could not affect eac h other instantaneously across astronomical distances . • Wher e there is a choice of results fo r the measurements o n one fragment, th e observed result, whatever it is, affects th e result of a measurement on the second. I t canno t therefor e b e sai d tha t th e secon d particl e possesse d certai n fixed values for its properties before the y were measured. The firs t property , nonlocality, i s perhaps the stranges t finding o f quantum mechanics to date. Spooky wa s the right word. Much has been made of this weird togetherness. The univers e ha s been envisage d as a collection o f particles bound t o each other by past associations but unable eve r to break those ties, no matter how far apar t they drift . A holistic cosmos , but boun d b y what? And wha t i s it that allows particles to communicate faste r tha n light , the suppose d fastes t mean s in th e universe? Are we capable of understanding reality? Is the scientifi c approach an approach to reality? Is there a way out of the maze? Familiarity Breeds Consent

As a schoolboy I often me t aggressive anti-Semitism i n the playground, sometimes from considerabl y older and bigger boys. My father's advice was simple : "Yo u can fight bette r than any o f them. Singl e out the leader . There's alway s one . Go up t o him and punch him really hard o n the nose." "An d what about the others?" "They won't d o a thing." The y didn't. I t worked i n three schools . Th e mindless bullyin g stopped immediately . I wa s dangerous , eve n grudgingl y admired . T o m e th e method seeme d completely senseless. I was always outnumbered, but m y father' s apparently irrationa l recipe worked. That's ho w I feel abou t quantu m mechanics . Our scientific fathers, thos e whom we revere—Schrodinger an d Heisenberg , Born and Dirac , Bohr and d e Broglie—have given us a recipe for success. It works every time, but i t flouts common sense. As I grew up I began to appreciate the rationale of my father's advice. It really did make sense. Will it be the same with quantu m mechanics? The augurs are not too favorable. How ca n thousand s o f scientists us e a theory that ha s irrationa l feature s t o it? Because wher e theoretica l result s ca n b e compare d wit h experimenta l observa tions, one can only pray that all theories were as reliable. No scientist would dream of stoppin g using quantu m mechanic s becaus e h e doesn' t understan d it s founda tions. We keep hitting the leader of the pack on the nose.

The Lan d of Parado x j

Among scientists ther e is no uniformity in response to this unsatisfactory situation. Th e predominan t opinio n b y fa r is: no opinion . Bu t many theoretician s ar e unhappy wit h the assumption that quantu m mechanics , as conventionally formu lated, i s a correct , fina l theory . Th e fac t that , t o dea l wit h quit e straightforwar d questions, like Schrodinger's cat, we might have to stray into multiple and continually splitting universes, make s many scientists as k whether quantu m mechanics is missing something important . Personally I feel tha t th e possibilit y tha t we ar e too limite d shoul d no t be dis carded. A s Lord s o f the Universe , it doe s no t flatte r u s t o b e tol d tha t ther e ar e things beyond not only our ken, but even our capacity to ken. Since Lucretius there has been an implicit belief among scientists tha t "i n the end" Nature will be comprehensible. This may not be true, if to "comprehend" mean s to reduce all explanations to concepts that are acceptable in terms of logic and current common sense. It is more likely that we will get used t o using concepts tha t w e don' t reall y understand, content in the fac t tha t the y allow us to "explain" what w e see as objective reality and to reliably predict the outcome of experiments. In the end we may be no more capable of understanding the big questions about the universe than Schwar z is able to write haiku . The paradoxes of quantum mechanics hav e provoked many thinkers to pick up their pens, Unfortunately for the mental health of HMS, in addition to serious, reasoned reflections on this subject, there is a steady stream of popularly available dubious thinking. Quantum Sociology We should suspect an intention to reduc e God to a system of differential equations. —Sir Arthur Eddington

There sometimes seems more danger of us doing the opposite. Quantum mechanic s has bee n a fertil e breedin g ground fo r those wh o se e in it s ambiguit y a steppingstone to social philosophy o r religion. Thus on e recent writer on the suppose d social relevance of quantum mechanics claims, "Through the precise and testable imagery of physics we may learn a new language for describing other, related domain s of ou r dail y experience. " We may, but I hope we don't . Ou r present language suffices, if used accurately. All we can borrow from science, in this respect, is a greater awareness of the places in life where reason should be paramount.8 Lately there has been an attempt t o use the wave-particl e duality a s a basis for building a new view of society. It is claimed that we too display duality—we are individuals, but we are also part of society. This parallel i s facile i n the extreme and can be repeated a d infinitum : a note i s a note, but i t is also part of a symphony; a grain of salt is a grain of salt, but i t is also part of a sausage. And a particle can look like a wave! And . .. therefore? And therefore nothing. Th e fact that we are both individuals an d members o f society is extremely important, but i t has nothing to do with quantum mechanics and the parallel is sterile. It is essentially a misuse of lan8

Incidentally, as William Empson showed many years ago in Seven Types of Ambiguity (1930), it is the very ambiguity of language that gives literature much of its subtlety and power.

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guage—the use of the word duality to create the impression that there is something sociologically significant in quantum duality. There isn't. There is no consequence of our social duality that owes anything to quantum mechanics. It could be a good theme for a poem, but HM S should tak e care; although sociolog y can use mathe matical modelin g to study th e dynamic s o f social intercourse , it ca n learn almos t nothing from physics . Einstein wa s much concerne d wit h question s o f morality an d meaning . When asked what effect relativity had o n religion, he replied, "None. Relativity is a purely scientific theory , and ha s nothing t o d o with religion." Nevertheless, there is a long history of fruitless attempts to relate the specifics of mathematics or physics to man's religious and mora l life . Thi s is the wacky side of the Pythagorean heritage. The most general lesson that man ca n learn from scienc e is the nee d to apply the highest standards of reason to those problems to which they can be applied.

JI.

The Elementary Particles What are little girls made of? What are little girls made of? Sugar and spice and all things nice, That's what little girls are made of.

Little girls are made of quarks and leptons. Likewise little boys, and everything else in the universe. The reign of the triumvirate of the proton, neutron, and electron was short-lived. In 1932, the year that Chadwick discovered the neutron, Carl Anderson detected a fourth particle , with the mass of the electron but positively charged . The positron, which Dira c had predicted , is stable if left o n its own but has a permanent suicid e pact wit h th e electron , bot h particle s vanishin g an d leavin g tw o y-rays . Th e positron wa s discovere d b y observin g th e particle s generate d by th e collisio n of cosmic rays with matter. Cosmic Bombardment

In 1910 Father Theodor Wulf, a Jesuit priest, ascended the Eiffel Towe r and detect ed more radiation than he had expected. Intrigued by this observation, Victor Hess made ten ascents in a balloon, between 1911 and 1912, some to over 5000 feet, an d in 193 6 he received the Nobel Prize for discovering cosmic rays. Cosmic rays fall o n us fro m oute r space. They are composed of particles traveling at very high speeds—mostl y protons, but with small percentages of the nuclei of severa l elements . The y have come a long way, probably originating in the star s within ou r galaxy, and the y ar e very powerful missiles . Nucle i hit by cosmic rays can readily spli t int o fragments , no t onl y int o protons and neutron s but als o into other particles. Cosmi c rays can also produce fragments by the conversion of some of their enormou s kineti c energ y into matter. This i s relativity showin g it s finger prints; the conversion of energy into mass can occur when extremely energetic particles are stopped in their tracks by collision. Because cosmic rays can be lost before the y reach the ground , because o f collisions with the molecules i n the air, many earl y experiments wer e don e on mountaintops o r by sending apparatu s u p i n a balloon. In 1937, using cosmic rays, Anderson, together with S. Neddermeyer, struck gold again, discovering another two particles: the muon and the antimuon. These two particles, one positively charged, the othe r negatively , had abou t one-fift h o f the mas s o f an electro n an d sponta neously disintegrated i n a matter of a millionth of a second. The hunt for new particles intensified.

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The Accelerators

It seemed that if you hit elementar y matter hard enoug h you could fragment it, but cosmic rays were not a n ideal projectile, an d th e need became evident for a manmade sourc e o f bombarding particles , allowing a choice in the control , type, an d energy of the projectile . Thus was born, in the 1950 s and 1960s , the age of the accelerator. A n accelerato r is simpl y a n extraordinaril y expensiv e evacuate d tube , surrounded b y powerfu l magnets . A variet y o f projectiles can b e accelerate d t o enormous speeds in these tubes. There are accelerators that can produce beams of electrons traveling at 0.999 999 999 86 of the spee d of light. The huge and growing expense of accelerators is a consequence of the need, or more accurately the desire , to attain higher velocities. With the use of very high-speed protons, neutrons, electrons, and othe r projectiles, hundreds o f particles have been characterized , and at one time it seemed tha t every new issu e o f Physical Review Letters or Nature, in cluded a report of a new particle. The speed o f the collidin g particles in an accelerator is so great that we have to take int o accoun t th e theor y o f relativity (se e Chapter 32), one resul t o f which i s that bodie s movin g nea r th e spee d o f ligh t increas e significantl y i n mass . Thi s means that , o n collision , tw o particle s ca n hav e a joint mass fa r larger than tha t which the y have when the y are at rest. It is thus not surprising that comparatively heavy particles can be formed as a result of such collisions. By the 1990s there were about 400 "elementary" particles, which suggested that the Creator picked up almost anything to hand as he built the cosmos. This wealt h of new toy s was excitin g but puzzling , but i f it gives the impressio n tha t particl e physics is an expensive kind of beachcombing, it is thoroughly misleading. Although a few of the new particles had been predicted o n theoretical grounds, at one time there seeme d to be no unifying principl e behin d the variety of masses and charges. Nevertheless, over the past few decades, the theorists have performed miracles of interpretation and have succeeded in bringing a degree of rational order into the welter of disparate dat a on elementary particles. The story is too long and complex, the theory too advanced, and the number of particles too large for the layman t o appreciate the fine r details—an d I include among laymen those scientists , like myself , wh o ar e not in the field . However , the genera l lines are clear and th e picture is fascinating. Our basic approach here is to give a brief overall view of the field, no t followin g the trai l o f detection but goin g to the bac k o f the boo k to se e who done it. It i s fai r t o sa y that i f you wan t t o kno w ho w th e worl d work s a t th e leve l of atoms and molecules, you will lose almost nothing by forgetting about several hundred particles and contenting yourself with the properties of the electron, the proton, and the neutron. On the other hand, you will be missing out on a very strange tale and whole lot of colorful characters . The Particles and Their Antiparticles

The elementary entities o f which th e universe is constructed can be classified into two groups (Figure 31.1) with names reminiscent of tribes of science fiction aliens : • Th e quarks. Quark s ar e neve r foun d alone . The y exis t i n variou s combina -

The Elementary Particles

Figure 31.1 Th e classification of the elementar y particles.

tions that form a large group of particles known a s the hadrons. Several hundred hadron s hav e hee n identified , o f which h y fa r the bes t know n ar e th e proton and the neutron. • Th e leptons. Ther e ar e onl y six known leptons , of which th e electro n is th e most familiar . Both quark s an d lepton s hav e antiparticles havin g th e sam e mas s bu t opposite charge. The first antiparticl e t o be found wa s the positron, the electron's antiparticle, which ca n be classified as an antilepton. Just as quarks are never found i n isolation, so antiquarks ar e never found alone , but th e various combination s o f these particles, th e hadrons , d o have detectabl e antiparticles . Thu s ther e i s an antipro ton. The neutron ha s no antiparticle, sinc e it is electrically neutral. Almost all the particles, hadrons or leptons, disintegrate spontaneousl y and rapidly and can only be studied immediatel y afte r the y ar e formed i n a collision experiment . The average lifetimes of particles and antiparticle s ar e identical, except in one famous case, relevant to the Creation, which w e will discuss later . The only other known objects in the physical universe are the entities tha t mediate the physical forces, of which we have so far met only the photon . Quarks and Leptons Leptons appea r t o be genuinel y elementar y particles , havin g n o smalle r components. Thus, as far as we know, quarks and leptons, and their antiparticles, are the irreducible components of matter. No one has ever observed either a single quark or a combination of more than thre e quarks . Combinations of three quark s are called baryons, and includ e th e proton an d the netitron. Those composed of a quark an d an antiquark are called mesons. Baryons and mesons together form the hadrons. The quark was postulated in 1964 by Murray Gell-Mann and Georg Zweig. Early in Zweig's career , his appointment t o a post in a Swiss university wa s blocked, on the grounds that he was a charlatan. Hi s first pape r on quarks was rejected; it was obviously nonsense. H e is now a professor in California, and the concept of quarks is a cornerstone of particle physics.1

1

The name quark comes from the following lines in James Joyce's Finnegans Wake: "Thre e quarks for Muster Mark! / Sure he hasn't got much of a bark / and sure any he has it's all beside the mark." Quark is also a kind of cheese. Quark and apricot flan is particularly good.

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Just as the periodic tabl e suddenl y made sense whe n th e electron , proton, an d neutron wer e discovered , s o th e quar k ha s brough t a wonderfu l orde r int o th e world of the elementary particles. Color

There is a science fiction story in which i t turns out that there have been, for 10,000 years, two human specie s occupyin g thi s planet , eac h invisibl e t o the other , an d with no channels o f communication.2 This is how electromagnetic and gravitational force s are . They don' t appea r to speak to each othe r in an y way. Electric fields have a counterpoin t tha t w e cal l charge . Gravit y has a counterpoint tha t w e cal l mass. Electric fields n o more act on mass than gravity acts o n charge. Each to hi s own. A priori there is no reason there should no t be othe r force s i n th e universe, each actin g o n som e property , other than mass or charge. Particl e physic s ha s shown that this is so. Until recently, we have been in the position o f a man who has had a clothespi n put o n his nose, been blindfolded, and then asked to sort ou t a bunch o f assorted flowers. H e could onl y g o on shap e an d size . Remove the pe g and th e blindfold , and h e find s tha t flower s hav e othe r properties—colo r an d smell . Thes e ar e revealed by the interaction with his sense organs. There are properties of the elementary particles that hav e revealed themselve s in their interaction s wit h eac h other , and tha t ar e completely different fro m mas s and electri c charge. These properties help u s t o classif y th e particles . Th e bes t know n ar e color, which w e wil l tal k about, and strangeness, which we won't. Two force s wer e know n a t th e beginnin g o f this century , th e electromagneti c force and gravity, but it became evident that the forces between quarks were far too strong to be due to either o f these. What holds quarks together inside hadrons, suc h as the proton? What is the nature of this new force, which is called the strong force? And on what does the forc e act? For quarks, particle physicists invented a new property, analogous to mass an d charge. A new propert y was neede d becaus e i f there wa s a new typ e o f force be tween quarks there had t o be something o n which i t could act. They called it color charge becaus e i t ha s nothin g whatsoeve r t o d o with color . Ordinar y charg e ha s two variations—positiv e an d negative . Colo r charg e ha s thre e variations—red , green, and blue—which have nothing to do with red, green, and blue, and might as well hav e bee n Harpo , Groucho , an d Chico . Thus , i n additio n t o mas s an d t o charge, quarks have anothe r property , color charge, that act s as an ancho r fo r the strong force. For short we will call it color. The Roll-call of the Quarks How d o you ge t several hundre d differen t hadron s ou t o f combinations o f two o r three quarks? By postulating that: There are six kinds of quark, each having a choice of three colors, and each having a fractional electric charge (Figur e 31.2).

Five of these quarks have been characterize d o n the basis o f experiments i n accel2 When I mentioned this story to a feminist friend o f mine, she declared that the two species were men and women.

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Figure 31.2. Th e classification of quarks .

erators. Th e sixth , althoug h no t ye t found , i s confidentl y predicte d t o exist . Th e names o f these quarks , and thei r symbols , are: u, for the u p quark; d, for the down quark; these are the only stable quarks. In addition ther e ar e four unstabl e quark s which appea r momentaril y i n accelerator s and wer e probabl y aroun d a t the cre ation o f the universe : s, for the strange quark; c for charm; b, for bottom (althoug h the more genteel call this quark beauty], an d t, for top, which some call truth. Truth has ye t t o be found , o r if you prefe r it , we hav e not reache d th e top . Three of the quarks (u, c, and t) have a charge of +2/3 (on a scale in which the charge on the electron is -1). The other three (d, s, and b) have a charge of -1/3. Every quark has ar t antiquark with the opposit e charge . Thu s th e antiquar k of u i s denoted u an d ha s a charge of-2/3. The belief that there are six kinds of quark and six kinds of leptons is part of what is known among theoreticians as the standard model of the elementary particles an d th e force s tha t ac t between them . Ar e the quark s and lepton s them selves buil t fro m simple r particles , lik e Russia n neste d woode n dolls ? W e don't laiow. In 199 5 i t was claime d tha t experimenta l result s supporte d the existenc e o f an elementary particl e with mor e mass than mos t atoms . This coul d be the sh y top quark but stronger evidence would be welcome. The letter s u , d , s , and s o on , ar e referred t o as the flavor o f the quark . Thus a quark has both flavor (which indicates , amon g other things , th e magnitudes o f its mass an d it s electrica l charge) and color charge (whic h indicate s ho w i t behaves with respect to the specific stron g force that quarks have between them.) Protons an d neutrons , the familia r brick s of matter, contain onl y up an d dow n quarks. Th e proto n i s built o f three quarks : uud , giving a total charg e o f +1. The neutron I s ddu , wit h zer o charge . Th e n+ meso n i s du , whic h als o give s a tota l charge of +1. All mesons have one quark and one antiquark. Given that there are 6 quarks and 6 antiquarks, each having a choice of three colors, and that they can be combined two at a time or three at a time, there are easily enough different possibl e combinations to account for the few hundred known "elementary" particles. Moreover, although the masses of the quarks are not accurately known, they cover a wide range of values, which woul d accoun t for the great variety o f masse s amon g th e hadrons . Th e quar k story , a s describe d here , i s schematically summarized in Figure 31.2. Back to the Trinity Unless you are interested in particles that generally last less than one millionth o f a second, modern particle physic s lead s to the conclusion that , after findin g and ra-

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tionalizing several hundred particles , the everyday world can still get by with only three. Once we had the proton, the neutron, and the electron. Today we can manage nicely wit h th e up quark , the dow n quark , and the electron . Bot h the proton an d the neutron ar e built of combinations of the two differen t quarks , and th e electro n has remained inviolat e since J. J. Thomson found it . That's it. With these three you can build the periodic table—every element in the cosmos. A positive electric charge and a negative charge cancel eac h othe r i n the sens e that they produce a body that is not acted upon by an electric field. Analogously, a combination o f three quarks, each having a different color , is "neutral" towar d th e strong force . Thi s neutralit y hold s fo r both th e proto n an d th e neutron , eac h of which has one red, one blue, and one green quark. Thus, at first sight , such "colorneutral" hadron s shoul d no t hav e an y "color " interactio n wit h othe r hadrons . If both the proton and the neutron are neutral in this sense, the question is : After al l this theorizing, what hold s the nucleus together? What force prevents tw o protons from rushin g apart? To answer that I refer you back to Figure 13.4b and Chapte r 13, where we discussed the (gentle ) van der Waal's force between neutral atoms. There we saw that even though the net charge on each of two atoms was zero, the individual electron s an d nucle i coul d attract and repe l i n suc h a way that th e ne t resul t was an attractive force. Thi s wa s because the tw o kinds o f charged particle have a certain amoun t o f freedom i n how the y distribut e themselve s in space . A n analogous situation holds for the interaction o f color-neutral hadrons. Just as the van der Waals force between atoms is much weaker than the internal force holding the electrons of each atom to their nuclei, so the force between two hadrons i s much weaker than th e forc e betwee n their constituents , the quarks . The forc e betwee n color neutral hadrons is a weak offshoot o f the stron g force. As the number of protons i n the nucleu s increases , th e electrostati c repulsio n betwee n the m eventuall y over comes the force s holdin g the neutrons and protons together, which is why it is becoming more and more difficult t o produce new elements of greater atomic number than those found or synthesized to date. The Shy Quark Quarks have never been observed outside the nucleus. When nuclei or single particles are bombarded with high-velocity particles, collisions ar e invariably followe d by the appearance of a wealth o f short-lived particles that often disintegrat e to give other species. The tracks revealed in bubble chambers are by now a familiar icon of the late twentieth centur y (Figure 31.3). Quarks never appear; they only give signs of their presence. The problem of "quark confinement" is one that has given rise to much speculatio n but a t the time of writing has not received a universally accept able solution. But we know that they are in there. There is a parallel between Rutherford's discover y of the nucleus an d the experiments tha t revealed the inner structur e o f protons. Rutherford's a-particle s generally went straigh t through the metal foil, excep t when they had a head-on, or nearly head-on, collision wit h a nucleus, i n whic h cas e the y wer e deflecte d throug h very larg e angles. I f a beam o f electrons o r neutrino s i s fire d a t protons , mos t o f them go straight through, but som e are violently internally deflected—presumabl y by the quarks. A popular picture of a hadron is of a bag containing three quarks. But what keeps quarks together?

The Elementar y Particles |

Figure 313. Charge d particles leave tracks in a bubble chamber. A negatively charged meson comes in from the bottom of the pictur e an d hits a proton at point O. The result i s a negatively charged meson and a particle that immediately disintegrate s into a neutral A° particl e (which leaves no track) and a positively charge d meson. The lambda particle move s a short distance before it disintegrates into a proton and another meson . (Photo from the Lawrence Radiation Laboratory, Berkeley, California.)

Contact Glue for Quark s If we accept the picture of forces being associated with specia l particles—the electromagnetic forc e with the photon , an d gravit y with th e (a s yet undetected) graviton—then w e ca n expec t tha t th e stron g force , whic h hold s quar k t o quark , will also hav e it s ow n messenger . I t ha s bee n demonstrate d experimentall y tha t th e strong force is mediated by eight entities. Th e gluons (from glue) are stable but have no mass and no charge. One may well ask what they do have, but that question arises i n ou r minds becaus e we gre w up i n a world tha t ha d mas s an d charg e as the only fundamental properties. Remember that photon s have no mass or charge, but they exist. There is no point i n going into great detail about gluons. The force that they are responsible for is enormous. Th e energy required t o separate two quarks ca n be as much a s 10,000 joules, or the work required to lift a 50 kilo woman to a height of 20 meters. Gluons can interact wit h eac h other, considerably complicatin g the pictur e of wha t goe s o n i n th e nucleus . Photons , i n contrast , d o no t interac t wit h eac h other. The theory that deal s with the interaction o f quarks is called quantum chromodynamics (chroma fo r color), or QCD, and i t is less develope d than its counterpart, QED, that deal s with electromagnetic interactions . The Leptons

The lepton s ar e simpl e compare d wit h th e quarks . Ther e ar e si x lepton s (on e of which i s the electron), each with it s antiparticle. The y show no signs of having an internal structure . One of the strangest individual s i n the Great Particle Sho w is the lepton known as th e electro n neutrino , commonl y jus t calle d th e neutrino . Th e mai n natura l

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source of neutrinos in our neck of the woods is the Sun. Every second, thousands of trillions of neutrinos fal l to Earth; they are passing through you now. They can also be produce d i n proto n accelerators. Neutrinos ar e probably the mos t penetratin g particle i n th e cosmos . Ther e ar e good reasons for this: th e neutrin o contain s n o quarks, and i t is therefore unaffected b y the stron g force. Bu t it is also electrically neutral and therefore blind to the electromagnetic interaction. In addition, the neutrino has so little mass that there is doubt as to whether i t has any mass at all. All this would sugges t that it had n o interactions of any kind, but i t can interact wit h quarks, by the mediatio n o f a particle known a s the Z boson. Nevertheless , since this action is very weak, the neutrino is an extremely introspective character , barely interacting with its surroundings. A neutrino could pass back and forth through the Eart h a billion time s and stan d a fair chanc e o f not interactin g with anything. As John Updike wrote: Like tall and painless guillotines, they fal l Down through our heads into the grass. At night, they enter at Nepal And pierce the lover and his lass From underneath the bed—you call It wonderful; I call it crass. The Weak Force

The fourt h o f the know n force s o f nature t o have been characterize d i s the wea k force. It operates within the nucleus. The relative strength of the four force s is indicated by the approximat e forc e i n newton s betwee n tw o proton s place d a t a distance of 10"15 meters from eac h other. They have to be that close, for the very shortranged weak and (indirect ) strong forces to have a chance of showing their strength: Gravity: 10" 34; weak force: Id" 10; electromagnetic force: 10 ; strong force : 10 3. Note that th e stron g force betwee n tw o proton s i s the "va n de r Waals' " shadow o f the enormous strong force between quarks. How doe s th e wea k forc e manifes t itself? Betwee n what i s i t a force ? Yo u can look upon the forc e a s one that is able to change the flavor o f quarks, for example, from a down quark to an up quark. It was first invoked to account for the phenomenon o f (3-decay, the radioactive ejection of an electron and a neutrino from an atomic nucleus. It is impossible to go into the brilliant theoretical analysis, mainly from work by Sheldon Glashow, Abdus Salam, and Steven Weinberg, that has been applied to the weak force, but it has been shown that just as electric and magnetic force s are really two aspects of the sam e physical phenomenon, so the weak force an d th e elec tromagnetic forc e ar e sister s under th e skin , manifestation s o f a single phenome non labele d the electro-weak force. It is not possible to really grasp the meaning of this withou t goin g throug h th e physics—whic h w e wil l no t do . Nevertheless , it should b e realized that this is a major ste p in the physicist' s desir e t o construct a unified theory of all the forces in the universe, a theory which would show that all forces ar e differen t aspect s o f on e force , a s Kan t an d th e Naturphilosophers be lieved. It still remains a belief, a reflection of the impulse to create order, and of the, perhaps mistaken, faith in the simplicity o f nature.

The Elementar y Particles |

Theory and Experiment

Why do we think there are six quarks if only five have been found? Recall the periodic table. Before they were found, certain "missing" chemical element s were predicted to exist becaus e ther e were obviou s holes in th e table . I t often happen s in science that ther e ar e very good reasons for supposing th e existenc e o f a particle, molecule, or process, without our having observed it. In recent times, the prediction of the existence of unrevealed particles and, more generally, the understanding o f the known elementary particles, has depended crucially on considerations of symmetry. The study of symmetry, as a branch of mathematics, began long before it became obvious in the twentieth centur y that symmetry was one of the most powerful tools that the physicist and chemist have in discussing the nature of matter. Symmetry puts restrictions on the possible properties of matter. If I tell you that an anima l mus t b e symmetrica l wit h respec t t o reflectio n i n a mirro r runnin g through its body, I am immediately putting limitation s on its form. If it has on e leg to the left o f the mirror plane it must have one, identical but mirror image, leg to the right, and s o on. The branc h o f mathematics tha t deal s wit h symmetr y i s calle d group theory. When applie d t o physica l objects , th e basi c questio n tha t grou p theor y ask s is : What changes leav e an objec t lookin g the same ? (The mathematicians woul d say : under what set of operations is the objec t invariant?) Many object s hav e som e geometrica l symmetry, but ther e ar e subtle r symmetries. Newton's laws are "symmetrical unde r time-in version," which is a posh way of sayin g that they are unchanged whe n time runs backward. They are unchanged by taking the equations an d changing th e time t, into -f . When we get to relativity, we will see that al l physical law s ar e lef t unchange d by certain changes. The fac t that a law remains unchanged by reversing time, or by performing experiments in a moving train , are , like th e conservatio n rule s tha t w e have noted , aids t o understanding the properties of physical systems . If a physical system has a certain symmetry with respect to space or time, that immediately puts restrictions on the way it can behave. We cannot go into group theory here. All I want to stress is that group theory has been used to classify the elementary particles into related families and that the theory help s u s predic t whe n ther e ar e particles—member s o f the family—tha t ar e missing. After all , if someone told you that h e was holding a n article that had th e symmetry of a square, and you could se e only three corners, you could predict that there was anothe r identica l corne r hidden b y his hand . Whe n particl e physicist s talk about "SU(3j" and the "eightfold" way, they are talking about symmetry, which has its roots very deep in the theory of quantum mechanics and relativity, but is not one of the allurin g siren s that w e will be droppin g in o n to sip wine with on this particular trip. The Final Force?

The British physicist Pete r Higgs has suggested that there is another undiscovered particle, now called the Higgs boson, whose properties are such as to give particles the appearance of having mass. If true, this could explain the origin of inertia. The

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search fo r the famou s Higg s boson is on e o f the justification s put forwar d fo r th e proposed giant Superconducting Supercollider—the SCSC or SCS. Another idea in the particle world, which has been the cause of many a seminar and symposium , is an entity on which great expectations wer e placed a few years ago: th e "string, " whic h ha s bee n followe d b y a n improve d model , th e "super string." I would not dream of attempting to go into detail about the superstring, but I bring it up to indicate the strange landscapes through which the theoreticians are wandering. There are variations of the theory, but all postulate a threadlike beast. Particles, i n th e standar d model , are supposed t o have no size ; they ar e point particles. As you might imagine, a particle with zero size can give funny answer s to some calculations . Thu s calculatin g the energ y o f such a particle ofte n cam e u p with the awkwar d answe r tha t th e energ y was infinite . Infinities are the curs e of theoretical physics, so why not assume that the really basic particles are not points but are threadlike? It would take about 10 20 of the hypothesize d "superstrings " to stretch fro m on e side of a proton to the other. These loops of something are supposed to be able to vibrate, and each of the modes of vibration corresponds to a different elementar y particle. The large number of possible modes of vibration could provide a basis for the hundreds o f different know n elementary particles, an d migh t eve n give a rational explanation for their masses, which u p to now have given no hint whatsoever of a pattern. Just as Pythagoras found that certain mathematical relationships were connected with certai n natural musical tones, so the allowe d vibrations o f the super string might, said the theoreticians, give the masses of the particles. Thi s hope has not materialized. The excitement created by the theory is, according to my theoretical colleagues, dying down somewhat. Mathematically it is complex; one variation claims that the strings exis t i n ten dimensions , anothe r that the y occup y twenty-six dimensions ! The real problem i s that s o far the theor y has no t com e up wit h an y new predic tions that have been experimentally verified. Rashomon Our ignoranc e is vast. —Karl Popper

We have divide d th e cosmo s into particle s and fields , bu t wha t justificatio n hav e we for preaching this doctrine? There is no doubt that it fits i n with our visual experience of the world—there are things that we can see and that take up space , and there are things that we cannot see but whose presence is evidenced by the behavior o f fallin g bodies , compas s needles , an d transformers . Bu t th e wave-particl e story teaches us to beware of simple conclusions, however obvious they seem. Consider the photon. We tend to regard it as a particle because we can detec t it when it hits a suitable device . A flash o f light on a screen would see m to indicate that a shell has fallen, no t a wave. And yet nothing in practice depends o n our belief tha t th e photo n is a "body," somethin g tha t Descarte s would sa y "had exten sion." In fact, the theoretician s prefe r t o view the photo n as a manifestation of the electromagnetic field , a kind o f bunching u p o f the fiel d or , if you prefer , a wave packet in the field . Thi s approac h abolishes the distinctio n betwee n particle s an d

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fields. Thi s i s not to o dauntin g i n th e cas e o f photons; they ar e no t suppose d t o have mass anyway. But the same idea has been extended to all "material" particles. The theor y wa s firs t propounde d by Heisenber g and Paul i i n 1929 . Theoreticians now trea t all particles a s though they were manifestations of a field. Thu s a proton is associated with a field an d can be regarded as a gathering together of this field. According to modern quantum field theory, every particle, whether it be electron, quark, muon, or whatever, can be regarded as being a bunching up o f a field , on which surreal note we take our leave of matter—in this book anyway. The theory of particles an d their interaction s has taken us far from th e simpl e ideas that guided the construction o f the atom in the first quarte r of the twentiet h century, when three particles and the coulomb force seemed to suffice. Modern particle theory is a soup containing quantum mechanics, relativity, and group theory, and it will probably never, at any time, be fully digestibl e by more than a few thousand people. What we have done here is merely to give a slight indication of its richness, fascination, and complexity . It is one of the great intellectual achievements of our time, even if its practical fruits fo r the last forty years have been negligible. Relevance Many scientists fee l that science should be useful i f possible. I am one of them, but the spiri t o f this book is, I believe, consistent with those scientists, o f whom I am also one, who regard science as a search that needs no practical justification. Particle physics ha s undoubtedl y produce d som e of the mos t imaginativ e an d subtl e ideas i n science , and the spectacl e of the elementar y particle s being "tamed" i s a magnificent exampl e o f physica l intuition , mathematica l awareness , an d grea t leaps of the imagination. It is also a very expensive hobby. The need to attain higher and higher energies, to liberate, for a fleeting moment, a new particle has resulted in the design of monster accelerators costing $10 billion or more. A few years ago, those with their hands on America's purse strings began to ask questions, an d th e particl e physicists ha d t o go on the defensive . Congressional committees , conscious of the nationa l deb t and th e demand s o f society for better socia l services , are not to o friendl y towar d the cr y of "science fo r science's sake." Perhaps thi s account s for the decidedl y straine d effort s o f certain particle physicists to justify research in particles as being much more socially useful than it is. The truth i s that t o date its practical application s hav e been meager. Neutrons have been used in cancer therapy, and positrons are revealing increasingly detailed information o n the workin g of the brain . Bu t it has bee n severa l decades sinc e a new particle has affecte d th e live s of anyone but th e discoverer' s professional colleagues. One point should be clear to HMS, if we had discovered only protons, electrons, and neutrons (p,e,n), and never found one more particle, it would have made little difference to HMS. Th e p,e, n tri o ha s underpinne d ou r understandin g o f atomic and molecular structure and dynamics , and has formed th e basis for much of th e technolog y an d medica l advance s tha t hav e change d al l ou r lives . I f you want to be a fundamentalist, you can say that the everyda y universe is built o f up quarks, down quarks, and electrons . If you throw i n th e neutrin o to account for |3 decay, you have enough components to account for most o f the history o f the uni verse. Th e res t o f the exoti c menagerie o f particles hav e affected n o on e excep t those wh o writ e articles-on-particles . Th e likelihoo d tha t th e nex t particl e tha t

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needs a multimillion dolla r accelerato r t o produc e (an d the n survive s fo r only a quadrillionth of a second) is going to be widely usefu l i s remote. Too remote, perhaps, t o justify th e enormou s expenditur e tha t could , a t least i n principle , b e di verted t o a large variety of other no less interesting , and possibl e mor e useful, sci entific projects . In October 199 3 the Unite d States House of Representatives voted t o withdra w support fo r the constructio n i n Texas of the hug e Superconducting Supercollider , which wa s to be the most powerful accelerato r yet built. This giant wa s to have a circular tunnel , 5 4 miles i n circumference . As one Representative said, "It' s goo d science, it's simply not affordable science. " The prospect of discovering all the fundamental particles and unifying all force s has drawn physicists into believing in the attainability of a theory that accounts for everything. These theories (fo r there will surel y be several!) are named theorie s of everything, or TOE for short. HMS should not be taken in by the nomenclature. Does anyone seriously believe that within th e next millennium TOE , which will be basically theorie s about particles an d forces , will be a more effective mean s o f studying medical, sociological, chemical, political, biological, economic, psychological, geological, and other problems than an attack made within the framework of these disciplines an d related disciplines? The use of the word everything in this context has always struck me not as grandly all-inclusive but as insufferably parochial . What kind o f priority should HM S give to the fundin g o f particle physics? Tha t is her ow n choice, but i t is as well to be aware of the propaganda . The proponent s of the new accelerators and TOE tend to write evangelical prose. They often imply , but hold back at the edg e of actually saying, that the discover y of the top quark , or the Higgs boson, will be the high point of man's history. Why do the rest of us have our doubts? Leon Lederman, the distinguished directo r of the Fermi National Laboratory (Fermilab) , has draw n a parallel between the superaccelerator s an d Gothic cathedrals: "Both provide spiritua l uplift , transcendence , revelation." Embarrass ing. A cathedral was the spiritua l cente r o f the whole community. Th e teaching of the priest , right o r wrong, directly affecte d th e dail y lif e o f his flock . Accelerator s express the fait h o f no one except a few thousand scientists. The results of their activities will almost certainly have little or no practical result, and will be truly understood by a negligible minority of mankind. Steven Hawking has declare d that if we can discover the Higgs boson we will know the "min d o f God." A scientist ca n take this as a piece of poetic licence, but HMS may have no guidelines to help him weigh such statements. If taken at face value, and I'm not so sure that Hawking didn't mean it that way, it shows a complete lack of proportion. If the Higgs boson represents the min d o f God, then I suggest that w e are in fo r a pretty dull party. Th e particle will probably be found, because the theorists have an impressive record of prediction. The populace will not rush into the streets waving flags . Many of them will spen d th e evenin g listening t o Mozart or Sonny Rollins—tw o o f the infinit e voices of God. The Croatian Visionary

Rudjer Joseph Boskovic, born in Dubrovnic in 1711, wa s a Jesuit priest, which is an occupation conduciv e t o the exercis e o f reason. H e traveled al l ove r Europe as a

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diplomat and a scientist. He was a remarkably active person, reminiscent of his acquaintance Benjamin Franklin, but he was a far better mathematician and a deeper thinker than Franklin. He advised the Vatican on the threat posed by the cracks in the cupol a o f Saint Peter' s i n Rome , mad e a plan fo r the drainin g o f the Pontin e marshes, and designe d a new harbor for Rimini. At the ag e of 24 he read Newton's Principia an d Opticks, both o f which wer e decisiv e i n determinin g hi s scientific activities. The latter book triggered his practica l work on the constructio n o f telescopes, bu t i t wa s th e Principia that wa s hi s secula r Bible . Boskovic published many papers and books, but his magnum opus was Philosophiae naturalis theoria redacta ad unicam virium in natura existentium, published i n 175 8 and , afte r a number of subsequent editions, printed in a revised form in Venice in 1763. In this book Boskovic showed a remarkably imaginative approach to physics, and though his ideas on atoms and forces had no experimental backing, they were an influence on a number of scientists. I t is not easy to show a direct line from Boskovic to Faraday's concep t o f fields , bu t Farada y was awar e o f Boskovic's book, as wa s Lor d Kelvin. Faraday' s belief that electricit y wa s a force, no t a substance, wa s i n lin e with Boskovic's view of things. Boskovic's picture o f atoms no t a s material entities bu t a s centers o f force wa s highly influential in the nineteenth century . Michael Faraday used it, acknowledging Boskovic's influence a t the Britis h Associatio n meeting in 183 7 a t which h e joined in a n attack on the materia l atom. Boskovic's attempt to construct a mathematical framewor k tha t would accoun t for the behavio r o f matter in term s o f one universal force , a central theme i n moder n physics, i s an underappreciated land mark in science . His conception of atoms as being a kind of gathering together of a field, rathe r than somethin g called matter that was separate from th e field , i s very close t o som e moder n ideas . I t may tur n ou t tha t wha t w e cal l matter i s indee d nothing bu t a knot in the void. Or is this all a fantasy dreamed up b y professors ? They continue to churn out psychedelic ideas, some of which live not much longer than muons. Is Science for Real ? And God-appointed Berkeley that proved all things a dream. -W. B . Yeats

We have drifted fa r away from the pictur e of little bouncy dumbbells that we started of f with i n Chapte r 1, the "molecules " tha t rushed around blindly i n a box. In the early twentieth centur y our dumbbells were replaced by three elementary particles—protons, neutrons, an d electrons—but the newborn quantum theory still lef t us wit h the tw o element s o f reality that w e had love d and know n sinc e w e were this high : matter an d energy . Then th e hol y trinity o f particles wer e replaced by usurping quarks and leptons , an d we were told that force s ar e mediated by particles, mass is interconvertible with energy, the vacuum can produce particles. And now particles are merely manifestations of fields. At thi s poin t realit y i s rapidl y runnin g throug h ou r fingers . Wha t ar e thes e fields? Are they more than mathematical constructs that have been put together so that when suitably manipulated the y give some of the answers? What is left ? A universe that i s a maelstrom of interacting fields? I n Chapter 12

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I suggested that you loo k at your hand an d the n reflec t tha t i t was mainly empt y space, but I left you with th e illusion tha t there were particles. Look again. Maybe you ar e looking at nothing bu t disembodie d lumps i n fields . I s that wha t w e are, cowpats in space , thromboses i n the cosmi c bloodstream? Is this the las t model? How real is all this? Science in the end is a construction of the human mind. Eddington saw this as a guarantee that it was rational. Our theories get better as judged by how much they can consistently explain. The ability of the quantum theory to explain th e periodic table make s it a better theor y than thos e tha t it displaced . I f there i s a reality ou t there, ou r abilit y t o predict it s behavior i s growing spectacularly. Fo r many o f us this is enough; we don't car e how the medicine cures the horse, as long as it does. We can always hide behind the positivist philosophy that says that the meaning of a propositio n is its metho d of verification. The experimen t has bee n define d in all its details, the dial s have said what the y had to say. That i s the meaning. Thi s is how , a t leas t a t th e beginnin g o f his career , Werne r Heisenberg sa w quantu m mechanics. Are we approaching the ultimate answers? One might think s o from som e of the disciples o f TOE. They remind me of a remark Max Born made in the late 1920s, to the effec t tha t "physic s a s we know it, will be over in si x months." T o which Einstein might well have answered, "B y whose clock?" For not all clocks seem to run at the same speed.

viii In the following chapters we leave behind the Newtonian universe where space and time are separate entities, and no one asked awkward questions like "How did it all start?" and "Where is it going?" Here we will travel through the space-time that Einstein built, and we will see how science has tried to answer what may well be unanswerable questions.

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32 Relativity Light is the principa l person in the picture . —Edouard Manet

Einstein fathere d two theorie s o f relativity. The first , whic h cam e ou t i n 1905 , i s the specia l theory of relativity, which generated muc h o f the popula r imager y of relativity: shrinking spears , lethargi c clocks, bodies accumulatin g mass, youthfu l space travelers, and s o on. The theory essentially concern s itself with what an observer sees when he looks at a system—a spacecraft, an aeroplane, a car, a comet, an electron, an d s o forth—tha t i s moving uniformly with respect t o him. I f Einstein had no t com e out with th e theory, someone else would have don e so ; the mathematics wa s standard , an d man y o f the idea s wer e sittin g aroun d waitin g t o h e drawn together. The second theory came out in 1916. Th e general theory of relativity is a theory of gravity, supplanting that of Newton and transforming the way that cosrnologists deal t wit h th e universe . Thi s i s th e origi n o f the warpe d spac e s o beloved b y science fiction writers . Einstein, in the genera l theory, completely rebuilt the way in which we mentally construct space and time, a transformation that he had begun with the special theory and that owed a debt to the work of the Russian-German mathematician Herman n Minkowski. 1 The general theory of relativity is one of the great monuments of the scientifi c imagination . Of what use is the theory of relativity? Very little to HMS. Its most notorious consequence, the equation E = me2, is the theoretical backing for the atomic bomb, but Einstein was no more responsible fo r the atomic bomb than Newton was responsible fo r intercontinenta l ballisti c missiles . Th e theor y wa s essentia l t o th e Dira c equation for the electron, and for quantum electrodynamics (QED). Neither of these subjects has disturbe d the sleep of HMS. Relativity affects the design of particle accelerators because particles traveling at speeds close to that of light gain in mass, which affect s thei r trajectories. Small effects o f relativity ca n b e detecte d i n th e electroni c structur e o f heavy atoms, bu t this is a very limited, esoteric subject. Otherwise relativity mainly appears in cosmology. Why all the fuss , then ? Because relativity has made us think agai n about where we live, which is in time and space. Because Einstein pulled aside the curtains arid revealed that, in describing nature, space and time are woven together, and matter and energy are one.

lr

['here is a story by Anatole France in which the aged King Herod is asked about Jesus but has difficulty rememberin g him, in differentiating hi m from th e other Judaic rebels. Einstei n was a pupil of Minkowski in Zurich, but the teacher barely recalled his student.

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Absolute Space and Time? But all the clocks in the city Began to whir r and chime: "O let not Time deceive you, You cannot conquer time." —W. H. Auden, "As I Walked Out On e Evening "

Time and space have tortured scientists, philosophers, and poets since the Greeks. Saint Augustine, in his Confessions, answers : Si non rogas intelligo in reply to the question: What is time? Locke expansively translates this as: "The more I set myself to think of it, the less I understand it. " Bishop Berkeley was more confident: "Time is the train of ideas succeeding each other." (But can you have the idea of "succession" if you don't assume the ide a of time?) Is time absolute, comin g of f God's production lin e i n a steady stream ? Newton thought so : "Absolute, true, and mathe matical time , o f itself, an d fro m it s ow n nature , flow s equabl y withou t regar d t o anything external, and by another name is called duration." Both Newton an d Sain t Augustin e held that tim e bega n at the momen t o f creation, a view subscribed to by one of the main medieval Islamic schools of philosophy and als o by many modern cosmologists. Newton also believed that space was absolute, existing out there—a ghostly framework, independen t o f man: "Absolut e space, in its own nature, without regard to anything external, remains always similar and immovable." Newton's concept of space, God's dwelling place as he calle d it, was clearly spelled ou t by John Keill in a lecture in 1700: We conceive Spac e to be that, wherein al l Bodies are placed . . . that i s altogether penetratable , receivin g al l Bodie s into itself , an d refusin g Ingres s to nothing whatsoever; that it is immovably fixed, capable of no Action, Form or Quality; whose Parts it is impossible to separate from each other, by any Force however great ; but th e Spac e itself remaining immovable , receive s th e Suc cessions of things i n motion, determines the Velocitie s of their Motions, an d measures Distances of the things themselves. For Newton and Galile o time and spac e were absolute. And i f an angel at the edge of the universe glance d a t his Role x at half pas t two in the afternoon , an d the n a t three o'clock, the same half hour would pass in Cambridge and in Padua. Interval s of time, an d distance , were everywher e what the y wer e o n Earth. Common sens e tells us that this is the nature of time and space; we don't expec t to become distorted when we run, or to find tha t when we return home afte r a drive, our watch ha s lost an hour. The world makes sense. But there was a feeling o f unease. Newto n realized that there was a problem i n locating thi s absolut e framework . I f a body move s with respec t t o anothe r body , how d o we know whic h is moving an d whic h i s stationary? Maybe they are both moving. Unless we have God's chalk marks on the stage, we cannot know: "It is indeed a matter of great difficulty t o discover, and effectuall y t o distinguish, th e true motions o f particular bodie s fro m th e apparent ; because th e part s o f that immov able space, in which these motions are performed, d o by no means come under the observation of our senses."

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Indeed they don't. Consider an astronaut in a spacecraft, seein g another spacecraft overtak e his own . H e can give an accurat e estimat e o f their relative motion, but he cannot state anything about the absolute motion of either craft , simpl y from his observation . Th e othe r craf t migh t be stationary , an d h e migh t be goin g backward. He has n o way o f knowing. He could of course ask Houston to give him th e speeds of both craft, as estimated from Earth, but that will not give him his absolute speed, onl y what h e aske d for : his spee d relativ e to Earth. He could fin d ou t th e Earth's motion with respect to the Sun and then work out his speed with respect to the Sun . But the Su n is moving within the Milky Way . . . An d s o on. There is no way that he can find the absolute framework. I cannot know if I am moving with respect to God's dwelling place because no one has seen it. Bishop Berkeley , Newton's faithfu l adversary , who migh t hav e mad e a better physicist tha n a cleric, dismissed absolut e time, space , and motio n a s fictions of the mind . Leibniz , als o consistentl y anti-Newtonian , rejected absolut e space , on the ground s that i t i s unobservable an d ca n hav e n o observabl e effects . On e ca n only say where something is in relation to other bodies. So it was with time. Time might stretch out like an endless line, but there were no fixed, sacred milestones on it. All we had, to give us some kind of arbitrary scale, were recurrent natural event s and man-made timepieces. There seemed to be an internal time, our consciousness of a sequence of events, one coming "after" another, but why suppose that this ha d any connection with the time of the physicists? Space arise s a s a concept i n tw o rathe r differen t bu t relate d ways. It may firs t have emerged with the need to specify the location of objects. The question is, does location hav e an y meanin g i n th e absenc e o f all materia l objects ? Ho w ca n I say where som e point is if I have nothing to refer i t to? If you wer e alone in a n otherwise empt y universe, how coul d yo u describ e where yo u were? (Except i n hell). Another concept of space arises in the contex t of a beer bottle. There is something called a "space" within th e bottle . This somethin g is capable of being filled. Th e bigger the bottle, the bigger the space. But the space is defined by the bottle. Once again, if we remove al l material objects, what meaning is lef t t o this space ? Try as you may, any attempt t o define i t relies o n the presenc e of a reference system . As Einstein said, "There is then no 'empty' space." Every definition of time come s down to a statement o f coincidence. Whe n I say that something happene d a t three in the morning, I mean that it coincided wit h a certain position of the hands on my watch, and that they could be correlated with a radio signal from Greenwich , and so on. Time eludes us. We don't understand wh y it flows , o r even what that phrase really means. But there is a class of phenomena that suggests that Newton was right about absolute space, that there really is a fixed framework out there. Centrifugeil Force Suppose that yo u ar e an astronaut an d yo u loo k out o f your window an d se e two unpleasantly purpl e littl e aliens , eac h holding o n to opposit e ends o f a rope, arid apparently circling about the cente r o f the rope . How do you know that it is they who ar e circling, and no t you who ar e circling them? Well, one thing is certain: if two childre n hol d th e end s o f a rope and circl e eac h othe r i n a playground, they feel a centrifugal force. The rope between them is taut and under tension. Are they undergoing absolute rotation? You can't ge t rid o f the tensio n i n th e rop e by sug-

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gesting that the children, o r the aliens, are stationary and you are going around. Rotation, i n contras t t o linear motion , appears t o be wit h respec t t o some fixe d absolute frame . Again Berkeley disagreed. Anyone rotating saw the so-called fixe d star s circling the othe r way. It was, he said , with respec t to the fixe d star s tha t we judged rotation, no t t o som e mor e fundamenta l spatia l frame . Berkeley' s idea s o n rotatio n were picke d up, a t the en d o f the nineteent h century , by Ernst Mach, who ha d a deep influence on Einstein. Mach was a no-nonsense positivist: all we could know was what we could observe , and sinc e the universe i s filled wit h matter, it would never be possible to observe a body rotating in a universe empt y of matter and ther e was no point in hypothesizing abou t it. If centrifugal force existe d in the real uni verse, it was, said Mach, due to the influenc e of the fixe d stars , which were themselves no t necessaril y fixed . Mach , in fact , credite d th e sam e star s with inducin g the property of inertia in matter, in contradiction to Newton, who sa w inertia as an inherent propert y of all matter. Mach's principle, as Einstein called it, has attracted renewed attention in recent years but has never been proved. 2 Apart fro m rotation , th e othe r phenomeno n tha t gav e paus e fo r thought wa s Foucault's pendulum . Jean-Bernard-Leo n Foucault (1819-1868 ) hun g a 28-kilogram iron bal l fro m th e dom e o f the Pantheo n i n Paris . Th e cabl e wa s 6 7 meters long, and the suspension allowed the plane of oscillation to change—which it did, slowly rotating. The change is such that it can be readily interpreted as a change in the orientatio n of the Earth, due to rotation. The pendulum keep s swinging i n th e same plane. On e might regard this as evidence that the pendulum "feels " absolute space an d remain s oriente d i n the sam e positio n wit h respec t to this framework . But i s th e trut h tha t i t feels , no t a fixe d absolut e space , bu t th e stars ? W e don' t know. You can see copies of the pendulum i n the United Nations building, the Science Museum in London, and other places. Because Einstein had a tendency to go for the big questions, he was bound to get involved wit h th e puzzle of space and time . He came to it through thinking abou t light. The Problem of Light

When Einstein was eigh t year s old, Michelson an d Morley' s experiment faile d t o detect an ether (se e Chapter 15). The physicists wer e in trouble. On the one hand , they wanted a medium for light waves to wave in; on the other hand, they couldn' t detect it.3 There has been much discussio n abou t whether Einstei n wa s awar e of, or took much notic e of , the Michelson-Morle y experiment. H e himsel f i s ambiguou s o n this, but i t is likely that h e would have produced his theorie s of relativity with or without the famous null experiment. 2

Einstein pointed out something od d about centrifugal force. Every other force seems to be an inherent property of all, or certain, kinds of matter. Gravitation is associated with mass, electromagnetism with charge, the strong and weak forces with the properties of elementary particles. But centrifugal force is apparently a product only of movement. 3 Faraday's intuition once again put him on the side of the angels: "The view which I am so bold to put fort h considers radiation a s a high species o f vibration i n the lines of force which are known to connect particles , and also masses o f matter together. It endeavors t o dismiss the ether but no t the vibrations" (m y italics).

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Figure 32.1. The two frame s are described as inertial becaus e they are moving at a constant velocit y with respect t o each other. The two me n see exactly the same behavior from the ball they throw.

Einstein thought abou t light for ten years before he produced the special theory of relativity, but the real origin of the theory lay in Newton's Principia an d Galileo's Dialogue Concerning the Two Chief World Systems. Einstei n did not accept the absolute spac e and tim e o f Newtonian physics , but, fatefully , h e di d accep t another basic axiom, conceived by Galileo and accepted by Newton: the concept of inertial frames, Thi s concept is absolutely central to the theory of relativity. Both Newton an d Galile o believed tha t if you ar e in a box ( a "frame") movin g with constant velocity with respect to the Earth , the law s o f motion that hold o n Earth hold in the box (Figure 32.1). Maybe you are reading this in a steadily moving car or commuter trai n tha t i s traveling i n a straight line. In your box, a body will obey the first law of motion: it will move with constant velocity unless acte d on by a net force . Leave a cup on your table, and it will not move with respect to you. because in the frame (th e train) ther e i s no horizonta l forc e actin g on it. Now drop your briefcase and it falls vertically to the floor , acceleratin g with the acceleratio n due to gravity, obeying the second law of motion, just as it would if the train were stationar]^ (Yo u will be repeating the seventeenth-centur y experiment s o f Gassendi, who droppe d object s from the masts of moving ships.) Throw a ball, inside th e train, an d it s pat h with respect to the train will b e identica l wit h tha t whic h i t would have followed, with respect to the Earth, had you thrown it outside the train. Newton's laws hold . We say that the box and the Eart h are "inertial frames." The room that you are sitting in is an inertial frame. The Earth and the train,4 provided it is moving at constant velocity, are inertial frames. Any two frames moving at constant velocity with respect to each other ar e inertial frames. A simple visual way o f grasping the concept of inertial frames is to realize that if you are in one you can never prove, solely from th e behavio r of bodies within th e frame, that yo u are moving. If the train carriage didn't vibrate and the blinds were drawn, you might think you were standing in the station, an d there is no experiment, confined to the train, that you can do to show that you are moving with respect to the Earth. *You will find that trains regularly steam through discussions o f relativity. This stems fro m Einstein's ow n original explanatory illustrations o f his theory.

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Physicists us e a number o f jargon-laden phrases to convey the precedin g idea . Some talk o f Galilean Invariance . Al l the y ar e sayin g i s that i f two observer s ar e moving a t a constant velocit y wit h respec t t o on e another , the wa y in whic h th e world behaves, within either of their respective frames, i s controlled by identica l physical laws. Note that to define inertial frames , we have no need to know the absolute speed of the two frames, onl y their relative motion. In inertial frames, there is no experiment that can be done, within the frame, that will reveal that it is in motion with respect to another frame. All physical laws are identical within the two frames.

The definitio n o f inertial frame s i s based on the fac t that each fram e i s moving at a constant spee d with respect to the other. If the train is not moving at a fixed velocity in a straight line, it is not an inertial fram e wit h respect to the earth. In an accelerating frame, al l you have to do is put a glass on your table to see that the train is moving; the glass starts to move across the table seemingly of its own accord, in the absence o f an external force . Thi s apparentl y contradict s Newton' s first law . I say apparently because , i n th e absenc e o f friction betwee n glas s an d table , someone standing o n the platfor m wil l se e a stationary glass , obeying the firs t la w with respect to the earth. Each observer must keep his eyes focused within hi s own fram e if he wants to decide whether a body in that frame is obeying a certain physical la w with respec t t o th e frame . Similarly , i n a n acceleratin g train , bodie s dro p no t straight down to the floo r but diagonally , even though the forc e o f gravity is acting vertically. Either of these tw o simple observations , within the frame, i s enough to reveal tha t th e fram e i s movin g wit h respec t t o the earth , thu s showin g tha t th e train an d the earth are not inertial frames . A spacecraf t movin g a t a constan t velocit y wit h respec t t o th e Earth , and th e Earth itself, for m a pair o f inertial frames . Th e laws in the spacecraf t shoul d there fore b e th e sam e a s thos e o n Earth . It i s tru e tha t astronaut s floa t freel y i n thei r smoothly moving spacecraft—behavio r tha t ca n hardl y b e sai d t o be earthlike . It isn't, but their world is controlled by the same basic laws, and their weightlessnes s doesn't show that the spacecraft is moving with respect to the Earth. Newton's laws still hold i n the capsule . The y ar e just too far away from th e Eart h for the forc e of gravity to be effective. I f someone jumps on the Moon, or throws a rock, the motio n in both cases is described completely by the usual law s of motion. The law of universal gravitation still holds, as it does in the spacecraft—it's jus t that, in the equa tion (equatio n (1) , Chapter 5) , we hav e t o replace th e mas s o f the Eart h with th e mass of the Moon. There is no experiment that you can do within the spacecraft whic h will give the game away. Only if you look outside ca n you tell that you are moving with respect to the Earth, and that count s a s an experiment outsid e th e frame . Thi s inabilit y t o perform a n experiment withi n the box that woul d sho w that yo u are moving is a pivot of Einstein's derivation of special relativity. The belief in th e unchangin g natur e o f physical law s i n inertia l frame s i s very deeply ingraine d i n physicists , bu t Maxwell' s proo f that ligh t travele d a t a fixe d and finite velocity threw a spanner in the works.

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The Image of the Undead Remember the pon d skate r i n Chapter 15, the cowardl y insect tha t rod e along on the cres t of a wave in the water ? If you had aske d it what th e velocit y of the wave was with respect to him, h e would answe r "zero." Notice that the wave never passes the pond skater. Einstei n was troubled by a similar problem: Wha t would happen if he were traveling at the spee d of light and attempte d to look at himself in a mirror? Imagine Einstein to be holding a torch that shon e o n hi s face . Ligh t is reflecte d off his face . But, if he was traveling at the speed of light, the light could never move ahead of him. It would never reach the mirror, and like Dracula and the undead, he would no t se e hi s fac e (Figur e 32.2) . Thi s i s th e kin d o f question tha t geniuses worry about while th e rest of us watch TV. Why did this problem worry Einstein? Note that if he is traveling at the speed of light with respect to the Earth, then he, and the mirror, are both in an inertial frame . But if he really couldn't see himself, then he had a way of knowing that he is in motion. For him, the observed speed of light would be zero, in contrast to the value observed o n Earth. An experiment withi n th e fram e ha s show n tha t h e is in motio n with respec t to another inertia l frame . Thi s means the collaps e of the principl e of Galilean invariance, which say s that such an experiment canno t be constructed. Einstein realized that th e proble m of Galilean invariance coul d be solve d i f he assumed tha t light traveled at its normal speed in his flying frame. I f this were so, then h e would se e himself, the spee d o f light would see m normal to him, an d h e would onc e again have n o wa y o f knowing tha t he wa s moving . Bu t there was a very serious problem with this solution. If light were to travel at its normal speed in Einstein's frame, then an observer on Earth would presumabl y se e the ligh t fro m Einstein' s flashligh t travelin g at twice the speed of light. If Robin Hood's arrows travel at 100 mph with respect to his bow, and h e shoots a n arro w forwar d fro m th e to p o f an expres s trai n travelin g a t 5 0 mph, he will stil l see the arrow traveling at 100 mph with respect to himself, but a spectator by the track will se e the arrow moving at 150 mph. Now that's O K for arrows, but i t doesn' t wor k fo r light. Th e reason i s contained i n ou r discussio n i n Chapter 15 . We saw there that the observed speed of light waves is independent of the motion of the source. This ca n be show n t o be true for electromagnetic waves by lookin g at Maxwell's equations . I n othe r words, to a n observe r on Earth, light could not travel faster than it s speed o n Earth; and if Einstein was traveling at the speed o f light with respect t o the Earth , then th e ligh t coul d no t leav e Einstein' s face; h e would b e riding on the cres t o f the wav e Ein d could no t se e his face . Ergo , Galilean invariance was a myth, there wa s an experiment tha t could reveal that you Figure 32.2. I n the stati c frame Einstein sees himself because the light from the torch is reflected, first off hi s face, then from the mirror, finally reaching his eye. In the frame moving at the speed of ligh t the light reaching his face can never leave it—he keeps catching up with it. Like Dracula, he will not see himself. At leas t that's what common sense says.

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were moving, even if you were in an inertial frame: just measure the speed of light. This problem was to bring down Newton's absolute space and time, so let's state it concisely: • Fo r a flashlight moving at the speed of light, Maxwell's equations show that, to an observer on Earth, the speed of the light from th e sourc e is equal to that on Earth. • I f the preceding is true, then for Einstein, who i s moving at the speed of light, the spee d o f a forward directed light beam is zero, and he would kno w that he wa s movin g with respec t to th e Earth . This contradict s th e principl e o f Galilean invariance, since Einstei n and the Earth are in inertial frames . Which was Einstein to throw out ? He could adjust th e spee d o f light fo r a moving observer, by modifying Maxwell's laws. Or he could reject Galilean invariance . The principle o f Galilean invariance was so deeply installed i n Einstein that he was not prepared to give it up. This meant that he had to leave all physical laws unchanged in the moving frame, an d that included Maxwell's laws! In other words, if Maxwell's laws were applied in the moving frame, they would predict the speed of light to be quit e normal , no t zero . Einstein woul d no t b e riding o n the cres t o f a wave. But now another dilemma emerged! If the spee d o f light wa s normal in the movin g frame, the n th e sam e beam tha t Einstein sa w to be travelin g a t the spee d o f light woul d b e traveling a t twice th e speed o f light t o someon e o n Eart h (thin k o f Robin Hood). Which , fo r the earth bound observer, would contradict Maxwell's laws. Remember, the speed of a wave is independent o f the speed of the source. Could a way be found to ensure that a beam of light traveled at the sam e spee d for th e ma n i n th e fram e (thu s rescuin g Galilea n invariance) , but tha t th e sam e beam a s viewed fro m Eart h also appeare d to be travelin g at the norma l spee d of light, as demanded by Maxwell's law? This sound s impossible, as though, standin g by the track, we saw Robin Hood's arrow traveling at 100 mph with respect to the Earth, and yet he also saw it traveling at 100 mph with respect to the moving train. With the boldness of genius that comes along only every few centuries, Einstein stood by his belief in Galilean invariance and declared that, whatever reason said: The observed speed of light is the same for any observer.

If Einstein was traveling at the speed of light, and carried a flashlamp, he would see the ligh t leavin g th e flashlam p a t 300,00 0 km/sec an d (thi s i s th e craz y part ) so would an observer on Earth. There are two pillars to the special theory of relativity: the concept of Galilean invariance and the belief that the velocity of light is the same for all observers.

Actually the secon d statement i s included in the firs t i f you believe absolutely in the principle of Galilean invariance, which state s that you can't tell if you are moving in an inertial frame. The Special Theory of Relativity Is Born

The need t o ensure tha t ligh t traveled at the sam e spee d fo r any observe r create d the theor y of special relativity. The theor y ensures the invarianc e o f the spee d of

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light in all inertial frames. Einstein would see his face, but from the Earth the speed of light from his flashlight would still appear to be 3 x 108 meters per second. How? Speed is estimated by measuring ho w long it takes something to travel a certain distance. The measurement o f speed thus requires a measurement o f length and of time. Now both Einstein and the observer on Earth are looking at the same beam of light. For them to measure the same speed relative to themselves, eithe r Einstein's ruler o r clock, or both o f them, must hav e differen t scale s fro m thos e o f his earth bound assistant . Give identica l ruler s t o two observers , in two inertia l frames , an d the y will look exactly the same provided each observer looks at his own ruler. But if an observer looks at his ow n ruler an d a t the rule r i n th e othe r frame, they will appear to be different . Likewise , if you look , from the vantag e of your frame, at a clock in another inertial frame, it will appear to be running a t a differen t rate from yours. If the difference s i n scal e are chosen properl y it is possible fo r both Einstei n an d the earthbound observe r to see the beam from his torch traveling at the same speed. This conclusion i s at the cor e of the specia l theory of relativity. Distance and time intervals in inertial frames depend on which frame the observer is standing in. Einstein ha d demolishe d th e Newtonian-Galilea n concept of an absolute time and an absolute space. We have n o intentio n o f getting into th e formalis m of relativity theory , but a t least it is worth seeing that the famous and central subject of "time dilation" is very easy to understand. Let us use Einstein's railway coach again (he did). In the moving train we will place a clock of a kind thought up by Richard Feynman (Figur e 32.3b) . Th e lam p send s ou t a regular strea m o f light pulses , eac h of which i s reflected of f a mirror and fall s ont o a receiver that emit s an audible beep and simultaneousl y triggers the nex t pulse . Th e time i t takes for one cycl e o f the mechanism will be our unit of time. The man on the platform has an identical clock (Figure 32.3a), but let's see how the clock on the train appears to him. In the eyes of the stationary observer (SO), th e light pulses takes a longer path between lamp and receiver, due to the motion of the train. However, according to Einstein, the veloci-

Figure 323. Feynmans clock. The regularly emitted photons are reflected off th e mirror and reach the receiver . To an observer on Earth the time taken for th e journey i n the movin g frame (b) is longer than that in the static frame (a) because the path is longer and the speed of ligh t is independent of the motion of the observer.

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ty of light is the sam e for all observers so that for SO, the light pulse in the moving frame take s longer to cover the path from lam p to receiver. The passenger does not see this extended path; he sees an identical path to that seen, for his own clock, by the man on the platform. The man on the platform looks at his clock and notes that with respec t to that clock , the cloc k on the train i s running slow ; it's no t beeping fast enough . In fact, if the trai n is running at three-quarters of the spee d of light, its time intervals will appear to him to be about one and a half times longer than those of the stationar y clock. To the man o n the train , lif e seem s perfectly normal. If the train is traveling a t 99% o f the spee d of light, the facto r rises to over 50. Note once again that these are identical clocks and the path of the light in his own clock looks identical to both observers. To the stationary observer, time has passed more slowly on the train. Th e whole argumen t depends on common sense plus on e totally uncommon assumption: that the speed of light o n the train appears to be the same to the man on the platform as it does to the man on the train. If you want to work out the differenc e between the clocks, the formula for the interval of time between beeps is:

where t is the interval observed on the stationary clock and f that , say 10 seconds for example , observed on th e moving clock, v is the velocity of the moving clock with respec t t o th e earthboun d observe r an d c is th e velocit y o f light. Not e that when v approaches the speed of light, (v^/c2) approache s unity and t approaches infinity. In other words, a clock traveling away from Earth at the speed of light would appear, to an earthbound observer, to have stopped. When v equals zero , and th e two frames ar e at rest with respect to each other, t = t, and we are back to the normal Newtonian world. This so-calle d time dilatio n i s the origi n of the famou s twi n paradox , in whic h one twin journeys into space at great speeds, returning to Earth to find that he has crossed fa r fewer day s of f the calenda r than hi s brother . Which cloc k was right ? Neither! They were both right, because there is no Master Clock, guarded by old Father Time and counting off the real seconds. To emphasize this, put yourself in the train. The man on the platform appears to be moving away from you , and you wil l see his clock going slower than yours, the reverse of what he experiences. There is no absolute time. We have not measured something calle d time, we have counted off events , comparin g two piece s o f apparatus. That, accordin g to th e positivis t philosophers, i s abou t al l w e ca n sa y about time. And , by the way , although we haven't shown it, there is no sacred length; that too depends on the observer. So Fast and N o Faste r

Einstein wen t a step further . H e emphasized no t onl y that ligh t canno t travel instantaneously between two bodies, but neither ca n force. Thus, suppos e tha t yo u coul d suddenl y switc h of f the charg e o n a proton . Would an electron, say a meter away, instantly feel that the electric field aroun d it had gone out? No. The field would die out in the time that it takes for light to travel between the two particles. Admittedly, this is a very small interval of time, but it is not zero . Why should th e forc e b e connecte d to the velocit y o f light? The easies t

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way to see this is to recall that the electromagneti c force i s mediated by photons, and they certainly travel at the speed of light. This is why Einstein saw the velocity of ligh t not onl y as being an uppe r limi t to the velocit y o f any body but als o as a limitation o n th e "velocity " o f forces. N o forc e ca n b e transmitte d betwee n tw o bodies faster than the spee d of light. For example, if our fiendish friend Dr. Moriarty decided to operate his antigravity gadget on the Sun, we would no t know about it for at least eight minutes, which i s roughly the time it takes for light to reach us from the Sun. This assum.es that gravity is propagated as we believe electromagnetic field s ar e propagated , taking tim e t o cros s space . N o othe r typ e o f signa l ca n reach u s faste r tha n th e spee d o f light—until you as k what i s happening i n Alai n Aspect's experiment (se e Chapter 30). Fact, Not Fiction

Time dilatio n ha s bee n observe d in severa l experiments. A particularly dramati c example is based on the spontaneous breakup of elementary particles, or of atomic nuclei (se e Chapter 12), a process that proceeds at a pace unaffected b y man. Each kind of elementary particle, when in isolation, has its own half-life. In 1937 Anderson and Neddermeyer detected a short-lived particle in cosmic rays. Muons have a half-life o f 2 millionth s o f a second , whic h mean s tha t afte r thi s tim e hal f th e muons in any given sample will have disintegrated . The elementary particles can be thought of as having an internal coi n thrower, different type s of particle having different rate s of throw. Heads, I disintegrate; tails, I live a bit longer . The thrower knows when t o throw because he ha s a clock. Pressure and temperatur e change s have no effec t o n the rate of this internal clock . In experiments at CERN, a beam of muons ha s been induced t o rush roun d a circular tube a t speeds of 99.94% of the speed of light. If you put thi s figure into equation (1), you will find that 1 second as observed on the coin thrower's watch (inside the muon) is seen as about 29 seconds by th e stationar y observe r watchin g hi s ow n clock . T o the coi n throwe r i n th e muon, disintegratio n goes on at the usual rate. To the experimenter , the lifetim e of the muon s should increas e by 29-fold , fro m 2 to nearly 60 millionths o f a second. The actual observe d differenc e betwee n experimen t an d Einstein's predictio n wa s in fac t les s tha n 0.2% . "Time" ha d slowe d down , if you wan t t o pu t i t that way . Mach would say that we have no right to bring time int o it; all that had happene d was that, a s seen fro m th e stationar y observers' viewpoint, on e clock ran twentynine times slower than the other. Either way, Einstein rules, OK. Mass

One o f the mor e notoriou s consequences o f special relativit y i s that th e observe d mass of a body depends o n its speed with respect t o the observer . We will not de rive this fact , but the mathematical treatment shows that as the body accelerates its mass increases. If it travels at the spee d o f light, its mass becomes infinite. This i s the origin of the statement that nothing can travel faster than the speed of light. Notice that the increas e i n mass is in the ey e of an observer in a frame with respect to which the body is moving. If you travel with the body, it is motionless with respect to you, and the additional mas s observed by the stationar y observer is not observed by you. You will see what is called the rest mass of the body. Again we see

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that what w e observ e depends o n the relationshi p betwee n ou r frame an d tha t of the object that we are observing. The mass increas e a t high speeds , predicted by theory, has been confirme d experimentally. As mentioned earlier , it has to be taken into account in designing particle accelerators , in whic h velocitie s clos e to that o f light ar e reached. Th e electrons in you r T V cathode tube trave l at roughly 7 % o f the spee d o f light, which means that they have about 7 % more mass than their rest mass. Electrons in a linear accelerator can reach speeds within on e part in a billion o f that of the spee d of light, and the y behave, experimentally, a s though thei r observe d masse s ar e ove r 1013 as large as their res t masses. Thi s i s as though a n ant increased its mass to \ million tons. New Laws for Ol d The second law o f motion ( a = F/m,) assumes that m, the mass of the body, is constant. We have seen that fro m a n observer's poin t o f view the mass depends o n the relative speed o f the body . If m increases , then, fo r constant forc e F , the acceleration a decreases . At the spee d o f light th e mas s i s infinite and th e acceleratio n is zero. The forc e appear s to have n o effec t a t all, with respect t o the stationar y ob server. Tw o hundred an d twent y year s after th e Principia, Einstei n rewrot e Newton's second law and unknowingly gave the explanation, but not the impetus to the atomic bomb: 5

The superscript 3/2 means take the expression in the brackets and multiply it by its square root. If you don't like this reminder of high school, it doesn't matter; the two important things to note are that: • Whe n v, the velocit y o f the body , i s equa l t o c, the quantit y in th e brackets vanishes, whic h mean s tha t th e acceleratio n i s zero . We can regar d this a s equivalent to the body having infinite mass. • I f v is zero, the equatio n reduces to Newton's a = F/m. Furthermore , even for quite large velocities, the equation is so clos e to Newton's as to make no practical difference . As a n example , fo r a body moving a t a velocity of one-tenth o f the spee d o f ligh t (i.e., 3000 km/sec, which is enormous by any normal standards) , the equatio n becomes a = 0.985F/m, which mean s tha t th e acceleratio n fo r a given forc e i s onl y about 1.5% les s than Newton predicts. This illustrates a general conclusion: when we are dealing with velocities well below the spee d o f light, the equation s o f special relativity reduce to those of Newton. Thus we see that Newton is not "wrong" ; his equations are very good approximations if we deal with bodies traveling at low speed. At low velocities al l the mechanical equation s of relativity reduce t o those of Newton . I t could b e sai d tha t w e neve r notice d tha t anythin g was wron g with Newton because we never traveled fast enough, and we never knew that we needed quantum theory because we aren't small enough. 5

Einstein's theories had almost nothing to do with the trails of research that led to nuclear weapons. Such weapons undoubtedly would have been developed in any case.

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The Unification of Mas s and Energy If we exer t forc e o n a body, then it s observe d mas s increase s whe n i t accelerates with respect to us, and a weird and wonderful consequence can be derived. The apparent increase in the mass is due to our having done work on the body. (Recall the definition o f work, as force times distance.) The work has appeare d a s both an increase in the kinetic energ y of the body, because its velocity is increasing, and a n increase i n mass . It is apparent that the work has been converte d int o energy and mass. Now wor k is a form o f energy and ca n onl y be converted into other forms of energy. This implies that the increase in the mass of the body can also be looked on as an increase in its energy. The conclusion is that mass and energy are two aspects of the same thing. The mathematics give s E = me2, where m is the body's mass an d c is the speed of light. We are so used to this equation that we are no longer amazed by its wonderful simplicity. I f there is a scientific analogue to minimalist art , then surely this equation, and Newton's F = ma, would take joint first prize at the Venice Biennale. Consider a practical example . A piece of coal has three kinds o f energy: potential, chemical , and "mass " energy . One kilo o f coal when burne d yield s abou t 30 million joules. This is its chemical energ y and is very roughly the amount of potential energ y that the coa l would have if it were at a height o f 3000 kilometers. Now let's turn the coal into energy by destroying its mass. This is not a chemical change like burning. Mass is genuinely disappearing . You can do the calculation immedi ately; you get me2 = 1 kilo x (3 xlO8 meter/sec) 2 = 9 x 10 16 joule, or about 3 billion times as much as the chemical energy. It is clear why great efforts are being made to duplicate, on Earth, the reaction in the Sun, in which part of the mass of hydrogen atoms is turned int o energy by nuclear fusio n (se e Chapter 34). The amounts o f energy obtained fo r a given quantity o f hydrogen are so large that the available hydrogen in the oceans looks infinite in this context. Incidentally, every second the Sun converts 5 million tons of its mass into energy. In a billion years, if the energy conversion proceeded at a constant rate, about 1.6 x 1023 tons would "burn" away. This amount is less than one ten millionth o f the Sun's mass. In nuclear reactions in the Su n or in nuclear reactors, the conversion of mass to energy is not complete. What happens i s that two entities mee t and produce products that have less total mass than that o f the reacting particles. Th e difference i n mass then appear s as the kinetic energ y of the particles produced. It is this kinetic energy that is the source of the power that we get from nuclear reactors. A New Conservatio n Law What are we to do about Lavoisier's law of conservation of mass and Clausius' s firs t law—the conservatio n o f energy ? Neithe r mas s no r energy , i n th e conventiona l sense o f these terms , is conserved in the nuclea r reaction s mentioned previously . Let's tak e a mor e extrem e example : a n electro n an d a positro n meet , annihilat e each other, and turn into a pair of photons, which ar e definitely radiation; no mass survives. W e canno t den y tha t mas s ha s disappeared , an d i f w e believ e i n th e equivalence o f mass an d energ y we must assum e tha t th e mas s ha s been entirely transformed int o the energ y of the two photons. We can take the input of "energy" as being roughly the su m of the masse s of the electro n and the positron. We ignore any contribution from th e kinetic energ y of the colliding particles, which wil l usu-

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ally be negligible. If we use E = me2, we fin d that the total energy equivalent o f the colliding particles is about 1.53 7 x 10" 13 joule. This mus t be equal to the energ y of the two photons, which , assumin g tha t the y ar e identical, i s given by 2hv. Using the value for Planck's constant, we find tha t th e frequenc y o f the photons is about 1.2 x 10 20Hz, which correspond s to yrays, agreeing with the observation that elec tron-positron annihilation produce s these rays. We see that what is conserved in nature is a mixture of mass and energy. (A physicist might tell you that the quantity conserve d is the energy-momentum force vector, but don't be cowed.) Normally, in the everyday world, there is no significant interconversion o f mass and energy, and we can keep both Lavoisier's and Clausius' s laws, but nevertheless, mass and energy are two aspects of the same phenomenon . The Defect and the Remed y The defect i n the specia l theor y of relativity, which onl y becomes apparent in th e general theory , is tha t it s law s begi n t o break dow n seriousl y i n th e presenc e of large masses. Although the equations of special relativity predict strange effects o n mass, the basic equations that Einstein constructed di d not contain mass. They predict change s i n th e apparen t mas s o f a body a t hig h speeds , an d the y le d t o th e equivalence of mass and energy, but the equations themselves, such as (1), include only space , time, th e relativ e velocitie s o f frames, an d th e spee d o f light. I n thi s sense they have an affinity to classical physics—there is an arena of space and tim e into which we put matter. Time and space become inextricably mixed in the equa tions, but not because of the presence o f matter. Matter does not affec t th e architec ture o r the cloc k o f the stadium ; onl y th e relativ e motio n o f inertial frame s doe s that. But Einstein had mor e rabbits in his to p hat . Th e general theor y show s tha t matter, by its presence, distort s "space-time. " Th e general theory provide s a very different accoun t of the working of gravity from that of Newton, and i t was thinkin g about gravity that le d Einstein to formulate the theory. General Relativity The professor came down in his dressing gown as usual for breakfas t but he hardly touched a thing. I thought something wa s wrong, so I asked what was troubling him. "Darling," h e said, "I have a wonderful idea." And after drinkin g his coffee, he went to th e piano and started playing . Now and again he would stop, making a few note s then repeat, "I've got a wonderful idea, a marvelous idea!" —Mrs. Einstein

The physics an d mathematic s o f the theor y o f general relativity, whic h was pub lished in 1916, ar e far more complex than those fo r special relativity. We will sim ply indicat e wha t th e theor y i s abou t an d wha t it s practica l consequence s are . I start by comparing two startlin g prediction s o f the theor y with experimental fact . Subsequently, I will use a tiny handful of equations, but at that point, those o f you who ar e violentl y allergi c t o mat h ma y choos e t o clos e th e boo k an d pla y gol f instead.

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The Proven Facts, Part I

Einstein's theory predicted tha t the pat h o f light would b e bent near massive bodies. Newton had also believed that his light corpuscles would be attracted by gravity, and Farada y looked unsuccessfully for the effec t o f gravity on light . Einstein' s prediction wa s teste d i n 1919 , durin g a n eclips e o f the Sun . Th e ma n wh o orga nized the experiment, which involved sending observers to Brazil and Principe, an island i n th e Gul f o f Guinea, was th e Englis h cosmologist Si r Arthur Eddington, who wa s a n earl y conver t t o relativity . Telescopes , directe d a t th e ri m o f th e eclipsed Sun , detected ligh t fro m star s that were known t o be slightly behind th e Sun. Because the starlight was bent inward towar d the Sun as it passed, the image of these stairs appeared to be just on the edge of the Sun (Figure 32.4). The measurements were made durin g a n eclipse s o as to blot ou t most o f the ligh t of the Sun , which woul d otherwis e hav e mad e the observatio n o f the star s impossible . Th e angle through which the light had turned was derived from their apparent position and the known position of the stars, as recorded on previous photographs. The angles through which the light was deflected were small, but enough to convince Eddington that the effect wa s real. The experiment had been o n a grand scale. An account of the observation s was presented a t a joint meeting of the Royal Society and the Royal Astronomical Society, in London, and the announcemen t o f the results by the astronome r royal, Sir Frank Watson Dyson, was a dramatic high point in the history of science. The deviations recorded by the two expeditions were 1.61 an d 1.98 seconds of arc, although the experimenta l erro r was rather large. Einstein had predicte d a deviation of 1.74 seconds o f arc. The chairma n o f the meeting , J. J. Thomson, proclaimed, "This is the mos t importan t resul t obtaine d i n connectio n wit h th e theor y o f gravitation since Newton's day [and] one of the highest achievements of human thought." That was o n 6 November 1919. Th e followin g day there wa s a n announcemen t i n th e London Times, and within days Einstein's nam e became known to more people at one time than that of anyone else in the history of science. The effec t i s no w s o frequentl y observe d a s t o hav e becom e commonplac e among astronomers. This is partly because of the use of radio waves, the detectio n of which i s quite unaffecte d b y the presenc e o f visible light . One of the source s of radio waves is a group of objects called quasars (quasi-stellar objects). In 197 8 the British astronome r Denni s Wals h detecte d a doubl e quasar , tw o closel y space d sources of light. Their spectr a were suspiciously similar , and the suggestio n arose that they were two images of the same object. This has been verified, an d there are

Figure 32.4. Th e light from the star s bends as it passe s the Sun , allowing us to se e stars that are behind the Sun. I have grossly exaggerated the bending angle.

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now thousands of related cases in which part or all of the light from a distant object has been deflecte d b y the presenc e of a large mass intervening between th e objec t and the Earth. It is as though these large masses acted as imperfect lenses. The phenomenon o f "lensing" was predicte d i n 193 7 by the Swiss-America n astronomer Fritz Zwicky , wh o base d hi s suggestio n o n Einstein' s theory . He sa w tha t i f two galaxies wer e aligne d suc h that , see n fro m th e Earth , one wa s behind th e other , then the gravitational field of the nearer one could distort the light from the farther . In the bes t tradition s o f science, he was ignored . Dennis Walsh's observation s restored Zwicky's good name. The Prove n Facts, Part II

Another prediction of general relativity is based on the prediction that a clock will run slowe r i f it i s move d fro m a weaker to a stronge r gravitationa l field . Thi s i s quite distinct fro m the slowing down due to relative motion that we encountered in discussing special relativity. Perhaps it would be better to say that the clock slows down as it moves into increasingly distorted regions of space-time, but I stick to the old-fashioned wa y o f talking. Thus consider a clock at ground leve l and on e high above the Earth. The theory says that an observer on Earth should fin d that the airborne clock is running faster , becaus e the gravitationa l field o f the Eart h weakens with altitude. The first really convincing experimental proof of this prediction was carried out in 197 6 by sendin g a clock up t o a height o f about 600 0 miles i n a rocket. At th e high point o f its flight , th e cloc k was running at nearly a billionth o f a second pe r second faster than those on Earth, as Einstein's theory predicted. If tim e i s slowe d dow n b y a n increas e i n gravity , then th e frequenc y o f light emitted by an atom is also reduced. You can think of it as a slowing down of everything connected with time. Slow the video and the tenor becomes a baritone.8 Thus a light source in a strong gravitational field (sorry , near a large mass) should exhib it a redshift, a lowering of frequency. This is not a Doppler effect suc h as that due to the relative movement of source and observer ; it occurs even fo r a source and observer at a fixed distance . The effec t ha s been observed in the light emitte d b y th e Sun, and far more markedly in the light emitted by the gravitationally lavishly endowed whit e dwarfs , wher e clock s appear t o be running slo w by ove r an hour a year with respect to us. There are no alternative explanations—as yet—for the observed phenomena pre dicted by the general theory of relativity. The effects ar e small, but they can be measured accurately, and they agree with the theory. What has all this to do with everyday life ? Nothing , except that ther e i s somethin g remarkabl e i n man' s abilit y t o create suc h subtl e explanation s fo r the way the planet s and th e star s stretc h tim e and play with light. The one area where the theory is absolutely essential i s in cosmology; the condition s at the time of the Creation were such that Einstein canno t be ignored. Space-time

Of al l th e term s that relativit y brings with it , the fourth dimension ha s bee n th e 6

Why don't the colors o f the video film change?

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most quoted , th e mos t misunderstood , an d i n a wa y th e simplest . I t ha s bee n latched ont o in particula r b y som e nonscientists, and use d t o give a false aur a of scientific authorizatio n to anything irrational. A s Eddington remarked, in the early years of the notoriety surroundin g relativity: "In those day s one had to become an expert in dodging persons who were persuaded that the fourth dimension wa s the door to spiritualism. " Every even t i n histor y need s fou r dimension s t o describ e it . A t th e Battl e of Hastings, King Harold was hit in the eye by a Norman arrow. We can use the exact map reference to locate the spot on the ground above which Harold's eye was at the time. This requires two map coordinates. A third number is necessary to determine the height of the eye above the ground. A scientist would probably label these three numbers a s x, y, and z . That takes care of the three dimensions tha t we need in ordinary space . However , we nee d a fourth number , the tim e that th e arro w struck. That is the fourt h dimension . Simple . All events tak e place i n fou r dimensions — three of space and on e of time. S o why wasn' t a fuss mad e about it until relativity carne on the stage? To answer that, we have to go back to the Greeks. Our scientific, as compared with our intuitive, concept s of space and tim e grew out of the way that the Greeks constructed geometry. The master was Euclid, whose axioms dominated geometry for well over 2000 years. Euclidean geometry is a selfconsistent system , by which I mean that if you accept the axioms, then all the rest follows logically. Man lives in a world in which Euclidean geometry is useful. Any measurement tha t involve s a plane, o r a body constructe d fro m planes , whether that body be a math lecturer's concept o r a real everyday object, can be handled by geometry, wher e th e qualifie r "Euclidean " i s rarel y used . Newton' s Principia i s heavily dependent on Euclidean geometry for its proofs. Euclidean geometry was subtly identified with the geometry of space. Man had looked around and seen that he lived on what appeared to be a flat plane. When he built a temple, he laid out lines on the ground. They were straight lines . When he drew a triangle, it was on a flat surface; the angles always added up to 180°. Euclidean geometr y i s buil t o n man' s experienc e o f his immediat e neighborhood , an d man extende d his straight-lin e univers e ou t into space, imagining that spac e ha d the sam e Euclidean geometry. Newton's universe is based o n Euclidean geometry. (a) (b

)

Figure 32.5. Th e length of the lin e in a given frame does not depen d on how I orientate my reference axes; in this case x and y, but i n general x, y, and z.

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The laws of motion spoke of bodies that, in the absence of forces, moved in straight lines. Gravity , according to Newton, acted in a straight line , and h e certainl y sa w the framework o f absolute space as built of straight lines. Th e point that is relevant to us is that in that univers e the shortest distanc e between two points i s a straight line. Let us look at that a little closer. The length of a straight line can be calculated if you know wher e its ends are . The formal way to do this is to first set up three axes, as in Figure 32. 5a. In a room it would be convenient to use the edge where two of the walls meet and the two edges where the sam e walls mee t the floor . Now mark off scales along these "coordinat e axes." To simplify th e explanation, I consider a straight lin e marked on a wall. The coordinates (x,y) of the two end points ar e determined a s shown i n the figure . Th e information i s enough to allow the length , 1, to be determined fro m th e (Pythagorean) expression: or, in a condensed notation: The generalization to three dimensions is: The firs t thin g to note is that thes e formula s d o not wor k for a line draw n o n th e surface o f a sphere o r in general on an y curve d surface . I n fact, w e could turn ou r argument around an d sa y that if (4) does give the length of a line having the short est distance between tw o points, then we are dealing with "Euclidean space." Now th e lengt h o f a line draw n o n a wall canno t possibl y depen d o n how w e choose our coordinate axes. Figure 32. 5b shows the same line enclose d by two different sets of axes. The length a s referred to the (a ) set of axes is given by: In the (b ) set of axes is given by: We see that in both set s o f coordinate axes the expression fo r the lengt h i s exactly the same . Only the numbers o n the right-hand side s o f the equatio n wil l alter , but the fina l lengt h must be the same . Again generalizing to three dimensions , w e can say that expressio n (4 ) is an invariant in Euclidean space. In other words, we can choose any fram e w e like, and th e Euclidean expressio n (4 ) will giv e the length of the line. This length is not dependent on what frame we choose. This is true as long as all the frames ar e static with respect to the line. The form of the invarian t (4 ) underlies th e Newtonian concept of space. In Newton's univers e the lengt h of a line had t o be same whichever observe r measured it , and the measure of its length was given by the Euclidean expression (4) , even if the frames were moving with respect to one another. Accordin g t o Newton , a lin e drawn o n the sid e of a train woul d appea r to have the sam e length whether o r not the train was moving with respect to the observer. The importance o f the invariant can be appreciated by considering th e proble m of calculating the path o f a discus. In Newton's universe the path o f the discus an d

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the distanc e i t travel s canno t possibl y depen d o n the observer , stati c o r moving. The method o f calculation i s based o n that belief, even if you don' t realize it. The method is founded on my conviction that the way I measure distance is invariant to any changes I may make in my frame, i n other words, any changes in either my coordinate system (where I put the x, y, and / axes) or my velocity. The independence of velocity is reflected in the fac t that the expression for the length of a line doesn' t include time. The invariant is my guarantee that I don't need a new system of equations every time I change my frame . When we get to special relativity, a problem arises. For two inertial frame s traveling with respect to each other, the length of a line as seen in the two frames i s different. As you have probably guessed, the line is shorter as seen from the frame no t containing th e line. Thus the length of the line, as defined b y expression (4) is not an invariant i n the theory of special relativity. The valu e of the expression , which gives the observe d length of the line, alters depending on which fram e yo u are in. What this really says is that the nature of space and time is not reflected by the invariant—it is , in fact , no t a n invariant i n the spac e and tim e describe d by special relativity. So what is an invariant i n special relativity? We can make a guess that if we are bringing motion into the picture we will have to bring time in somewhere. Instead of considering two points, let us look at two events occurring at differen t places and times, one at the point (x^, yt, z 1) at time ^ an d the other at point (x2, y2, z2) an d a t time t (Figur e 32.6). Now, by analogy with the expression for the lengt h of a line, define a quantity s, by: where At is t^ -l^ c is the speed of light, Ax =x2 - xl an d so on. It can be shown that this quantity has the sam e value no matter wha t inertial frame th e observe r is in. The individual value s of the coordinate s o f the points an d th e times of the events, as seen from you r frame , ma y be differen t fro m thos e seen by someon e in another inertial frame, but the su m , s2, will always end up th e same. Explicitly: if, according to an observer in a certain framework, a n event took place in that framework at the point (x a, ya, zj an d the time t a , and another event occurred at the point (x 2, y2,

Figure 32.6. Fo r frames moving with a constant velocity with respect to eac h other, a given observer will find the same value for the quantity s 2 separating two events an d defined in equation (5).

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z2) and t2; then for a second observer, traveling in another frame at a constant velocity with respect to the first, the expression (5 ) would give exactly the same number s2. In general, two suc h observer s would no t se e the sam e lengt h o f line. Neither would they see the same difference i n time between the two events. Expression (5) is Einstein's improvement on Newton's invariant; i t is the invariant o f special relativity . It is calle d not a length but a n interval. I t includes thre e space dimensions and the "dimension" o f time. Now you see where the "fourth dimension" comes from, an d why w e speak of space-time. I t has nothing to do with spiritualism. All that has happened i s that we need to mix space and time together in one expression in order to obtain a quantity that looks the same to all observers.7 Incidentally, although we are not in a Euclidean space, we are still in what can be called a "flat" space, a space where lines can get shorter depending on the observer but will not become curved. The shortest distance between two points is still a conventional straight line; we have not yet "warped space-time." Here endeth all the mathematics we are going to encounter in special relativity. There i s nothing in th e leas t mysteriou s here , nor particularl y complex. The expression fo r s is used in calculations, and the results are quite independent o f any visual significance you may attach to s. Neither HMS nor most scientists are likely to have to use the invariant of special relativity. The fact is that two observers moving at much less than the speed of light with respec t to each other will see the sam e distance between two points an d th e same time interval between two events. They can go back to expression (4) and forget about the infinitesimally small "mixing" o f space and time that becomes important only as the relative speed of the observers approaches that of light. Flexible Space-time For centuries it was assumed that there was only one kind of geometry. This is not true. Had man live d o n a planet tha t wa s onl y 10 0 meters in diameter , he migh t have grown up thinkin g i n curved lines. Stan d o n the North Pole of such a planet and draw two "straight" lines. They would be what we call lines of longitude. From where we stand we see two straight lines diverging. Euclid tells us that two straight line divergin g from a point wil l diverge forever. Bu t if you follow thes e two lines , they firs t diverg e and the n converg e to meet a t the Sout h Pole. Two straight lines can contain a n area. Now you will sa y that this is cheating; these are not straigh t lines i n the norma l sense. What you mean is that they ar e not Euclidean straigh t lines. I agree, but I would point out two things. First, a straight line can be defined as a line o n which th e shortes t distanc e between an y two point s o n i t only runs through points on the line. This is true of the traditional straight line, but it is also true o f the "curved " lines o f longitude o n a sphere i f you accep t that yo u canno t leave the surface of the sphere . Second, if Euclid had been born on our miniplanet, he probabl y would hav e constructe d a n altogethe r differen t syste m o f geometry, based o n differen t axioms . Th e theorem s o f this geometr y would b e a t varianc e with the familiar an d much-hated theorems we learned at school. To start with, he would hav e drawn triangles, squares, and othe r "straight line " figures, an d foun d 7

For the interested reader : the laws of physics are second-order differential equation s with respect to time (Newton) or interval (Einstein).

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that o n a sphere, in contras t to "Euclid," th e su m of their angle s depende d o n the size of the figure . Euclidean geometry is convenient fo r flat surfaces , hut clearl y we need other geometries for other surfaces. Other geometrie s wer e constructe d i n th e nineteent h centur y h y a numbe r of mathematicians, th e outstandin g tri o bein g th e Russia n Nichola s Lobachevsk y (1792-1856), the Hungarian Janos Bolyai (1802-1860), and the Germa n Bernhar d Riemann (1826-1866). They had been preceded by Gauss, but he never publishe d anything systematic on non-Euclidean geometry. Non-Euclidean geometry was largely ignored by other nineteenth-century mathematicians, le t alon e physicists, an d i t was onl y when Einstei n was lookin g for a geometry with properties that suited general relativity that a friend introduce d him to the work of Riemann. When he was twenty-eight years old, Riemann published a paper entitled "O n the Hypotheses Which Lie at the Basis of Geometry." The ideas therein were to be the basis for a great deal of modern mathematics and fo r our present conception of space-time. To give a hint of the differenc e fro m Euclid , consider Riemann's axio m tha t al l line s ar e finit e i n lengt h bu t endless . Worried ? You wouldn't b e if you live d o n a sphere. Wal k along any line, an d yo u will fin d tha t you will return t o the poin t o f origin (th e line is finite ) bu t tha t you r lin e ha s n o ends. Now let us see why the general theory of relativity needs to forsake Euclidean geometry. Fasten your safety belts, space-time is about to be warped. Comment on the General Theory If asked to sum up th e general theory in two sentences, I might sa y something like this: "In the inertial frames of classical physics and o f special relativity, Newton' s laws held i n any frame, but the y d o not hold fo r an accelerating frame, sa y an aircraft takin g off. One o f Einstein's achievement s i n th e theor y of general relativity, was to construct physical equation s that hold i n any frame, eve n one that i s accelerating." That's on e way the physicists se e it, but we don't have to look at it through their eyes. The theory is sometime s sai d t o be a new theor y o f gravity, and i t doe s reveal gravity in a brilliant ne w light . Bu t above all it is a revolution in the way that w e need t o vie w th e relationshi p betwee n space-tim e and matter . I n the Newtonia n universe, spac e an d tim e ar e separate , absolut e concepts . I n specia l relativity , space and time get mixed up, but the extent of the mixing depends onl y on the relative speeds of the inertial frames—it doe s not depend on the mass of bodies. In the theory of general relativity, matter distorts space-tiime.

The effec t ca n be ignored for small masses, which mean s that special relativity , or even Newtonian physics, usually suffice s fo r these cases. There ar e at leas t tw o possibl e response s t o th e statemen t tha t matte r distort s space-time. One is to attemp t t o for m a visual impressio n o f space-time and the n ask what the presence of mass does to it. The other is to say that the human mind is not adapted to thinking i n terms of space-time or its distortions—Einstein presumably gave us some trustworthy equations, so, let's see what they can do. In the en d we are going to use them t o explain observe d fact s o r predict ne w ones ; their suc cess has nothing to do with questionable geometrical images. The second approach is undoubtedl y easier; a theor y stand s o r fall s o n it s explanator y an d predictiv e

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successes. However , it is tempting to try to form visual images to go with the theory, so I will attemp t to give a short account o f the simples t visua l interpretatio n of general relativity. It is this interpretation tha t contain s the psychedelic feature s of the theory, the warping of space and the bending of light. The origi n o f the genera l theor y i s containe d i n a n observatio n w e mad e i n Chapter 5 , namely, the fac t tha t someon e i n a fallin g elevato r would no t fee l th e force o f gravity. This se t Einstei n thinkin g abou t th e connectio n betwee n gravit y and frame s o f reference. Newton had see n gravity as a force, but Einstei n realize d that the effect s o f gravity could apparently be reproduced by the acceleration of the frame of reference. Acceleration is embedded deep in Newton's laws of motion, but Newton was limited to Euclidean space. What happens t o the laws of motion when we go to other geometries? When I fly from Londo n to New York, the plane usually passes ove r Newfoundland an d Ne w England. On the ma p i n th e airline' s brochure , thi s look s like th e long way around, a very curved path. Of course, the reason is that the map is a distorted representation o f the surfac e o f a sphere. The fligh t pat h o n a globe is also a curve but onl y because a plane canno t take the shortest straigh t line pat h throug h the Earth . It flies alon g a great circle, which i s the shortes t pat h permitte d b y th e shape of the globe. We say that the geodesies of a sphere are great circles. In general, for any space , geodesies are the shortes t line s betwee n tw o points, takin g int o account th e limitation s impose d by th e geometr y of the space . Fo r example , th e shortest path between two points on th e surface of a cylinder is, in general, part of an ellipse, as you can guess from stretching a piece of string between two points a t different height s on a tennis ball canister. In th e geometr y o f Euclid , w e lear n tha t th e shortes t distanc e betwee n tw o points is a straight line. We could tur n this statement on its head and say that the fact tha t the shortes t distanc e betwee n tw o points i s a straight line means tha t we are living in a "flat" world, that what we call "space" is the familiar space in which Euclid's geometry works. If you like, you can picture this familiar space as containing an invisible rectilinear scaffolding. I n such a Euclidean space, the geodesies are what w e ar e use d t o callin g straigh t lines . W e saw tha t befor e Einstei n an d th e physicists cam e along, there were mathematicians playin g with other spaces. More correctly, they had constructed geometries based on modifications of Euclid's set of axioms. Thus they threw out the famous axiom about parallel lines, which implie s that parallel lines never meet. If you stand on the equator of a sphere and draw two closely space d paralle l line s o f longitude, they will indeed b e parallel, but i f you follow the m t o the poles, they meet. Again, don't be tempted to say, "But they are not paralle l lines"; the y are , on a spherical surface. Rela x your mind, tak e a puff , and journey into distorted geometries. Imagine that you were born on a sphere that had a diameter of 20 feet. Th e shortest distanc e between two points would alway s be a curved line, a geodesic, and resist the temptation to say, "Yes, but I could tun nel through the sphere and make a straight line." Not permitted! Now, throw awa y the sphere but leave the invisible geodesies. When you go for a "straight line " walk with you r girlfriend, yo u will fin d yoursel f back where yo u starte d afte r walkin g "straight" for about 63 feet. You have been controlled by the geodesies . Now g o back to Newton' s firs t la w o f motion. I t say s tha t a body move s i n a straight line if no force acts on it. You could rephrase this to say that if a force is not acting, the bod y moves alon g a geodesic in Euclidean space. No w take this spac e

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and distor t it, bending the geodesies. One can envisage a new first law , which say s that when there is no force acting on a body it travels not in a straight line but along a geodesic which, i f space is warped, need not be straight i n the Euclidean sense . This puts a new light on the paths of the heavenly bodies. As an example, consider the cas e of a comet passing objects i n its flight . I t would effectivel y ignor e a small asteroid, but the Sun has a dramatic effect , turnin g the comet about it and sendin g it off in an entirely different direction . Newton would attribute the effec t to gravity, Einstein woul d sa y that both th e asteroi d an d th e Su n have distorte d space-tim e and. its geodesies, but th e degre e of the distortio n depend s o n the mass o f the dis torter, and the Su n has a far greater effect . The warpin g of space-time is , according to Einstein, a result o f the presenc e of mass. Not e again that th e specia l theor y say s nothin g o f this effect . Th e mos t famous exampl e of the warpin g of space-time is the bendin g of light a s it passes th e Suri. Newto n ha d predicte d tha t th e Sun' s gravitationa l forc e woul d deflec t th e "corpuscular" ray s of light coming from the stars. Einstein saw this differently. Th e Sun distorted the space-time around it, "curving" it, so that light followed a curved path. Why d o we talk about the distortio n o f space-time an d no t o f space? There are two ways of facing this question. They are not really different, bu t they give differ ent insights. The first is to go back to the subject of invariants. Invariants allow us to calculate what a n observer sees when h e is in the same or a different fram e fro m wha t he is observing. They also say something fundamenta l about the physic s o f the spac e and tim e that we live in. Newton's is the comfort able, familiar invarian t that treats space and time separately because they don't get mixed u p i n ou r everyda y life . Newton' s univers e wa s Euclidean, an d w e foun d that the invarian t i n that universe wa s the length o f a straight line. Einstein came along with the theor y o f special relativity , accepted Euclidea n space, but showe d that the Newtonian length was not invariable. It depended on the relative motion of the line and the observer. There is, moreover, no expression that is invariant for inertial frame s unles s i t include s time . Instea d o f taking the distanc e betwee n tw o points, Einstei n took th e interval betwee n tw o events . Specia l relativit y weave s time and space together when we want to account for what we see. General relativity broadens ou r outloo k t o accoun t fo r the effect s o f mass an d acceleration . Ex pression (5) , for the interval, contains no reference to mass. Einstein remedied this in th e theor y o f general relativity. H e looked for a way o f expressing what a n ob server would se e not only if he were moving with respect to another fram e but also if there were masses involved. As with the universes of Newton and o f special relativity, there is an invariant in general relativity, and its form tells us a great deal. We will not us e it, but i t is worth writing down, just to make some nonmathematical points. Here it is in its simplest form: 8

8

I have simplified th e notation. The 10 coefficients, A,B,... K are written g°°, g11, g22 , g33, g01, g02, ...g23. Together they are known a s the metric tensor.

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(c is the speed of light). The essential point is that the coefficients (A,B,...K) contain the masses of the bodies that have to be taken into account. When the coefficient s are estimated for two event s taking place very far from an y masses, the coefficien t A becomes -1; B, C, and D become 1, and E to K become zero. The expressio n re duces to the invariant, (5) , of special relativity. The invariants of Newton and specia l relativity were universal—they applied to any place, any time, and any velocity. The invariant o f general relativity has a universal form , but th e coefficient s depen d o n the siz e and locatio n o f the masses in volved in the location under consideration . Thu s the interval between tw o event s in empt y spac e i s a n invarian t o f the simpl e typ e (5) , as see n fro m an y inertia l frame i n empty space, but (5 ) is not an invariant i n a region of large masses. Th e effect o f the masses is to change what we observe as far as position an d time are concerned, from wha t we would see if the masses were absent. However , if the detail s of the masses ar e put int o the ne w invarian t (6) , it is invariant fo r any two frames . Two events taking place near the massive planet Jupiter will be separated by an interval s , given by (6) , as measured fro m an y frame , eithe r o n Jupiter o r moving i n any othe r locality . Thu s ever y physical syste m ha s it s ow n value s fo r the coeffi cients. Invariants tell us abou t the kin d o f geometry that we are using. When I fly fro m New Yor k t o Te l Aviv, th e plan e roughl y follow s a geodesic , followin g part o f a great circle. Now imagine placing the Earth in a coordinate system of the kind typified i n Figure 32.5.1 could note the coordinates o f the two cities and then attempt to find th e distanc e between the m usin g the Newtonian invarian t (4) . I would get the wron g answer. Th e number tha t I get is equal to the straight-lin e distanc e be tween th e cities , the lengt h o f a tunnel betwee n them . Fro m a mathematician' s point of view, the mistake I have made is to assume that the invariant o f Newtonian space applied to a curved geometry, the surface of the sphere. There is an invariant that ca n be constructe d fo r spherical geometry , and I need i t to find th e lengt h of my flight . A n invarian t reveal s th e geometr y within whic h it applies . I f someone gives me th e expression s (4 ) or (5) , I know that h e i s working within a Euclidean space, a straight-line world. What can we say about the world in which (6 ) is an invariant? First, it is a world that is not Euclidean. The geodesies are not straight lines, and furthermore thei r shape depend s o n the specifi c localit y in which w e are interested. Wha t emerge s fro m a detaile d analysi s i s that , i n general , th e geodesie s ar e more curved the greater the amount of mass i n the locality, and become straight in the complet e absenc e o f mass . Einstei n actuall y constructe d a n invarian t tha t would guarantee geodesies conforming to the paths o f the planets. Each planet ha s a different path , but that is taken care of by the flexibility of the invariant, which allows different coefficient s t o be constructed from differen t masses . This i s the origi n of the concep t o f "warped space-time. " I t is apparent tha t al most an y amoun t o f distortion i s possible , bein g limite d onl y b y th e amoun t of mass in a certain locality. Some of the greatest "warpers" are black holes. Einstein's theor y does not includ e th e forc e o f gravity as a separate property of matter. I t says tha t mas s mold s space-tim e i n suc h a way tha t th e geodesie s ar e shaped lik e the observe d path s o f moving bodies. Th e space-tim e geodesies nea r the surfac e o f the Earth ensure that bodies fall vertically. The Earth itself moves in the curved geodesies created by the Sun, as do the other planets.

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Science for Pleasure

Homo supermarketus doe s not nee d th e theory of relativity. But the theor y represents scientific creativity at its most awesome. Einstein's incredibl e physica l intu ition, his single-minded pursuit o f what he believed to be the manifestation of God through nature—Spinoza's God—his welding of mathematics to observed fact , hi s intellectual courag e i n forsakin g accepte d scientifi c dogma ; all thes e combin e t o produce a theory of power and great beauty. Einstein believed, like Pythagoras and a long line of thinkers, in the unity of nature, in the possibility o f combining all the force s o f nature into one grand synthesis. For about thirty years he tried to construct a unified fiel d theory that would explain electromagnetis m as he had explaine d gravity, in term s of space-time. He failed completely. His Achilles' heel was quantum mechanics. The man who in . his youth ha d quantize d ligh t coul d neve r accep t th e probabilisti c interpretatio n of quantum mechanics , and h e lef t tha t subjec t untouched for decades, except for repeated attempts t o convince the res t o f the scientifi c world tha t they were wrong. He could not work with a theory that he believed t o be seriously flawed , a theory that stretche d belie f in a commonsense reality "ou t there." Einstein was a realist: he believed in a real world, independent o f the observer. But he saw it as a continuum, a kin d o f field i n which , puttin g i t crudely , matter manifeste d itsel f a s th e bunching together of the energ y in the field . H e didn't se e quantum mechanic s a s having a vital role in this picture, but it is almost certain that no unified field theory can ignore quantum mechanics. It remains to be seen whether Einstein was right and nearly everyone else is wrong.

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Cosmology The discovery o f a new dish does more for the happines s of mankin d than the discovery o f a star. —Jean Anthelme Brillat-Savarin, early nineteenth-century gastronome

One can' t hel p sympathizin g wit h the famou s chef. Mos t of us ar e chilled b y th e silent ocean s of space. I can hear James Joyce's Stephen Dedalus, reflecting on th e universe's "vas t inhuman cycle s of activity." Be honest: the surfac e of the Moon is about as intrinsically interestin g to HMS as the Utah salt flats. The rest of the sola r system is unfriendly; and non e o f us will travel to the stars . The image of space is bleak, serving as a metaphor for spiritual isolation : I am alone on the surfac e of a turning planet. What to do but, like Michelangelo's Adam, put my hand out into unknown space , hoping for the reciprocating touch? R. S. Thomas, Threshold There is a persistent hope that we are not alone in this colossal wasteland o f hydrogen gas. Our fea r o f psychopathic aliens i s balanced by a wish tha t ther e be someone els e t o kee p u s company , preferable a small , docil e creatur e with bi g Hollywood puppy eyes . We would lik e to have clos e relatives out there, which is why the standar d alie n has huinanoid features. Who comes out of a UFO? A little green man. As k anyone. Like the Vikings and the Polynesians, we have just begun to set sail, in primitiv e boats, extending this planet's thin fil m o f life, but as yet only to our nearest neigh bor. And the monsters that populate the far reaches of space are no less strange than the dragon s an d anthropophag i fantasize d b y Hakluy t an d hi s Elizabetha n col leagues. Wh o ha s no t hear d o f pulsars an d supernovas , o f red giant s an d whit e dwarfs an d th e voraciou s blac k holes ? Th e structur e an d behavio r o f thes e denizens of the cosmic deep are the clues to the history of the universe an d may, in the fa r future, determin e th e fat e o f man, i f that poo r forked creatur e doesn' t self destruct before an asteroid obliterates us. Cosmology is largely a product of this century. This is not a snub to Ptolemy, Kepler, Brahe , Copernicus, Newton, Halley , and generation s o f Babylonian, Greek, Chinese, Arab , and May a stargazers. It was th e observation s an d speculation s of these men that culminated in Newton's grand synthesis. But it was not until the advent of giant telescopes in the twentieth centur y that the immense siz e of the uni -

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verse became apparent. It was not until we began to analyze the radiation fro m th e stars that thei r chemica l compositio n wa s revealed. Onl y the adven t o f quantum mechanics allowe d a n understanding o f the processes that produc e energy within the star s an d contro l th e siz e o f white dwarfs . Not unti l th e detectio n o f radio waves from spac e did we know of thousands o f dark stars. Only the theory of relativity permitted us to comprehend the structure and functioning o f black holes, the slowing dow n o f the rotatio n o f pulsars, th e rea l meaning o f the "expandin g uni verse." An d i t wa s th e detectio n o f microwave radiation comin g fro m spac e tha t gave us ou r most direc t hin t tha t the univers e bega n with a Big Bang. Twentiethcentury cosmolog y is on e o f the grea t breakthroughs, a breakthrough tha t i s stil l proceeding. Of the fou r force s know n t o physics , onl y on e is important i n determinin g the large-scale structure of the universe. Gravity is the sol e major forc e acting between the differen t objects , planets , stars , galaxies, and s o o n tha t mak e u p th e coars e structure of the universe. It is not the only force. Thus light can and does exert pressure, and th e magneti c field o f the Sun , for example, canno t be ignored, but thes e are negligible factors; it is gravity that is the heavyweight. In wha t follows , detail s wil l b e avoided . W e will loo k a t som e curren t idea s about the birth of the univers e an d will review the mai n type s of bodies found in the heavens. We begin with our ow n planet , to which, a s far as massive colonization i s concerned , w e ma y wel l b e confine d fo r at leas t a coupl e o f centuries t o come. The Earth A New Theory of the Earth, from the Original to the Consummation of All Things, Wherein the Creation of the World in Six Days, the Universal Deluge, and the General Conflagration, as laid down in the Holy Scriptures, are shown to be perfectly agreeable to Reason and Philosophy. —Title of a book by the astronomer William Whiston (1696 )

A few months ago I was sitting at home in Haifa when I heard what sounded like a truckload of stones being tipped out. A small avalanche of rocks was running down the slop e of the mountain o n which I live. The room moved, slightly but perceptibly. The las t seriou s earthquak e i n Israe l was a couple o f hundred year s ago, but minor eart h tremors are quite frequent. Haif a is situated not too far from the Jordan valley, which lie s roughly i n lin e with the Great Rift Valle y o f East Africa. Thes e two valleys ar e the meetin g place o f two tectonic plates. The surfac e o f the Earth is covered by about half a dozen large plates and many smaller ones. These plates are huge areas of more or less stable crust floating on a layer of partially liquid rock, the asthenosphere. The tectoni c plate s consis t of the lithe-sphere, a soli d laye r about 7 0 kilometers thick, and above that the crust, a thin layer of earth, rock, and clay. The predominant rock on or near the surface is granite, composed primarily of oxygen, silicon, and aluminium. Tendin g to be lower down, but frequently appearing a s outcrops , i s basalt , a roc k consistin g mainl y o f oxygen, silicon, iron , an d magnesium. The plates move, at speeds of a few centimeters a year. Where they meet below oceans, thei r surface s ar e generall y neare r th e asthenosphere , whic h send s u p

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molten material into the joins between plates. This cool s down and solidifies, and somewhere somethin g ha s t o give . Ofte n th e othe r edge s o f the plat e ar e force d downward an d slowly melt. The jostling together of plates can result in the buildup o f tension a t their mutual boundaries, as when a drawer is jammed. The sudden releas e of this tension can be catastrophic. Japan lies on the boundary between the Pacific and Eurasian plates. San Francisco and Los Angeles lie on the boundary between the Pacific and American plates. A number of large and smal l plates come together in the area of Greece, Turkey, and the Middle East. All these areas are prone to earthquakes. Massive collisions o f plates in prehistory resulted i n the folding up o f the Earth's surface. Th e Himalayas, the Andes, and the Rockies all lie along plate boundaries. The tectonic plates are floating, and have been since they formed during the cooling of the molte n Earth. The dynamic stat e of the Earth's surface is made dramati cally evident by looking at a map of the eastern coast of the American continent an d the western coast of Europe and Africa . A s Sir Francis Bacon noticed, in their general shape they match each other, as though there had once been one great land mass that had split from north to south and drifte d apart . The similarity o f fossil remain s and mineral deposit s on the two sides added to the suspicion tha t what is two was once one. There is no doubt now, in the light of accumulated fact , that this thesis is correct. The molte n asthenospher e i s abou t 20 0 kilometers wid e an d cover s a n inne r layer, the mesosphere, which is more solid in texture and has a width of about 2000 or mor e kilometers . The mesosphere , lithosphere , an d asthenospher e ar e collectively called the mantle of the earth. Inside this mantle is the outer core, which ap pears to be liqui d metal , and which surround s th e inner core of the Earth, a solid ball of metal, probably mainly iron but perhaps containing nickel, about 2500 kilometers in diameter. Man has not succeeded in drilling down to depths o f more than 20 kilometers . Ou r knowledg e of the Earth' s interio r come s almos t entirel y fro m seismology. The behavior o f shock waves generated eithe r by natural event s o r by deliberately setting off explosions is , in th e hand s o f experts, a source of information on the large-scale structure of the Earth. It's a little like the use of ultrasound i n medicine. The Earth was onc e entirely molten. Th e fac t tha t the interio r o f the Eart h still contains molte n material , which gushe s ou t occasionally , is the result o f the continual productio n of heat by the decay of radioactive elements. Thi s i s what foole d those nineteenth-century scientist s wh o tried to work out the age of the Earth fro m its present temperature and its estimated rate of cooling. They didn't realize that it had it s own source of heat. Th e heat of the core , which ha s a n estimated tempera ture in the range of 3000-7000° C, sets up convection currents i n the less than rigi d mantle, which i n turn are responsible for the movement o f the tectonic plates . The Wobbling Magnet As the Elizabetha n William Gilber t guessed, the Eart h is a magnet. Th e magneti c poles ar e no t fixed ; the y meande r fo r several mile s ever y year. Furthermore, th e North and South Poles have switched place s about ten times during the past 3 to 4 million years. We know this because, long ago, rocks that were then molten wer e magnetized b y th e magneti c fiel d o f the Earth . When they coole d an d solidified ,

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they preserved the footprint s of the magneti c field a t the time , and from independent evidence we can date the rocks. Successive layers of rock sometimes have opposite direction s o f magnetization. We don't kno w why thes e switche s occurred . They tak e abou t a thousan d year s t o complete , whic h i s fas t o n th e geological timescale. It has been suggeste d that the theory of chaos may apply, but there is as yet no physical model to which the theory ca n be applied. Another change , which man shoul d watc h nervously , is the progressiv e weakening o f the strengt h o f the field, which in the last 150 years has fallen by some 7 percent. The Earth's magnetic field dominates that of the Sun for many thousands of kilometers above the Earth' s surface , Th e Earth's magnetic fiel d ha s a vital protective role. Th e Su n eject s a continuou s strea m o f proton s an d electrons , th e "sola r wind." Thi s win d i s augmented periodicall y by the emission s from sunspots an d solar flares. The particles of the solar wind ar e almost completely deflected past us into spac e by the Earth' s magnetic field . Unusuall y strong gusts of the sola r wind can cause what ar e known a s magnetic storms, which ca n disrupt electrica l communication systems, and create spectacular lighting effects i n the heavens—for example, the northern lights. Fluorescent lighting is based on the passage of electrons through an inert gas, such as neon. The invading electrons blast some of the atomic electrons out of their orbits, and the resultant fall of other atomic electrons into the empty orbit s release s th e photon s whic h giv e such a ghastly color to faces i n all night cafes . Thi s phenomeno n occur s on a massive scale when a powerful gus t of solar wind penetrate s ou r atmosphere . Thi s is the origi n o f the grea t auroras that hang in northern skie s at times of enhanced sola r activity. If the Earth' s magnetic fiel d continue s t o weaken, we may eventually fin d tha t the solar wind is blowing uncomfortably strong. The effect of a considerable rise in the numbe r o f charged particles reachin g the Eart h could be an increase in radiation-induced illnesse s an d in the mutation rate, not to speak of the possible effect s on our electronic civilization. But this is not the only threat from space. Voltaire believed that the Earth had remained as it was when it was created except fo r the effect s o f 150 days of the Deluge , but th e fac t i s that ther e hav e been massive global changes over the past few billion years. Life in general has managed to adap t t o the slo w changes that have characterize d the histor y o f the Earth , the huge change s i n climat e typifie d b y the ic e ages , the shiftin g continents , an d th e rise i n the oxyge n content o f the atmospher e a s plants establishe d themselve s o n Earth. Occasionally, however, major catastrophes have occurred, and there may be more on the way. The main threat, apart from man's greed, is from space. The Earth-Crossers In 1801, in Palermo, Sicily, the monk Giuseppe Piazzi peered through his telescope and foun d a new heavenly body within the solar system. Ceres is about 1000 kilometers across , compare d wit h ou r Moon' s 320 0 kilometers . Thi s barre n roc k proved to be the largest of a huge number of bodies, the asteroids, careering around the Su n i n path s lyin g between Mar s and Jupiter . Th e problem i s that ther e i s a group of asteroids, the Earth-crossers, whose paths cross the path of the Earth. In June 1908 a farmer sittin g on his porch in the Tunguska region of Siberia was knocked of f his chai r by a powerful shock wave. Eight kilometers abov e the Earth an object, possibl y an asteroid, and probably about 70 meters across, had heated u p

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and exploded after enterin g the atmosphere. The sound was heard 100 0 kilometers away, trees were flattene d fo r 30 kilometers around , and th e intens e hea t ignite d the forests. And all this from a n object that never reached Earth. To penetrate our atmosphere an asteroid would have to have a minimum diame ter o f about 20 0 meters. Ther e ar e plent y o f those around . W e can ge t an ide a of what woul d happe n i f a n asteroi d wit h a diamete r between 1 0 to 1 5 kilometers struck us . I t is now generall y accepted tha t a collision wit h suc h a n asteroi d occurred some 65 million years ago, leaving a crater about the size of the Netherlands, 6 miles deep and 19 0 miles across, off the Yucatan Peninsula in the Gulf of Mexico. The energ y released wa s equivalen t t o abou t 200 million ton s o f TNT. Roughly a quarter of a million cubi c kilometers of dust was thrown high into the atmosphere , forming a cloud that darkened the Sun for months an d brought a mini ice age. The dinosaurs were wiped out ; they couldn't accommodate to the change in climate. There are something like 180 identified Earth-crossers, none of which i s predicted to hit th e Earth during the nex t century . But small asteroids ar e difficult t o detect, an d a n asteroi d measuring , say , onl y 3 kilometer s acros s an d travelin g a t 150,000 kph coul d raise enough dust to blot out the Sun for months. On e hesitates to think what it could do if it fell on a city. In 1992 a large group of scientists, unde r the auspices of NASA, produced a battle plan to combat Earth-crossers. Six sophisticated telescopes at widely separated site s would searc h solel y for asteroids. Possible paths would be predicted and the dates of collisions estimate d years ahead. Is this fund-raising scaremongering ? Not if you believe those astronomers wh o clai m that there are as many as 5000 as yet undetected Earth-crossers of over half a mile diameter. Our only feasible defense against such an object would be to launch a nuclear missile and hope to blow it to pieces or divert its path. Maybe the technology that destroyed Hiroshima will one day save this planet fro m another ice age. At the very edge of the solar system there is a host of comets, some of which visit our neighborhood . Som e swoo p in , swoo p out , an d ar e neve r see n again . Som e swing around periodically. Ovid recounts how Venus came down invisibly into the Roman Senate to remove Caesar's soul from his body. As they ascended, his soul ignited and became a comet. Gaia

The realization is spreading that the Earth is a collection of delicately balanced interdependent systems . The ocean s an d th e atmosphere , the radiatio n o f the Sun , geophysical processes, the activitie s o f living forms—al l these constitute a system of great complexity in which change s in one part may have effect s tha t are not always eas y t o predict . Thu s a dro p i n globa l temperatur e ca n caus e significan t amounts of the ocean to be added to the polar ice caps. This would resul t in a lowering o f the leve l o f the oceans , which i n tur n woul d lesse n th e pressur e o n th e seabed, especially along the continental coasts . This coul d make it easier for pressurized subterranea n molte n roc k to burst out , so that lowe r globa l temperatures could be correlated with increased volcanic activity. On the other hand, increase d volcanic activity pushes more dust into the skies; if this dust contains large proportions o f sulfur-containin g gases, i t wil l resul t i n th e formatio n o f tiny droplet s (aerosol) of sulfuric aci d in the upper atmosphere. These are good at scattering and absorbing sunlight and thus contributing to the cooling of the Earth.

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This comple x interdependenc e wa s apparentl y firs t seize d o n by th e eminen t Scottish geologis t Jame s Hutto n (1726-1797 ) t o justif y th e suppositio n tha t th e Earth behaved as a single organism. This idea, in the hands of James Lovelock, has recently been turned int o a fashionable hypothesis, which sees the Earth as being an organism , wit h mechanism s o f self-defense. Th e biologis t Lyn n Marguli s ha s joined Loveloc k in developing an d promoting the theory, goin g under the name of Gaia (a Greek goddess), and a t one time i t received a great deal o f publicity i n th e media. But , as Richard Dawkins has pointe d out , the Eart h can hardly be consid ered t o b e a n organism , sinc e i t doesn' t reproduce . I t i s difficul t t o se e wha t i s gained i n scientifi c terms by definin g a n interdependen t grou p o f phenomena a s one single organism, if their mutual relations ar e known o r being researched anyway. A central point o f the theory seems to be that the Earth defends itself, just as an organism does, but this is highly questionable. The Earth and its inhabitants ad just to changes, and som e o f those adjustment s are successful, bu t i t doe s not follow that the y have th e natur e o f the biological defens e mechanisms produce d by evolution (se e Chapter 26) . It is difficul t t o believe tha t th e Eart h a s a whole ha s evolved in this way. There are signs tha t interest i n Gaia is waning. Nevertheless, if its emphasis o n the unity of the natural world gets through to some of those who determine national policies , i t wil l b e doin g a majo r service . Gaia , wit h it s holisti c aura , ha s in evitably been taken up by the New Age dreamers. Would they have noticed it if, instead of being named afte r a Greek goddess, the theory had been called coordinated interactive non-linear dynamic s in the terrestrial bio- and geospheres? The Sun

The Sun, which is 864,000 miles (1,382,000 km) in diameter, has a mass of nearly 2 x 10 30 kilograms, equal t o about 70 0 times th e tota l mas s o f all th e othe r planet s combined. Th e Philosopher s o f Jonathan Swift' s Laputa , lik e Helmholtz , feare d that the Su n would burn out, but this will probably not happen fo r a billion o r so years. The Sun's interior temperature has been estimated a t between 8 and 1 5 million K , although th e averag e temperature o n the surfac e i s only about 600 0 K, The Sun has an intense magnetic field that reverses its polarity every eleven years. This field play s a major par t in the Sun' s activities, being responsible fo r the formation of sunspot s and th e hug e archlik e flare s o f radiant matte r that appear temporarily on the Sun' s surfac e and ca n reach hundreds o f thousands o f kilometers above the surface. Fo r reasons that ar e not clear , the temperature i n these coronas can be as hot as 2 million K , and i n short bursts can even reach about 2 0 million K. It is electrons accelerate d b y the magneti c field s i n thes e corona s tha t produc e the radi o waves present in the Sun' s radiation. I t is from thes e outbursts o f matter above the Sun's surfac e tha t spurt s o f matter ar e thrown fa r out int o space . This sola r win d has been detected beyond Pluto by the spacelab Voyager. The Sun is the only star that we can, at present, study at close hand, and much of what w e learn ca n be applied t o other stars, all of which, eve n with the best telescopes, appear to us as little more than dots . Thus, for example, the sudden , huge, short-lived rises in temperature that are observed i n some stars can often probably be interpreted i n terms of the solar flares that can be seen quite clearly on the Sun .

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The Planets

It is convenient to define the distanc e of the Earth from th e Sun , which i s ahout 93 million miles , as one astronomical unit ( 1 AU). Thus if the Earth is 1 AU from th e Sun, then the distances of the nearest four planets to the Sun are Mercury, 0.39 AU; Venus, 0.7 2 AU; the Earth ; Mars, 1.52 AU. These comparativel y smal l planets , of which th e Eart h is the largest , for m a tigh t littl e grou p aroun d th e Su n an d ar e called the terrestrial planets because they have an outer coat of rock over a predominantly metalli c core . The y consis t mainl y o f the element s silicon , oxygen , an d iron, the oxygen being primarily tied up in the silicates that form rock (see Chapter 13). Mercur y (abou t a thir d o f the diamete r o f the Earth ) and Mar s (abou t half) , being considerably smaller than the Earth, cooled faster an d displa y little volcani c activity. Mars has enoug h of a gravitational field a t its surface (about 38% of that of the Earth) to hold o n to a sparse laye r of carbon dioxide . Venus, which is roughly the siz e o f the Eart h and ha s a comparable gravitational field , ha s a dee p atmos phere o f carbon dioxide . Moving outward, the next fou r planets , the gas giants, ar e all much large r than the Earth . They contai n hig h proportion s o f the tw o lightes t elements , hydroge n and helium : Jupiter, 5.20 AU; Saturn, 9.52 AU; Uranus, 19.16 AU ; Neptune, 29.99 AU. Notice how the gas giants are spread out over far greater distances tha n the terrestrial planets. Neptune is 2,789 million miles from the Sun . The ga s planets hav e soli d core s bu t thick , partiall y gaseous , partiall y liqui d wrappings, with properties appropriate to a science fiction film . Thus Jupiter's core is surrounded by an enormous ocea n of liquid hydrogen, which is under th e pressure resulting fro m Jupiter' s gravitational field . Thi s liquid metallic hydrogen ha s strange properties, being able to conduct electricity. It may well be responsible for Jupiter's powerful magnetic field. Strange auroras move over the polar regions, and great bolts of lightning fall fro m the atmosphere, which is about 90% hydrogen an d 10% helium, with trace s of other gases. The gravity of the Earth cannot hol d thes e gases very effectively, bu t fo r its first hundre d o r so million year s of existence, th e chemical compositio n o f the Earth' s atmosphere ma y have resemble d tha t o f present-day Jupiter. Jupiter gives out a great deal o f energy, but it s sourc e is probabl y the slow contraction of the planet, not the nuclear reactions that produce the Sun's radiation. (You can envisage this contraction in terms of matter falling "down" and losing potential energy, just like a boulder or the weight in Joule's experiment. Th e lost energy appears as increased kinetic energy.) Jupiter has sixteen moons, ranging in diamete r fro m 6 miles t o abou t 330 0 miles, compare d wit h ou r moon' s 217 0 miles. I t was Galileo who foun d th e fou r larg e moons o f Jupiter, which he name d the "Medicea n planets" after th e famil y o f Grand Duke Cosimo II d'Medici o f Florence. He also sent the grand duk e a telescope, which was perhaps hi s way of applying for a research grant. He was duly appointed chief mathematician o f the University of Pisa and philosophe r o f the grand duke . The six innermost planets , including the Earth, have been known sinc e prehis tory. It was not until th e eighteent h centur y tha t Uranus , th e sevent h planet , was found. Isaac Newton made the firs t reflectin g telescope , based o n curved mirrors . Fol lowing Newton's lead, the grea t astronomer Si r William Herschel mad e a 10-foot long reflecting telescope, 6 inches i n diameter, with which , i n 1781 , h e found th e

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first plane t discovered sinc e prehistoric times . Herschel , who a s a young man i n Hanover earned a living by playing the oboe in a military band, settled in England and subsequently became the best telescope maker of his time, his crowning effor t being a huge, 40-foot-long, reflectin g telescop e with mirror s 4 feet across . He discovered Uranus, a planet encircled by somber, coal-colored rings. Mars is an example of seeing what yo u want to see. The nineteenth-century as tronomers Camill e Flammarion , Giovann i Schiaparelli , an d Perciva l Lowel l al l looked at Mars and claime d that they sa w signs o f life and intelligence . Thei r evidence was a network of suspiciously straigh t line s coverin g great distances on the surface o f the planet . Lowel l published a numbe r o f convincing drawing s o f th e planet i n his book Mars and Its Canals (1906) . On the basis of these drawings, th e lines see n o n Mar s are almos t certainl y th e wor k o f intelligent beings . An d the n came the camera, which has one great advantage over man: it has no expectations. Entile Zola said, "We cannot claim to have really seen anything before having photographed it." One can certainly argue with this opinion, 1 but in science the camera can give an objectivity that sometimes elude s the scientist . Photographs o f Mars do not resemble Lowell's drawings at all. The canals finall y faded int o scientifi c limb o whe n Mar s wa s photographe d b y twentieth-centur y space missions, showin g that scienc e fact i s sometimes scienc e fiction . Nevertheless, photographs taken fro m satellite s in orbit around Mars have show n the pres ence o f deep twisting scar s that resemble drie d u p riverbeds , and i t has been hypothesized tha t water , th e sin e qu a no n o f terrestrial life , wa s onc e par t o f th e Martian environment. There are plans to send an unmanned Russian-buil t robot to Mars in 2001 , its mission being to drill beneath the surfac e to search for fossilized primitive life-form s suc h as algae. In the meantime, as noted earlier, what appear to be fossilized microorganisms have been detected in rocks from Mars. All eigh t planet s revolv e i n plane s tha t ar e n o mor e tha n 3 ° from tha t o f th e Earth, which suggest s that they were all formed togethe r from th e sam e revolving disk of matter. This nebular hypothesis tha t sees the solar system as condensing out of a whirling plate of hot gas, has fallen in and out of favor over the past century. As yet there is no universally accepted theory of the origin of the solar system. Far outsid e th e othe r planets i s Pluto , a t a n averag e distance fro m th e su n of 39,37 AU. Pluto was discovered only in 1930. It is the smallest of the planets, only about the size of the Earth's Moon. Its orbit, like that of Mars, is more elliptical than those o f the othe r planets, and i s also at a marked angle to those o f the res t o f the planets. It may have a different origi n from the other planets, which should set you UFO buffs thinking . Or you might care to reflect on the Titius-Bode law, formulated in the eighteent h century. Thi s say s tha t i f you tak e the number s 0,1,2,4,8,16,32,64,12 8 . . . triple each number , add 4 , and finall y divide by 10 , the resultant number s giv e the dis tances of the planets (including the asteroid Ceres) from the sun in A.U. This works very well excep t for Neptune. Does this mean tha t Neptun e is in som e importan t way different fro m the other planets? Or is the "law" just a coincidence? Light takes about twelve hours to cross the solar system, a negligible time by intergalactic standards. The nearest star to Earth is the Sun; the next nearest, Proxima 1

As Baudelaire, who was not a realist, did. Fo r him photography was "industry's imbecile revenge upon art." Whic h didn't prevent him sitting for a portrait.

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Centauri, in the Centauru s constellation, i s 4.8 light-years away, which i s some 12 million time s farthe r than th e Moon. This compariso n illustrate s th e magnitude of the tas k facin g ma n i f he wishe s t o reac h destination s outsid e th e sola r system , which on e day he might have to do. No othe r plane t i n th e sola r syste m ca n suppor t life . Ou r presen t technolog y gives little hope of massively colonizing another home outside the solar system. I n the meantime, we are endangering ou r survival o n Earth. Perhaps Arthu r Koestler was right: Homo sapiens ma y be one of the specie s i n the galaxy that are mentally unstable biologica l misfits , i f there ar e an y othe r species . W e have ha d n o tele phone calls up to now.

34 The Cosmos and Peeping Tom

In 168 2 th e write r Ihara Saikak u published hi s Life of an Amorous Man. Saikaku was not on e to be bound by convention. I n a country where the cherr y blossom is almost sacre d h e starte d on e story , " I was s o bored wit h cherr y blossoms tha t I stayed away from the capital all spring." The fifty-four chapter s of his book recount the eroti c adventure s o f one Yonosuke , from the ag e of seven. By the ag e of fifty four, he had had encounters with 374 2 women and 72 5 men, which i s suggestive of an unstoppabl e attac k o f hiccups rathe r tha n o f promiscuity. I n on e episod e th e precocious hero, aged nine, stand s o n a roof watching a maidservant i n her baththrough a telescope. The telescope had been put to educational use, perhaps riot for the first time, but this seems to be the first suc h appearanc e in literature. Galileo— as far as we know—pointed his telescope up, not down . Our knowledge of the universe stil l comes mainly via the telescope. Perhaps no branch o f science depend s s o much o n a singl e invention , especiall y whe n i t i s used in conjunction with the camera. Objects that are too dim for the ey e to see through a telescope may be recorded on a photographic plate because, unlike the eye, the plate accumulates the effec t of every photon striking its surface. Thus, a photographic plate can be left expose d for a considerabl e time , durin g whic h i t slowl y record s th e evidenc e o f very di m sources. Th e familia r photograph s o f galaxies ar e al l take n wit h lon g exposur e times. They are hardly visible against the night sky. The word telescop e means to "se e far, " which allow s u s t o include withi n th e term instruments tha t collect radiation other than visibl e light. The most spectacular of these is the radio telescope, two major examples of which are the huge disk at Jodrell Bank in England and the VLA (very large array), in New Mexico, which consists of twenty-seven receiver disks, each 25 meters in diameter and arranged along three arms each about 21 km long. Every range of frequencies i n the electromagnetic spectrum is now used to probe the universe, but we have to use instruments carried by satellites or rockets to observe any other than visible, radio, and some IR radiation. Othe r wavelengths fai l to penetrate the atmosphere . Before Galileo turned hi s telescope to the night sky in 1610 , the universe wa s a much smalle r place . There ar e fewer tha n 500 0 stars visible to the nake d eye, although it must have been assumed that there were many more, in view of the common European belief that eac h person had hi s ow n personal star. 1 By comparison with today' s telescopes , Galileo's simple lense s wer e toys. What he sa w as single points of light, twentieth-century astronomer s see as huge agglomerations of separate stars. The size of the discernible universe has expanded with the passing of the 1

In the fift h century , Bishop Eusebius of Alexandria asked if "there were only two stars at the time of Adam and Eve."

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centuries, and in the early years of this century, hints began to accumulate that the universe was much larger than it appeared. On on e o f hi s journeys , Magella n recorde d tw o smeare d dot s o f light , no w known a s th e Smal l an d Larg e Magellani c Clouds . I n 191 2 th e America n as tronomer Henrietta Leavitt (1868-1921) estimated the distance to these clouds and showed that their apparent siz e could be accounted for only if they were billions of miles across. They were later shown to consist o f vast stretches o f glowing gas and stars. B y the beginnin g o f this century , the significanc e o f the sola r syste m ha d completely faded. I t was clea r that we were a tiny part of a galaxy, the Milky Way, but it was not certain whether this galaxy constituted the whole universe . On a favorable night it is possible to make out a great band of light across the sky. The Milky Way is in fac t disk-shaped , its center being thicker than its edges . The reason we see a band is that we are ourselves situated in the Milky Way, about twothirds o f the way to the edge , and ar e looking more or less sideways through it, as was firs t guessed by Thomas Wright of Durham in 1750 . Only eight y years ag o the America n astronome r Howar d Shaple y though t tha t the Milk y Way was the universe ; i t i s abou t 120,000 light-years across, which i n those day s wa s prett y big . H e wa s hugel y wrong . H e shoul d hav e listene d t o Thomas Wright , who guesse d tha t ther e wer e othe r Milk y Ways, "too remote fo r even our Telescopes to reach." Scattered throughou t th e sk y ar e spira l objects , th e spiral nebulae. Shaple y claimed tha t the y wer e comparativel y near, being essentiall y a part o f the Milky Way. Not everyone agreed with him. At a meeting of the American National Academy of Science in 1920, Heber Curtis suggested not only that the spiral nebulae were much farthe r away than Shapley though t bu t tha t they wer e in fac t galaxies—"is land universes" (the phrase is Kant's). 2 Was he right? Measuring the Immeasurable

How far are the spira l nebulae? How large is the universe? We cannot begin to answer these questions unles s w e can measure the distance o f heavenly objects . The breakthrough was made by Henrietta Leavitt, who was interested in a rather special class of stars, the Cepheids . The intensity o f the ligh t comin g fro m Cepheid s rise s and falls regularly with time, with a period that varies between stars, usually being a fe w day s but sometime s a s much a s three to fou r months . Leavit t found nearl y 2500 Cepheids . Concentratin g o n on e o f the Magellani c Clouds , sh e foun d tha t there was a very close relationship between brightness and period for the Cepheids in the cloud. The brighter a Cepheid was, the longer its period. The distanc e o f the Magellani c Cloud is so great that the star s there ca n be regarded a s all being effectively th e sam e distanc e fro m th e Earth . If you ar e in Los Angeles, everybod y in Carnegi e Hall i s abou t th e sam e distanc e fro m you . Thi s means that if one Cepheid is four times brighter than another, it is not because it is nearer t o yo u bu t becaus e i t i s intrinsicall y fou r time s brighter . Suppos e tha t a Cepheid in the cloud has a certain brightness and a period of one week. Now look at another Cephei d in some more distant galaxy . If it has th e sam e period, we can 2

As we have seen, Kant started his academic career more as physicist than philosopher, and one of his firs t publications was General History of Nature and Theory of the Heavens (1755).

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assume it has the same intrinsic brightness, and yet it is dimmer than it should be. We can deduce tha t the Cephei d is farther awa y from us than those in the Magel lanic Cloud . Moreover, assuming tha t it s real , intrinsic brightness i s the sam e as that o f a Cepheid o f similar period , in the cloud , we ca n work out its relative distance from Earth. A star o f the sam e intrinsic brightness that i s twice as far away will be four times dimmer. A method had become available to measure the relative distances o f stars, albeit a restricted class o f stars. It is slightly complicate d b y th e effects o n brightness of interstellar dust clouds, but i t was a huge step forward. The nex t ste p i n ou r stor y wa s mad e b y th e unlikely-name d Vest o Melvi n Slipher (1875-1969) , wh o di d to the light from spira l nebulae wha t Newton did to sunlight. H e placed a prism in his telescope and obtained spectra. Slipher saw the kind of lines that are shown in Figure 15.6, which he readily identified as lines du e to hydrogen and helium and , to a lesser extent other elements. No unrecognizable lines were found, o r have been foun d since . The spectra of the star s is completely arialyzable i n term s o f the spectra l line s belongin g to know n chemica l elements . What was unexpected wa s that the frequencie s of the line s that he observe d were all shifted very slightly from those obtained from the chemical elements in earthly laboratories. This strongl y suggested that the sources of light were moving with respect to the observer and that frequencies were being altered by the Doppler effect (see Chapter 15). The shift varied from galaxy to galaxy. They were apparently traveling at different speed s with respect to the observer on Earth. The strange thing about Slipher's observations was that in practically every case the frequencie s wer e al l lower tha n the y shoul d hav e been . Ther e wa s wha t i s called a redshift, s o named because red ligh t appear s at the low-frequenc y en d of the visible spectrum. Now the observed frequency of light emitted by a source moving away from th e observer is redshifted. Slipher' s findin g therefore suggeste d that nearly al l the spiral nebulae were moving away from us. Two spiral nebulae had a blueshift, indicatin g tha t they were apparently moving nearer to us. On e of these was the Andromeda nebula that is approaching us at about 360,000 kph. Why wer e nearl y al l th e observe d spira l nebula e movin g away from us? An d were the y par t o f th e Milk y Way , a s Shaple y thought , o r wa y ou t ther e i n extra-Milky Way space, as Curtis had suggested? The Dynamic Universe

In 191 9 Edwi n Hubbl e (1889-1953 ) cam e t o th e Moun t Wilso n Observatory . He used a ne w 100-inc h telescope , the mos t powerfu l instrumen t availabl e a t tha t time, t o loo k fo r Cepheid s i n galaxies . I n thi s way , usin g Henriett a Leavitt' s method, h e hoped t o measure th e distance s to galaxies. Were they really a s far as Curtis though t the y were ? In December 1924 Hubble announce d tha t h e ha d ob served a Cepheid that had a period of about one month. From its brightness he estimated that it was nearly \ million light-year s away. That figure has since been corrected to 2 million light-years. The star was in a galaxy officially name d Messier 31, but i t i s better know n a s the Andromed a nebula (Figur e 34.1). I t i s much to o far away to be part of the Milky Way, and, as Hubble showed, it is probably very similar in its shape to the Milky Way, although a little larger. With one stroke, our home galaxy had been demoted to a desperately isolated whirl of stars lost in an unimaginably huge void.

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Hubble showed that the universe wa s populated with galaxies, "island univers es," that were several hundred millio n light-year s away from us . Today the known visible universe encompasses galaxies that are thousands o f millions o f light-years away. As soon as Hubble started publishing hi s observations , Slipher's Dopple r effec t suddenly becam e o f intens e interest . Wer e these incredibl y distan t galaxie s al l moving awa y fro m us , a s Slipher' s result s implied ? Wa s the univers e no t onl y much larger than people thought but also expanding? The lin k betwee n Hubbl e an d Sliphe r wa s mad e b y th e physicis t Howar d Robertson. He did what all self-respecting scientists woul d hav e done—h e made a graph. Th e magnitud e o f the Dopple r shift ca n b e use d t o calculat e th e spee d a t which a light sourc e is moving away from a n observer. Robertson plotted the esti mated speed of the galaxies against the distance s of the same galaxies as estimated by Hubble . H e wa s astonishe d t o fin d tha t the farther the galaxy was from the Earth, the greater was the redshift. Abou t the same time, Hubble noticed the sam e correlation. I n 192 9 he announce d tha t ther e wa s " a roughly linea r relatio n be tween velocitie s an d distances. " Th e spee d o f recession wa s proportiona l t o th e distance of the galaxy. This is now known as Hubble's law, but there is a good case for callin g i t th e Robertson-Hubbl e Law. Robertson didn't complain . Perhap s h e was aware of the fac t that Hubble was a very good boxer. Since antiquity , astronomer s ha d believe d that th e movemen t o f the heavenl y bodies was overwhelmingly cyclic. The moon circled the Earth, the planets circle d the Sun . The fixed star s were fixed. No w the universe ha d been revealed to be not so muc h a carouse l a s a firework s display. Som e o f the galaxie s tha t Hubbl e observed wer e recedin g a t speed s i n th e regio n of 100 million kph . Bu t what doe s Hubble's la w mean ? If all th e galaxie s are moving awa y fro m us , doe s thi s mea n that we are at the center of the universe? And why are they moving? Imagine a circl e o f folk-dancer s skippin g backward , awa y fro m eac h other , maintaining the circle but expanding it. The first point to grasp is that every dancer sees all the other s retreating from him . It is not necessary to stand in the middle of the circl e to experienc e this distancin g o f each dance r fro m al l the others . Notice also that the farther away two dancers are from each other, the faster the distance between them increases. Thi s argumen t ca n immediatel y be generalized to thre e dimensions. The interpretation o f Robertson's (Hubble's) finding was that the universe, lik e the circle of dancers, was expanding. This was a great turning point in our efforts to write the history of the universe. Again, note carefully that the fact that all the galaxies appear to be receding from us does not mean that the Earth is at the center of the universe. Every dancer sees all the other dancers going away from him , but none is at the center of the circle. An observer on any galaxy will see what Hubble saw. The next question i s unavoidable: On what dat e did the universe star t expand ing, and what did it look like at that time? Regarding the time scale: on the basis of the presen t state of the universe, and the observe d rate of expansion, cosmologist s have run the video backward and estimated that the universe began its expansio n

3 When life first emerged o n Earth, the densit y o f matter in the expandin g universe was abou t twice wha t it is today.

The Cosmo s and Peepin g Tom [

about 15,00 0 billion years ago.3 Everything is presumed to have started with an incredible explosion, th e famou s Big Bang, a phrase coined by Fred Hoyle. The firs t man to present this startling image of the Creation was a Belgian Jesuit priest, engineer, and astronomer , Georges Lemaitre (1894-1966), who propose d that the uni verse started as a sphere, a "primeval atom," about thirty times bigger than the Sun. The physicist Georg e Gamow subsequently presente d a related, and now defunct , model tha t i n hi s an d othe r people' s hand s develope d into th e presen t Bi g Bang theory. How do we know that there was a Big Bang? Alternative theories have avoided the "something-out-of-nothing" conundrum b y replacing it with a n equally incomprehensible enigma: the eternal universe, with no beginning and hopefully no end. For man y year s Einstei n defende d thi s concep t o f a static univers e bu t relin quished i t in the fac e o f the experimenta l evidence . At present the Big Bang theory is the favore d versio n o f the Creation . You can regard time and spac e as beginning with th e Bi g Bang, but I know that whatever th e cosmologist s d o to convinc e u s that ther e wa s nothin g befor e th e Bi g Bang—because ther e wasn' t a "before" — HMS, an d th e majorit y o f scientists, wil l neve r fee l reall y comfortabl e with th e something-out-of-nothing scenario . The phrase "th e expandin g universe " shoul d no t be taken to imply that every thing i n the univers e i s expanding. Th e Milky Way is not expanding , arid neithe r are the othe r galaxies . Neither were the dancer s i n ou r analogy. But they are certainly moving apart from eac h other. There i s a commo n misconceptio n abou t th e meanin g o f "expansion" i n thi s context. There is a natural tendency to see the galaxies flying through space. Here a much-used analogy helps; the universe is likened to a fruitcake baking in the oven. The currants ar e not moving through the expandin g dough ; they are moving with the dough. Now replace the dough with space, and you have the right picture. I t is space that is stretching. I know it doesn't fit in with daily experience, but that's the way the cosmologists say it is. As space stretches, it stretches the light waves corning to us from the galaxies, and they drop in frequency. That is the real explanation of the redshift; it is not a genuine Doppler shift. Another strang e consequence o f the expandin g universe i s that there are galaxies moving so fast tha t their ligh t can never reach us. This implies that, compared with us , they are traveling faster tha n th e spee d o f light, thus apparently breaking the conditio n impose d b y th e specia l theor y o f relativity. Th e difficult y ca n b e overcome if you accept the fac t tha t they are traveling with space and no t through space. It doesn't matte r i f this i s puzzling; the poin t t o grasp is that there ma y be parts of the universe that we will never see, and those parts may be far larger than the visible universe. They may be very different, but we may never know. We can onl y see the univers e fro m th e Eart h or from th e observatorie s that w e send ou t int o ou r immediat e locality . I s this a typical view ? Would the univers e look completely differen t fro m anothe r vantag e point? Einstein thought abou t thi s and propounded his cosmological principle, which states that wherever you are in the universe you will see pretty much the same overall picture, rather like a man in a huge crowd. It says that the distributio n o f galaxies is fairly unifor m throughout the universe , whic h conform s with wha t w e se e from here. Th e principle seem s reasonable but cannot be proved since we cannot (yet ) travel all over the universe. It certainly sweetens the lif e of the theoretical cosrnologist.

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The Galactic Host The eternal silence of these infinite spaces terrifies me. —Blaise Pascal, Pensees They cannot scare me with their empty spaces Between stars—on stars where no human race is. I have it i n me so much nearer home To scare myself with my own desert places. —Robert Frost, Desert Places

All the individua l star s that you see with th e nake d ey e are in the Milk y Way, including ou r Sun and the neares t sta r (Proxim a Centauri). There are about 10 0 billion othe r stars in ou r galaxy. All tha t you ca n discer n o f other galaxie s ar e a few blurred smudges of light. The Milky Way is a typical galaxy, shaped like a disk with a swollen center , where most of the star s in the galaxy are found. The wispy spira l arms ar e characteristic o f th e majorit y o f galaxies . W e liv e i n a normal galaxy , which jus t means that there is not much happening to its structure. The Milky Way turns in space, one revolution taking about 300 million years . It is this rotation that is probably responsible for the for m of the arms of spiral galaxies. Observation indicates tha t all stars, in our galaxy or elsewhere, have a life cycle: birth, followe d by a hectic, glitterin g lif e whic h i s ende d b y on e o f two kind s o f death. The small stars go relatively quietly. The biggest stars, Gloria Swanson-like, leave the stag e with a spectacular final fling . Star s are made primarily from hydro gen atoms with a minority contribution fro m helium. These were the two main elements lef t ove r fro m th e Bi g Bang, an d the y wer e distribute d thinl y throughou t space. Th e forc e tha t brough t hosts o f them togethe r to for m star s i s gravity. The process o f star formatio n ca n b e picture d a s a kind o f gravitational snowball , al though this picture is far from proven. A cluster of atoms that happened t o come together by chance woul d tend to pull othe r atoms in their direction . A s the mass of this cluster grows, its gravitational pull also increases, and so does its effectivenes s in persuading more free atom s to fall into its lair. Huge quantities o f matter eventu ally accumulate. The gravitational pull of the cloud not only draws in more material from it s surroundings bu t also compresses the cloud to higher and higher densi ties. This process of collapse is not simple; it does not resemble a deflating balloon. Part of the ga s forms a disklike structur e that begins to revolve and i n many case s breaks u p int o tw o lumps , formin g a doubl e star . Anothe r possibilit y i s tha t th e disk condenses into a planetary system. As the newbor n sta r contracts , the pressur e and temperatur e at its cente r rise . The spee d o f atoms, and therefor e their kineti c energy , grows as they fal l towar d the center of the nascent star, and we know that the temperature of a gas is reflected in the average kinetic energy of its molecules. A typical star could have a temperature o f 10 million degree s Celsius at its center . This i s hot enoug h fo r the proton s and other particles to react. The consequence is energy production by processes in which mass is turned int o energy. In the Sun, and billions o f other stars, the initia l step i s the fusio n o f two proton s (hydroge n nuclei) and th e subsequen t los s o f a positron an d a neutrino t o form a deuterium nucleus , tha t is , a proton an d a neutron (see Figure 12.5):

The Cosmo s and Peeping Tom | proton + proton = deuteron + positron + neutrino

This i s the hardest step . The other steps follow fairl y quickly , and in the complete process, which convert s protons into cc-particles (helium nuclei), there is a net loss of mass that turns up a s energy, just as it does in atomi c weapons. In E = me2, the mass is multiplied by an enormous number, the spee d of light squared. One kilo of matter is equivalent t o 9 x 1016 joules, enough to run a 100-watt lightbulb for nearly 3 million years . The nuclear reaction is characteristic of the long adult life of a star. The tremendous kinetic energy of the particles in the hot gas prevents the gas cloud from collapsin g completel y unde r th e pul l o f gravity. They are moving too fas t t o stick together. That i s why th e glowin g star i s stabl e onl y a s lon g as i t ca n glow, which mean s until the hydrogen runs out. The great majority of stars, including ou r Sun , ar e "burning " hydroge n to give helium. The astronomers call them main sequence stars. The Death of the Average Star The stabilit y o f a star depend s o n a continua l figh t betwee n gravitation , whic h tends t o pul l i t inward, an d radiatio n an d th e kineti c energ y of its atoms , whic h produce a net outward pressure. If a star tends to shrink because of gravity, then its core would b e compressed an d this would increas e the crowdin g of the gas of nuclei. These would mee t an d reac t more often , produc e kineti c an d radian t energy faster, an d pus h the star outward again. The lifetime of the star , and the manner of its death, depends on its size. Stars star t t o di e whe n thei r centra l stor e o f hydrogen begins t o ru n out . Th e small one s have less fuel, but the y burn i t more slowly. The most massive stars, as befits thei r image , are big spenders and liv e a n intense but shor t life . Ou r middleclass Su n lie s i n th e intermediat e range , its expecte d lifetim e o f 10 billion year s being about 1% of that of the smallest star s but about a thousand time s longer than that of the most massive stars. The small stars die the simples t deaths . When most of the hydrogen in the core has turned t o helium, there i s an upsurge of energy production aroun d the core , a kind o f protest against the coming oblivion, like Beethoven on his deathbe d shaking his fis t a t heaven. This results i n a huge swelling up o f the oute r layers of the star, which consequentl y cool somewhat , s o that th e frequencie s o f the ligh t tha t they emi t move down into the red part of the visible spectrum. So are born the red giants, and in about 5 to 10 billion years our Sun will swell up in this way and approach, or envelop, the orbit of the Earth. In the early part of this process, the radiation fallin g o n the Eart h will increas e thousands-fold, and lif e wil l vanish. Late r we, together with Mercury and Venus, will vaporize. Red giants can be up to a hundred times larger than the original star, but because the huge gas cloud i s so far from th e center of the star it starts to drift away . All that is lef t i s a tiny, intensel y ho t body , usually abou t th e siz e o f the Earth , which i s nothing to brag about o n the cosmi c scale . It has become a white dwarf, whit e because i t is very hot. Bu t this hea t i s not du e t o nuclea r reactions ; the fue l tan k is empty. The star is living o n past glory, glowing because it has not yet cooled down enough to disappear, a process that is long but inexorable. The hottest objec t so far found in the Milky Way is a white dwarf , imaginativel y

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named RE1502+66. This i s so hot that i t is not eas y to see. Looking back at Figur e 15.8a, we can see that the range of frequencies emitte d by a heated body moves upward a s th e temperatur e rises . Th e surfac e temperatur e o f RE1502+6 6 is abou t 170,000 K, compared with the Sun's 6000 K. It is almost too hot to emit frequencie s in the visible range and indeed i t emits mostly UV radiation. A typica l white dwar f i s a s big as the Eart h but ha s th e mas s o f the Sun . Th e compressive forc e o f gravit y i s staggering . A tablespoo n o f whit e dwar f weigh s about 1 5 tonnes, a million time s mor e tha n a spoonfu l o f sugar. Th e nucle i i n a white dwarf are about a hundred times closer together than they are in normal matter. The electrons ru n free, as do the conductio n electrons in a metal. We can treat them theoretically as though they were free electrons in a box. The latter problem is well known to first-year physic s students. Thus doe s quantum mechanics becom e a tool for handling the structur e of stars. Incidentally, the most energetic electrons in a white dwar f are moving so fast tha t relativity theory is needed to account for their properties. We have see n that whe n mai n sequenc e stars—thos e tha t "burn " hydrogen t o give helium—die, they turn int o re d giants and the n int o white dwarfs . As in th e entertainment industry , some stars are "bigger" than others , and, as you know, the really bi g star s hav e somewha t differen t biographie s fro m th e averag e star . Th e analogy is not bad, for as we now see , the really big stars live in the fas t lane ; they have more intense lives and die more spectacular deaths . The Death of the Great Stars For much of its life, a really massive star follows the same pattern as any other star, so that when it s central store of hydrogen runs out it too forms a red giant. However, because of its enormous bulk, the pressur e and temperatur e a t the cente r of the star rise far above that o f lighter stars, so far above that "helium burning" becomes possible. Hydroge n "burning" need s a temperature of 10 to 20 million K. This is not enough to give the doubl y charged helium nucle i (a-particles ) enough kineti c energy to overcome the electrostati c repulsion betwee n them. However , at 10 0 to 200 million degree s they have enoug h kinetic energ y to run a t each other withou t playing chicken. Thei r fusio n reactio n gives carbon nuclei , although th e reactio n requires the collision of three helium nuclei, which i s far less probable than a twobody collision . Carbo n was probabl y th e firs t comparativel y heavy elemen t t o be formed afte r th e Big Bang. At the temperatures obtaining in giant stars, another he lium nucleu s ca n ad d o n to the carbo n nucleu s to give an oxyge n nucleus. Thes e fusion reactions release even more energy, again by the conversion o f mass to energy. When th e temperatur e rises t o about 50 0 million degrees , it is hot enoug h for carbon nuclei , whic h hav e a charg e o f six, t o interac t with eac h othe r an d for m heavier nuclei, such as neon, sodium, and magnesium. At around 1 billion degrees, oxygen nucle i ca n combin e t o giv e silicon , phosphorus , an d sulfur . A t tempera tures i n th e regio n of 3 billion degree s metals, includin g chromium , manganese , iron, cobalt, and nickel form . More and more types of nucleus ar e produced and i n each case fusion produce s energy , but th e heavies t nucleu s tha t ca n be formed i n this way is that of iron, because the fusio n o f nuclei heavier than iron does not give energy—it needs energy. Heavier nuclei ar e formed b y the additio n o f neutrons t o existing nuclei, a process helped by the fac t tha t a neutron i s not repelled electro -

The Cosmos and Peeping Tom |

statically. Th e trapped neutron s ca n then conver t to protons, thus increasin g the total positive charge on the nucleus (th e atomic number). At this stage massive stars have heen likened to onions, successive layers being composed predominantly of one element. The core is dominated by iron, and going outward we cros s layers of silicon, neon an d carbo n until, i n th e oute r regions of the red giant, the atmosphere is helium and hydrogen. This theory of stellar nucleosynthesis—the production of the chemical elements in the stars—which was published i n 1957 , is mainly du e t o Willy Fowler, with considerabl e help fro m Fre d Hoyle. It is the stars that have generated almost all of the periodic table. The party does not last. At a certain stage the engin e stops and on e of the most spectacular event s i n th e cosmo s follows. Suddenly , within a matter o f seconds, the cor e of the sta r implodes. The result is a flash o f energy that tears through the whole star. A huge explosion smashes the star to pieces, and for a period of hours to days it can shine brighter than the whole of the galaxy in which it resides. A supernova has been born. Such events are rare, but I can vouch for the excitement in the cosmologist community when they do occur, as one did in February 1987. The firs t recorded supernov a was observe d by Chinese astronomers on 4 July 1054 , in th e Taurus constellation. Incidentally, the earlies t verifiable report of an eclipse—-tha t which occurre d in 1361 B.C.—was also recorded by Chinese astronomers. The Fate of a Supernova The explosion of a supernova sends out a cloud of hydrogen, helium, and heavy elements. Gravity now repeat s its trick, pulling parts of the clou d inward o n themselves and creatin g new stars , in a repetition of the process in which the firs t stars congealed fro m th e matte r that was created in th e Bi g Bang. Thus the heav y stars not only live and die , they can reproduce. New stars are continually replacing old, a process that is not expecte d to stop for tens of trillions o f years, when al l the hydrogen in the universe has been "burned. " In contrast to the origina l star , the ne w star' s offsprin g star t of f with heavy elements. It was through the life cycles of the massive stars and their offspring that the elements that are heavier than hydrogen and helium were synthesized and spread through the universe. The cycle can be repeated by the star's progeny. If some of the new stars are massive enough, they too will produce heavy elements, adding to the stock tha t the y receive d a t birth. An d s o i t goe s on . Bu t despit e th e impressio n given by the soli d natur e o f our planet, the heav y elements ar e in a complete minority in the universe, which is dominated by hydrogen and helium. Helium exists as single atoms. The next most common molecule i n the universe, after th e hydrogen molecule, is the carbon monoxide molecule, CO. From some of the ne w stars , planetary systems evolve. In on e o f the planet s of one such star, stocked with the full range of stable chemical elements, a homicidal biped evolved. The collaps e o f the cor e of a heavy star, and th e los s o f the oute r cloud o f gas, leaves a tiny object, usually no more than about 20 miles across and consisting entirely o f neutrons. Neutro n stars, or pulsars, th e firs t o f which wa s discovere d in 1967, ar e fantasticall y concentrated. Thei r diameter s ar e abou t 2 0 million time s smaller than those of the red giants that fathered them. In Chapter 5 we noted that the escape velocity from Earth is 25,000 mph. This is the minimum initial velocity

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of a projectil e that wil l allo w i t t o escap e fro m Earth' s gravitationa l field . Fo r a white dwar f and a neutron star, these velocities are in the region of 10 million an d 200 million mph, respectively. Pulsar s are well over a hundred millio n times mor e dense than white dwarfs. The enormous density is the result of stupendous gravitational pressure. It is this pressure that appears to have forced the electrons and protons o f the star' s cor e to combine, giving neutrons. A tablespoon o f a neutron sta r would weigh about 3 billion tons, about ten times the weight of the Earth's population. Densities of this magnitude confirm the emptiness o f ordinary matter that was first revealed by Rutherford. Th e density of a neutron star is not far from th e densi ty inside a normal nucleus . Pulsars spi n aroun d a n axis up t o several thousand time s a second. The y hav e tremendous magnetic fields, and electrons caught up in them accelerate toward the magnetic poles of the star. Maxwell said that accelerating charges generate electromagnetic radiation, an d pulsars generat e two beams of radio waves emerging fro m opposite sides of the star. The rotation of the star with respect to the Earth results in regular pulses of radiation being picked up down here, hence the name pulsar. Pulsars als o occasionall y sen d ou t giganti c amounts o f visibl e light , equivalen t t o many thousand s o f times the tota l ligh t emitte d by the Milk y Way. Since pulsar s have hug e gravitational fields, the y can dra w i n gas from a neighboring star . Thi s gas acquires great kinetic energy , and whe n it s temperature reaches abou t 1 0 million K, the atom s of the gas start to emit X-rays. Black Holes Therefore there exists, in the immensit y of space, opaque bodies as considerable in magnitude, and perhaps equally as numerous as the stars . —Laplace

When the core of a supernova has a mass exceeding that of about three times that of the Sun, it is believed that a black hole is formed ("Black " because when light is directed at a black hole it never comes back). Both Laplace, and before him the Reverend John Michell,4 surmised tha t the attractive force o f a heavenly body could be so large that the light coul d not flow ou t of it, but the y were vindicated only in the twentieth century . Laplace actually calculated the condition for the escape velocity of a body to be large enough to prevent light leaving it and o n the basis of questionable assumptions actually arrived at the right answer. In 1915 Einstei n showed that one of the more dramatic consequence s of his theory of general relativity was the formation o f black holes from large masses of matter. Black holes reached the cover of Time. Their notoriety is understandable; a n object tha t swallow s no t onl y matte r bu t als o light , deserve s medi a attention . Th e basic principle behind black holes is that when ther e is enough matter concentrat ed in one place it allows nothing to escape from it; the escape velocity (see Chapter 4

John Michell (1724-1793) , wh o was a lecturer in Greek, Hebrew, arithmetic , and geometry at Cambridge, made a telescope i n 1780. H e attempted to detect the pressure o f light, studie d magnetic force , and wrote Essay on the Cause and Phenomena of Earthquakes (1760) , which many regard as the beginning o f scientific seismology. He also designed th e apparatus wit h which Henry Cavendish estimate d th e density o f the Earth.

The Cosmo s an d Peepin g Tom [

5) becomes greate r than the spee d o f light. O f course, if no ligh t ca n ge t ou t o f a black hole, you can't see it, so we have to look for indications o f its presence, rather like detecting the wanderings o f a poltergeist. The most common method b y which black holes have been detecte d is through the movement o f visible stars . The enormou s gravitationa l pull o f black holes ha s been invoked as the cause for the unexpected paths of some stars. Thus a star in the Musca constellatio n ha s bee n see n t o be rapidly circling nothing a t a velocity of nearly 1 million miles pe r hour. Obviously , it is being strongl y attracte d to something. Calculation, using the old-fashioned laws of motion, shows that the invisible object has a mass of about three times that of our Sun. This is about as modest as a black hole can get. The formation of black holes is supposed to come about by the collapse of a massive star . The matter i n the cor e of a supernova is drawn togethe r by gravitational force. A s th e centra l mas s contracts , th e gravitationa l fiel d a t th e surfac e o f th e dying star increases. The smaller a given mass is, the greater the gravitational pul l at its surface.5 At a certain stage you can imagine the formation of an imaginary surface, abov e the surfac e o f the blac k hole. Thi s i s termed the event horizon, o r the Schwarzschild radius. An y object , o r radiation, tha t penetrate s the even t horizo n from outside is lost forever. It is as though the black hole has isolated itself from th e space-time aroun d it . Nothing can return fro m thi s ravenous land . You might care to see the even t horizo n as being the consequenc e o f the escap e velocity reaching the spee d of light. When no light leaves the star , we ca n no longer see it—a black hole ha s formed . Thi s proces s canno t reac h it s fina l stag e i f there i s insufficien t mass to start with. Thu s th e mas s o f the Eart h is far too small fo r its gravitationa l field t o induce contractio n o r significantly slow dow n light . It can be shown tha t the minimu m mas s neede d to for m a black hole i s roughly three times that o f the Sun. In contrast, there are black holes that have been calculated to have masses up to about a billion times that of the Sun . When matter is caught in the pull of a black hole and descends toward its center, it becomes compressed, heating up so much that, at around 1 0 million K, it starts to emit high-energy radiation. Thi s i s probably the origi n of the bursts o f X-rays that have been detecte d fro m th e directio n o f suspected black holes. It is claimed tha t mysterious bursts of y-rays are also caused by the energy released when black holes swallow stars , but th e staggerin g amounts o f energy associated with these burst s are not at present explicable . Half a dozen black holes have been identifie d in th e Milky Way, to varying degrees of certainty. There may be a black hole, having a mass about a million time s that of the Sun , at the center of the galaxy. If, as is the custo m of black holes, it eats anything that comes its way, it will get heavier, bigger, and more dangerous. Strange thing s happe n i n blac k holes . I f we follo w Einstei n an d attribut e th e bending of light to the bending of the geodesies of space-time by mass, we can construct a graphic picture o f a black hole in which space-tim e is so curved that ligh t never escapes . Thus , o n th e even t horizon, a beam o f light directe d tangentiall y along the horizon woul d circl e aroun d an d around . Yo u would b e able to see the 5 From Newton's law of universal gravitation, the fiel d at the surface of a sphere of matter depends both on its mass and on the distance from the center of the sphere. If the sphere contracts by a factor of 1000, the field goes up by a factor of 1000 squared, or 1 million.

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back o f your head . Ligh t attemptin g t o escap e fro m th e blac k hol e woul d slo w down and become static at the event horizon because its velocity is equal to the escape velocity at that surface. An object approaching the event horizon fro m outside would accelerat e becaus e o f the gravitationa l attraction an d woul d approac h th e speed of light as it neared th e horizon. Once having crosse d th e horizon, it would become invisible to an outside observer. What happen s t o matte r tha t fall s int o a blac k hole ? Firs t o f all, i t i s tor n t o pieces. Thi s effec t i s a result o f the enormou s increas e i n gravitationa l forc e be tween two points at different distance s fro m th e cente r of the hole. If you dived i n headfirst you would elongate as though on a rack, until your body disintegrated. As the parts moved inward they would disintegrat e further, into cells, then molecules , then atoms, nuclei, quarks, and so on. What happens a t the center? We don't know. It has been suggeste d that matter is crushed ou t o f existence. Yo u don't believe it? I'm no t sur e tha t I do , usin g m y commo n sense . Man y physicist s doub t i f th e presently accepted laws of physics hold at the center of a black hole. To complicate things, Stephen Hawking has suggested that in certain circumstances radiatio n can escape from a black hole. I f you fee l confuse d you have a n absolute right to do so. Cosmology, especially the area of cosmology that deal s with, or thinks i t is dealin g with, the Creation is not onl y often bewilderin g to HMS; it a rich source of (almost polemical) controversy between the leadin g scientists i n the field . A taste o f these sometimes barel y gentlemanly exchange s ca n be savore d i n The Nature of Space and Time by Stephen Hawking and Roger Penrose (1996], in which the authors dis agree on almost every important issue from th e Creation to Schrodinger's cat. Black holes apparentl y ea t matter, but wher e di d matte r com e from i n th e firs t place? Where did the universe come from? Easy: the Big Bang.6

6

A magazine competition, intende d to find a new name for the Big Bang (considered b y some to be sexually suggestive) , resulted i n over 10,00 0 entries, including "Th e Blast from th e Past," "Orgasmus Universalis" and "Hubbl e Bubble. " The judges settled fo r the Big Bang.

J55 The Impossibility of Creation When there was no heaven, no earth, no height, no depth, no name, when Apsu was alone, the sweet water, the first begetter. --The Babylonian creation myth, twelfth century B.C .

As a ten-year-old child I lay in bed an d sweate d ou t my nightly terro r of death. It was not hell tha t worrie d me, but oblivion . I didn't believe in lif e afte r death . My reason refused to be humiliated b y a cowardly compromise with m y fears . Bu t in the Sloug h of Despond I found hope: the complete inexplicability of the Creation. 1 asked John Donne's question: How can something appea r out of nothing? For if that was possible, which i t appeared to be, then anythin g was possible—even life afte r death. The fea r o f death faded , but I remain, as most of us do , mystified by the fac t of the Creation. The Bible didn't help me. In my search for a more convincing story I discarded th e Egyptians, Babylonians, and Hindus, although in my wanderings I was attracted t o the Gnostics, an early Christian sect whose origins actually predat e Christ an d wh o recognize d a secondary god , the Demiurge , who wa s responsibl e for th e creatio n o f evil. The Demiurge answers som e very awkward questions. Bu t not how being emerged from nonbeing . What preceded the Creation, or has that statement no meaning? Like "How high is green?" Was time born a t the Creation ? And space ? Aristotle said that tim e was created with the cosmos, and so there was no "before." Modern theories of the Creation tend to agree with him, but no one has provided a readily comprehensible solution t o Donne's question: What was nothing—and how doe s something emerge from it ? To which Lock e replied: "Bu t you will say , Is it not impossibl e t o admit of the making of any thing out of nothing, sinc e we cannot possibly conceive it? I answer, No: Because it is not reasonabl e to deny th e powe r o f an Infinit e Being, because we cannot comprehend its operations."1 And onc e w e hav e a universe, ca n w e understan d it s physica l limits ? No t i n everyday three-dimensional imagery . General relativity allows us to create forms of space-time that resemble the surfac e of an orange, thus ensurin g a space-time that has no boundaries bu t i s finite . Ther e i s no edg e to this surface , n o en d o r beginning. With a little goodwill you can feel yourself walking on the surface. It is a picture tha t anyon e ca n construct , bu t whic h i n th e en d doesn' t reall y squas h ou r childish(?) question: What's outsid e the orange, Dad? 1

Saint Augustine (354—430) , referring to people who ask "What was God doing before he mad.e heaven and earth?" explain s that "I keep awa y from the facetious reply. . . . 'He was preparing hel l for people wh o ask awkward questions.' . . ."

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The easiest way out is to accept our limitations. The explanations of the cosmologists—and ther e i s a choice—ma y b e convincin g mathematically , bu t w e wil l never be comfortable with them because they are not constructed withi n th e kin d of (separate] space and time that we experience. Our, quite unjustified, gu t feelin g that spac e an d tim e ar e absolut e Newtonia n playin g field s doe s no t encourag e friendly feeling s towar d professor s with incomprehensibl e equation s assurin g u s that we live in a warped space-time that started from a fluctuation in a vacuum. None o f the presen t theorie s pretend s t o giv e a commonsens e answe r t o th e problem of nothing an d it s emergence into something. Th e concept o f fluctuations in a vacuum (see Chapter 30) is, to most people, totally unacceptable as an explanation o f the Creation . I am also aware of the storie s that begin, "A wedding ring ha s no beginning. There are objects which exist which have n o beginning s o why no t the universe? " Once again, the min d ca n swallo w it , but no t th e instincts . I t has been suggeste d that a model fo r the appearanc e o f matter is t o mak e a video o f a black hole swallowing an d destroying matter, and then run the cassette in reverse. This is the so-called white hole, an entity predicted by Einstein's general relativity. It makes a good subject fo r an animated cartoon , but d o you believe it ? Where did the white hole come from? Sir Arthur Eddington wrote, "The beginning seems to represent insuperable dif ficulties unless we agree to look on it as frankly supernatural . We may have to let it go at that." Not very satisfactory, but I defy an y cosmologist to explain the momen t of Creation in the language of HMS. Those scientists concerned with the origins of the physical universe begin their investigations just after the Creation, not just before. The story that they have to tell will unquestionably be modified as we learn more and think deeper , but i n its essentials i t seem s a t present t o give a good rough explanation o f the wa y tha t this universe developed. As we saw, there may be others. Let's see what ou r tribe's creation myth says. The Big Bang

When we speak of the Bi g Bang theory, we are speaking of a family o f theories, differing fro m eac h other on a variety of issues but al l accepting the general picture of an initial cataclysmic creation of "something," about 15 billion years ago, followed by a furious expansion . One version, which is regarded as the "standard theory," is associated wit h th e name s o f Friedmann, Robertson , Walker, and Lemaitre , wh o were, respectively, Russian, American, English, and French. This is the theory that forms the basis of our discussion. I t is the most straightforward of the various theories, and i s what mos t peopl e are talking about when they mention th e Bi g Bang. The majority of cosmologists feel that the outline s o f the standard theory ar e plausible and that there is some strong supporting evidence for its general validity, but that there are some very difficult question s remaining and there may be more waiting round the corner . It should not be thought of as a stable theory, but i t seems to contain a fai r amoun t o f truth. Wha t follows is the scientifi c equivalen t o f a firs t draft. It is being tinkered with as I write. The postulate d early histor y o f the univers e i s conveniently divide d int o eras , where we have to stretch that word to include minute fractions of a second as well as periods of hundreds o f thousands o f years. The earl y eras ar e the shortest , an d

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the subsequent era s get longer and longer. Everything is more closely packed at the beginning, and the rate of events slows down as time progresses. It is not wise to ask what came before the Big Bang. In some circles it is even regarded a s gauche, a sign of scientific naivete. I f you wis h to avoi d the imag e of a cosmic countr y bumpkin , yo u mus t profes s t o believ e th e curren t mythology , which claim s that space, time, matter, and energy were all born with the Big Bang, and that the expansion o f the universe wa s not an expansion into space but an expansion of space . I would no t blam e yo u i f you preferre d th e homel y image s of Genesis; just don't say so in smart company. We begin no t a t zero but jus t afte r that , a t 10" 43 seconds. This perio d o f time is called th e Planc k time. (Divid e one second by ten multiplie d by itself forty-three times). Th e theoreticians ar e not too united abou t what t o say after "I n the beginning there was .. .". They understandably mumble about it being difficult t o apply normal concepts of space and time, or matter, to this period. As for time zero itself, the standar d theor y ask s u s t o believ e tha t th e "universe " ha d infinit e density , which i n everyday terms means that it had no volume. Some suggest that the concept o f time breaks dow n near zero . If you ax e uncomfortable with this, don' t b e afraid to say so. Most sane human beings are. From 1CT 43 to 10" 35 Seconds

It is supposed that a t the beginning o f this period, called the grand unified theory (GUT) era, all four known physical force s were united into one force. You can suppose that there was only one kind of field (no t a gravitational field plu s an electromagnetic field , etc. ) and that this field produce d a single particle that mediate d a single typ e of force. On e o f the mai n object s o f theoretical physics i s to construc t such a field. The drive to do so is largely based on the belief in simplicity. But as A. N. Whitehead onc e said: "Seek simplicity, and distrust it. " During this period , gravity separates off as a distinct force , s o that there ar e effectively two force s in the universe: gravity and a combination of the othe r forces . At the end of the period, however, the strong force separates out. This separation of diverse forces out of a single unified force has been the subject of much devising of analogies. Some refer to the process as the "crystallizin g out" of forces a s the temperature drops, as if, at high temperatures, everythin g is melted together. It may be easier to see it as the separatio n out of the particles that mediate the forces , jus t as at a later stage different materia l particles also separate out. On the other hand, taking into accoun t the view that all particles ar e packets in fields, yo u may prefer to think o f differen t field s separatin g ou t o f the soup . Analogie s are no t reall y tha t helpful. It' s a case of working on the subjec t for thirty years, by which time you are used to it. Like quantum mechanics . As th e temperatur e continue d t o fall , smal l particles—th e quark s an d elec trons—began to appear. Where did these particles come from? From the conversion of th e energ y of photons t o mass. These particle s ha d hug e kinetic energy , which militates agains t their formin g stabl e clusters . Group s of three quarks , as there ar e in protons and neutrons, would be unstable under frantic bombardment by violently energetic photons. The theory assumes that, whatever i t was that made up th e universe i n the beginning, i t ha d unifor m densit y throughout . I n othe r words , whereve r yo u wer e and whichever wa y you looked, the view was exactly the same, as if you were ern-

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bedded in strawberry Jell-o. This means that the universe expanded at the same velocity in all directions. From 10~35 to 10~32 Seconds The frenzied activit y during this instant of time makes the explosion o f a hydrogen bomb look like the pop of a Christmas cracker. Whatever existed at the beginning of this period had a temperature of something like 1028 degrees Celsius, which is completely unimaginable . Everythin g was compresse d int o a spac e estimate d t o b e about a s big as a pearl—yes, al l th e matter/energ y that exist s i n th e presen t uni verse. It must have been hell to get to the bar. Then, according to a theory put forward by Alan Guth of MIT in 1981, came inflation; the universe expanded by a factor o f about 10 30. To get some idea o f what thi s means, i t i s as though a hydrogen atom expanded into a sphere 1 0 million times the diameter of the solar system. There has been a suggestion that durin g this expansion gravit y was a repulsive force, blastin g th e nascen t univers e outwar d a t colossa l velocity . It is durin g thi s first perio d that most of the expansion of the universe took place. The calculation s have to take into account the stupendou s concentratio n o f mass, which force s th e theoretician t o bring i n both the genera l theory o f relativity (t o give a descriptio n of space-time ) and th e quantu m theory (t o give an explanatio n o f the behavio r of matter). At 10"10 Second s

The weak force separates from the electromagnetic force about this time, so that we have all four force s that we have today. At One-Hundredth of a Second By this time, the pearl had expande d to roughly the size of our Sun, but this figur e depends on which particula r variation of the theory you are reading. Some say that the universe was already the size of the solar system at 10" 10 seconds. It is not worth taking these differences to o seriously. No one knows much about the exact, or even approximate, correlation of size and time, but all agree that the universe expande d very fast indeed at the beginning and then slowed down, keeping going until now . The temperature ha d falle n t o a trifling 10,00 0 billion degrees , and wa s fallin g rapidly, perhaps to 30 billion degree s at one-tenth of a second. As fierce as this latter temperature is, the equivalent conditions can be replicated on Earth. More accurately, it is possible to accelerate particles to the kind of speeds they should hav e at these temperatures . Th e densit y o f matter a t this stag e was abou t a billion time s that o f the Earth—in other words, a teaspoon of the universe would have weighe d about 16,000 tonnes (i f weighed on the nonexistent Earth). By the en d o f the firs t second , the nascen t universe wa s probably a hectic mix ture o f radiation , electrons , positrons , an d neutrinos , wit h comparativel y tin y numbers o f neutrons an d proton s forme d fro m th e rapidl y disappearin g isolate d quarks. Thes e proton s an d neutron s ar e essentially thos e presen t i n the univers e today. Regarding the electrons and positrons: ou r experience i s that when particle s are create d fro m th e destructio n o f photons , the y com e i n particle-antiparticl e pairs, one positively and one negatively charged. In one way this is convenient. We need roughl y equa l numbers , otherwis e th e univers e woul d hav e bee n strongl y charged—remember, th e numbe r o f proton s (positivel y charged ) wa s relativel y

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small. This presents a difficulty: Wher e have all the positrons gone? They are pretty difficult t o find these days. At One Second The temperature had falle n t o about 10 billion degree s Celsius, and th e densit y of the univers e wa s abou t 100,00 0 times that o f the Earth . One teaspoon of universe would have weighed about 1.5 tonnes. B y now the average photon di d not contain enough energy (remember E = me2) to produce any of the known particles, so at this stage there was no further productio n of matter. At 100 Seconds The temperature was now dow n to about 1 billion degrees , similar t o that a t the center of the hottes t known stars . This is the stag e at which th e nucle i o f the firs t chemical element s wer e formed , no t fro m radiatio n bu t fro m existin g particles . Two kinds o f synthesis ar e o f interest t o us : th e formatio n of deuterium nucle i (a proton plus a neutron) and helium nuclei (tw o protons plus two neutrons). A delicate balance is involved here. At too high a temperature a deuterium nucleus will , if formed, immediatel y disintegrate into its components. At too low a temperature the repulsion between protons will not allow the helium nucleus to form. A billion degrees accommodates both conditions . Afte r th e formatio n of the tw o nuclei, a n excess of neutrons wa s probably left over . Now, stable as the neutro n i s when i t is inside a nucleus, it has a lifetime of only about a quarter of an hour when it is on its own, so the exces s neutrons broke down to give protons (and electrons). The proton, o f course, is th e nucleu s o f the hydroge n atom. Very smal l amount s o f other light nuclei, suc h a s that o f lithium (thre e protons plus thre e neutrons) may also have been formed. It was still too hot for electrons to become attached to these two nuclei, they would have been knocked off immediately. The average speed of a proton at 1 billion degrees is about 18 million kph. Thus, according to theory, the net result of the activit y up to 100 seconds was a sea o f radiation i n whic h ther e wer e deuteriu m nuclei , heliu m nuclei , protons , electrons, an d positrons . Somethin g like 99 % o f the matte r i n th e univers e wa s made in the first hundred seconds . None of the nuclei o f elements heavier than helium existed. A Test of the Theory to This Point The theoreticians hav e calculated that at this stag e the ratio of hydrogen nuclei to helium nuclei shoul d hav e been ten to one, and that it is unlikely to have changed significantly sinc e then . Furthermore , the rati o o f deuterium t o hydrogen a t tha t time is calculated to have been 1 in 50,000. We can detect the elements in the stars by examining the spectrum of their light; furthermore, w e can estimate their relative abundances fro m th e intensit y o f their spectral lines. The ratio of hydrogen to helium atoms in the present-day universe is about ten to one. The amount of deuterium is about 1 in 50,000. To be fair, we have to admi t tha t som e of the ligh t arrivin g here fro m th e star s has take n millions of years to get here so that we are looking at what they were like long ago. Nevertheless, the theor y say s that th e ratio s o f hydrogen to helium t o deuteriu m have no t changed significantl y since th e firs t 10 0 seconds, s o the fact s ar e stil l consisten t with the theory—a very impressive achievement.

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Time Goes By: From 100 Seconds Onward As the temperature continued t o fall, som e of the electron s managed to hang on to the nuclei , an d th e atom s o f the chemica l element s hydroge n an d heliu m wer e formed. Electrons and positrons began to annihilate eac h other to give photons. At the en d o f this process, perhaps afte r 300,00 0 years, there wer e no positron s left , just hydrogen and helium atom s and photons, i n roughly the sam e ratio as today, namely, about 1 billion photons fo r each proton or neutron. This mutual annihila tion of electrons and positrons , to leave the presently observed excess of electrons, obviously implies that there must have been more electrons than positrons to begin with, otherwise both species would have disappeared completely and there would be no electrons to clothe the nuclei of the elements. This would have resulted in a positively charged universe, whereas the universe appears to be effectively neutral . Is there any explanation o f why the number of positrons and electron s differed ? In those events in which radiation produce s particles, it does so in pairs—particle and antiparticle, two by two. Nevertheless, there are examples of asymmetry in the particle world. For example, in 1947 an unstable particle was found in cosmic radiation. Th e K ° meson ha s a lifetime o f 10" 10 seconds, which i s abou t twenty time s shorter than that of its anti-particle, thus breaking the symmetry that characterize s matter and anti-matter. (This is known to the experts as CP violation.) This doesn' t directly explain the proposed inequality in the numbers of electrons and positrons, but i t doe s sho w that th e particl e worl d is capable o f slipping ou t o f the straight jacket of perfect symmetry. After 300,000 Years The universe is now made of atoms and radiation. The temperature is a mere 3000 degrees Celsius . Recal l the shift y professor' s whisky-lade n breat h (i n Chapter 1), which ha d t o fight it s way through an astronomical number o f collisions befor e i t reached hi s skeptica l wife . Photons in the interior o f the Su n have the sam e problem. The y ar e s o frequentl y scattere d b y collision s tha t the y tak e a n averag e of about 1 million years to reach the surface an d escape. This was what it was like up to about 300,000 years after th e Bi g Bang, at which point th e disappearanc e of the great majority o f electrons an d effectivel y al l the positron s cleare d the fo g of particles so that photons coul d move from one end o f the universe to the other without continually bumping into things. We can say that the universe became transparent. The universe has also continued to expand, albeit far less dramatically, but a highly significant change had taken place in the nature of the cosmos. Up to about 300,00 0 years, radiation ha d dominate d the universe. The photon s had s o much energ y that i f you sa t dow n with E = me2 yo u woul d fin d tha t the y could easily turn into known particles. When they did appear, particles were in far too energetic a n environment to form atoms , let alone clusters o f material. Bu t the temperature fell , an d from roughly 300,00 0 years onward atom s coul d for m with out fea r o f being smashed t o pieces , an d the y coul d als o com e together i n stabl e clumps, pulled by gravity. The stars and th e galaxies were being born. And radiation was not energetic enough to give matter. Radiation and matter were divorced . The universe was still about a thousand times smaller than it is now. The transparency o f the universe , coming at a time when the temperatur e wa s

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about 300 0 degrees, means that a flood of photons was fre e t o roam through space. Which brings us to a very remarkable finding . Another Test of Theory The range of frequencies that are found in the radiation emitte d by a body depen d on its temperature. If the temperature of the universe was really 3000 degrees when the great flood of photons was released, then the radiation should hav e been mainly in th e visibl e rang e and shoul d stil l exist . Th e existence o f such radiatio n had been predicte d b y th e Russian-bor n America n scientis t Georg e Gamo w (1904 1968), the firs t person to suggest that the Big Bang had been associated with extraordinarily hig h temperatures . Two of Gamow's students, Ralph Alpher and Robert Herman, did some calculations an d estimated that the temperature of this radiation should no w be 5 K. When you se e reference to the "temperature " o f radiation you can thin k o f it i n term s o f a heated body , preferabl y a. blackbody. Th e radiatio n emitted by such a body is related to its temperature, so that radiation "a t 300 K" is radiation with the sort of frequencies that you would measure coming from a body maintained a t 300 K. Alpher an d Herma n publishe d thei r wor k i n th e Britis h magazin e Nature i n 1948. It did not create a stir, although it was one of the most significant predictions ever made in th e fiel d o f cosmology. In 1964 , Arno Penzias (anothe r refugee fro m Hitler) an d Rober t Wilson, working at the Bel l Telephone Labs at Holmdel, were disturbed by a background buzzing that interfered with their attempt s to operate a newly constructe d instrumen t designe d t o pick up wea k radio waves fro m oute r space. The background nois e cam e from al l directions . Attempt s t o eliminat e th e noise failed, including sweepin g out pigeon droppings from the receiver and shooting the two pigeons responsible. Finally , Penzias phoned Bernie Burke, a radio astronomer in New York. Burke suggested that the noise was radiation lef t ove r fro m the Bi g Bang. Penzias phone d Rober t Dicke, the well-know n Princeto n physicist . Dicke had n o doubts . Th e strang e fact i s that Penzia s and Wilso n were no t firmly convinced; the y were just relieved t o have som e kind o f explanation, s o that they could carry on trying to pick up radi o signal s fro m galaxies . The radiation wa s i n the microwave and IR range, and in fact it had been observed previously, in particular by E. A. Ohm in 1961, als o at Bell Labs. This was another exampl e of "It's no t wha t yo u see , it's how yo u se e it." Ohm , and the others who had detected inexplicable noise , regarded it as a nuisance. Penzias and Wilson happened t o be doing their experiments a t a time when there was considerable theoretical interes t i n othe r laboratorie s in th e possibilit y o f finding such radiation . Whe n the y an d Dicke' s group published thei r result s an d conclu sions, they did so in two consecutive papers in the same journal. Gamow was furi ous; he had no t been mentioned, an d neithe r ha d Alphe r or Herman. Their work had been forgotten. It is a curiosity that Penzias and Wilson were awarded a Nobel Prize for a discovery that had bee n predicte d long before, an d fo r observing radiation that had been observed by Ohm in 1961 but not recognized for what it was. The irritating noise was radiation coming from the universe abou t 300,000 years after th e Big Bang. However, the temperature of the universe a t that time was probably about 3000 K, so why d o we se e radiation a t a temperature o f only 2.7 K? Because th e univers e wa s muc h smalle r a t th e tim e an d th e radiatio n tha t fille d i t

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then, cooled as the universe expands . One way of looking at this cooling is to realize that, accordin g to the theory , space itself expanded a s the universe expanded , so that the wavelength of all radiation was stretched. This mean s that the frequen cy, and therefore the energy , of the radiation was lowered. The radiation, known as the cosmi c background radiation (CBR) , was foun d to be isotropic, whic h mean s that whicheve r way the receiver is turned i t picks u p th e sam e intensity o f radiation. This is almost as it should be, but not quite . The universe today is not isotropic. It is not like a featureless bowl of strawberry Jell-o, which i f you were embedded in it, would loo k exactly the same in all directions. You only have to see the stars to realize that. Einstein's cosmologica l principle say s tha t th e univers e look s prett y muc h th e sam e i n al l directions , whic h should be interpreted in terms of a man at the center of a Christmas pudding, not a bowl of Jell-o. The raisins ar e roughly evenly distributed throughou t the pudding . The CB R is radiatio n tha t come s t o u s fro m th e tim e whe n th e univers e becam e transparent, about 300,000 years after the Big Bang. But this is exactly when matter was aggregating into the huge clumps tha t we call the stars and the galaxies. Thus the CBR should not be isotropic; it should no t come equally from al l directions bu t should be uneven. The gravitational field of the young galaxies should have slowe d down th e photon s leavin g their neighborhoo d an d thus effectivel y reduce d thei r frequencies, whic h we can interpret a s a lowering of their temperature. We should see cool spots in the map of the CBR. The search for this unevenness, o r anisotropy, was not easy. A specially commissioned satellite, the Cosmic Background Explorer (COBE), was loade d with sensitiv e instrumentation . I n 199 0 it sen t back a perfec t blackbody spectrum of radiation at a temperature of 2.726 K. No anisotropy was de tected, th e radiatio n looke d exactl y th e sam e i n al l directions . Somethin g wa s wrong. The negative results wer e threatenin g the Bi g Bang theory. COBE went o n taking measurements, about 7 0 million i n it s first yea r in space. They paid off . As the dat a accumulated, tiny variations i n the temperature o f the radiation bega n to emerge. By tiny I mean about 30 millionths of a degree below the averag e temperature of the CBR—small , but undeniably real. The announcement o f the COB E measurements was a major medi a event , being given prominence o n the fron t pag e of many newspapers. Steven Hawking declared, "It's the greatest discovery of the century—if not o f all time. " George Smoot announced th e results a t a meeting o f the America n Physical Society on 24 April 1992. He said, "Well, if you ar e a religious perso n it's lik e seeing the fac e o f God." His excitemen t ca n be understood . Th e univers e wa s speakin g across 15 billion years. The radiation is one of the most important discoverie s ever made in cosmology—it is the oldest "object" that we can see. Eternal Expansion

Will the universe stop expanding one day? And what then? The way that this question has been approached is through the realization that the universe has an inborn tendency to collapse, just as a star does, under the influence of its own gravitation. So we ca n ask , as we aske d o f a projectile in Chapte r 5, are the galaxie s travelin g fast enough to escape? We sa w tha t ther e wa s a minimum velocit y below whic h a n objec t coul d no t leave Earth. Above the escap e velocity, an objec t travels on forever; below it , it re-

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turns. Now the Big Bang resulted in a cloud of matter and radiation, which we call the universe, spreading outwar d an d continuin g t o do so until today . For any object, sa y a planet o r star, there is a net gravitationa l forc e exerte d o n it by al l th e other objects, and tending to slow it down and pull it back to the center of the universe, wherever that may be. There are two extreme possibilities concerning the future o f the universe . On e i s tha t th e gravitationa l pul l o f matter wil l eventuall y bring expansion to a stop. In other words, the escape velocity is too great for the expansion t o keep going. Just as the stationar y arro w at the to p o f its vertical fligh t starts to fall back to Earth, so the universe will slow down, and when it is stationary it will start to contract. Finally, so this plot goes, the universe will return to being a tiny, immensely compresse d ball. Thi s i s the Bi g Crunch, and a universe that expands and then collapses is termed a closed universe. An alternative scenario is based on the assumption that the mass of the universe is not enough to stop eternal expansion an d it will go on forever; i t will "escape. " This is an open universe. In which universe are we living? The answer depends on how much mass there is. When a rough estimate is made, on the basis of the visible objects in the cosmos, it is clear that the mass is far too small to prevent eternal expansion; the universe should expand forever. But what does theory say? The equation s o f general relativity , whic h forme d th e basi s fo r th e standar d model of the Big Bang, do not i n themselves contain a prediction of the amoun t of matter i n th e universe , any more than Newton' s law s o f motion tell u s wha t th e mass o f the Eart h is. I t is Guth' s additio n o f inflation that alter s things. A theory might give a vast range of answers to the question of how much mass the univers e contains. The one obtained when inflatio n i s taken into account is extraordinary. 2 The answe r i s that the universe is neither ope n nor closed ; it is flat, which i s the formal way of saying that the mass is just enough to prevent infinite expansion but not enough to result in eventual contraction. The mass needed for this delicate balance is called th e critical mass. The prospect for us i s that th e presen t rat e of expansion wil l get slower and slower , approaching zero but neve r quite reaching it. The calculatio n give s a densit y fo r the presen t universe o f about 10" 23 grams pe r cubic meter, or an average of three molecules of hydrogen in ever y cubic meter of space. If the theor y can be trusted, then w e have a problem: this calculated, (and critical) mass is about eight to nine times larger than the observed mass of the universe. Should we believe theory or experiment? Experiment says that there is not enough observed mass to stop the universe expanding forever . Theor y says that ther e is . Now we ca n tinker with th e theory i n order to convince it to give us the amoun t o f matter that we have observed in th e universe, but then we lose two other accurate predictions because the GBR, the hydrogen-helium ratio, and th e critica l mass com e as one indissoluble packag e tha t emerges conveniently from th e theory . Another, Baconian, point o f view is to give observation precedenc e and admit that the calculation could be wrong and the universe i s really goin g to expand endlessly . Th e theoreticians ar e stubborn , and o n the whol e the y prefe r t o clin g t o th e theor y an d loo k for th e "missing " matter , which has come to be known as dark matter. 2 The theory, developed mainly by Alan Guth, is also extraordinary i n that inflation gives a flat universe whateve r initial conditions w e start with. This seems to preclude proving anythin g about the beginning o f the universe. The fingerprints have been rubbed of f the gun.

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Dark Matter In 199 3 a huge mass o f glowing gas was detected , far out i n space . From the tem perature i t i s clea r tha t th e ga s molecules ar e movin g a t enormou s velocities , s o high, in fact, that the clou d has no chance of hanging together. Yet it does, and th e investigators suggest that it is held by the attraction of an invisible mass of material amounting to 2 0 trillion Suns . Previousl y there had bee n observation s of individual bodies whose paths ar e inexplicable unles s i t is assumed tha t the y ar e near to other, invisible an d very massive, bodies. As far back as the 1930s , the astronome r Fritz Zwicky had used the term missing matter in this context. How much o f this invisibl e stuf f i s floating around ? And what i s it? There have been many suggestions, from ne w kind s o f matter to our old friends th e neutrino s and black holes. There are huge numbers of neutrinos in the universe, but the problem is that it is becoming more and more probable that they have no mass.3 So they can be ruled out for the moment, but the physicists have the privilege of suggesting all kinds of new and unknown particles without risking ridicule. In order to tackle the problem of missing matter, they have invented a t least three hypothetical enti ties, none universally accepted. And new fact s ar e continually emerging. One type of observation, supportive of the widespread existenc e of dark matter, is related to the famou s bendin g o f light nea r the Sun . The bending o f light by large masses t o produce distorted images of stars is known as lensing (Chapter 32). The indirect evidence fo r th e occurrenc e o f thi s phenomeno n i s growing . Case s i n whic h th e "something" doin g th e lensin g i s invisibl e strongl y sugges t th e presenc e o f dark matter—almost by definition! Another indication o f dark matter comes from theo retical calculations on the stability of certain spiral galaxies, which turn out to have masses that are unable t o gravitationally hol d the m togethe r but coul d be stable if there were large amounts of dark matter wrapped around them. In short, it could be that the universe i s at present abou t 90% to 95% invisible . Until we know reliably ho w much mas s ther e i s in the universe , we won't kno w whether Guth' s prediction i s correct—that the universe contain s th e critica l mas s that ensures that it is "flat." Awkward Questions

I have skirted around som e very complex issue s an d faile d t o mention som e very weird idea s about the nature of Creation and abou t the past , present, an d futur e of the universe . A s one , no t particularl y weird , example , Einstei n onc e postulate d that there was a repulsive forc e i n the universe, opposing the inward pul l of gravitation. He needed suc h a force to maintain hi s model of a static universe, a model he later abandoned , stating that th e repulsive forc e wa s the worst mistake h e ha d ever made. There are some physicists who , while rejectin g the idea o f a static universe, suspect that such a repulsive forc e may in fact exist. It has never been direct ly detected, but who knows? It sometimes seems that in cosmology anything goes. I emphasize agai n tha t th e Bi g Bang theory is in fac t severa l theories, an d tha t they can't al l be correct, eve n if there ar e signs that w e may be on the righ t track. 3

It has been proposed by some investigators that neutrinos switch around between three forms and that they do have a very small mass. The jury is still out.

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One question to which w e may never have an answer is the following: If there is a Big Crunch, will the universe be so hot and s o concentrated that the condition s of the Big Bang will be recreated? And di d "our" Big Bang follow such a crunch? And how many time s ha s th e cycl e bang-crunch-ban g bee n repeated ? Thi s i s th e phoenix with a vengeance. Was the Universe Made for You and Me?

Newton's demonstration that the gravitational constant, G, applied to the solar system as well as to gravity on Earth, was quoted as proof that there was one supreme designer. In recent time s scientist s hav e foun d wha t som e se e as convincing evidence for more than chance in the structure of the universe. It has been pointed out that if the relative strengths of the force s i n the universe had not been as they are, then life would never have developed. Furthermore, there is no a priori physical reason for the universe to be as it is. If gravity had been somewhat stronger , the stars would hav e been compressed more strongly, and, because collisions would have been more frequent, they would have burned out far quicker. The life of the universe might not have been long enough to allow life to develop. If gravity had been somewha t weaker, the star s would neve r have formed—n o sola r system, no planets , no Eve , no Adam . If the stron g force ha d bee n a bit stronger, protons would b e able to hang onto each other without: the necessit y o f neutrons being around. The single proton, the nucleus o f hydrogen, would have been unstable with respect to a double proton. Hydrogen would not have existed. If the strong force ha d been a bit weaker, nuclei woul d neve r have formed. Th e only chemical element in the universe would have been hydrogen—no life! In short, it looks like something of a miracle that the fundamental forces had the strengths that they did, strengths tha t appea r t o b e almos t essentia l fo r the existenc e o f a univers e conducive to the emergenc e of life. Several prominen t physicists , includin g Stephe n Hawking , have pushe d th e idea, apparently first voiced in 195 7 by Robert Dicke, that we are not dealing with luck here. The so-called anthropic principl e has been develope d into a variety of theses, each supporte d by all kinds o f coincidences that are shown not onl y to be highly improbable, but als o to be conditions fo r the existence of life. The physicis t John Wheeler has gone several steps further than most and made the extraordinary suggestion that a universe i n which life could not develop would never have come into existence. One thing is certain: no one would have known if it had been created. The idea is related to those o f another physicist , Robert Dicke, whose chain of reasoning starts with the question : If there i s no on e to see it, what poin t i s there being a universe? Thus the conditio n for there being a universe is that ther e be a living creature capable of appreciating that the universe exists. In that case, all the laws of nature and al l the force s would have to be such tha t this cosmi c superob server—who is literally the creato r of the universe—shall have evolved. HMS may be unaware that sobe r scientists hav e this sudde n urg e to walk o n the wil d side . Their imagination has been stimulated in part by some intriguing (Pythagorean) relationships betwee n the numbers that characterize the universe. A simple example revolves around the number 10 39, which is roughly equal to the ratio of the electrostatic forc e betwee n a n electro n and a proto n t o th e gravitationa l force betwee n them. But it is also roughly the ratio of the radius o f the known universe to the ra-

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dius of the electron and, lo and behold, when squared it gives 1078, which i s about the number o f particles estimated to be in the universe. Thes e ideas have been expanded, but I will not follow that trail here. The anthropi c principl e an d particularl y th e cosmi c numbe r gam e hav e pro voked either the awe that comes from seein g the light or the ridicule engendered by Scientology. My own feeling , for what it is worth, is that the anthropic principl e is fascinating, unprovable , an d unlikely . Th e principl e alway s seem s t o me to be a substitute for the religious belief in the special creation of man. It is a theory that allows the hard-bitten materialist with the sof t cente r t o lead God back on the stage, and to use the value of physical constants t o hint that our advent had been predicted in handwritten (Hebrew , of course) holy scripts, slightly before the Bi g Bang. As for cosmic numbers, they are an easy target for ridicule, but I would say that, in one sense at least, that ridicule is misplaced. The question of why the universe is like it is is far from trivial . Thus all electrons have the sam e mass. Why? And wh y that particular mass? And what determined the ratio of the gravitational to the electromagnetic force? Again the simple answer is: that's how it happened, but in this case that is not satisfactory. I am not suggesting that there was a guiding hand, but that w e don' t understand th e mechanis m by which th e hosts o f elementary particles turned ou t to be like the standardized products of a production line rather like the idiosyncratic pebbles on the beach. We have no answer to these questions, and finding a solutio n wil l tel l u s somethin g fundamenta l about th e structur e o f the cosmos. It must be admitted, even by all those with whom I share disbelief , that at present by far and away the most likely hypothesis is that Zeus rules. Cosmology Comes of Age

The twentieth centur y has see n our knowledge of the present and pas t o f the uni verse gro w int o a self-confiden t disciplin e wit h som e ver y significan t achieve ments t o it s credit . We have n o reason t o suppos e that w e hav e see n a s far as we can, nor to conclude tha t we have detecte d more than a small portion o f the dar k matter whic h w e believe i s ou t there. Nevertheless, an impressiv e star t ha s bee n made on rationalizing the cosmos. The Hubble telescope, circuiting 300 or so miles above Earth, has extended by a factor of about a thousand the volume of space open to our view. And we are exploring not only space but also time, for the farther away the objects we observe, the longer the light has taken to arrive here. When we gaze at distan t galaxies , or a t th e birt h o f a far-of f supernova , we ar e watchin g object s and event s as they were billions o f years ago. And al l this is being been don e fro m the Eart h and som e satellite s mainl y confine d to the sola r system—a ludicrousl y limited platform o n which to put our instruments . Cosmologists have ventured t o construct theories explainin g th e histor y o f the universe. On e of the tests of a theory is whether it can assimilate new facts natural ly. The Big Bang theory was capable of doing this with the CBR and with the ratios of hydrogen to helium, an d hydroge n to deuterium. It should be remembered that we are dealing with events that happened som e 1 5 billion year s ag o under condi tions fa r removed fro m anythin g man ca n creat e or observe today. The miracl e is that the theory is moderately successful, but the theoreticians would be the first to admit that it is not successful enough. If the theoreticia n ha d on e wish , i t would probabl y be t o star t off with a set of

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equations, incorporating within the m the axiom s of quantum mechanic s an d general relativity, and to show that the birth an d developmen t o f the universe was an inevitable consequenc e o f these equations , whic h woul d provid e hi m wit h th e wave function o f the universe. From this wave function he would derive the masses and othe r propertie s o f all the particles . Ther e are physicists wh o believ e that this dream of an overall theory, or something very like it, will become reality. In his inaugural lecture, o n taking the chai r o f Lucasian Professor o f Mathematics a t th e University o f Cambridge i n 1982 , Stephe n Hawkin g expresse d th e opinio n tha t "there are some grounds for cautious optimis m that we may see a complete theory within the lifetim e of some of those presen t here. " Other eminent physicists hol d similar views . Bu t Hawking's optimis m was base d o n a theoretical developmen t that looked very promising at the time but has been slowl y evaporating. A history of repeatedly dashed optimism , is, as Popper have would explained, no guarantee that th e nex t chambe r wil l no t revea l th e gold-encruste d sarcophagu s o f th e pharaoh. I t might be argue d i n genera l tha t sinc e scienc e ca n explai n mor e an d more phenomen a i t must, by definition , be approachin g a n explanatio n o f everything. Don't hold your breath.

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IX Decision Time for Plane t Earth

No other human activit y rivals science in its ability to erect cities of the imagination o n one hand an d mold our material existence on the other. This century began with quantum mechanics and draws to its close with the sequencing of the human genome. We have been handed a set of tools with which we can relieve man's estate or create misery. Whether we build a golden city or a gallows depends on us, and the minimum, we can ask of ourselves is to understand no t only the political environment i n which we live but also the awesome potentia l that science holds. Man's attitude toward science matters, but that attitude is varied in the extreme and, unfortunately, often dangerousl y unbalanced. Le t us take a walk through the sociological garden, starting with the naysayers.

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36 The Tree of Death When man ;ate from the tree of knowledg e h e elected to find a short-cut to the Godhead. He attempted to ro b the Creator of the divine secret, which to hi m spelled power. What has been the result ? Sin, disease, death. —Henry Miller

Ironically—considering that it was Miller who wrote these sentences—sin, disease, and death are today more associated with sex than with Miller's target, science. But he i s fa r fro m alone ; antagonism t o scienc e i s widespread, an d a t the en d o f our journey it is worth pausing to see why the search for knowledge is not universally applauded. I came up against the opposition early on. My father's table talk installed in me a number of archetypal heroes of whom th e elite, for me, were Louis Pasteur, Jesse Owens, and Te d "Kid" Lewis, the last being a ferocious Jewish boxer who live d i n th e sam e slum s i n the Eas t End o f London where I spent m y childhood . M y father gav e me boxing lessons, an d I developed into an aggressive middleweight, but Pasteur won out . The emotion-laden story of the bo y bitte n b y a rabi d dog , an d mad e whol e b y Pasteur' s primitiv e vaccine , turned me toward science . At twelve years of age I lay in bed an d sa w myself performing a series o f incisive experiment s wit h a few test tube s an d a microscope, culminating in a dramatic evening at the Albert Hall. "This is it, ladies and gentlemen, the cur e for cancer." I raised high the vial of clear violet liquid. Tie r after tier of luxuriousl y bearde d nineteenth-centur y scientist s an d luxuriousl y bosomed beauties rose to create a torrent o f applause. My father encourage d my choice; like Bacon, he believed that science was intended for the relief of man's estate. It was thus with complete bewilderment that , at the age of sixteen, I came across the word s o f William Blake: "Art is the Tre e of Life, Scienc e is the Tre e of Death." No ambiguity, no mincing o f words. As I grew up, I came to realize that my "rabi d dog" view o f science was far from universal . Wha t was particularly riling , in adolescence, was that the opposition seemed to be drawn heavily from the ranks of my favorite poets. Only occasionally was there a note of grudging awe for science, as in W. H. Auden's well-known confession : "When I find myself in the compan y of scientists I feel lik e a shabby curate who has strayed by mistake into a drawing room full o f dukes." The nonscientist's attitude s towards science range from admirin g puzzlement to virulent antagonism . To the scientist , som e of these attitude s are understandable, some are irifuriatingly irrational. All have their importance, because science affect s our dail y live s an d i s also heavil y dependen t o n publi c funding . Publi c fundin g can be influenced by public opinion. What forms that opinion?

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Is Science Safe? The Mad Scientist Syndrome When I was a child the ma d scientist was a figure of derisio n and contempt, a fictional joke. How times have changed. The world i s now full of these mad scientists—mad doctors tampering with embryos, mad physicists and chemists working out more refined methods of termination Wha t can be done about these loonies? —Reader's letter, London Evening Standard, 31 January 1994

Diagonally acros s th e roa d fro m on e o f the house s I lived i n a s a child , wa s th e Odeon "pictur e palace, " where fo r a penny I spent m y Sunda y mornings , a t th e kid's show. The program was preceded by a recital o n the Wurlitzer organ, which mysteriously an d garishl y ros e ou t o f the groun d an d san k back int o th e depth s about ten minutes later . I was allowed a packet of Smith's Crisps. Horses starred in most o f the films . Occasionall y a scientist wa s featured . At the Odeon , scientist s were no t normal : the y ha d spad e beards , pince-ne z spectacles , bush y hair , an d crude German accents. Thei r laughter had two modes—sinister or maniacal. The y were given to periodical fits o f eye rolling during which they were likely to throw switches o r pour bubbling liqui d fro m on e smoking flask t o another. Sometime s I struck gold and was treated to the spine-chilling announcement : "Wit h this I shall be Master of the World!!!" "This" was either the bubbling liquid o r a metal breadbox to which wer e glued a few clock dials an d from which leape d a n occasiona l anemic spark . The conventio n was neve r broken—scientists were kooks , dangerous foreign kooks. The scientist a s a threat to civilization i s more than a "B" movie stereotype. The satanic mills o f the Industrial Revolution , the clou d above Hiroshima, the DDT in animal fat , carcinogenic foo d additives , thalidomid e babies , an d a series o f other horror stories have, for many an HMS, rightly or wrongly, formed th e image of science. The scientist himsel f may be seen not a s literally mad but a s too concerned with his research or his position to act responsibly with th e box of matches in his hands. How, the public asks, can a man get up i n the morning , eat his cornflakes , hug his kids, kiss his wife , an d driv e to his Defens e Department laboratory where he is working on a virus that causes paralysis of the respiratory system? Is this not a kind of madness? The questio n o f the danger s of irresponsible science 1 recur persistentl y i n th e media. Unfortunately , emotionalism, ofte n fuele d b y misleadin g an d inaccurat e sensationalism an d preconceived attitudes , has usually prevented meaningful debate. Add to this the disagreements between experts, and the occasional dishonest y of big companies and loca l or government authorities, an d i t is often no t apparen t who to believe, or what attitude to adopt to certain areas of scientific research. Sus picion i s certainl y understandabl e whe n i t come s t o project s tha t threate n ou r health, o r even ou r existence . Bu t before yo u for m a n opinion , firs t ge t the facts . Second, don' t simplify . An d don' t blame science i f business-driven technolog y is really to blame. 1

I use the term irresponsible science as a shorthand for the catastrophic scenarios of the previous paragraph. In that science cannot in itself he irresponsible, it is a misleading phrase, but it is convenient.

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Take pollution. I t is an easy word to write o n a placard o r spray on a wall (wit h ozone-friendly spray) , but i t i s a comple x subjec t that shoul d no t b e mindlessl y simplified. Som e source s o f pollution , fo r example , th e centuries-ol d custo m of burning woo d to obtain heat, can hardly be laid at science's door . The smoke-laden skies of industrial England were not create d by science. Pollution i s not a n inven tion of modern science , an d th e dange r o f burning fossi l fuel s woul d no t eve n be apparent if the scientist ha d not researched the atmosphere and the physical properties o f carbo n dioxide . A significan t par t o f the damag e t o th e atmospher e i s caused by volcanic gases and th e gaseous emissions o f cattle. Man is not the onl y culprit. Of course , there ar e pollutio n problem s tha t ca n certainl y be lai d a t science' s door, including th e chemicals partially responsible fo r the ozone hole, the creation and indiscriminat e us e o f DDT, and th e effect s o f hormone-disrupting chemicals i n the foo d chain . In no cas e was the scientifi c project initiate d with the knowledg e that there was an environmental threat . The worst aspect of the DDT story was th e money-powered effor t o f big business t o downpla y th e danger s of the insecticide . The sam e thin g i s happenin g wit h th e tobacc o companie s an d smoking . Thi s i s where HMS, acting within a democratic society, has a pivotal role to play. Much o f the blam e directe d a t irresponsibl e scienc e ha s bee n poste d t o th e wrong address. Scienc e is not synonymous with technology. The stereotypical scientist is interested in how nature works; the stereotypical technologist is interested in makin g mor e profitabl e soap powders . A s a scientist, I am offende d whe n sci ence i s falsely accuse d an d th e rea l criminal, irresponsible technology, roams th e streets free . Th e tan k wa s no t invente d b y a scientifi c "loony, " neithe r wa s th e sword, th e musket , th e bow, the" bayonet, o r gunpowder. And neithe r scienc e no r high-technology i s responsibl e fo r alcohol , heroin , cholesterol , saturate d anima l fats, cholera , th e commo n cold , poliomyelitis , leprosy , influenza, the populatio n explosion, or AIDS. Where is a sense of balance? Plague, hunger, gunfire, religiou s or political fanaticism , and man's inhumanit y t o man have killed many more people than have died from atomi c weapons o r faulty vaccination. Which is not to say that atomi c weapon s ar e a blessing o r that vaccinatio n technique s canno t be improved, but it is hardly a n advertisement fo r human reason whe n th e antivaccination lobby highlights the handful of fatal vaccinations an d glosses over the million s who have been protected from diseas e and death . And yet Miller's indictment canno t be waved away. The Tree of Knowledge Miller is not alone i n claiming that th e scientist ha s ignored the lesso n o f Genesis in stealing from th e tree of knowledge; that nature has its secrets and i t was not intended that they should be revealed. Man has transgressed and brought down catastrophe upo n himself . Suc h statements , yo u migh t say , ar e mad e b y thos e wh o know little or nothing abou t science an d are happy to have found a mystical excuse for remainin g ignorant . Having sai d which , i t i s undeniabl e tha t man' s curiosit y has not always led him straight toward the earthly paradise. The Judeo-Christian myth define s knowledge as something tha t wa s stolen , for which ac t Adam an d Ev e were expelle d fro m Eden . (No t surprisingly fo r a mal e chauvinist society , it was the woman wh o was blamed.) In the crueler Greek varia-

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tion, Prometheu s pai d th e pric e o f eternal tormen t fo r stealin g th e secre t o f fir e from the gods. The myth of Prometheus speak s to us because it condenses, in the hideous sufferings o f the protagonist, the danger and the occasional sense of transgression that accompany our probing of the natural world. And it symbolizes, as myths ofte n do , a ver y real problem, a problem tha t requires a rational answer , no t on e based o n sloppy mysticism : 7 s the scientist to be permitted to investigate everything in nature? The question worries HMS, and he has reason to worry. The spontaneous reply of the Baconian observer is "yes, all nature is there for us to study." Bacon himself was not so sure. In New Atlantis he puts this opinion int o the mouth o f his natural philosopher: "W e have consultations, which o f the inven tions an d experience s whic h w e have discovere d shal l be published, an d whic h not: and take all an oath of secrecy, for the concealing of those which we think fit to keep secret : thoug h som e o f those we d o reveal sometimes t o the state , and som e not." In contrast, Descartes held tha t th e secret s o f nature wer e in fac t th e mathe matical laws that lay beneath the visible reality, and he had no doubt that, by using his powers of observation and his reason, man could and should reveal this knowledge. But in those day s science ha d a negligible practical effec t o n society. Today, HMS may no t be s o liberal, and som e scientist s ar e deepl y trouble d b y the ques tion. Newto n held tha t a scientis t shoul d no t revea l that par t o f his wor k whic h could conceivabl y lea d t o dangerou s practica l developments . Rober t Oppen heimer, afte r Hiroshim a an d Nagasaki , expresse d hi s doubt s i n religiou s terms : "The physicists hav e known sin." That is a powerful statemen t of the fact that, like some political an d religiou s doctrines , som e scientific researc h ca n lead to suffer ing and death. It is this that should worry us and that demands rational debate. Obviously the scientists mus t have a part in such debate; the scientist is both the Stealer o f the Secrets , since tha t is his vocation, and the Keepe r of the Secret s by virtue o f his expertise . But he cannot thereb y assume th e rol e of an Elder of the Tribe, and it is certainly debatable whether he should be allowed an absolutely fre e hand. Inquir y is one of our most basic instincts, an d there will be those who will protest agains t restrictions, in the name o f academic freedom. 2 Bu t science i s no longer, as it was in the seventeent h century , a harmless activit y of a few curious minds, i n modest private or university laboratories . Very large sums of money are put int o government-sponsored researc h and into the research laboratorie s of private companies. The type of work being done in some laboratories can have an enormous impact on our lives, just as the obscure experiments of a handful o f European scientists in the 1930s unlocked the atomic era. And now the double helix is here. There should be public input into the question o f academic freedom i n science. Would you like to live near a laboratory that was putting a defective huma n gen e into a virus or bacteria? Would you like your son to work on biological or chemical weapons? Shoul d experiment s o f this kin d b e forbidden ? I refuse t o hide behin d the excus e that i t is not I who will make the decisio n t o randomly wip e ou t civilians. A scientist cannot, or should not, be unaware of the possible uses of his work, although thi s i s a very difficul t area . Rutherford' s experiment s le d t o th e atomi c bomb, but he couldn't have known it. At present the tree is available to everyone. Whether the scientist shoul d be fre e 2

Defined a s the right to speak before you think.

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to pick what frui t h e wants i s a question that should concer n al l of us. HMS has a role in that discussion, and he is also needed as a watchdog. Controlling Technology

HMS must be politically active, and scientifically aware, if he is to control technology. It was political action that began the elimination o f the more obvious curses of the Industria l Revolution—whic h wa s a technological , no t a scientific , revolution—and allowed u s to guiltlessly enjo y it s benefits. (To pretend tha t ther e were no benefits is just bloody-mindedness.) It was political action in the 1960s, sparked by Rachel Carson's Silent Spring, that triumphed over the U.S. Department of Agriculture and the big chemical companie s that profite d from th e wild overus e of insecticides. Informed politica l actio n i s essential , an d ye t to o ofte n w e hea r anti science opinions that have not got past the mad scientist stage . This is not amusing. It is dangerous, because it directs anger at the wrong targets. It is essential tha t the public have a rational, informed, and unprejudiced voice in discussion of the uses and misuse s o f scientific research . These matters are, as they say, too important to be left to the scientists . Scientific researc h i s here t o stay. Our modest ai m here is to dra w attention t o the fact that HMS has a central role to play in the future o f that research. In matters that affec t ou r dail y lives, HMS should certainl y have his say , but the eas y demo nization o f scienc e or scientists is not a worthy starting point. The consequences of science an d technolog y are too important to be judged from a seat i n th e Sunda y morning kid's show. Down with Science;?

The genuine drawback s associated with science and technology have engendered dreams o f turning back the cloc k on scientific discover y s o as to return to a better, more natural world , forsaking the craze d Dr. Hackenschmidt for the nobl e savage. This is sentimental naivete . Without the benefits o f science we would retur n no t t o a Technicolor, William Morris land of pink-cheeked fol k dancin g farmers but t o a world in which th e majority of men (as in the Third World today) would live "short brutish lives," hounded by disease , kille d of f by infections that ar e now controllable , livin g in bug-infested habitations and clothes and unsanitary cities, and lucky to have a life span of four decades—i f childbirt h wa s survived . On e o f my childre n underwen t open heart surger y at the ag e of six; the othe r tw o suffere d fro m influenz a in their early years. My guess is that non e o f them woul d hav e survive d ha d the y bee n born a century ago. Primitivism ha s it s pleasures, but, in terms of health, an d socia l an d educational deprivation , i t is too costly for most of us. Natur e is red i n tooth an d claw. Nevertheless, there are those who clai m that to o high a price has been pai d for th e improve d standard o f living of HMS. It is fashionable in hand-wringing circles to detect a spiritual void at the center of the consumer society, and to implicate science in the creation of that void. Which brings us to the science trashers. The Science Trashers

Science is an overhyped facade, a self-supporting club that covers up its errors and

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is continually fallin g ove r itself. This ha s been the them e o f a number o f authors who have made a profession out of trashing science . Thei r books, because of their provocative content, sell well an d get reviewed and quote d in the media. Fo r this reason alone they need to be confronted. The trashers must not be allowed to mislead HMS. Science i s a huge , remarkabl y varie d activity . A t presen t man y hundred s o f thousands o f research project s ar e going on, i n dozen s o f countries. Th e projects range fro m th e mos t abstrus e aspects o f quantum mechanics t o th e effec t o f foo d composition o n human health. Th e quantity of observational dat a is staggering. A standard ploy of the trashers is to pick out conflicting data, or data that are suspect because of faulty procedures. Does any rational person believe that all the data collected b y scientist s i n all the studie s ever made would b e faultless ? I n almost all cases the opposing camps eventually converge. There are always scientists ready to detect the mistakes of other laboratories! If there is any human activity that is self critical it is science, but the trashers dig up conflicting studies, question the objec tivity o f the scientist , an d declar e the deat h o f science . I n fact , thei r whol e ap proach is heavily dependent on the showcasing of the (expected) failures of science and o n the maliciously blind underemphasis o n its successes. Faile d theories fue l their critical fires. They revel in tales of shaky concepts, multiple theories designed to explain the same phenomena, fraudulent results, laws that are not exact, antibiotics that induce resistance, backbiting scientific rivals, grant-grabbing professors, imperialistic head s of laboratories. You name it, and th e trashers wil l di g it up for you. For them anything less than perfection i s failure. With this sort of approach it is possible to discredit the totality of human cu/ture.Wha t about those weak (an d stolen!) plots in Shakespeare? Or Tchaikovsky's sugary sentimentalism? And, good God, didn't the Egyptians know anything about perspective? Every human activity, because it is human, is imperfect. There have been scientific frauds—sometime s euphemisticall y termed hoaxes—and there have been in competent scientists. This no more discredits science than a plagiarizing musician discredits music. The trashers harp on the inerti a of the scientifi c establishment, an inertia that I have documented in this book. There is inertia, but fo r every case that I have quoted, the truth finally cam e out. And unlike politics or religion, there are no immovable fact s i n science , there is no principl e tha t canno t be questioned . Eve n Newton's law s wer e modifie d afte r 25 0 years . Th e trasher s se e thi s a s a sig n o f weakness. A normal man would see it as a sign that the cosmos is immensely diffi cult to understand, but that we are understanding more and more, as evidenced by our exponentially increasing ability to predict the behavior o f the material world. That ability does not always grow in the way suggested by the schoolbook's idealized account of science: the miraculous succession of observation, theory, and ex periment. In this, at least, the trashers ar e right: scientific progress can sometime s be messy, shortsighted, and the result o f accident rather than planning. But look at the incredibl e structur e that ha s evolve d over the centuries , and compar e that t o the petty-minded and basically dishonest niggling of the naysayers. The trashers si t opposit e their word processors (th e fruit o f Basic Scientifi c research, fo r short , BSc) , turn o n th e ligh t (BSc) , wea r artificia l fabrics (BSc) , tak e their blood pressur e medicatio n (BSc) , phon e thei r friend s (BSc) , loo k at th e T V news (BSc) through their plastic glasses (BSc), listen to their radios (BSc) , get their

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injections agains t influenza (BSc) , and s o on an d on . And wha t ar e they typing ? About the failure of science! If they had any self-respect, they would live in a virgin forest, writin g thei r manuscript s o n parchment with a quill, forgoin g any modern medicine o r comforts , hereft o f electroni c communications . T o tak e on e o f th e greatest and most successfu l human adventure s and pic k trivial hole s i n it, like a thin-lipped aun t runnin g he r finge r ove r a dust y shelf , requires a special kind of mean-mindedness. Science , b y it s ver y nature , demands criticism , bu t no t b y someone wh o woul d condem n th e Ta j Mahal for demolition because som e of the stories are cracked. The Ice-Cold Clock? In rn y final yea r a t high schoo l a n intens e an d talente d gir l taking "Arts, " as we called them i n those days, told me that I was "too bright to take science." I quoted the mathematician G. H. Hardy, "Archimedes will be remembered when Aeschylus is forgotten." (Frankly , I would have given my vote to Aeschylus, but I was o n the defensive.) Th e argumen t lef t on e phrase permanently i n my memory: "Your universe," she said, putting a pale hand on my forearm, "you r universe is an ice-cold clock." Two year s late r I was studyin g chemistr y a t Universit y Colleg e London. One evening, afte r watchin g th e young Tom Courtney in the Colleg e Drama Club's performance o f Ring Round the Moon, we ende d u p i n th e "Orang e Tree. " Towards closing tim e Jill, who wa s readin g English, leaned acros s the stick y table and , i n Chelsea tones slurre d by gin, asked, "And what's th e Moon to you, Silver? A lump of sodiu m chlorid e or something?" Sh e raised he r near-empt y glass, "Buy me an other one. We'll drink to your mechanical soddin g universe." I bought her another two. "Whatever the Sun may be," sai d D. H. Lawrence, "it is certainl y not a ball of flaming gas." Helios, the sun god, has more sex appeal than a cloud of gas, however hot. Lawrence spoke for my frien d Jill , and fo r many other s wh o se e science systematically chipping away a t the mysterious, bu t generally benign, unknown an d arrogantly replacing it with the dull , prosaic, down-to-earth known. The mechanical universe, the "ice-col d clock," is not something you want to curl up wit h o n a winter's night. Genesis 9:13 reads: "I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth." The scientist's rainbo w is the result o f the differen t refractiv e indice s of the variou s frequencies of light that make up solar radiation. But man evidently prefers mystery to math, and the intrusion of science into the movements of the planets and the stars, into the living cell and into that final sanctuar y o f the spirit , th e mind , ha s undoubtedly cas t a chill ove r that warm, blurred garden, the theocentric universe. The scientist, ruthlessly buying up desirable property, appears to many people to be building a n automated factory i n the middl e o f the garden . Fo r thi s reason , scienc e has , fo r some, become an un wanted neighbor . And indeed , mos t scientists woul d mak e very hard work of explaining how the concep t of the sou l fits int o the material universe, where there is nothing bu t "atom s an d th e void. " Wa s this wha t Blak e meant when h e sai d that science wa s th e tre e o f death? The deat h o f religion? O f imagination? Both hav e been frequently suggested. Science, since the fifteent h century , has been see n as a threat to the dogmatic Judeo-Christian account of the Creation and the universe, and even to religion itself:

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That vast moth-eaten musical brocade, Created to pretend we never die . Do these line s fro m Phili p Larkin' s "Aubade " encapsulat e th e rea l fear ? Tha t th e mechanical universe dispenses with the immortal soul? Many distinguished scien tists think not.3 And even if science has genuinely discredited revelation, does that discredit science? As to imagination, it is true that the first recorded stoned writer, De Quincey, declared tha t scienc e wa s th e greates t threa t t o th e facilit y t o dream , bu t h e wa s wrong. Conside r th e followin g improbabl e scenario : A n astronome r observe s events that took place 5 billion years ago (it takes that long for light from the star he is observing to reach th e Earth , light generate d by explosion s o n an unbelievabl e scale, at incomprehensible distances) . The astronomer lives o n a tiny planet, i n a universe tha t i s mostly gas or empty space , Eliot's "vacant interstella r spaces , the vacant into the vacant." And yet on this planet, out of immense fier y continents of molten rock, over hundreds o f millions o f years, a solid crus t solidified , the wil d clouds rained dow n to form tempest-swept primeval seas, and in those seas an incredible process began. Matter, the cloth of the universe, tentatively, tenuously developed, by a slow improbable transformation, into a form so complex and so organized that i t can comprehend its own history and, however pitifully, pla n it s own future. Thi s is the strangest dream of all. It is a story that has the power of primitive myth, o f Gilgamesh , o f Adam . It is a dream created only by science. Ther e i s enough wonder in the physical world . It was a poet, Wordsworth, not a scientist, wh o wrote : "the beaut y in for m o f a plant or an animal i s not made less but more apparent a s a whole by more accurate insight into its constituent properties and powers." And Voltaire wrote to Newton: "I do not se e why th e stud y o f physics shoul d crush th e flower s of poetry. Is truth such a poo r thin g tha t i t i s unabl e t o tolerat e beauty? " Scienc e i s certainl y ou r prime weapon against superstition and irrationalism, but in a world i n which sci ence flourishes—with o r without a God—love and fea r stil l remain, as do pleasure and regret, poetry and humor , art and music. Th e arts are not lessene d b y the sciences. Blak e was mistaken: man's ineradicabl e gift, hi s questin g curiosity , th e di vine discontent, is the common source of the arts and the sciences. The Obscurity of Science? The public aspect s o f science ar e important enoug h for HMS to make the effor t t o understand th e issue s involve d an d no t t o fal l fo r the shallo w antagonis m o f the naysayers. The effort i s vital. The expert may know more about his subject than the layman, bu t hi s politica l an d socia l judgmen t ar e n o bette r tha n tha t o f his la y friends. Th e nauseatin g prostitutio n o f Nazi and Sovie t scientist s t o the immora l aims of their states reinforces the theory that DQ, the decenc y quotient, is not positively correlate d with IQ . Scienc e polic y needs th e inpu t o f HMS. This doe s no t mean that business executive s and factory foremen should brush up o n their quantum mechanics, but you don't nee d a degree in science to understand th e need for, Immortality has been subjected to political attack: "the idea of the soul's immortalit y i s a superstition encourage d by rulers to keep their subject s docile." So wrote the sixteenth-centur y Paduan radical Pietro Pomponazzi.

The Tree of Deat h |

and to participate in, say, open discussion on the way that new drugs are marketed and tested , whether geneti c analysis o f employees should be allowed, or whethe r huge sums should b e devoted to areas of science that are almost certai n to be of no practical use . HM S might protes t tha t scienc e i s to o obscur e fo r him t o attai n a meaningful understandin g o f a specific subject, within the constraint s o f his working day. It is true that very few laymen can sight-read and understand th e WatsonCrick paper on the doubl e helix structure of DNA. So should HM S give up? No! Bertrand Russell opined tha t if a scientist coul d not explain what h e was doing in layman' s term s the n h e didn' t reall y understan d wha t h e wa s doin g himself . This is not quite accurate, but all the same, most of the important topics in science can be made intelligible to the layman, and this is particularly true of those areas of science relevant to the welfare of this planet. The obscurity of science is an obstacle but definitel y not an insurmountable obstacle , otherwise there wouldn't b e popular science magazines. HMS must not use this obscurity as an excuse to mindlessly slam science and avoid rational debat e on scientific problems. Know Your Enemy

If you choose to criticize science or scientists, because you feel that in a specific instance they are damaging the community, materially or spiritually, d o it from a position o f strength. Kno w what yo u ar e talking about . Don't let the "science-is-an unmitigated-curse" extremists o r the "tre e o f knowledge" mystics ge t at you , an y more than yo u would blindl y accep t ever y statement mad e by the dru g compan y scientists o r their lawyers. If someone tells you that "thos e mad scientists " ar e responsible for modern man's exposure to dangerous levels of radiation, go to the library. You'll find tha t sinc e the daw n o f life abou t 55 % o f the radiatio n t o whic h living things are exposed come s from th e naturally occurring gas radon, about 8% from cosmi c rays, about 11 % from naturally occurring radioactive isotopes i n ou r food, and s o on. The major man-made source of radiation encountered by HMS are the X-rays used for medical diagnosis. And, by the way, I have met only one scientist who was certifiably mad, and he was harmless. Those who waffl e abou t forbidde n fruit ma y be excuse d for using the languag e of myth, but not for facing some of mankind's most urgent problems by opening the doors of emotion and closing the gates of reason. Iconoclasts are essential, but only if they aim at being as informed, as rational and as passionate as a Rachel Carson. If yo u stil l hav e a gut feelin g tha t we ar e being punished fo r having stolen fir e from th e God s and apple s from th e tree , you might care to reflect that , apparently just fo r kicks , benevolen t natur e ha s bestowe d o n u s earthquake , hurricane , drought, disease , famine, overpopulation , an d th e threa t o f annihilation b y collision with asteroids. T o conclude, a s Henry Miller did, that scienc e is responsibl e for the major ills of mankind is lazy thinking. Far from damnin g us, the fruits of the tree of knowledge could be our salvation. Prometheus and Adam should deman d a retrial.

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37 "What the Devil Does It All Mean?"

The popular image of science is formed primarily by science-based technology. As evidenced by what we buy, what we use, and what we covet, we are a gadget-based civilization. To suggest that the tida l wave of consumer good s is responsible fo r what has bee n seen by some as the emptiness at the heart of modern life is facile i n the extreme. No other era has had so readily available to it great music, great art, and great literature. Cheap travel, the mass electronic media, and mass publishing have spread the products of the creative arts deeper and wider than at any time in history. However, it is true that i n general those who have benefited from technology couldn't care less about its scientific basis. Rare is the dancing teenager or madrigal buff wh o can tell you that the canned music he or she is listening to comes by courtesy of the basic science that eventually led to the transistor, the semiconducto r laser, and magneti c films. Most of the main concepts o f modern science ar e as familiar t o the man in the street as the language of the Aztecs. Sometimes, as in the case of theoretical particle physics, it doesn't really matter. Sometimes, as in th e case of genetic engineering, it really does, and unfortunately scientific ignorance is typical of a society whose attitudes toward science can hardly be said to be balanced or informed. The naysayers have been given their say . Now we turn the microphone ove r to HMS, to the humanists, to the philosophers, and to the scientists themselves . HMS Looks at Science

Georges Braque and Pabl o Picasso calle d eac h othe r Wilbur and Orville , after th e Wright brothers. They were not alone in their aeromania. On 28 September 1909, a Prague newspaper published a n article by Franz Kafka calle d "Th e Aeroplane s at Brescia," a n accoun t o f a n airplan e race . Kafk a wa s clearl y hooked . I n th e same yea r the lur e o f the machin e wa s spelle d ou t explicitl y by th e Italia n poe t Emilio Marinetti. The Futurist Manifesto totall y repudiated the pas t and declare d that ar t should creat e an authentically moder n sensibilit y founde d on the beauty and vitalit y o f th e machine . Bu t HM S di d no t need a manifest o t o arous e hi s lust fo r gadgets, and i t i s th e plethor a o f technological product s tha t issu e fro m Sony, Genera l Motors , and othe r industria l lab s tha t dominate s HMS' s image of science. In the early 1920s the automated production line turned America into an objec t of mass envy and admiration . Technology, not art or basic science, was confirmed as civilization' s statu s symbol . Few heede d th e word s o f Dean Inge, i n th e 192 0 Romanes Lecture : "The Europea n talks o f progress because b y th e ai d o f a fe w scientific discoverie s he has established a society which ha s mistaken comfort for civilization." The avalanche gathered force. The radio and later the television set, initially ob-

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jects of curiosity an d envy , became prosaic and indispensable item s in household s that often lacke d a single book except for the two holy texts of the era: the Bible and the Sear s catalogue . Th e washin g machine , th e spi n drier , air-conditioning , th e long-playing record, the magnetic tape cassette, the microwave oven, the compact disc, the video recorder, the fax, electronic mail, and the cellular phone have added to the domestic, and hence immediately obvious, benefits of technology. Add medical instrumentation , antibiotics , syntheti c hormones an d vitamins, syntheti c fabrics an d colors , the automobile , the airplane , and , fo r a very select few , the spac e shuttle. W e live—and breathe—i n a n environmen t tha t everywher e exhibit s th e work of Homo technologicus. As judge d b y it s practical achievements , scienc e ha s a stron g clai m t o b e a worldwide success story. The amount of government and private-sector funding for scientific research far outstrips anything spent in previous centuries. There are science correspondent s o n all the "quality " newspapers , an d scienc e slot s ar e standard in the program scheduling o f most major TV networks and radio stations. Scientists ar e regularl y interviewed , o n th e new s o r o n tal k shows , primaril y o n medical o r ecological matters. Foo d products contain analyse s of sodium, choles terol, polyunsaturates, fiber , and calories . There is a flood of books (of which this is another), and a variety of magazines, devoted to the popularizatio n o f science an d technology. Science museums have interactive, pedagogic exhibits. In England and Israel it is possible to take a degree in science by following the courses of the Open University on TV. Nevertheless, HMS is aware that technology has its drawbacks, and at the end of the century there is, as compared to its beginning, a vastly increased public awareness of the danger s of applied science. 1 The responsibility o f the scientis t towar d society is a topic that occupies scientists and nonscientists alike . As earl y as 192 5 Bertrand Russell wrote, "At present (science ) i s teaching ou r children to kill each other, because many men of science are willing to sacrifice th e future of mankind t o their own momentary prosperity." He was obviously unaware of th e scal e o f scientific salaries , bu t al l th e sam e i t canno t b e denie d tha t ther e have been many scientists who have conveniently closed their eye s and ears to the concerned voices around them : No tyrant ever fears his geologists or his engineers . W. H. Auden, Marginalia As a scientist I regret that the welter of science-based technology is too often th e window throug h which HMS sees science. In the twentieth century the wonderful ly unifying, if often strange , ideas of science have not become common currenc)'. HMS and the Idea s of Scienc e Consider the followin g quartet of notables, each representing a different aspec t of 1 When I graduated from Universit y College London, I, together with the others who had been awarded first-class honors, received a letter from th e Biological and Chemical Warfare Establishment. It was superficially tempting in that it offered a relatively assured future, a reasonable salary, and a promise that I could, if allowed to, publish my research results—in the Journal of Pathology.

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the creativ e life o f the seventeent h century : John Donne, John Dowland, Sir Peter Lely, an d Si r Isaac Newton. Admittedly, James I said o f Donne that his verse s re sembled the peace of God, for "they pass all understanding,"2 but mos t of Donne's writings ar e immediately understandable. Dowland, the great lutenist, wa s ahea d of his time with his occasional deliberate discords , but his compositions wer e immensely popular, his Lachrimae being a best-seller in Europe. Newton's mechanics was not overl y obscure, and an educated man coul d recognize its contribution t o our understandin g o f the cosmos . Finally, anyone ca n enjo y th e Playmat e o f th e Month portraits of Sir Peter Lely. All in all , the scientifi c and cultura l activities of his day were accessible to seventeenth-century HMS. Now take a prominent mid-nineteenth-centur y quartet : Dickens, Mendelssohn, Courbet, an d Darwin . Courbet initially cam e under criticis m fo r his depictio n of his subjects, but he presented no visual puzzles to the beholder. The others were all a part of middle-class culture. I could have chosen Maxwell as a difficult-to-under stand scientist , but a n educated layman could grasp the meaning o f his laws. Th e educated mid-Victorian may not hav e agree d with, o r comprehended, everythin g happening on the scientific and cultural front, but he broadly understood what was being written, painted, and played. Move to the early years of the twentieth centur y and weigh this quartet, chose n from th e majo r figure s o f the time : James Joyce (after 1922) , Alba n Berg , Picass o (after 1907) , an d Einstein . The connectio n wit h HM S has collapse d completely . Language failed to communicate, music was (t o the ears of the time) cacophonous, painting (t o the eyes of the time) was incomprehensible, a description that also fitted th e theor y o f relativity . Alternativ e quartet s d o littl e t o help : Ezr a Pound , Schoenberg, Braque , an d Schrodinger ; o r T . S. Eliot, Stravinsky, Kandinsky , an d Heisenberg. I coul d hav e chose n a mor e accessibl e artist , sa y Matisse , but mos t works of his that we enjoy today were regarded as difficult i n those days. Of course there wa s a n ongoin g popular cultur e o f traditional literar y forms , crooners , an d paintings o f puppies, but th e intellectua l mountai n climber s wer e completely ou t of sigh t of the bas e camp . Contemporar y comment, from layma n an d criti c alike , leaves no doubt whatsoever that the creative world, both scientifi c and humanist, appeared to HMS to have forsaken its senses. Obscurity seemed to be obligatory. As the centur y progressed , the twentieth-centur y eye acclimatized to much of modern art, and th e twentieth-centur y ea r accepted Stravinsky an d Berg—eve n if one doesn't often hea r people whistling Schoenber g in the bath. The era of willfully obscure poetry slid quietly into history and although dadaism in its purest for m became passe, Beckett and lonesco played to full houses . Onl y science, especiall y physics, continued to drift awa y from HMS . The tribe does not understand th e language of the priests . The Obscurity of Physic s "... We get a trifle weary, at Mr. Einstein's theory." —Herman Hupfeld, "As Time Goes By"

2

The king obviously liked this comment, for he also used it in respect of Francis Bacon's Novum Organ um.

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The outstanding scientifi c concepts born i n the twentieth century , apart from th e genetic code, have been i n th e fiel d o f physics. Fo r HMS, most o f these develop ments remain profoundly obscure. Despite the shelves of "popular" books on quantum mechanics , th e Bi g Bang, chaos , blac k holes , an d s o on , th e averag e reader finds himself in a state akin to that of a medieval peasant attending mass in a great Gothic cathedral: he is awed, he knows that somethin g terribl y important i s being said, but he understands ver y little because it's all in Latin. He takes the wafer an d remains mystified. In on e wa y th e failur e t o communicat e doesn' t reall y matter . N o on e wil l b e asked to vote on whether o r not he wants Big Bangs and chaos in his neighborhood and, a s th e charismati c Richar d Feynma n said , som e scienc e i s jus t no t under standable. If Feynman didn't understand, then we are all excused. After ninet y years , relativity an d quantu m mechanic s stil l remai n enigma s t o HMS, and, along with chaos and cosmology, have done almost nothing to form hi s thought processes. The conceptual bases of modern physics remain the preserve of a limited section of the scientific community. Newton's achievements and methods were well enough understood t o be a real source of fuel fo r the fire s o f the Enlightenment. Darwin and Faraday were within comparatively easy grasp of the layman. That can hardly be said of Einstein and Heisenberg, Schrodinger and Poincare. In October 1847, Maria Mitchell built an observator y on desolate Nantucket Island. Sh e gazed out and discovere d a previously unknown comet . By 1900 it was clear that few averagely educated ladies, or gentlemen, could set up their ow n scientific laboratory and hope to compete with the professionals. Science had become a profession. HMS was puzzled. So was the world of the arts. The Humanities Look at the Sciences Language and science are abbreviations of reality ; art i s an intensification of reality. —Ernst Cassirer

In the nineteenth centur y the cracks between science and the humanities were obvious, and by the mid-twentieth centur y the once happy couple were barely speaking, althoug h ther e ar e som e prominen t exceptions . Berthol d Brecht envie d th e duty of the scientist t o look at any theory, however successful, and challenge its validity: " A technique fo r gettin g irritate d b y familiar , 'self-understood, ' accepte d facts was built up by science with great care and there is no reason why art should not adopt that immensely useful attitude." In The Sacred Wood, T. S. Eliot revealed a knowledge of chemistry. In a striking image he compares the poe t to a chemical catalyst: "Jus t a s the platinu m catalys t use d t o induce th e combinatio n o f oxygen and sulphu r dioxid e to give sulfuric acid, 3 is left unchange d at the end o f the reaction, so the poet's mind would , after creatin g the poem, emerge inert, neutral, and unchanged." But despite simila r examples , it has to be said tha t th e interest , and understanding, o f most creativ e artists i n th e twentiet h centur y has been superfi cial or nonexistent. 3 An irritatingly pedantic note: The product of the reaction is sulfur trioxide. This has to be dissolved in water to give sulfuric acid.

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Undigested scientific concepts have been used to embroider texts or to create interest as titles of paintings, sculptures, or television series. The double helix makes occasional guest appearances in poetry. Time is frequently warped in space epics . One of the few writers who has made more than trivial use of modern science is the playwright To m Stoppard, but h e enjoys , an d i s highly successfu l at, juggling abstract ideas. (He has confessed that he is expecting a professional scientis t to get up in th e middl e o f a performance of one o f his play s and shou t "Bollocks!" ) It is th e suggestive terminology of science, the occul t connotations of the term s uncertainty, warped space, cloning, an d black holes, that hav e generall y bee n th e mean s through which scienc e has mad e a n appearance . In spite o f Apollinaire's conclu sion that relativity was the spiritual precursor of cubism, it is certainly not, except in rar e cases, the understood concept s of science that hav e fertilize d ar t o r litera ture. This is not to say that the humanities hav e suffered. Th e problem is that when a complete and influentia l section of the communit y is ignorant of the intellectua l content of science, its attitude toward important scientific and technological issues becomes unbalanced. A Painful Divorce? World War I did nothing to beautify the image of science in the eye of the humanist . The deep disillusionment wit h th e direction i n which Europ e had been drive n by its accepted values led to a wave of romanticism, antithetical, amon g other things, to rationalis m i n genera l an d deterministi c scienc e i n particular . Th e flagshi p of the reactio n t o scienc e wa s Oswal d Spengler' s widel y rea d Decline of the West (1918), in which nonrational, mystical ideas were touted as the antidote to the scientific subversion o f civilization and nature. Spengler's demotion of reason and his singling out o f deterministic causalit y as the serpen t in the garde n came at a time when advance s in the quantum theory appeared to be burrowing under th e deter ministic foundation s o f classica l scienc e fro m within . Bu t fe w humanist s wer e aware o f the ful l meanin g o f the collaps e o f Newton's mechanica l universe ; th e more popularly sensational aspect s of relativity took the limelight : th e bending of light, the effec t o f space travel on aging. In the meantime, Spengler and pseudoscientific mystics such a s J. W. Dunne spoke to the antirationalisti c leaning s o f many intellectuals in the humanities. The gap widened. In 1959 , C. P. Snow, the physicis t an d novelist , gave a now famou s lectur e enti tled "The Two Cultures and the Scientific Revolution," describing, as he saw it, the profound schis m betwee n th e humanitie s an d th e sciences . Sno w suggested , among other things, that a fully educate d man should hav e a knowledge of the sciences, and he made it clear that most humanists didn' t meet this criterion. He underlined th e antagonis m o f the Britis h literary establishmen t t o science an d tech nology, and it s ignorance of the achievement s and conceptua l richness o f science. There was a furious response from Dr. F. R. Leavis, who ruled the English literatur e roost a t Cambridge for a good part of the mid-twentiet h century. 4 Leavis let loose : "The intellectual nullity i s what constitute s any difficulty ther e may be in dealin g with Snow's panoptic pseudo-cogencies, his parade of a thesis: a mind to be argued with—that is not there." Evidently Snow had touched a sensitive spot , but Leavis 4

The axiom of the French farce-writer Feydeau could be applied to Snow and Leavis: "Whenever two characters must under no circumstances meet, I immediately bring them together."

"What the Devi I Does It Al I Mean?" |

had a point. The rather cardboard characters in Snow's novels and his stodgy reference to the perio d 1914-1950 as a "misguided period " i n the history o f literature hardly made him the ideal emissary between the two camps. The two-cultures row spread rapidly into the intellectual magazines and the media. A decade later, Leavis was still on the defensive. He let it be known that, in his opinion, the English department wa s the heart o f his university, the center about which al l else revolved. The statement is symptomatic of the gap. It is pitiful t o claim that th e Englis h department a t Cambridge was the heart of the university durin g a n er a when Watso n and Cric k were determining th e struc ture of DNA and, in the same university, Frederick Sanger was performing the firs t aminoacid sequencing of a protein (insulin), for which he received the Nobel Prize. Arid if that isn't enough, the astronomer Martin Ryle was reaching into deep space, detecting scores of radio stars, work for which h e was knighted an d als o awarded the Nobel Prize. These people were changing the futur e o f humanity, an d altering the way we see the cosmos. During that period there was no one doing any signifi cant original writing i n th e Englis h department. Ther e was , o f course, criticism , criticism of criticism, and so on—infinite reflections in parallel mirrors. Was th e professo r o f Latin equall y convince d o f the centralit y o f his subjec t when Isaac Newton was occupying himself with trivia such as the law of universal gravitation? An d b y th e way , who was the professo r of Rhetoric at Padu a whe n Galileo first turne d a telescope on the nigh t sky? One often despair s o f academics. Consider another professor, Michael Oakshotte, a distinguished write r on philosophy who, when referring to science, declared that there was no room for "vocational training in a university." Science, said Oakeshotte, dealt with "objects and observations," not "idea s an d thoughts" ! On e can only throw u p one' s hands; perhap s Charles Snow was right about the two cultures, but surely the time has come to expect a little more awareness on both sides.5 It may be that one of the roots of the fairly prevalent antagonism of academic hu manists to science is an unconscious resentment of the emergence of a high-profile, worldwide communit y tha t sometime s implicitl y o r explicitl y claim s t o b e in volved in a pursuit that is more important than the humanities, not only in respect to its applications but also in a wider sense. It is all right (but not in my opinion accurate) if a distinguished historian like David Thomson writes that in the twentieth century, "the scientist . . . came to dominate the whole spher e of creative endeavour." Fo r scientists to expres s simila r sentiment s smacks of cultural imperialism . Unfortunately, science is seen as somewhat larger than life by some who practice it. Science in the Mirror I iike my face in the mirror, I like my voice when I sing. My girl says it's infatuation— I know it's the rea l thing. —Kit Wright, "Ever y Day in Every Way" 5 Newton set a bad example, branding poetry as "a kind of ingenious nonsense" but he could have pleaded that: he was only paraphrasing fiaint Bernard, who in the twelfth century spoke of the "lies of poetry."

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The increasing obscurit y of much o f twentieth-century scienc e leaves ample room for th e scientis t t o present science to HMS in, ofte n justifiably , glowin g terms. But HMS may lack the knowledge to meaningfully question the justification. The publicity given to science, the increasing intrusion o f science into the lives of HMS, the marvelous consistency of the scientist's cosmos—al l these have had their effec t o n the scientist's imag e o f science. Scientist s occasionall y grossl y overestimat e th e value of their research. Lately this seems to be an occupational risk that is particularly sever e amon g particle physicists . Hyperbol e ofte n ha s budgetar y a s well a s philosophical implications . False Gods "My nam e is Ozymandias, king of kings : Look on my works, ye Mighty, and despair!" Nothing beside remains. Round the deca y Of that colossal wreck, boundless and bare. The lone and level sands stretch far away. —Percy Bysshe Shelley

HMS should b e o n his guar d against Ozymandiism. I n the ol d day s I might hav e said that there were patent medicine salesmen in town. Consider the interesting example o f the superconductin g supercollide r (SCSC ) mentione d i n Chapte r 12 , a project tha t illustrate s no t onl y the clas h o f scientific and budgetary interests bu t also th e sellin g o f science t o the public . Th e hope wa s tha t this mighty machin e would induc e th e "fina l particle, " the Higgs boson, to appear. Professor Leon Lederman, a Nobel prize-winnin g theoretical physicist, has dubbe d the Higg s boso n "the God particle." No less! With such PR, one can understand wh y the thought of this shy but tempting morsel flicking aside its fan and revealing itself for a billionth of a second , i s inducin g ecstas y i n th e audienc e o f particle physicists . Bu t th e striptease coul d be a trifle pricey , perhaps i n exces s of $11 billion. An d th e lad y may not deliver everything expected of her. Proponents of the SCS C spent much effort i n lobbyin g the powers-that-b e in orde r to be assured o f sufficient fundin g for the giant accelerator. They cannot be accused of underestimating th e importance of the apparatus. A prominent physicist has used the phrase "propaganda war" in referring to the statement s o f the SCS C lobby. What is HMS to make of all this? Is the deification o f the Higgs boson warranted? Is the expens e justified ? I hope that the Higgs boson will one day be found. It will be a magnificent technical an d theoretica l triumph, lik e a great Bobby Fischer game . But let's ge t it i n perspective: tax-paying HMS should b e aware that th e discover y wil l no t hel p t o solve any outstanding proble m in medicine, chemistry , biology, or any other fiel d of huma n endeavor , excep t theoretica l particl e physic s an d possibl y cosmology . There i s almos t n o doub t whatsoeve r tha t th e discover y wil l b e o f no practica l value to HMS. This is not the discover y of atomic structure, which allowed an explanation o f the periodi c tabl e an d thu s created modern chemistry , materials sci ence, molecular physics, an d molecular biology. Admittedly, scienc e has othe r justifications besides utility , althoug h I have acquaintances wh o se e th e concep t o f "useless " basi c scienc e a s a n effete , elitis t avoidance of the real problems with whic h scientist s shoul d be occupied. I do not agree with them , partly because useless scienc e has ofte n turne d ou t to be useful ,

"What the Devil Does It All Mean?" [49

and partl y becaus e I believe i n th e disintereste d searc h fo r knowledge. Bu t th e "elitist" objection to the search for the Higgs boson has nothing to do with the feel ing among many scientists that the significance of the search has been greatly overplayed by some very prominent physicists . Maybe subconsciously awar e of the probabl e practical irrelevance of the Higgs boson, and seeking to justify th e preposterous expense involve d i n looking for the God particle, another Nobel Prize-winning physicist has gone on record as predicting that when the Higgs boson is discovered, "the new s that nature is governed by impersonal laws will percolate through society, making it increasingly difficult t o take seriously astrology or creationism o r other superstitions." On e can see the scene, the da y after th e Higgs boson is discovered and the National Enquirer announces: "Bouncy Boson Bared!" The bookshops will be emptied of occult books, the horoscopes will vanish from the daily papers, the Creationists will crumple, the streets of San Francisco will be littered with the discarde d paraphernalia o f loony sects. Not the day after, and not a century after. The Age of Enlightenment, and o f trie reason-worshiping French philosophes, was followed by the irrational Reign of Terror. Many of the heroes of the sixteenth- and seventeenth-century scientific revolution were deeply interested in the occult, in the so-called Hermetic writings, and in magic in general; one only has to look at the lives of John Dee, Boyle, Bruno, Paracelsus, Kepler, and many others. Boyle had an ongoing correspondence with magicians and alchemists an d only avoided an attempt to contact the other world by his fea r that he would get through to evil spirits. Newton, the heralder of the Age of Reason himself, believe d firml y i n th e mysti c aspect s o f alchemy an d o f Pythagorean thought. Of the 1752 books in his library, 170 were on occult subjects, including the Kabbala, Rosicrucianism, and plain old-fashioned magic. In 1890, a president of the Royal Society, Sir William Crookes, was inducted into the Hermetic Order of the Golden Dawn. The physicist Si r Oliver Lodge was taken in by pretty girls wearing skimpy costumes and pretending to be psychics, and I know two respectable practicing physicists wh o believe that Uri Geller can psychically bend spoons. If anything was a publicly trumpeted triumph of reason in this century, it was the experimental confirmation of Einstein's prediction of the bending of light going past th e Sun, and yet (amazingly enough), it was followed by the rise of the Nazi party, based on irrational racial myths. Th e Rosicrucians flourished, millions read their dail y horoscope, and Scientology went on its brainless way. One onl y has to go through the "astrology " or "occult " shelve s of Barnes and Noble or Doubleday to see that, in the da y of the genetic code, antibiotics, and nu clear power, the general public still provides a sure market fo r the irrational . The cold truth is that the Higgs boson will hardly stir HMS. It is far too late in the history of science and societ y to expect the discover y of a useless (t o HMS) particle to create anything more than a weeklong flurry of, probably inaccurate, newspaper articles an d a few TV interviews. Thi s i s not, for HMS, Newton setting the heaven s and terrestrial mechanics i n order, or Darwin putting man in his place. This is not the gif t o f the genetic code. Reason will not advanc e one millimeter. HMS beware! This i s science lookin g in the mirro r an d seein g itself ver y much larger than life . Not infatuation , but tru e love. Severa l physicists have doubt s abou t whethe r th e scientific gain s following the discover y of the Higgs boson will be staggeringly significant. Th e particle is important, but no t that important. I would suggest that titles as grandiose as "The God particle" be reserved for a general method, if there is

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one, of defending man agains t viral disease. If anything is guaranteed to bolster the image of reason and counterbalance the negative connotations that science aroused after the atomic bomb, it would be the victory over AIDS and other major diseases . And i t is arguable that fa r more could be done for the menta l health o f man by diverting som e o f the billion s devote d t o accelerators , t o plai n old-fashione d improvements in the elementary school system. Reason is built block by block in the kindergarten, not proton by proton in a supercollider. Particle physics is a major par t of the scientifi c endeavor and a towering example o f the abilit y of the min d of man t o seek out order in the cosmos ; but i t is evidently seen as even more than that by at least one of its very distinguished practi tioners. In his fascinating book The First Three Minutes, Steve n Weinberg writes: Men and women are not content to comfort themselves with tales of the gods and giants , or to confin e thei r thought s t o th e dail y affair s o f life; the y als o build telescopes and satellites and accelerators, and sit at their desks for endless hours working out the meaning of the dat a they gather. The effort t o understand th e univers e i s on e o f the fe w thing s tha t lift s huma n lif e a littl e above the level of farce, and give s it some of the grace of tragedy. Which puts th e human race in it s place! Accelerator builders on one side and on the other those who, when not occupied with the daily affairs o f life, comfort themselves with myths. Could w e perhap s hav e a lis t o f the "few " othe r occupation s i n lif e tha t ar e worthwhile? I know teachers and nurses who have done more to give life meanin g than a lab ful l o f data analysts . And wha t i s to become of my wife, wh o i s an actress, an d m y acquaintances, amon g them businessmen , doctors , workmen, writers, painters, housewives, all of whom desperately want to throw down their colorby-number copie s o f Jack th e Giant-kille r and buil d accelerator s an d si t a t thei r desks for endless hour s analyzin g data, to give some meaning to their lives ? And what of Verdran Smilovitz, the last remaining member of a string quartet, the othe r members o f which ha d bee n killed , who playe d his cell o i n the ruine d street s of Sarajevo t o "show tha t civilizatio n was not dead" ? It may be that ther e is no purpose in the lon g run, that we are, in a few million o r billion years, doomed to extinction, but i t i s no t th e accelerato r builders wh o wil l hav e lifte d u s abov e the level of farce. This example of "Mirror, mirror on the w a l l . . . " reminds me o f J. D. Bernal, the Marxist physicist wh o predicted , and anticipate d with approval, government b y scientists , wh o woul d "emerg e as a new specie s an d leav e humanit y behind."6 Well, at least we know one of those who has contributed to the farce . Overevaluation is not confined to some particle physicists. ( I say "some": I have colleagues in the field. ) A number of gene sequencers have also started to walk on water. Again: HMS, beware! Earlier on I mentioned the Human Genome Project, the attempt to determine the complete base sequence o f human DNA. It has been claimed, by some of those in volved in the sequencing, that this knowledge is the key to what it is to be a human being. 6

Bernal would have felt at home in the kingdom of Bensalem in Bacon's New Atlantis, where th e only statues raised were to inventors.

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The huma n genom e controls most , but no t all , o f our physica l characteristics . But the genome is not the man. A genetic factor is probably involved in our thought mechanisms, but not in a simple fashion. Identica l twins have identical genes, yet when brought up i n differen t environment s the y can exhibit very different behav ior.7 How would a complete knowledge of their genes explain who they are, or who any of us are, in any meaningful human sense? Human beings ar e more than thei r genetic components , even i f some of those components contro l most o f their physica l an d som e of their menta l characteristics. This is not to say that there is an additional unidentifiable component, call it the soul if you will. It is just to stress that we are the most complex systems in th e universe an d that tha t complexit y is partially built-in an d partially , but very substantially, th e result of our interactions with the inanimat e worl d an d with other human "systems. " T o claim tha t suc h a system ca n be completel y understood in terms o f the serie s o f bases o n DN A is no t eve n a scientific statement. D o the se quencers really believe that the workings of the human brain can be completely described once the gene sequence is known? Ask those working on the brain. There is evidence that the development of the central nervous system in the embryo is partly a random process, and that the "wiring " of the brain is affected b y the nature of the experiences that feed into it. The fallacy o f those who believe that "the genome is the man " i s their implici t acceptanc e that gene s are conceptually equivalen t to elementary particles. The particles are the 011/ 7 basis of all matter; their properties completely control the propertie s of individual molecules . Genes are not the onl y determinants o f man's nature—and , incidentally, scienc e i s not th e onl y jewel in his crown. Big Fleas Have Little Fleas...

The canonization of the genome is consistent with the old reductionist hope that it will be possible to explain everything in Creation in terms of the properties of the simplest component s o f matter. Reductionism is a creed that tend s to be popula r with particle physicists . Part of the accepte d syste m of beliefs o f medieval man , at least i n Europe , wa s the existence of the Chain of Being. This was a hierarchical ordering of the Creation from th e lowest level, the inanimate world, up through plants and animals to man and the angels. There was, of course, no implication o f evolution here. Every member of the chai n had been created individually. It is tempting to revive this idea in the light of modern science, with th e additional premise that at each level of complexity, systems can be explained o n the basis o f the propertie s of the leve l below them. With the possible exception o f the angels, everything on Earth, and probably in the Heavens, is made of quarks and leptons. Now just as we can explain the struc ture and behavio r o f atoms in terms of the elementar y particles, and th e behavior and structure of molecules in terms of those of atoms, the reductionist's dream is to carry on climbing upward along our ladder and explain th e structure and behavior of living cells and living organisms in terms of their component molecules. The top of the ladder no w beckons; perhaps we can explain man an d his mind i n terms of 7

This was one good reason given by Aristotle for doubting the validity o f astrology.

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the nature of cells—and ultimately quarks? And then scienc e will have explaine d everything. Is this a meaningful program? Niels Bohr thought not, stating that biology would never be entirely explained in terms of Chemistry. Schroedinger disagreed , but w e don't have to go up to the level of mind to run int o difficulties. We saw when dealing wit h entrop y that th e macroscopi c behavior o f a larg e ensemble o f particles cannot b e deduce d fro m th e propertie s o f the individua l particle s themselves. A t least from a practical point of view, reductionism has to be put o n hold for the moment. Some might say forever. The belief in reductionism has something of the Cartesian desire to start with a simple, verifiabl e basi s an d systematicall y construc t fro m i t th e whol e Creation . We don't yet know if this can be done, but th e seemingly rational suppositio n that complex systems can always be completely explaine d i n terms of the properties of their simple r components is at present not proved. In any case, the statement tha t King's College Chapel was built by J. Quark and Company , even if true, adds nothing whatever t o ou r real understanding o f the plan , purpose , and wonde r o f that glorious structure. Which does not imply that it is a fruitless exercise to climb up and down the ladder of the sciences. Most levels of science have benefited from looking down to the level below, and th e cross-fertilizatio n of different disciplines , a s exemplifie d by biophysics, i s a distinctiv e aspec t o f twentieth-century science . Standin g o n th e ladder of the sciences , molecular biology, for example, has profite d immeasurabl y from lookin g down to chemistry and molecular physics. Science and Philosophy Weigh Each Other Up In thi s century , the attemp t t o understan d th e natur e o f the physica l worl d ha s pushed us toward the borders of philosophy. Can science talk to philosophy? In the age of quantum mechanics this is not a pointless question . Scientists o n the whole have little time for philosophy. Put bluntly, philosophy seems irrelevant to science. And yet the scientist's feeling that the nature of the Big Bang and th e subsequen t evolution of the univers e i s approaching a solution, the geneticist's successful probing of the human genome , the doctor' s manipulation of embryos, the claims that we are beginning to understand consciousness—al l these have maneuvered scienc e into confrontation s with th e ethic s o r the epistemolog y of the philosophe r and th e morality of religion. Science and philosoph y persis t i n flirting with each other, even if science has rarely profited. The twentieth century has seen a growing stream of books purporting to link science wit h God , with meaning , and wit h ou r plac e i n th e cosmos . A t th e reall y woolly end of the spectrum is the science-reveals-God literature. The classic modern statement was made by a geologist, the Jesuit Pierre Teilhard de Chardin, whose book Man's Place in Nature (1966 ) attained temporar y cult status. Here we are i n the lan d o f unprovabl e statements , abus e o f language , an d everythin g tha t ha s given mysticism a bad name . That there is poetry, awe, and myster y in science is part of its appeal, but i t is intellectually sloppy to take, for example, a concept lik e energy, use it in a loose metaphorical sense, and pretend that the word energ y that appears in you r text is the sam e as , or has the remotes t resemblance to , the wor d

"What the Devi l Does It All Mean? " |

energy that appears in a scientific paper. To do so is merely a highbrow equivalent of the T V psychic, emoting about "focusing cosmic energy." More incisiv e thinker s have considere d th e relationshi p betwee n scienc e an d philosophy. "What the Devil Does It All Mean? " A person may be supremely able as a mathematician, engineer, parliamentary tactician or racing bookmaker; but if that person has contemplated the universe all through life without ever asking "What the devil does it all mean?" he (or she) is one of those people for who m Calvin accounted by placing them in his category of the predestinately damned. —George Bernard Shaw, The Adventures of the Black Girl in Her Search for God

You can almost hear Shaw' s Iris h accen t as he say s "divil." Can science help i n a search fo r meaning ? Ha s scienc e an y relevanc e t o th e "bi g questions " tha t th e philosophers use d to ask? For many, the answe r to Shaw's question lies not in science o r philosophy bu t i n religion (onc e define d as man's attempt to speak to th e weather). But most o f us, lookin g at history, can se e no meaning issuing fro m religion's diverse gods. Science can certainly engender awe for the workings of the universe, and this is one step alon g the pat h to the rose-tinted sentimentalism of the "How-marvelous is-thy-handiwork" school of thought, with its suppositio n o f a benevolent Desiigner. It is a pleasant, warm, harmless trap into which to fall. But Science has revealed nothing that i s unambiguousl y indicativ e o f purpose. I f we ar e hones t wit h our selves, we have to accept that al l evidences of design seem to be due to evolution, coincidence, o r an orde r inherent i n natur e itself , Th e law s of motion, Maxwell's laws, the secon d law of thermodynamics, the doubl e helix—none of them give the slightest support to the hypothesis o f a Creator, except insofar as we throw up ou r hands and say, "Well, it must have been created by someone." And this returns us to the deist fold . Nevertheless, althoug h fait h appear s to have almos t no interfac e with science, scientists in this century are being forced to ask questions that are normally regarded as the territory of the philosophers. Fo r example, is science a valid means of examining reality ? In this centur y quantu m mechanic s ha s le d u s a very long way from commonsens e reality. One has to say of certain experiments, "If this is reality, it is beyond our comprehension." Are Kant's phenomena, the appearance of things, perhaps wildly differen t fro m hi s noumena, the tru e nature o f things? If so, is science, alon g wit h othe r huma n activities , a kin d o f dream , albei t a ver y usefu l dream? I n th e worl d o f elementary particles , wha t doe s "reality " mean ? Sense data? Readings on instrument panels ? Ah, solving that questio n Brings the priest and the doctor In their long coats Running over the fields. 8 8

From "Days," by Philip Larkin, from The Whitsun Weddings, Fabe r & Faber, London (1969).

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And, one might add, the philosophers and the scientists. And what do the philosophers make of science's picture of reality? Through a Glass Darkly Philosophers consistently see the method of science before their eyes, and are irresistibly tempted to ask and answer questions in the way that science does. This tendency ... leads the philosopher into complete darkness. —Ludwig Wittgenstein, The Blue Book Philosophy is virtually empty without science. —A.J. Ayer

For a t leas t 30 0 years , philosopher s hav e flirte d wit h th e scientifi c method . Wittgenstein recognize d this an d wa s no t pleased , but hi s dir e warnin g remain s largely unheeded, and it is typical of twentieth-century philosophy that many of its major practitioners, including Wittgenstein himself, had mathematical or scientific roots, and some have taken science very seriously indeed. In contrast, most contemporary scientists regard philosophy as completely irrelevant t o science , or indeed t o lif e i n general . Things starte d differently . Partiall y spurred on by the rise of physics, three major seventeenth-century philosophers se t out to construct universal system s of thought that would provid e all-inclusive ac counts of the eternal truths of religion, the finding s of science, and the problems of metaphysics. They all tried to incorporate ethics within their schemes . Descartes, Leibniz, an d Spinoz a al l failed . An d non e o f them succeede d i n linkin g scienc e with philosophy in a practical sense, although all of them tried. The natur e o f knowledge might b e though t t o be a basic concer n no t onl y of philosophers but als o of scientists. Indeed, the primary objective of the British empiricists wh o followe d Locke was t o fin d a method o f differentiating between , on the one hand, reliable and meaningful propositions concerning reality and, on the other, proposition s tha t wer e eithe r meaningles s o r beyond ou r abilit y t o verify . Most scientists ignored this epistemological swamp until this century, when quantum mechanics seeped over the border into philosophy. Three centra l question s tha t hav e resiste d philosoph y sinc e Socrate s have become the respectable concern of science as much as of philosophy: What is matter? What i s mind? What criteria ar e there fo r truth? The scientis t ha s ha d littl e hel p from th e philosophers . Moder n philosophy i s either irrelevan t t o science o r antiscience, i n spit e o f the fac t tha t man y twentieth-century philosopher s wer e con cerned with the nature of science or mathematics. The first major book on philosophy published i n this century was Fundamental Laws of Arithmetic (1903) by the German logician Gottlob Frege (1848-1925). Frege attacked two old problems: What is the nature of mathematical truth? and What are numbers? His work on the bases of mathematics was fatally wounded by Bertrand Russell, an d subsequentl y Freg e became concerned with question s o f language, a central concern of many philosophers i n this century and a turning away from th e traditional problem s o f knowledg e (Ho w and wha t d o I know? ) to question s o f meaning (Wha t am I saying?). Frege is regarded as the founde r of "analytical" phi losophy, but he has had little direct effect o n science. Bertrand Russell (1872-1970), althoug h not primaril y concerne d with science , believed in the unity o f science and philosophy; they were merely two related as-

"What the Devi l Does It All Mean? " I

pects o f ou r knowledg e o f the world . Lik e Frege , h e mad e hi s firs t professiona l mark with wor k on the base s o f mathematics i n hi s grea t tome, Principia Mathematica (1910—1913), written with A. N. Whitehead. Russell's empirical philosophy was based o n observed qualities (sense-data) , not o n the suppositio n o f an unobservable substanc e o r substance s tha t "have " thos e qualities . H e wanted t o con struct entitie s ou t o f sense-data, not ou t o f objects tha t were onl y inferred, in hi s eyes unjustifiably, fro m thos e sense-data. This approach is reminiscent o f Heisenberg and Bohr : only observables mean anything . Unfortunately, Russell then complicated matters by saying that sense-data are different fo r different people ; everyone ha s hi s ow n persona l sense-data . Mos t people , especiall y scientists , ge t impatient a t this kind o f approach to reality. The vast majority o f scientists believe in a real, external world that i s analyzable through our senses. Russell in the en d decided that, to save the foundations of science, one had t o accept the existence of permanent object s an d substance . Contrar y to Wittgenstein , he recommend s the scientific method (in On Scientific Method in Philosophy [1914]) to those attacking philosophical problems . Philosophers should , he said , be "impregnated wit h th e scientific outlook. " But his philosophy has had no practical effect o n science. Moving back to the Continent , one of the most influential philosophers during the pas t decade s was yet another mathematician , the Moravia n Edmund Husser l (1859-1938). Husserl's plea to make "all-embracing self-investigation" the basis of science, i f acceded to , would probabl y put a n en d t o mos t natural scienc e as we know it. Husserl closes his best-known book, Cartesian Meditations (1931) , with a quotation fro m Sain t Augustine : "D o not wis h t o g o out ; g o back int o yourself. Truth dwells in the inner man." A catastrophic working philosophy for a scientist. Husserl's student Martin Heidegger (1889-1976) wa s an opponent of science and the technological society. His temperament led him along the dangerous path of German romanticism, which ende d with his flirting with Nazism. Some have excused this aberration by supposing that he looked to the Nazis to combat the anti-cultural, technological society of the time . If this is so it only confirms th e suspicio n tha t many brainy men are incredibly naive.9 It is disconcerting to think of a philosopher telling his students, as Heidegger did in 1933, "Do not let doctrines and ideas be the rules of your being. The Fuhrer himself, and he alone, is the present and future German reality and its rule." His students were required to salute him. In a 1966 interview fo r Der Spiegel, Heidegge r dissociated himsel f fro m hi s statement s o f the 1930s—absent-mindedly forgetting to mention that he was a Gestapo informer.10 Heidegger's writings fall into the highest German tradition of obscurity. Thus his description o f the sel f i s "a being suc h tha t i n it s being its being i s in question. " Which is OK if you like that kind of thing.11 9

I have a pamphlet entitle d "What Are You Going to Do about It?" written in 193 6 by the undoubtedly bright Aldous Huxley, suggesting that the way to defeat Hitler and prevent war was to organize small discussion groups of people dedicated t o the idea of peace. Doubtless, Panzer General Rommel trembled in his boots. 10 I cannot refrain fro m notin g anothe r example of the discrepancy between the professional and political IQ s of apparently rationa l men. Russell , at a public meeting, declared that Kennedy and Macmillari were ". . .wicked and abominable. The y are the wickedest people that ever lived i n the history of man." Which lets Pol Pot and Himmler off the hook. "Those who have a weakness for debunking may appreciate Paul Edward's opinion tha t Heidegger has given us "huge masses of hideous gibberis h whic h must be unique in the history of philosophy."

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Heidegger sa w the great metaphysical questio n a s being why ther e i s anything rather than nothing. He believed that man had los t the sense o f being, of just existing. Th e fault , a s he sa w it , la y mainly with scienc e an d technology . Th e centra l question on which he focussed—the meaning of being—is an ancient and hauntin g one and he faced it straight on, accepting that we come from oblivio n and return to oblivion: "these thing s ar e not otherwis e bu t thus. " It is a stance, reminiscent o f Camus and Sartre , that speak s to those among us who se e no evidence for the su pernatural. A major twentieth-centur y philosophica l movemen t which was largely created by scientists and has had a strong, but sometimes questionable, effect o n scientists in this century is Logical Positivism. It is far more understandable than most continental philosophies. Erns t Mach, whom we have already met, is often regarde d as the spiritual father o f the movement, but d'Alembert , the joint instigator o f the Encyclopedia, an d Auguste Comte were not blameless. Th e school was initially cen tered in Vienna under the leadership o f Moritz Schlick (1882-1936). Logical positivism is empiricism taken to extremes. It places strong emphasis on observation an d measurement. Scientists, especially physicists, ofte n ten d to sympathize wit h th e basi c principl e o f logical positivism: tha t the meaning of any proposition is its method of verification. A s the Vienna Circle's English disciple, A. J. Ayer, put it: " . .. a sentence is factually significant to a given person if, and only if, he knows how to verify th e proposition which i t purports to express." This ha s clear echoes of Heisenberg's approach to quantum mechanics, in which the "mean ing" of an observation is taken to be simply the result of an experiment don e on a known system with a known piece of apparatus an d a defined procedure. The Vienna Circl e considered that two kinds o f verification were acceptable: experience and logical necessity. Propositions which are true in the limited sense that they are condemned to be true by the meaning of the symbols contained within the proposition, woul d b e terme d analytic propositions , i n Kant' s vocabulary. On the othe r hand, if I observe that any two o f a given set of bodies fall with the sam e acceleration, then I am using experience to verify the proposition that all bodies in that set fall with the same acceleration. Propositions of this type, depending for their trut h on the observed facts o f nature, are examples of Kant's synthetic propositions . This reduction o f possible knowledg e to eithe r tautologie s o r proposition s whic h ar e empirically verifiable i s directly traceable to David Hume who aske d of a proposition: "Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence"? No. Commit it then t o the flames : fo r it ca n contai n nothin g but sophistr y and illusion. " Thes e criteri a cu t th e groun d fro m unde r metaphysics . Question s such a s the meaning of existence are reduced t o nonquestions, sinc e the y are not susceptible t o either logica l analysis o r experimental verification. More down-toEarth question s als o los e al l meaning , suc h as , "Wha t i s righ t an d wrong? " As Schlick said , suc h question s hav e n o answers , not because the y ar e difficul t bu t "simply becaus e the y are not questions" ! Schlick considere d tha t a practical sys tem o f ethical behavio r coul d b e buil t u p fro m man' s experience , bu t i t ha d n o philosophical validity . This is a difficult attitud e to challenge. Some outstanding physicists accepte d logical positivism, either implicitly or explicitly. The y were i n practic e phenomenologists—dealing solel y i n observable s and the observed relationships betwee n them; they had given up o n the noumena

"What the Devi l Does It All Mean?" I

of Kant , th e suppose d hidde n reality . Th e sam e "blac k box " attitud e t o realit y shows up in the behaviorist schoo l of psychology, associated particularly with J. B. Watson and B. F. Skinner, in which it was not done to speak of mental states, since they could not be directly observed. A difficult y tha t the logica l positivists neve r solved wa s how t o accommodate science in their system. Since most of them had been scientists, they wanted to preserve science as meaningful, but it was not easy. Many of the basic concepts of Science cannot be verified either logically or by observation. As we saw, Mach rejected the concept of atoms because they were neither observabl e nor, in his opinion, logically necessary. Kaufman n famousl y misse d ou t o n a Nobel Prize because he was a logical positivist in outlook and refused to interpret his experiments in terms of a particle (th e electron) that he could not see (see Chapter 12). If yo u wan t t o anno y a logical positivist, as k him i f the verifiabilit y principl e stands u p t o its own criteria fo r verifiability. You could also point ou t that unles s you first understan d a proposition, you have no idea how to verify it . This means that a proposition ma y really have meaning, but because you don't understand i t you don't know how to verify it , and thus assume that it has no meaning. The logical positivists belong to the school of philosophers who have tended to concentrate less on problems than on how to solve them. The tradition goes back at least as far as Hume. In this context the so-calle d "scientific method," whic h ha s the reputatio n o f being a successful means o f problem solving , has ha d a n attraction fo r some modern philosophers . Thu s th e "logi c o f scientific discoverjr " ha s long been a primar y concer n o f the philosophe r Kar l Popper . We met Poppe r i n Chapter 2 , where we discussed th e best-known aspect of this work, the question of the verifiability of scientific theorems. In the scientific community, Popper is probably fa r and awa y the best-know n an d respecte d modern philosopher , partly because he i s a blessed exampl e o f the fac t tha t writing impenetrabl e pros e is riot a precondition for being a German-speaking philosopher. As might be expected, modern American philosophy contains a strong streak of practicality, often bringin g it closer to science than modern European philosophy. The recognize d leader o f the pragmati c school o f philosophy wa s Willia m James (1842-1910), the older brother of the novelist Henry James. To sum it up in its most concise form: A proposition is true if the results that follow from it are useful. Thi s is an ideal philosophy for a practicing scientist—or for an automobile manufacturer. Since scientists usuall y continu e using a theory as long as it is useful, the y are implicitly usin g the criterio n o f pragmatism t o determin e whethe r th e theor y is true. Onc e the theor y doe s not giv e correct (useful ) results , i t i s discarded . John Dewey (1859-1952 ) wa s eve n neare r t o th e scientifi c fram e o f mind, i n tha t h e stressed the need to accept that any idea could be proved to be mistaken; one might approach, but possibly never reach, truth. A concern with the method of finding the truth often goes hand in hand with an interest in the wa y that we use language . In fact, som e would se e modern AngloSaxon philosophy as far too concerned with the meaning of words and far too little concerned wit h th e classic moral questions tha t stil l remain unanswered. Bu t the dilemmas of quantum mechanics have sharpened our need to define our terms. The outstandin g nam e i n linguistic s i n recen t year s ha s bee n tha t o f Noam Chomsky, who has revolutionized our attitude toward language. His theory of the deep structur e o f languages suggests that w e have inborn , inherite d grammatical

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patterns whic h ar e commo n t o al l languages . Chomsk y addresse s th e natur e of knowledge: " . .. the general character of knowledge, the categories in which it is expressed o r internally represented, and th e basic principles tha t underlie it , are determined by the natur e of the mind. " This is a direct negation o f Locke's belief that there is no innate knowledge of either principles o r ideas. Locke famously insisted that when w e come into the worl d our minds ar e "white paper, void o f all characters, without an y ideas, " a view o f man echoe d b y Sartre' s insistenc e tha t there is no built-in human nature, that we are completely free. Anti-Lockean views were expressed by the grea t physicist Wolfgan g Paul i (1900-1958) in a n essay on Johannes Kepler : "The process o f understanding i n nature , togethe r with th e joy that man feels in understanding,... seems therefore to rest upon a correspondence, a coming into congruence of preexistent internal images of the human psyche with external object s and thei r behavior. " Th e suspicion tha t ma n impose s a structure on the universe is related t o the controversies, considered in Chapter 9, surrounding the ideas of philosophers such as Kuhn and Feyerabend. If anyone delved profoundly into the meaning of language—obsessively and un necessarily so, in Karl Popper's view—it was Wittgenstein. He had been deeply impressed by the work of two o f the greatest scientists o f the lat e nineteenth century , Heinrich Hertz and Ludwig Boltzmann. It was not so much their science that concerned him a s their attitud e toward Science . Boltzmann in particula r felt tha t all that we were really doing when we stated physical laws was using a series o f linguistic representations of reality. To relate force an d mass , as Newton had don e i n his law s o f motion, was to relate labels i n suc h a way that w e could use the rela tions for predictive purposes. To read anything more into the terms force an d mass was to presume more than we can know. One is reminded once again of the logical positivists although it is a mistake to put Wittgenstein in their camp. Wittgenstein put i t this way: "Philosophy is a battle against the bewitchment of our intelligence by means of language." Wittgenstein was basically antiscientific . He knew that science wa s partl y driven by a desire t o generalize, and h e rejected generalization. Scientifi c question s were of no great interest to him; they merely addressed th e working of the natura l world. Wittgenstein spent much of his later years examining the way in which language may shape our reality. This is not a subject that is irrelevant to science. The use of words like matter, space, mass or life, i s charged with connotations that arise from our education and the way those words have been used i n the past. It is worth remembering tha t Einstein' s questionin g o f the meanin g o f the wor d simultaneity was more than idle philosophizing. Is Philosophy Relevant to Science? There have been times when science and philosophy were alien, if no t actually antagonistic t o each other. These times have passed. —Max Planck (1936)

I have done a gross disservice to some of the outstanding intellectuals of this century. I have taken video clips o f their life' s wor k or summarized tiny piece s of com-

"What the Devil Does It All Mean? " |

plex philosophies i n a few glib phrases, but , a s explained earlier , in certai n area s this book is not a map, but a sign-post. Ask the nex t scientis t yo u mee t if philosophy ha s affecte d hi s lif e o r work. Get ready fo r a blan k stare . Thi s complet e avoidanc e o f philosoph y ma y hav e t o change. We must be prepared t o fac e a growing number o f philosophical problem s arising from the ethical aspects of modern science. Less controversially, we saw the difficulties whic h quantu m mechanic s ha s introduce d int o ou r idea s o f reality, and, fo r some of us, th e natur e o f reality is , perhaps, the philosophica l question . Shimony, i n The Reality of the Quantum World (1988) , writes , "W e live i n a remarkable era in which experimental results are beginning to elucidate philosophical questions." He was referring to the challenging fact that the questions raised by the fundamental s o f quantum mechanic s ar e now impingin g very directly o n th e nature of the relationship o f the observer's perceptions to the external "real" world. This is an old question, but we have hardly advanced since, on the one hand, Locke wrote that the "bulk, figure, number, situation, and motion" o f bodies are real properties "whether w e perceive them o r not," and, on the other, Berkeley avowed that " . . . as to what is said of the absolute existence of non-thinking things without any relation t o thei r bein g perceived, tha t seem s perfectl y unintelligibl e . . . nor i s i t possible they should hav e any existence, out of the minds or thinking things which perceive them. " Ther e i s n o knowin g where , i f anywhere , thes e tw o divergen t roads t o the understandin g o f matter will lead . But, because of quantum mechanics, they are becoming scientific a s well as philosophical questions . An Endles s Road or a Dead End?

My feeling is that the attempt to understand the basic nature of reality may well be a losing game. It could be that we have reached, or are fast approaching , the limit s of human comprehension . Dare I suggest that we may never be capable of forming a "commonsense," easily visualize d pictur e o f what w e choos e t o cal l reality? Perhaps becaus e we ar e part o f the syste m o r because w e haven't go t the righ t hard ware. Thomas Hobbes wrote, in De homine (1658), that language "is the connexion of names constituted by the will of men to stand for the serie s of conceptions o f the things abou t which w e think" (my italics). The conceptions are, perhaps, as far as we ca n get . It is possibl e that , a s in th e cas e o f quantum mechanics , w e wil l jus t have to be satisfied with theories that give the right answers even if we don't really understand why . As a working scientist I sympathize with th e approach of the American philosopher, V. O. Quine (1908 — ), who see s " . . . the conceptua l scheme o f science a s a tool, ultimately, fo r predicting futur e experienc e in th e ligh t o f past experience. " Up to now that tool has been enormously effective . A Note on Complete Uncertainty The foundations of science are uncertain, but mathematics has often been looked to as a system which was potentially foolproof . B y which I mean that if a suitable set of axiom s coul d b e found , an d way s o f manipulating the m agree d upon, the n i t would be possible to state unambiguously whethe r a statement involving th e subjects covere d by the axioms , was tru e o r false. Thu s i t was take n for granted tha t once the integers, and th e rules for handling the m (addition , multiplication, etc.) ,

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had been defined , an y statement about the integer s could b e proved to be true or false, th e proo f onl y involvin g th e axioms . Mathematics thus ha d a certainty denied to an y other human constructio n o f the mind; it was a completely self-suffi cient system , requiring no extraneou s factors t o be taken into accoun t i n proving anything that lay within the scope of its basic axioms. In particular it was superio r to science in this respect—especially after Popper . The man who upset the applecart, in 1931, was the Austrian mathematician and logician Kurt Godel (1906-1978). There are a number of equivalent ways of stating his result, perhaps the clearest of which i s that no finite se t of axioms is sufficien t to form the basis for all true statements concerning integers. No matter how many axioms for m th e basi s o f mathematics , ther e wil l b e statement s abou t integer s which cannot be proved to be either true o r false. Thi s i s an amazing finding an d for mathematicians at the time, a severe psychological jolt.12 In addition t o the suspicio n tha t w e may never full y understan d th e physical universe, we are now faced with the fact that we are forever limited in our ability to construct a noncontradictory syste m o f mathematics. Th e twentiet h centur y ha s been maliciously unkind to Man's intellectual pretensions. Toward th e en d o f his life , Gode l feare d tha t h e wa s bein g poisoned , an d h e starved himself to death . Hi s theorem is one o f the mos t extraordinar y results i n mathematics, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt Godel's gifts might be aborted.

lz lncidentally, Godel does not say that there cannot be a limited syste m of axioms, within th e whole set of axioms, which ca n be used to prove any statement involving only those axioms, provided that we can hope to use the remaining axioms, if we are in trouble proving that something is true or false within the framework of the smaller set. The problem is that, if we take all the axioms, we have none lef t ove r to help us .

X Cross My Hand with Silver

In which some thoroughly unreliable predictions are hazarded.

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38 The Future We all believe that it isn't possible to get to the moon; but there may be people who believe that it is possible and that it sometimes happens. We say: These people do not kno w a lot tha t we know. And, let them never be so sure of their belief—they are wrong and we know it. If we compare our system of knowledge with theirs then theirs is evidently the poorer one by far. —Ludwig Wittgenstein, "On Certainty"

This will b e a very short chapter—no t because the apocalyps e is upon u s but because th e succes s rat e o f futurology is probabl y o n a pa r wit h tha t o f astrology. There was at one time, especially in the 1960s , a fashion for committees of savants to issue documents purporting to predict the broad lines of the future. Th e authors usually considere d i t advisabl e t o us e extensiv e dat a processing , as i f shak y assumptions could somehow be corrected by expensive hardware. I am prepared to bet a modest sum that there is not one document issued befor e the fal l o f the Berli n Wall that predicts even the rough timin g of that event, or th e subsequent disintegration of Eastern Europe. On the other hand, it is quite possible that a n astrologe r did. Afte r all , the sixteenth-centur y French cour t futurologist , Nostradamus, in his last prophecy, foresaw that England would be the dominating world power for 300 years, which, if taken as the perio d from Elizabeth to Victoria, works out fairly well—plus or minus, as the scientists say. (He added that the "Portuguese will not be content," which I'm quite prepared to believe.) He certainly did much better than Wittgenstein. Really successful prophec y went out with th e Old Testament, partially because human histor y is chaotic in the scientific sense, continually demonstratin g oversensitivit y t o initial conditions , a fac t appreciate d by Blaise Pascal when he declare d that the whole course of history would have been changed if Cleopatra's nose had been a different shape . Vive le nez. Predicting the futur e o f basic science is a losing game. The twenty-first century may bring a successful unified field theory, and perhaps hidden variables will save quantum mechanics . W e might really understand th e Bi g Bang, dar k matter, an d the mind. My guess is that there will be multiple theories of everything, several for each universe, and tha t foreigner s wil l be blamed fo r everything, in all universes. But I really don' t know , an d thi s i s typica l o f the marvelou s unpredictability of basic science. Any da y a stranger may knock on the doo r and irrevocabl y change your life . As to applied science, there are a few safe bets about developments in the early years of the coming century: the scientifically based development of new materials; the understanding an d contro l of the immun e system ; the sprea d of gene therapy; ecology-related research, and s o on. A fairly obviou s list . The crysta l ball als o re-

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veals tha t computer s wil l ge t faster , pain t wil l become mor e durable , an d deter gents will wash even whiter. Inessential gadgets will proliferate and remain socially essential. Many o f the ne w direction s in applie d scienc e will hav e t o be carefull y moni tored by HMS. We have spoken of some of these areas, particularly those based on the human genome, but the information explosion is also a phenomenon that needs watching, and one that has already begun to change our lives. A combinatio n o f basi c scienc e an d technolog y ha s create d wha t ha s bee n termed th e thir d industria l revolution . W e watch distan t war s in realtim e in ou r living rooms. I can si t dow n opposit e a compute r terminal in Haif a an d ta p int o huge databases , assembled i n distan t countries . M y computer an d I are par t o f a vast pseudoneural network that is spreading over the globe with almost threatening speed. The information explosion i s changing the way we live. The availability of information can be a blessing. The ability to access libraries and data that are in another tow n o r anothe r continen t i s no t onl y a gif t t o academics , doctors , media workers, and writers; it also expands dramatically the educational means available to nine-to-fiv e man . Without movin g fro m you r armchair, you ca n mak e use o f a huge library, with recorded plays, concerts, documentaries, and sports events. Information i s flowing int o terminals everywhere, but this is not always a good thing. Difficul t question s o f privacy an d o f censorship inevitabl y aris e when a n easily accessible worldwide networ k exists. Ho w much abou t my lif e an d health , recorded in a government computer, should be available to anyone who is curious? Should pedophile s an d rabi d racist s b e allowe d t o channe l thei r message s int o every home? A subtler question is that of creativity. I'm not at all sure that I know what terminal watching is doing to children's minds. Observe a child, sitting for an hour or so in front o f a video game—usually consisting of some brutal, strutting figure beating the living daylight s ou t of an equally punklike automaton. My own children hav e avoided thi s plague , but wil l theirs ? Wil l they lac k th e creativit y that goe s int o building a sledge, or a primitive boat, out o f whatever materials are available? Are we receiving too much and creating too little? A youngster reading this might say, "I don't believe it. He wants to ban computers and go back to 'the good old times.'" I don't. As I sit typing this on a word processor, I thank Faraday for technology, as I do when I am ordering airline tickets or getting into my car, but I do not believe that the new times are necessarily better in every respect. I do believe that the monitoring of information technology is a legitimate concern of HMS, and that, where children are concerned, we must striv e to maximize the educationa l an d recreationa l advantages of the "informatio n highway" an d figh t t o minimize it s deleteriou s effects. Makin g sadistic pornograph y available to children doe s not come under my definition o f free speech . A final thought . Th e tw o most self-confiden t activitie s of mankind ar e religion and politics . N o on e i s sure r o f himself tha n a believer . Thi s self-confidenc e i s based on a fundamental rigidity, a stubborn refusal t o really hear the other side, to admit for one moment that there might be something basically wrong with the accepted dogma. A believer may be prepared to say that we are all the children o f one God, but he doesn't usually switch from Islam to Catholicism. Science, on the other hand, is completely open-minded—despit e the history o f inertia. An y monument can b e demolished , any belief forsaken. I t is exactly this liberatin g acceptanc e of

The Future |_5]]

the possibilit y tha t ou r minds ca n mislead u s that underlie s th e magnificent successes of science. Scientists ar e not invariably ecstatic when their scientific beliefs are undercut b y better theories o r new facts . Bu t in the end, the scientific community gives in to change because, on the average, we refuse t o be irrational—or to be seen to be irrational by our colleagues. It is the (rehictant!) willingness to be shown to be wrong that has so often led us in the direction o f being partially right. Science, like art, is continually seein g the world anew. This is part of the joy of science.

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Annotated Bibliography

I hav e gon e fo r readabilit y an d accessibility , i n genera l avoidin g referrin g t o sources that ar e only available in specialized librarie s o r archives. I have kept the list short , sinc e almos t al l the books mentioned serv e as jump-off point s t o other sources. At th e university leve l ther e i s a plethora o f undergraduate textbooks dealing with the scientific ideas presented in this book but they are not usually the kind, of books that appeal to the layman. The live s o f hundreds o f scientists an d shor t summarie s o f their work are contained i n th e Dictionary of Scientific Biography, th e sixtee n volume s o f whic h were publishe d betwee n 197 0 an d 1980 , b y Scribner . Scientist s wh o die d afte r 1980 are not included. Part One

Hollis, Martin. Invitation to Philosophy. Basil Blackwell, 1991. A short, lucid, jargon-shunning introduction. A pleasure to read. Kuhn, T . S. The Structure of Scientific Revolutions. Universit y of Chicago Press, 1970. An easily digestibl e classic , althoug h ther e i s much to argue with i n hi s approach. O'Hear, Anthony. An Introduction to the Philosophy of Science. Oxford University Press, 1989. A good starting point for those interested i n the subject . Contains a useful bibliography. Popper, Karl . Conjectures and Refutations. Routledg e and Kega n Paul , 1962 . A basic course in Popper's view of things. Popper, Karl . The Logic of Scientific Discovery. Hutchison , 1959 . A modern classic. Helpful o n the theory of probability. Quinton, Anthony . Bacon. Oxford Universit y Press, 1990. A short, excellent summary of Bacon's life and thought . Williams, Bernard. Descartes, The Project of Pure Enquiry. Penguin Books, 1985. A book that cuts no philosophical corners . Not always easy, but stimulating. Part Two

Brecht, Berthold. Th e Life of Galileo. Methuen, volume 1, 1960. This play, which presents Galile o in a n unflattering light, migh t ge t you arguin g about whethe r he should hav e recanted o r not. "He who does not know the truth i s merely an idiot. But he who knows it and calls it a lie, is a criminal". Cohen, I. Bernard. The Birth of the New Physics. Penguin Books, 1987. A readaible and scholarl y account of the transition fro m the physics of Aristotle to the era of Galileo and Newton.

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De Santillana, Giorgio. The Crime of Galileo. Heinemann, 1958. A good account of one of the critical intellectual confrontations in scientific history. Diderot, Denis. Lettres a Sophie Volland. Gallimard , 1984. Nothin g to do with science, but a unique windo w o n th e ma n behin d th e Encyclopedic, an d o n hi s times. The English translation appears to be out of print. Fauvel, }., R. Flood, M. Shortland an d R . Wilson, eds. Let Newton be! Oxford Uni versity Press, 1990 . A n entertainin g collectio n o f essays o n variou s aspect s of Newton's work. The accounts of his non-scientific or pseudo-scientific interests are particularly interesting. Gay, Peter. The Enlightenment, An Interpretation. W. W. Norton & Co., 1977. A fascinating, authoritativ e tex t whic h include s a detaile d discussio n o f Newton's role, as seen by a historian. Merton, Rober t K. Science, Technology and Society in Seventeenth-Century England. Harper an d Row , 1970. Thi s i s a classi c stud y b y on e o f the leadin g experts in the field . Popper, Karl . Objective Knowledge. Clarendon Press, Oxford , 1979 . Read the sec tion showin g ho w Keple r generalized o n th e basi s o f sketchy data , an d ho w Newton built o n Kepler's laws knowing them to be approximations to the truth. So much for "the scientific method." Turnbull, H. W., ed. The Correspondence of Isaac Newton. Cambridge , 1960. Th e letters bring the reader a little closer to the introverted human being behind the stereotype of the "great scientist." Part Three

Friedel, Robert, and Pau l Israel. Edison's Electric Light: Biography of an Invention. Rutgers Universit y Press, 1985 . A n excellen t boo k showing ho w a brain wav e was turned into a commercially viable product. Latour, Bruno , and Stev e Woolgar . Laboratory Life. Princeto n Universit y Press , 1986. This highly unusual book is a sociological study of a major scientifi c laboratory by a French philosopher an d a n English sociologist. Skeptical i n tone, but almos t alway s objective , it shoul d b e rea d b y al l scientist s (t o embarrass them), and all interested layme n (to amuse them). Merton, Rober t K. Sociology of Science. Chicag o University Press , 1973 . A n ab sorbing book that has a solid, well researched feel about it. Williams, L. Pearce. Michael Faraday. Basi c Books, 1965. An interesting, solid bi ography tha t place s emphasi s (perhap s to o much ) o n th e influenc e o f Naturphilosophie o n Faraday's thought. Part Four

Gordon, J. E. Structures. Penguin Books,1978 . A dated but ver y readable, informative and completely non-technical tour of part of the world of materials. Harrison, J . F. C. Late Victorian Britain. Fontan a Press , 1990 . A n interestin g ac count of the social circumstances an d shifts a t the end of the 19t h century . Knight, David . The Age of Science. Blackwell , 1986. A good summary o f the ad vance of science in the nineteenth century.

Annotated Bibliography |

Lucretius. O n the Nature of the Universe. Trans, b y Ronal d Latham . Pengui n Books, 1951. O f no scientifi c value, but a landmark in man's attemp t to understand reality without invoking the supernatural . Wilson, David . Rutherford, Simple Genius. MIT Press, 1983 . Ambiguousl y titled biography of the great no-nonsense experimentalist . Part Five Atkins, Peter. The Second Law. Scientific America n Library , 1984. Th e autho r i s acknowledged as an outstanding science writer . Thi s book, on entropy and en ergy, will require the nonscientist to concentrate, but it's worth it. Gleick, James . Chaos: Making a New Science. Abacus , 1987. A n excellen t intro duction t o chaos , spice d wit h anecdote s abou t those wh o hav e contribute d t o the theory. Honderich, Ted. How Free Are You? Oxford Universit y Press, 1993 . A really clear discussion o f the problem of determinism. Mandelbrot, Benoit . The Fractal Geometry of Nature. W . H. Freeman , 1982 . Th e inventor of the term fractal reveal s the wonders of the fractal world. Ruelle, David. Chance and Chaos. Penguin Books, 1993. A first clas s work of popularization by a distinguished theoretica l physicist . Wilson, S. S. "Sadi Carnot," Scientific American, vol. 254 (1981): 134. Carnot, who more or less invented th e secon d law, could have been a TV "personality" ha d he lived today. Part Six Bannister, Rober t C . Social Darwinism: Science and Myth in American Social Thought. Templ e University Press, 1979 . Chronicles th e ris e o f the phenomenon in the United States, its origins in the work of Herbert Spencer, and its connections to eugenics and racism. Darwin, Charles . On the Origin of Species. Harvar d Universit y Press , 1975 . Facsimile of the first edition. This book hardly needs an introduction fro m me . Unless you are a naturalist, best taken in small doses . Dawkins, Richard. The Blind Watchmaker. Penguin Books , 1991. A superbly readable defense of Darwinism by a confirmed evolutionist an d atheist . A model of scientific popularization . Gosse, Edmund. Father and Son. Penguin Books , 1989. A classic Victorian autobiography, which includes a touching account of one man's unsuccessful struggle to accommodate both his religious faith and the new doctrine o f Darwinism. Kamin, Leon. The Science and Politics of IQ. Wiley, 1974. A sober, reasoned book that has had much influence on sober, reasonable people. Kitcher, Philip. Abusing Science: The Case Against Creationism. MIT Press, 1982. If you need ammunition agains t the creationists, yo u will find plenty here. Lucas, J. R. Wilberforce and Huxley, A Legendary Encounter. Historical Journal, 22(1979): 313 . Agains t my principles I include a n article i n a learned journal. My reason is that thi s accoun t o f the championshi p figh t suggest s that it ende d nearer a draw, rather than the knockout usually attribute d to Huxley.

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Miller, Jonathan. Darwin for Beginners. Random House, 1982. The doctor who became a theater directo r occasionally return s to his roots, in this case producin g an amusing popular book illustrated wit h cartoons. Olby, Robert. The Path to the Double Helix. University o f Washington Press, 1975 . A very thorough analysis of the differen t trail s that lead to the great discovery. Tennyson, Alfred, Lord . In Memoriam. Norton, 1973. Apart from th e famous poem this editio n include s a wide rang e o f critical essays , includin g discussion s o f the effec t o f mid-Victorian scienc e o n th e poe m an d o n th e poet , wh o wa s a friend o f Darwin. Watson, James . The Double Helix. Weidenfel d and Nicolson , 1968 . Th e stor y of one of the majo r advance s in the history o f science a s told by one of the men responsible. Fascinatin g science , but not always completely fair when i t comes to personal matters . If you want th e stor y as Crick might have told it see the book by Olby. Part Seven

Badash, Lawrence . "Werner Heisenber g and th e Germa n Atomic Bomb. " Physics and Society, 16(1987) : 10 . Some clai m tha t h e deliberatel y slowe d dow n th e project, others say not. Perhaps w e will never know. Boscovich, R . A Theory of Natural Philosophy. Translatio n o f the 176 3 edition . • MI T Press, 1966. Plenty of interesting raisins in this imaginative text . Einstein, Albert, and Leopol d Infeld. The Evolution of Physics. Simo n and Schus ter, 1967. Originally published i n 1938 , this is a lively and comprehensibl e his tory of the main theories in physics, with a touch of philosophy throw n in . Feynman, Richard. The Character of Physical Law. Penguin Books, 1992. Feynman was a genius—and he knew it. He was one of the most gifted physicist s an d explainers o f physics o f the pas t decades . Thi s boo k discusse s genera l issue s i n physics and also shows us how Feynman's brilliantly intuitive mind worked. Hey, Tony , an d Patric k Walters . The Quantum Universe. Cambridg e Universit y Press, 1987 . A visually attractiv e an d absorbin g accoun t o f the histor y o f th e quantum theory, with emphasis o n its role in particle physics . Weinberg, Steven. The Discovery of the Subatomic Particles. W. H. Freeman & Co., 1990. Writte n fo r nonscientists . Primaril y th e stor y (well-told ) of the proton , neutron an d electron. Quarks barely get a mention. Part Eight

Barrow, J. D. and F . J. Tipler. The Anthropic Cosmological Principle. Oxfor d Uni versity Press, 1986 . Tr y reading thi s and se e whether i t convinces yo u that th e universe was designed for man. Einstein, Albert , an d Pete r Smith . Relativity: The Special and General Theory. 1917. I f you ca n ge t hold o f it, this i s relativity straigh t fro m th e ma n himself . The special theory in particular i s lucidly explained . Gribbin, John. In Search of the Big Bang. Corgi, 1987. Gribbi n is a well-known an d effective popularizer . Lovelock, James. Gaia. Oxford Universit y Press , 1982 . A book by the originato r of

Annotated Bibliograph y |

the theory . A rich sourc e o f information o n plane t Earth , although personall y I'm not convinced by the basic idea behind Gaia. Miller, Ron, and Willia m K. Hartmann. The Grand Tour: A Traveller's Guide to the Solar System. Workma n Publishing , 1981 . Lavishl y illustrate d wit h pho tographs and spectacular graphics . Pais, Abraham . Subtle Is the Lord. Oxford Universit y Press, 1982 . Thi s i s a n au thoritative descriptio n o f Einstein's work , wit h considerabl e referenc e to hi s personal life . A layman will fin d som e parts obscur e an d ma y ge t more out of the book by Clifford. Will. Weinberg, Stephen . The First Three Minutes. Fontana , 1983 . Weinber g is a Nobel Prize-winning theoretica l physicis t wit h an easy writing style . Thi s accoun t of the Big Bang has been overtaken by subsequent theory but remains a good overall pictur e o f the conventiona l pictur e o f the Bi g Bang afte r th e firs t one-hun dredth of a second. Will, Clifford . Was Einstein Right? Putting General Relativity to the Test. Basi c Books, 1986 . Part Nine Broad, William, and Nichola s Wade. Betrayers of the Truth. Simon an d Schuster , 1982. The authors revel in cases of scientific fraud an d claim that the scientific establishment i s no t equippe d t o detec t fraud . The y ten d t o wildl y overstat e their case , but the incidents the y discuss mak e uncomfortable reading for a professional scientist. Carson, Rachel. Silent Spring. Houghton Miflin, 1963 . A monument to her fight for ecological sanit y i n a countr y wher e bi g business didn' t wan t t o kno w abou t anything but profits. Hoffmann, Roald . The Same and Not the Same. Columbia University Press, 1995. The author i s a Nobel Prize-winning chemist , with a poet's eye . This delightful book of short essay s linking the scientific and humanistic worlds is a good book to curl up with. Holton, Geraldo. Science and Antiscience. Harvard University Press, 1994. A distinguished autho r skillfully undermines thos e antiscientists whose case is built on unreasoning prejudice . Johnson-Laird, Philip. The Computer and the Mind. Fontana Press, 1993. Despite my avoidanc e of the natur e of the mind , I canno t resis t recommendin g thi s readable, but no t alway s easy , book on mentality becaus e i t is an important il lustration o f the effec t o f science (i n th e guis e o f the electroni c computer ) on man's image of himself. Maxwell, Nicholas . From Knowledge to Wisdom. Oxfor d Universit y Press , 1984 . The author contends that the fac t that science is divorced from ethica l values is not a point in its favor but a guarantee of disaster. I disagree, but you may think otherwise. Morgan, Michael , Josep h Moran , an d Jame s Wiersma . Environmental Science. William C . Brown, 1993. A wide-ranging, well-illustrate d discussio n o f the en vironment and the dangers it faces. Olsen, Richard G., ed. Science as Metaphor: The Historical Role of Scientific Theo-

517

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d Bibliography

ries in Forming Western Culture. Wadsworth, 1971. A collection of generally absorbing essay s that cover s a wider rang e than thi s book sinc e i t include s psy chology. Russell, Bertrand. Why I Am Not a Christian. Routledge, 1992. Not too relevant t o this book , apart fro m a discussion o f determinism, but ho w luck y th e secula r are to have this sharp-witted iconoclas t on their side . Russell, Bertrand. A History of Western Philosophy. Allen an d Unwin , 1961 . Lively, hold s th e reader , but hasn' t muc h t o sa y abou t moder n philosophers . M y professional philosophe r friend s tel l me that Russell was sometimes too sure of himself, but don't let them put you off . Ziman, John . An Introduction to Science Studies: The Philosophical and Social Aspects of Science and Technology. Cambridg e University Press, 1985 . A n im pressive survey.

Index

a-particles, 140,146, 301 Academie Royale des Sciences, 61,148 Acceleration, 38f f Accelerators, 402, 411, 494 Accumulator, 124 Acquired characteristics, inheritanc e of, 270,287 Adams, Henry Brooks (1838-1918), 230 Adams, John (1735-1826), 61 Addison, Joseph (1672-1719) , 62 Advancement of Knowledge (Bacon) , 51 Aeschylus (525-45 6 B.C.) , 177, 485 Aesop (6th cent. B.C.) , 254 Agamemnon (Aeschylus), 37n Agassiz, Jean-Louis (1807-73) , 25 8 Age of Reason (Paine), 60 Air resistance, 8 Albert, Princ e (1819-61), 124,128 Albertus Magnus (c.1200-1280), 180 Alchemy, 103,113ff, 149 Aldrin, Edwin (Buzz), 39 Alfred the Great (849-99), 17 6 Algarotti, Francesco (1712-64) , 56 Alpher, Ralph, 469 Al Qazwini (c.1203-83) , 69 Altaian, Sidney, 347 Alva, Duke of (1508-82), 203 American Academy of Arts and Sciences, 6 1 American Philosophical Society , 61 Amino-acids, 125,163 Amp, uni t of electric current, 82, 88n Ampere, Andr6-Marie (1775-1836), 72, 88ff, 93,108 , 123 Anaximander (c.610-54 6 B.C.), 135,169 Anaximenes (c.585-52 8 B.C.), 135,169 Anderson, Carl, 376, 401, 427 Anderson, Hans Christian (1805-75) , 87 Anderson, W. French, 309 Andromeda nebula, 453 Aniline dyes , 125 Anselm (1033-1109), 53 Anthropic Principle, 473

Antibodies, 164 , 332 Anticipations (Wells) , 291 Antileptons, 403 Antimatter, 37 7 Antimuon, 401 Antiproton, 377 , 403 Antiquark, 403 Apollo 11, 32 Apology for Raymond Sebond (Montaigne), 51 Aquinas, St. Thomas (1225-74), 31ff, 35, 53,180 Arago, Dominique (1786-1853), 88,121, 193 Archimedes, 485 Arian heresy, 59 Aristarchus o f Samos (3rd cent. B.C.), 282 Aristotle (384-322 B.C.) , xiii, 16 , 23, 29, 31, 33, 43, 46, 52, 54, 57, 62,105, 116,136,170, 180. 253 , 256, 288, 319, 338,463,497n Armstrong, Neil, 30, 32, 39 Arnold, Matthew (1822-88) , 28 7 Artificial intelligence , 336 Artificial life , 33 6 Aspect, Alain, 397, 427 Asteroids, 249, 340, 445ff; Earthcrossers, 445 Atom, structure of , according to Bohr, 364ff Atomic bomb, 146 Atomic nucleus, 139ff ; unstable nuclei , 146ff Atomic number, Z, 151 Atomic theory, 136f f ATP, 323 , 326 Attila (c.406-53) , 175 Attractors, 244 Aubrey, John (1626-97), Brief Lives, Descartes, 15; Bacon, 17n Auden, Wystan Hugh (1907-73), 69, 418, 479 , 489

520

Index Averroes (b.1126), 136 Avery, Oswald Theodore (1887-1955) , 293 Avicenna (980-1037) , 256 Avogadro, Amadeo (1776-1856), 120 Ayer, A.J. (1910-89), 500, 502 |3-rays, 146, 30 1 Babbage, Charles (1792-1871) , 120,122 Back to Methuselah (Shaw) , 277 Bacon, Francis (1561-1626), 15ff, The Great Instauration, 17, Novum Organum, 17, 21, 25, 44, 51, 52, 54, 55, 58, 63, 66, 69,115,136,138, 150, 183, 184 , 444, 482, 490n, 496n Baekeland, Leo (1863-1944), 165 Bagehot, Walter (1826-77), 285-29 0 Bagley, William, 313 Bahrdt, Karl (1741-92), 59 Balmer, Joseph (1825-98) , 366 Bardeen, John, 100 Barry, Dave, 251 Baryons, 403 Bases (components o f DNA), 29 3 Bastian, H.C. (1837-1915), 350 Baudelaire, Charles (1821-67), 449n Bayle, Pierre (1647-1706), 52 Beckett, Samuel, 490 Becquerel, Antoine-Henri (1852-1908) , 140 Beginnings of Life (Bastian) , 350 Bell, Alexander Graha m (1847-1922) , 123 Bell, John, 397 Bentham, Jeremy (1748-1832), 286 Berg, Alban (1885-1935), 490 Berkeley, Bishop Georg e (1685-1753), xvi, 21, 22, 46, 419ff, 50 5 Bernal, John Desmond (1901-71) , 496 Bernoulli, Daniel (1700-82) , 83, 202ff Berry, Michael, 23 9 Berzelius, Jons (1779-1848), 320 Big Bang, 226, 230, 236, 455, 464ff; Big Crunch, 230 , 471 Billy the Kid (William H. Bonney, 1859-81), 8 Binet, Alfred (1857-1911) , 313 Biotechnology, 307 Black-body radiation, 199 , 359 , 369 Black holes, 48, 460ff, 47 2 Blake, William (1757-1827) , 61, 69, 73, 74, 76,479,485,486

Boerhaave, Hermann (1668-1738) , 66 Boethius, Aniciu s Manliu s (480-524) , 175ff, 23 5 Bohr, Aage, 379n Bohr, Niels (1885-1962) , 38, 142, 357, 364ff, 375 , 379n, 383, 398, 498, 501 Boltzmann, Ludwig (1844-1906), 223n, 504 Bolyai, Janos (1802-60), 43 7 Borges, Jorge Luis (1899-1986), xv Born, Max (1882-1970), 374, 382, 385, 414 Boskovic, Rudjer Joseph (1711-87), 236, 412 Bothe, Walter (1891-1957), 143 Boullee, Etienne-Louis (1728-99), 5 6 Boyle, Robert (1627-91), 9, 25, 46, 54, 58n, 60, 74,103,114ff, 128,198n , 202, 259n , 495; Boyle's law, 9, 202, 204 Bradlaugh, Charles (1833-91), 130 n Brahe, Tycho (1546-1601), 44, 56, 442 Braque, Georges (1882-1963), 488, 490 Brecht, Berthold (1898-1956), 491 Bridgewater, Eighth Earl of (1756-1829), 337 Brillat-Savarin, Jean-Anthelme (1755-1826), 442 Brown, Robert, 201, 260 Brownian motion , 201f f Bruno, Giordano (1548-1600) , 495 Buckingham, Duke of (1628-87), 115 Buddha, Gautama (c.563-483 B.C.), 170 Buffon, Comt e George (1707-88), 63, 68, 258ff, 274 , 289 Bunsen, Robert (1811-99), 196 Buridan, Jean (c.1300-85), 136 Burke, Bernie, 469 Burns, Robert (1759-96), 61 Butler, Samuel (1612-80) , 116 Butler, Samuel (1835-1902) , 285 Butterfield, Herbert, 51 Byron, Lord (George Gordon) (1788-1824), 127 Cadbury company, 12 7 Cagliostro, Count (Giusepp e Balsamo) (1743-95), 75 Cairns-Smith, Graham , 346 Caloric, 210 Calvin, John (1509-64), 53 Camus, Albert (1913-60) , 77, 180, 502

521

Index

Candide (Voltaire) , 60 Cannizzaro, Stanisla o (1826-1910), 120 Carbon dioxide, 118,150,155 , 202, 319, 322, 324 , 343ff, 352 , 448, 48 1 Carlisle, Anthony (1768-1840) , 89 Carlyle, Thomas (1795-1881) , 72, 73 Carnot, Sadi (1796-1832), 222 Carson, Rachel (1907-64), 483, 487 Carter, Elizabeth (1717-1806), 56n Cartesian Meditations (Husserl) , 501 Cassirer, Ernst (1874-1945) , 491 Catalysis, 208 Catullus, Gaius (c.84-54 B.C.), 179 Cathode rays, 138f f Catholic Church, 14 , 53, 54, 63, 66, 254n, 310 Cavendish, Henry (1731-1810), 83 Cavendish Laboratory, 129,137,140, 144, 29 2 GBR, cosmic background radiation , 470ff Cech, Thomas R., 347 Cell theory o f life, 126 , 260 Cell division, 300 ; development o f organism, 326ff; Ho x genes, 327 Cell structure an d function, 325ff ; membrane, 325 ; nucleus, 32 6 Cepheids, 452f f Ceramics, 162 Ceres, 445 Chadwick, James (1891-1974), 144, 401 Chain o f Being, 497 Chakrabaty, Ananda, 316 Chambers, Robert (1802-71), 285n Chandrasekhar, Subrahmanyan, 2 9 Chaos, 233f f Chardin, Pierre Teilhard d e (1881-1955), 498 Chardonnet, Comt e Louis-Marie-Hilaire Bernigaud de (1839-1924), 125 Chargaff, Erwin , 294 Charge, electric; static , 82ff ; mobile, 83f f Charles I of Anjou (1226-85) , 8 6 Charles II, King (1630-85), 65,115 Chatelet, Marquise d u (1706-49), 56 Chaucer, Geoffrey (c.1340-1400) , 177 Chemical change , 206 Cherwell, Lor d (F.A. Lindemann) (1886-1957), 125 Chomsky, Noam, 30, 314, 50 3 Christ, Jesus (1st cent.), 170, 417 n Christian Virtuoso (Boyle), 114

Christianity as Old as the Creation (Toland), 59 Christianity not Mysterious (Toland) , 59 Christie, Linford, 378 Chromosomes, 126, 262; X and Y chromosomes, 262 , 265; crossingover, 266 Churchill, Winston (1874-1965) , 143 Cicero, Marcus (106-43 B.C.), 175 Clairaut, Alexis-Claude (1713-65) , 56 Clarendon laboratories, 130 Classification o f species, 256f f Clausius, Rudolf (1822-88), 214, 224, 429 COBE, cosmi c background explorer, 470 Cockcroft, John Douglas (1897-1967), 152 Codons, 298, 303 Color, in elementary particles , 404 Concorde, 7 Colbert, Jean-Baptiste (1619-83), 17 Coleridge, Samuel Taylor (1772-1834), 69, 71,108,109, 126, 218 n Communism, 5 On Computer, mechanical, 12 2 Comte, Auguste (1798-1857), 502 Condillac, Etienne de (1715-80), 63 Condorcet, Jean, Marquis de (1743-94) , 68, 76, 77, 288 Connors, Jimmy, 204, 211 Consciousness, xvi i Conservation laws , 84; for charge, 84; for matter, 118; fo r energy, 213; for mass and energy, 429 Control of organism's interna l environment, 327ff ; nervou s system , 330; hormones, 331ff ; defens e mechanisms, 331; antibodies, 33 2 Conversations in Chemistry (Marcet) , 89 Cooper, Leon, 100 Cope, Wendy, 109n Copernicus, Nicolau s (1473-1543), 16, 45, 53ff, 56 , 57, 105, 177 , 256, 282, 442

Corday, Charlotte (1768-93) , 67 Correns, Carl (1864-1933), 264 Cosmic rays, 302, 401, 487 Cosmology, 41, 442f f Cosmological Principle, 455, 470 Coulomb, Charles-Augustine (1736-1806), 82 Coulomb, unit o f electric charge , 82

522| Inde

x

Coulomb's law , 83, 372, 392 Council o f Trent (1551), 5 3 Courbet, Gustave (1819-77), 490 Covalent bond, 158 Cowper, William (1731-1800), 69, 74 CP violation, 468 Craig, John (d.1731), 35 Creationism, 227ff , 250 , 279, 283, 495 Creech, Thomas (1659-1700) , 179 n Cremonini, Cesar e (1550-1631), 16 Crewe, A.V. , 13 7 Crick, Francis, 105 , 292 , 349, 493 Critique of Pure Reason (Kant) , 18 Crookes, William (1832-1919) , 75, 154n, 290,495 Curie (Joliot-Curie), Irene (1896-1956), 144ff, 148 , 379 n Curie, Marie (1867-1934), 135, 140 , 144 , 148, 379 n Curie, Pierre (1859-1906), 140 Curtis, Heber, 452 D'Alembert, Jean (1717-83), 58, 502 Dalibard, Thomas Frangoi s (1703-79), 84 Dalton, John (1766-1844), 119ff, 125, 128 Daniell cell, 124 Dark matter, 472 Darwin Among the Machines (Butler), 285 Darwin, Charles Robert (1809-82), 19, 49, 122, 131ff, 264, 269ff, 282 , 289, 291,313,344,490,491 Darwin, Erasmus (1731-1802) , 61, 269ff , 288 Darwinism, 121,130ff ; socia l Darwinism, 131 , 289f f Das Kapital (Marx) , 94, 290n Davies, John (1569-1626), 177 Davisson, Clinto n (1881-1958) , 379 Davy, Humphry (1778-1829) , 72, 73, 89ff, 108 , 115n , 151 , 21 1 Dawkins, Richard, 348, 447 De Broglie, Louis (1892-1987), 378; equation, 379 , 390 De Consolations Philosophiae (Boethius), 176 De Corpore (Hobbes) , 235 De Historia Stirpium (Fuchs) , 253 De Homine (Hobbes), 235, 505 De Humanis Corporis Fabrica (Vesalius), 256

De Institutione Musica (Boethius) , 175 De La Tour, Maurice Quentin (1704-88), 65 De L'Esprit (Helvetius) , 67 De 1'Esprit des Lois (Montesquieu), 66 De Magnate (Gilbert) , 86 De Materia Medica (Dioscorides) , 253 De Quincey, Thomas (1785-1859) , 74, 486 De Rerum Natura (Lucretius) , 86,136, 179ff De Revolutionibus (Copernicus), 25 6 De Veritate (Herbert), 59 De Vries, Hugo (1848-1935), 264 DeCandolle, Augustin Pyram e de (1778-1841), 290 Decline and Fall of the Roman Empire (Gibbon), 61n Decline of the West, (Spengler), 230, 492 Deductive reasoning, 23f f Dee, John (1527-1608), 495 Defoe, Daniel (c.1660-1731), 62 Deism, 51, 59ff, 62 , 234, 499 Deimos, 237 Delacroix, Eugene (1798-1863), 42 Delille, Jacques (1738-1813), 50 Demiurge, 46 3 Democrates (c.460-370 B.C.) , 116,135, 136 Desaguliers, John Theophilus (1683-1744), 35 Descartes, Rene (1596-1650), xvii, llff , 21, 31, 33, 51, 53, 59, 63, 88, 115 , 116,143n, 172n, 198n, 203, 307, 320, 410,482,500 Descent of Man (Darwin) , 282, 313 Design Hypothesis, 33 7 Determinism, 103 , 233ff , 38 3 Devil (Satan), 13,15 DeW7s, The (Dostoevsky) , 291 Dewey, John (1859-1952), 503 D'Holbach, Baron Paul (1723-89), 57, 64,65, 75, 76,234 Dialogue concerning the Two Chief World Systems (Galileo) , 421 Diaper, William (1685-1717) , 257 Dicke, Robert, 469, 473 Dickens, Charles (1812-70) , 133, 490 Diderot, Denis (1713-84) , 25, 57, 58, 65, 66, 75, 76, 236, 269, 292 Diffraction, 193 ; o f X-rays, 193; of electrons, 37 9

523

Index

Diffusion, 20 2 Dioscorides, Pedanios (firs t cent . AD), 86n, 253 Dirac, Paul (1902-84), 81n, 376 , 401, 417 Discours de la Methode (Descartes) , 54 Discourse on the Sciences and the Arts (Rousseau), 69 Disordered (amorphous ) solids, 162 Dissenters, 128 Dissipative structures , 22 9 DNA; components of , 293; general structure of , 293; protein synthesis , 295; exon s and introns, 296 ; the genetic code, 298; instability, 302 ; recombinant DNA , 307,105,160, 164, 193 , 259 , 272, 279, 288, 292ff , 315,324,326,493 Donne, John (c.1572-1631), 54, 55, 72, 113,179n, 463,490 Doppler, Christian (1803-53) , 194 Doppler effect , 194 , 45 3 Dore, Gustave (1832-83), 133 Dostoevsky, Fyodor (1821-81), 290 Double Helix, 292ff , 499 Double Helix (Watson), 292 Dowland, John (c.1563-1626), 355, 490 Drude, Paul (1863-1906), 158 Dryden, John (1631-1700), 62,115 Duality, 380, 399 Dunne, J. W., 492 Diirer, Albrecht (1471-1528) , 255 Dyson, Frank Watson , 431 Earth, the, 443ff; earl y history, 340; magnetism of , 444 EGG, 85 Eddington, Arthur (1882-1944) , 389, 399,414,431,433,464, Edison Electric Illuminating Company , 124 EEC, 85 Ehdich, Paul (1854-1915), 126,164 Einstein, Alber t (1879-1955), xiii, 34, 48, 49, 81, 89, 91, 95, 101, 106 , 124, 132, 135, 169, 183 , 357 , 359ff, 374, 379, 383 , 387, 391, 395ff , 400, 417ff , 455,490,491,495,504 Einstein, Mrs., 430 Electric battery, 85 Electric current, 83ff , 123ff Electrical resistance, lOOf f

Electricity and Magnetism (Maxwell) , 94 Electrochemical reactions , 90f f Electron, 96; and magnetism, 97 ; angular momentum of , 364; g-factor, 393 ; 137ff, 392 , 401, 41 1 Electron gas, 158 Elemens de la philosophie d e Neuton (Voltaire), 55 Element, chemical, 116 , 150 ; transformation of , 152; man-made, 151,154; quantum mechanica l mode l of, 367ff ; synthesis of in stars, 458 Elementary particles, 401f f Elements, the Four, 113,116,149 Elements, the Five, 149 Elements (Euclid) , 53, 77 Elephant on the Moon (Butler), 116 Eliot, George (1819-80), 290 Eliot, Thomas Stearn s (1888-1965) , 486, 490, 49 1 Elizabeth I (1533-1603), 17, 86, 176 Elizabeth, Saint (1207-31), 35 Ellis, Havelock (1859-1939), 131 Ellis, William Webb, 269n Empson, William, 399 n Encyclopedie (Diderot , ed.), 58, 65ff, 76 , 108 Energy, 209ff Engels, Friedrich (1820-95), 133, 290, 342 Enlightenment, 50f f Entropy, 215ff, 223 , 351 Entropy (Rifkin) , 23 1 Enzymes; and evolution, 278 ; inhibitors, 328; effectors , 329,164 , 328 Enquiry into the Nature and Causes of the Wealth of Nations (Smith) , 74 Epicurus (c.342-270 B.C.), 17 9 Epistola Petti Peregrini de Maricourt (Peter the Pilgrim), 86 EPR experiment, 395f f Equilibrium, 218 , 221ff; dynamic, 22 8 Erasmus, Desiderius (c.1466-1536) , 255 Escape velocity, 48f f Essay Concerning Human Understanding (Locke], 50 , 51, 58, 63 Essay on Man (Pope) , 62, 63 Essay on the Cause and Phenomena of Earthquakes (Michell) , 460n Essay on the Principle of Population (Malthus), 270 Essays (Montaigne) , 51

524

Index Essays and Reviews (Various authors), 284 Estienne, Henry II (1528-98), 51 Ether, 198 Euclid (3rd-2nd cent. B.C.) , 53, 54, 77, 170, 175,433 Eugenics, 291 Eusebius, Bishop (5th cent.), 451n Evelyn, John (1620-1706), 11 5 Everett III, Hugh, 388 Evolution; time scale of, 274ff; manmade, 275; perversion of , 289ff; of DNA, 19 , 105, 257, 268ff, 30 1 Excellence of Theology (Boyle), 11 4 Expanding universe, 454f f Fabian Society , 291 Faith, 25 Faraday, Michael (1791-1867), 83, 87n, 89ff, 101 , 106 , 125ff , 133 , 169 , 413, 420n, 431, 491, 510; electric motor, 90; dynamo, 90; transformer, 90 Faraday effect, 9 3 Fat Sumo, the curse of, defined, 10 Father and Son (Gosse) , 284 Fermi, Enrico, 146 Feydeau, Georges (1862-1921), 492n Feyerabend, Paul, 19,177, 504 Feynman, Richard, 357, 378, 389, 393, 425,491 Fields, xvii, Electromagnetic, 19; magnetic, 87n, 91ff; electric, 91ff; quantum field theory, 411 Finnegans Wake, 403n First Three Minutes (Weinberg) , 496 Fischer, Bobby, 494 Fisher, R. A. (1890-1962), 265 Fission, nuclear, 146 Flammarion, Camille (1842-1925), 44 9 Flat-Earth theory, 19 Flaubert, Gustave (1821-80), 59 Flavor, of quarks, 405 Footprints of the Creato r (Miller), 283 Force, 29ff; electromagnetic , 81 , 87,102, 393; line s of, 91; van der Waals, 159, 406; strong , 404, 406; weak, 408ff ; electro-weak, 408; centrifugal, 419 Foucault, Jean-Barnard-Leon (1819-68), 127,420 Fourier, Jean-Baptiste (1768-1830), 67 Fourth dimension, 43 3 Fowler, Willy, 459 Fox, Sidney , 34 3

Fractals, 248f f France, Anatole (1844-1924), 417n Frankenstein (Mar y Shelley), 127 Franklin, Benjamin (1706-90), 60 , 61, 75, 82, 84, 87, 124n, 129, 413 Franklin, Rosalind (1920-58) , 292f f Frauenhofer, Joseph von (1787-1826), 194 Free radicals, 98 Free will, 234ff, 39 1 Frege, Gottlob (1848-1925), 500 French Revolution, 67ff, 73ff , 117,119 Fresnel, Augustine Jean (1788-1827) , 193 Freud, Sigmund (1856-1939), 358 Friedmann, Alexander (1888-1925), 464 Frisch, Otto, 146 Froben, Johann (1460-1527), 255 Frost, Robert (1874-1963), 456 Fuchs, Leonhard (1501-66), 253 Fundamental Laws of Arithmetic (Frege), 500 Futurist Manifesto (Marinetti) , 488 y-rays, 96,146, 188, 301 , 401 G, the gravitational constant, 43, 73 Gaia, 446 Galen (c.131-200), 113, 254 , 256 Galilean invariance, 422 Galilei, Galileo (1564-1642) and Inquisition, 14n ; trial, 15, 25, 31, 32, 33n, 38ff , 43 , 47, 53ff , 56 , 57, 74, 95, 101, 104 , 105,114, 118,176, 235, 260, 282 , 284, 418ff, 448, 451 Galilei, Vincenzo (d.1591), 176 Gallon, Francis (1822-1911), 291, 311 , 313 Galvani, Luigi (1737-98), 84ff , 107,123 , 156 Gametes, 263 Gamow, George, 455, 469 Gases, 3ff Gassendi, Pierre (1592-1655), xv , 31, 203,421 Gauss, Karl Friedrich (1777-1855) , 43 7 Gay-Lussac, 120 Geiger, Hans (1882-1945), 140 Geller, Uri, 495 Gell-Mann, Murray, 132, 403 Gemma (Melena), 131 Gene therapy, 309f f General History of Nature (Kant) , 452n

525

Index

Genes, 262ff; dominan t an d recessiv e genes, 264ff ; repressers, 302; inducers, 304; cloning, 307ff ; Hox genes, 327; 'death gene,' 335; 'life gene,' 335 Genetic code, 298ff, 49 6 Genetic engineering, 307 Genetic Privacy Act, 316 Genome, 272, 496; sequencing o f human, 302 , 316f f Geometry: Euclidean, 433, 436ff; non Euclidean, 436ff Germ theory of disease, 12 6 Germer, L.H., 379 Ghiorso, Albert, 151 Gibbs, Josiah Willard (1839-1903), 129 Gibbon, Edwar d (1737-94) , 60, 61n Gilbert, William (1544-1603), 86,128, 444 Gladstone, William Ewart (1809-98), 130, 285 Glashow, Sheldon, 408 Gluons, 407 Gmelin, Johann, 163 Goddard, Henry, 313 Godel, Kurt (1906-78), 50 6 Goethe, Johann Wolfgang vo n (1749-1832), 69ff, 95n , 109, 184n , 230, 270,292,378 Goldsmith, Oliver (1728-74) , 65 Goncourts, the: Edmond de (1822-96 ) and Jules de (1830-70), 12 7 Goryu, Asada (1734-99), 45 n Gosse, Edmond (1849-1928) and Philip (1810-1888), 130, 284 Graham, Dr.. 86 Graviton, 407 Gravity. See Universal gravity Gray, Asa (1810-88), 271 Greenhouse effect , 36 8 Gregory, Horace, 179 Greuze, Jean (1725-1805), 76n Griffith, Fred , 293 Grimm, Baron de, Frederic-Melchior (1723-1807), 61 , 63 Grotius, Hugo (1583-1645), 59n Group theory, 409 Guericke, Otto von (1602-86), 9 , 83 Guevara, Che (Ernesto) (1928-67), 7 7 Gulliver's Travels (Swift) , 62 , 203 GUT, Grand Unified Theory, 465 Guth, Alan, 466, 471

Haber, Fritz (1868-1934), 208 Hadrons, 403ff Haeckel, Ernst (1834-1919), 287 Hahn, Otto (1879-1968), 146 Haldane, J. B. S. (1892-1964), 268 , 342, 353 Halley, Edmund (1656-1742), 42 , 46, 56, 442 Halley's comet, 42 Hallwachs, Wilhel m (1859-1922), 36 1 Halske.J. G.,123 Hamilton, Lady (c.l761-1815), 86 Hamilton, William Rowan (1805-65), 72 Harding, Sarah, 106 Hardy, Alister, 280n Hardy, Godfrey Harold (1877-1947) , 147, 485 Harriot (or Hariot), Thomas (1560-1621), 42 Harve}?, William (1578-1657) , 58n , 128 Le Hazard et la necessite, (Monod), 350 Haydon, Benjamin (1786-1846), 73 Hawking, Stephen, 31 , 412, 462, 470, 473,475 Hegel, Georg Wilhelm Friedric h (1770-1831), 71,126 Heidegger, Martin (1889-1976), 501 Heine, Heinrich (1797-1856), 7 0 Heisenberg, Werner (1901-76), 376, 389, 391, 396 , 411, 414 , 490, 491, 502 Hell, Maximilian (1720-92) , 87 Helmholtz, Hermann von (1821-94), 95, 212,274,447 Helvetius, Claude Adrian (1715-1835), 67 Hemophilia, 266 Henry, Joseph (1797-1878), 87, 90 Herbert of Cherbury, Lord (1583-1648), 59 Hereditary Genius (Galton), 313 Herepath, John (1790-1868), 204 Herman, Robert, 469 Hermes Trismegistus, 114 Herschel, William (1738-1822), 188 , 448 Hertz, Heinrich (1857-94), 95,124,138, 188,198, 361, 504 Hess, Victor (1883-1964), 401 Higgs, Peter, 409 Higgs boson, 148, 409, 494ff Hippocrates (c.460-377 B.C.) , 254, 319 Histoire Naturelle (Buffon) , 63 , 258 Histona Stirpium (Fuchs) , 253

5261

Index

Historical and Critical Dictionary (Bayle), 52 History of the Corruptions of Christianity (Priestley), 119 Kitchener, Elizabeth, 68 HIV, 33 4 Hobbes, Thomas (1588-1679), 26, 53, 54,63, 77,235,250, 505 Homer (8th cent. B.C.) , 56 Hooke, Robert (1635-1703), 9, 46, 55, 74, 115 , 122 , 158, 212 , 260, 278n Hooker, Joseph Dalton (1817-1911), 283 Horace (65-8 B.C.) , 180 Hormones, 331f f Hoyle, Fred, 341ff, 455 , 459 Hubble, Edwin (1889-1953), 453ff Hubble's law, 454 Hughes, Ted, 109 Humanitarianism, 13 3 Hume, David (1711-77), 20, 22, 35, 49, 52,56,236,502,503 Humours, the Four, 113 Hunter, William (1718-83) , 255 Hupfeld, Herman, 490 Husserl, Edmund (1859-1938), 501 Hutcheson, Francis (1694-1746), 286 Hutton, James (1726-97), 274 , 446 Huxley, Aldous (1894-1963), 501 n Huxley, Thomas (1825-95) , 283ff, 285 , 286,289,320,324 Huygens, Christiaan (1629-93), 17, 55, 58n, 74,115, 183,190,198 Hydrodynamica (Bernoulli) , 203 Hydrogen bond, 159 Hypnosis, 8 7 Hypothetico-deductive metho d , 23 Immune system, 332 ; phagocytes, 332; lymphocytes, 332 In Memoriam (Tennyson) , 285 Individual, a s hero, 72 Inductive reasoning, 17ff Industrial Revolution, 68 , 73, 74,122ff , 483; secon d Industria l Revolution , 123ff; the third, 510 Inertia, 34f f Inertial frames, 421 Infeld, Leopold (1898-1968), 95 Inge, Dean, 488 Invariants. Se e Relativity Invisible College , 115 lonesco, Eugene, 490

Ionic bond, 157 Ions, 96ff, 15 7 IQ, 312ff IR (infra-red) radiation, 96,189 Irrational numbers, 173 , 240 Irreversible processes , 21 5 Isotopes, 152 Jacobins, 67 James, William (1842-1910) , 230, 503 James I (1556-1625), 17, 86, 490 Japp, F. R. (1848-1925), 320 Jeans, James (1877-1946), 340 Jefferson, Thoma s (1743-1826), 55 Jenner, Edward (1749-1823), 133 Jesuits, 65f f Jimenes, Juan Ramon (1881-1958), 184 Jodrell Bank, 451 Johanson, Donald, 13 In Johnson, Ben (Sprinter), 7 Johnson, Samuel (1709-84) , 35, 62,123 Joliot (Joliot-Curie) Frederic, 144ff , 14 8 Joshua (13th cent . B.C.), 19 0 Joule, James Prescott (1818-89), 209, 211,213 Joule, unit o f energy, 209 Joyce, James (1882-1941), 403n, 442, 490

Juliette (de Sade), 66 Jung, Carl Gustav (1875-1961), 149 Jupiter, 249 , 448; and Galileo, 1 6 K, the electrostati c constant, 83 Kafka, Franz, 488 Kamerlinghe Onnes , Heike (1853-1926), 100 Kamin, Leon, 313 Kandinsky, Wassily (1866-1944), 490 Kant, Emmanuel (1724-1804) , 35, 58, 76, 77, 87, 106ff, 274 , 371, 408, 452, 499, 50 2 Kaufmann, Walter (1871-1947), 138, 503 Keats, John (1795-1821), 73, 126 Keill, John (1671-1721), 418 Kelvin, Lord (William Thomson ) (1824-1907), 93,198 , 212, 339 Kepler, Johannes (1571-1630), 16, 44, 56, 57, 58n, 86, 104, 118, 442 , 495 Kepler's Laws, 45 Kinetic Energy, 209 Kinetic Theory o f Gases, 24, 206 Kingsley, Charles (1819-75), 284, 285

527

Index

Kirchhoff, Gusta v (1824-87), 196 Koch, Robert (1843-1910), 126 Koch snowflake, 248 Koestler, Arthur, 450 Kolbe, Adolph (1818-84), 320 Kuhn, Thomas S. , 22,103,105ff, 504 La Barre, Jean-Frangois Le Febvre, Chevalier de (1747-66), 6 0 Lagrange, Joseph (1736-1813), 67 Lakatos, Imre, 106 La Mettrie, Julien Offroy d e (1709-51), 57,66,234,250 Lamarck, Jean-Baptiste de (1744-1829) , 269,278,287 Lamborghini, 7 Laplace, Pierre-Simon (1749-1827) , xiii, 61,67,234,236,237,460 Larkin, Philip, 486, 499n Lasers, 192 Laue, Max van (1879-1960), 193, 292 Lavater, Johann (1741-1801), 71 Lavoisier, Antoine-Laurent (1743-94) , 67, 74, 117ff, 120, 125, 210, 295, 429 Lawrence, David Herbert (1885-1930), 485 Leavis, F.R., 492ff Leavitt, Henrietta ((1868-1921), 452ff Lederberg, Joshua, 317 Lederman, Leon, 412, 494 Ledoux, Claude-Nicolas (1736-1806), 117 Leeuwenhoek, Antony van (1623-1723) , 58n, 115, 259 Leibniz, Gottfried Wilhelm (1646-1716) , 21, 46, 52, 58, 60, 64, 65n, 107, 135, 357,500 Lely, Peter (1618-80), 490 Lemaitre, Georges (1894-1966), 455, 464 Lenard, Philipp (1862-1947) , 361 Lenin, Vladimir Ilyich (1870-1924), 77 Lennon, John, 321n "Lensing,"432,472 Leonardo da Vinci (1452-1519), 15, 255 Lepeshinskaia, Olga , 342n Leptons, 403ff, 4007f f Lessing, Gotthold Ephraim (1729-81), 56 Lettres Philosophiques (Voltaire), 55 Lettres surles Anglais (Voltaire) , 55 Leucippus (5th cent. B.C.) , 136 Lewis, Carl, 7, 33 Lewis, Gilbert Newton (1875-1946), 149

L'homme machine (de La Mettrie), 57 L'hopital, Marquis d e (1661-1704), 37 Lichtenberg, Georg Christof (1742-99) , 25,85 Liebig, Justus von (1803-73), 12 5 Life, 226ff , 251ff , 319f f Light; as an electromagnetic wave, 95; invariance of speed of , 187, 423f:f; bending of , 431 Limit cycle, 246 Lind, James (1736-1812), 68 Linnaeus, Carolus (1707-78), 257 , 269 , 270 Liquid crystals, 165f f Lisbon earthquake, 60 Literary and Philosophical Societ y of Manchester, 61 Lobatchevsky, Nicholas (1792-1856) , 437 Locke, John (1632-1704), 17 , 50, 51, 55, 58, 63, 65, 69, 74, 126,149, 204, 463, 500, 504, 505 Lodestone, 81 Lodge, Oliver Joseph (1851-1940), 75, 495 Logical Positivism, 139, 502ff Logistic map, 242 Loman, Willy, 5 Lonsdale, Kathleen, 86n Lotka-Volterra model, 245 Louis XIV (1638-1715), 114 Louis XV (1710-74), 66 Louis XVI (1754-93), 75,117 Lovelace, Ada (1815-52), 122n Lovelock, James, 446 Lowell, Percival (1855-1916), 449 Lucas, Tony, 178 Lucretius (c.96-55 B.C.), 68, 86,116,136, 178ff "Lucy," 131n Lunar Society, 61 Luther, Martin (1483-1546), 14, 53 Luzzi, Mondino dei (c.1270-1326), 254 n Lyell, Charles (1797-1875), 130 , 274 , 284, 285 Lyon, Amy . See Lady Hamilton Lyrical Ballads (Wordsworth), 72 Lysenko, Trofim (1898-1976) , 288, 342 Mach, Ernest (1838-1916), 34, 139, 420, 427,502,503 Mach's Principle, 42 0

5281

Index

Machiavelli, Niccolo (1469-1527), 1 7 Madonna, xv Magellan, Ferdinand (c.1480-1521) , 452 Magellanic clouds, 452 Magic Mountain (Mann) , 71n Magnetism, 81, 86, 97 Magnetic monopole, 81n Maillet, Benoit de (1656-1738), 269 Malpighi, Marcello (1628-94), 260 Malthus, Thomas Robert (1766-1834), 131,270 Man versus the State (Spencer) , 131 Mandelbrot, Benoit, 248 Manet, Edouard (1832-83), 417 Mann, Thomas (1875-1955), 71n, 319 Man's Place in Nature (Chardin) , 498 Mao Tse-tung (1893-1976), 104 Marat, Jean-Paul (1743-93), 67,11 7 Marcet, Jane (1769-1858), 89 Marconi, Guglielmo (1874-1937), 18 8 Marcus Aurelius (121-180), 254 Margulis, Lynn, 341, 446 Marie-Antoinette (1755-93), 109 n Marinetti, Emilio (1876-1944), 488 Marlowe, Christopher (1564-1593) , 113 Mars, 40, 237, 249, 344; canals on, 448 Mars and its Canals (Lowell), 449 Marsden, Ernest, 140 Martin, George, 174n Martyrdom of Man (Reade) , 121 Marx, Karl (1818-83), 94,104, 290 Mary Stuart (Schiller), 71 Mass: apparent, 427; and energy, 429 Matisse, Henri (1869-1954), 490 Mattioli, Pierandrea (1501-77) , 25 3 Maupertuis, Pierr e de (1698-1759), 49, 55,269 Maxwell, James Clerk (1831-79), 19, 83, 94ff, 101,109 , 124,127,129, 132, 169,188, 198, 206, 232, 341n, 393 , 460, 490 Maxwell's equations, 94ff , 222 , 357, 372, 393, 499 ; and electromagnetic waves , 95, 191,422 Mayer, Julius (1814-78), 212 McCarthyism, 104 McClintock, Barbara, 302 Mead, George Herbert (1863-1931), 289 Means, arithmetic an d harmonic, 172 Measurement, i n quantum mechanics , 380ff Mecanique analytique (Lagrange) , 94

Mecanique celeste (Laplace), 61 Medici, Cosimo II de (1590-1621), 448 Meiosis, 267 Meitner, Lise (1878-1968), 147 Melanchthon, Philip p (1497-1560), 53 Melena, Elpis (1818-99), 131 Mendel, Gregor Johann (1822-84), 26 2 Mendelian inheritance , 262f f Mendeleev, Dimitri (1834-1907), 153f f Mendelssohn, Barthold y Felix (1809-47), 49 0 Mendoza, 312 Merchant of Venice (Shakespeare), 177 Mercury, 41 Mersenne, Marin (1588-1648), 172n Merton, Robert, 58n Mesmer, Friedrich Anton (1734-1815), 75,86 Mesons, 403 Metallic bond, 158 Metamorphoses (Ovid) , 175 Metaphysical Foundations of Knowledge (Kant) , 107 Metaphysical Society , 285 Metric system, 67 Metrodorus of Chios (5-6th cent. B.C.) , 51 Meziriac, Claude-Caspar de, 8n Michelangelo Buonarroti (1475-1564) , xiv Michell, John (1724-93), 46 0 Michelson, Albert (1852-1931), 129, 198; Michelson-Morley experiment , 198,420 Microwaves, 96 Miescher, Johann Friedrich (1844-95) , 293 Milky Way, 452, 456 Mill, John Stuart (1806-73) , 286 Miller, D.C. (1866-1941), 198 Miller, Henry (1891-1980), 479, 487 Miller, Hugh (1802-56), 283 Miller, Stanley, 343, 346 Millikan, Robert Andrews (1868-1953) , 139,362 Milton, John (1608-74), 69, 241 Minkowski, Herman n (1864-1909) , 417 Mitchell, Adrian, 169 Mitchell, Mari a (1818-89), 491 Mitochondria, 279 , 326 Modern Utopia (Wells) , 291 Molecular shape, 164 , 332

Index

Molecules, 3ff; motion of, 6; average speeds, 7 ; collisons, 8,154f f Momentum, 37 8 Monod, Jacques, 350 Monodologia physica (Kant), 58 Montaigne, Miguel de (1533-92), 51 Montesquieu, Charle s de Secondat , Baron de (1689-1755), 66, 289 Montmor Academy, 115 Montmor, Henri-Louis Habert de (c.1600-79), 115 Moon, 39, 86,118, 210, 237, 340 Morley, Edward (1838-1923), 198 Morris, William (1834-96) , 123n Morse, Samuel Finle y Breeze (1791-1872), 123 Morveau, Guyton de (1737-1816), 153 Moseley, Henry (1887-1915), 142 Moses, 59 Motion: atomic and molecular, 202 ; and chemical change , 206 MRI (magnetic resonance imaging) , 99 Muir, Edwin (1887-1959), 218 Muon, 401,427 Murray, Les, 41 Mutations, 267 , 272, 301 Nageli, Karl von (1817-91), 325 Napoleon Bonapart e (1769-1821), 61, 85,123 Nature of Space and Time, (Hawking andPenrose), 462 National Secular Society , 128 Natural selection, 27 3 Naturphilosophie, 70ff , 76 , 107ff, 212, 261, 287,408 Nazism, 50ii Necessity of Atheism (Shelley), 68 Neddermeysr, S., 401, 427 Nelson, Horatio (1758-1805), 86 Neptune, 249 Nero (37-68 A.D.), 253 Nerve activity, 126, 330; neurotransmitters, 33 0 Neutrino, 407, 472 Neutron, 96,144, 401, 405, 411 New Atlantis (Bacon) , 115,184,482,496n New Theory of the Earth, (Whiston), 443 Newman, Ernest (1868-1959), 131 Newton, Isaac (1642-1727), xiii , 9, 14, 29ff, 37ff , 42ff , 50-67 , 69ff, 79 , 93, 95 , 101, 103 , 106,114,115 , 126, 127,

529

176ff, 183,184,192 , 198, 203 , 204, 214, 224, 233, 234, 362, 393, 418ff , 428, 442, 448, 490, 493, 495, 504 newton (uni t o f force), 39 Newtonian mechanics , 19, 29ff, 41,105, 106, 220ff , 233 , 357, 371, 372 , 484, 499; defects in, 20 ; first law , 30ff , 203; second law , 37ff , 203 ; third law, 40, 15 3 Newtonianismo per le dame (Algarotti), 56 Nicholas I, Tsar (1796-1855), 129 Nicholson, William (1753-1815) , 89 Nicole d'Oresme, Bisho p (c.1330-82), 114 Nietzsche, Friedric h Wilhel m (1844-1900), 233, 277 Nivernais, Due de (1716-98), 117 NMR (nuclear magnetic resonance) , 98 Noddack, Ida, 146 Non-locality, 398 Nostradamus (1503-66) , 509 Novum Organum (Bacon), 17, 490 Nucleus, atomic , 96,139f f Oakshotte, Michael, 493 Oersted, Hans Christian (1777-1851) , 72, 87ff , 98 , 106ff , 16 9 Ohm, E.A.,469 O'Keefe, Georgia, 257 Omphalos (Gosse) , 284 On Scientific Method in Philosophy (Russell), 501 Oparin, Aleksandr (1894-1980) , 342 Oppenheimer, Robert, 482 Opticks (Newton) , 413 Oratorio de comparando certo in physicis (Boerhaave), 66 Orbitals, atomic, 374 Orchestra (Davies), 177 Order and disorder, 223 Organic chemistry, 163f f Orgel, Leslie, 347 Origin o f life, 339ff ; lif e fro m space , 341ff; abiogenesis , 342ff ; self organization, 350f f Origin of Modern Science (Butterfield) , 51 Origin of Species (Darwin) , 264, 271, 278, 282ff, 29 3 Ostwald, Wilhelm Friedric h (1853-1932), 119

Index

530

Ovid (c.43 B.C.-17 AD), 175, 446 Owen, Richard (1804-92), 283 Oxidation, 118 , 319 , 344 Ozone hole, 196 Paine, Thomas (1737-1809) , 60, 77 Paley, William (1743-1805), 337 Palmer, Samuel (1805-81), 73 Paracelsus (c.1493-1541) , 74, 75, 107, 116,255,495 Parthenogenesis, 30 4 Parallel universes, 38 7 Pascal, Blaise (1623-62), 456 , 509 Pasteur, Louis (1822-95), 87 , 126,133, 342n, 350 Patenting animals , 316 Pauli, Wolfgang, 411, 50 4 Pauling, Linus, 149, 292 Pearson, Karl (1857-1936), 291 Pease, E.R., 121 Penrose, Roger, 462 Pensees (Pascal), 456 Penzias, Arno, 469 Pepsi-Cola, 19n Pepys, Samue l (1633-1703), 58n, 46 Perelman, S.J. , 147 Perfect numbers, 171f f Periodic Table of the Elements, ISlff , 404, 409 Perkin, William Henry (1838-1907), 125ff Perkins, David, 314 Perpetual motion, 9 Perrin, Jean-Baptiste (1870-1942), 135 , 141 PET (positron emission tomography) , 147n Peter the Pilgrim, 86 Pfeffer, Wilhel m (1845-1920), 325 Phaedo (Plato), 175 Philips, Katherine (1631-64), 81 Philosophes, Les, 63ff, 75ff , 49 5 Philosophiae naturalis (Boskovic), 413 Philosophy, an d Science , 498f f Philolaus o f Crotone (5th cent. B.C.) , 177 Phlogiston theory , 117 Phobos, 40, 49, 237 Photoelectric effect , 360f f Photons, 361 , 393ff , 410 Photosynthesis, 32 2 Physics and Politics (Bagehot), 290 Physiologus (2n d cent. B.C.?) , 253

Piazzi, Giuseppe (1746-1826) , 445 Picasso, Pablo (1881-1973), 258, 488, 490 Piccard, Jacques, 180 Pirandello, Luig i (1867-1936), xvii Planck, Max (1858-1947), 132, 358, 363, 364, 504 ; Planck's constant , 36 0 Planck time, 465 Planets, 447f f Plato (c.427-34 7 B.C.) , 51, 52,170,174, 175, 184 Pliny the Elder (23-79), 157n Pliicker, Julius (1801-68) , 137 Pluto, 249, 449 Podolsky, Boris, 395ff Poe, Edgar Allen (1809-49), 339 Poincare, Henri (1854-1912) , 82,135, 220, 238ff, 49 1 Polanyi, Michael, 50n Polarization o f radiation, 194 , 38 1 Pollution, 48 1 Polymers, 163; man-made, 165f f Pompadour, Antoinette, Marquise de (1721-64), 65, 66 Pomponazzi, Pietro (1462-1525), 486n Pope, Alexander (1688-1744) , 56, 60n, 62, 7 3 Popper, Karl, 18ff, 25,105,108, 235, 289,475,503,504,506 Porta, Giambattista della (c.1540-1615), 20,180 Positron, 376, 392, 401, 411 Potential energy, 210 Pound, Ezra (1885-1973), 490 Pragmatism, 503 Pratt, Mike, 174 n Predictability, 240 Preformist theory, 260 Prelude (Wordsworth), 72, 77 Pressure, 203 Priestley, Joseph (1733-1804), 61, 64, 74, 83, 84, 118ff, 12 8 Prigogine, Ilya, 230 Principes de Philosophie (Descartes), llff, 3 3 Principia Mathematica (Newton) , 30, 34, 44, 46, 51, 56, 57, 60, 63, 71, 94, 106,126, 234, 236, 282, 413, 421, 433 Principia Mathematica (Russell and Whitehead), 501 Principles of Geology (Lyell), 28 5 Principles, The Three, 116

531

Index

Probability, 205 , 216ff; i n quantu m mechanics, 374f f Prometheus, 482 , 487 Prometheus Unbound (Shelley), 68 Proteins, 163; self-replicating, 348 Protestant Church , 53; German Protestants, 70 n Proton, 96,143,401,405 Prout, William (1785-1850), 142,143 Psychopathology of Everyday Life (Freud), 358 Ptolemy, Claudius (2nd cent. AD), 45, 56, 170, 442 Pulkovo observatory, 129 Pyrrho of Elis (4th cent. B.C.) , 5 1 Pythagoras (c.582-500 B.C.), 74, 103, 108, 128n , 170ff , 410 , 44 1 QCD, 407 QED, 393, 417 Quantum fiel d theory, 411 Quantum mechanics , 41, 357f f Quantization o f energy, 358; of angular momentum, 364 Quarks, 402, 403ff; confinement , 406 Quetelet, Adolphe, xi Quine, V.O., 505

Radio waves, 95,188 Radioactivity, 140; half-life of , 146 Radon 301, 487 Raleigh, Walter (c.1552-1618), 116 Ranelagh, Lady Katherine (1614-91), 114 Raspail, Frangois-Vincent (1794-1878), 260 Ray, Joh n (c.1627-1705), 257 Reade, William Winwood (1838-75), 121 Reality of the Quantum World (Shimony), 505 R6camier, Madame Julie (1777-1849) , 88 Receptors, 305, 325 Red Queen theory, 305 Red shift , 194 , 453f f Reductionism, 497f f Reid, Thomas (1710-96) , 47n Rejection of transplants, 33 4 Relative atomic weights, 120 Relativity, 19, 41, 393, 400, 402, 417ff; Special Theory, 424ff; Genera l

Theory, 48; 65, 376, 430ff, 437ff ; "white hole, " 464; invariants, 434ff ; events, 435; geodesies, 438 Renan, Joseph Ernest (1823-92), 169 Reproduction: sexual, 304; parthenogenetic, 304 Republic (Plato) , 175 Republic (Cicero) , 175 Respiration, 118 Ribosome, 299 Richardson, Samuel (1689-1761), 76n Richter, Georg (1711-53), 84 Riddle of the Universe (Haeckel) , 287 Riemann, Bernhard (1826-66), 43 7 Rifkin, Jeremy, 231 Ritter, Johann (1776-1810), 87n, 90, 109n,188 RNA, 276; ptRNA, 297; mRNA, 297; tRNA, 298; RNA as a catalyst, 347 Robertson, Howard, 454, 464 Robinson, Nicholas (c.1697-1775), 35 Rockefeller, John D. (1839-1937), 131 Roe, Ann , 314 Rontgen, Wilhelm Konrad (1845-1923), 124ff, 188 , 29 2 Roman de la Rose, 177 Romanticism, 70f f Rosen, Nathan, 395f f Rousseau, Jean-Jacques (1712-78), 54n , 55,57,65,69, 71, 76, 77 Royal Society, 61, 62, 85,115ff, 122, 148,211,260,431 Ruelle, David, 249 Ruskin, John (1819-1900), 130, 285 Russell, Bertrand (1872-1970), 215 , 236, 487, 489 , 500, 501 n Rutherford, Ernest (1871-1937), 135 , 139ff, 147,152 , 362, 406, 460, 482 Ryle, Martin, 493 Sacred Wood (Eliot) , 491 Sade, Marquis de (1740-1814), 57, 66 Saikaku, Ihara (1642-93), 451 Salarn, Abdus, 408 Salisbury, Robert , Marquess of (1830-1903), 133 Salts, 157 Sanchez, Francesco (1552-1632), 5 1 Sandemanians, 108 Sanger, Frederick, 493 Sartor Resartus (Carlyle), 72 Sartre, Jean-Paul (1905-80), 15, 502, 504

532

Index

Sceptical Chymist (Boyle) , 74, 116, 259 n Schelling, Friedric h (1775-1854), 71, 72, 107f f Schiaparelli, Giovanni (1835-1910), 449 Schiller, Friedrich von (1759-1805), 71 Schlegel, August Wilhelm (1767-1845) , 71 Schleiden, Matthias Jakob (1804-81), 260

Schlick, Moritz (1882-1936), 502 Schoenberg, Arnold (1874-1951), 490 Schopenhauer, Arthu r (1788-1860), 55, 277, 339 Schrieffer, John Robert, 100 Schrodinger, Erwin (1887-1961), 352, 372ff, 380 , 385, 490, 491, 498 Schrodinger's cat, 385f f Schwann, Theodo r (1810-82) , 260 Schwarzschild radius, 461 Science and Politics oflQ (Kamen) , 313 SCSC (superconducting supercollider) , 148,410,412,494 Seferis, George, 337 Segre, Emilio, 151 Selfish Gene (Dawkins), 348 Semiconductors, 16 0 Semi-metals, 160 Seurat, Georges (1859-91), 132 n Seven Types of Ambiguity (Empson) , 399n Sex, 304f f Sextus Empiricus (2nd cent.), 51 Sforza, Ludovic (1542-1608), 255 Shadwell, Thomas (c.1642-92), 116 , 178, 253, 260 Shakespeare, William (1564-1616) , 69, 71,113,484 Shapley, Howard, 452 Shaw, George Bernard (1856-1950), xvi, 277,285,499 Shelley, Mary Wollstonecraft (1797-1851), 127 Shelley, Percy Bysshe (1792-1822), 68ff , 73,126, 170,494 Shimony, Avner, 505 Shockley, William, 312 Siemens, Erns t Werner von (1816-92), 123, 13 3

Silent Spring (Carson), 483 Singer, Isaac Bashevis, 25 Sir Isaac Newton's Philosophy Explain 'd for the Use of Ladies (Algarotti, tr.

Elizabeth Carter), 56 Sizi, Francesco, 15 Slipher, Vesto Melvin (1875-1969) , 453 Smart, Christopher (1722-71) , 268 Smilovitz, Verdran, 496 Smith, Adam (1723-90), 74 Smithsonian Institution , 129 Smoot, George, 470 Snow, C.P., 492ff Social Statics (Spencer), 289 Socrates (c.470-39 9 B.C.) , 53, 500 Soddy, Frederick (1877-1956) , 143, 147 Solvay, Ernest (1838-1922), 135 Some Considerations about the Reconcilableness of Reason and Religion (Boyle), 114 Some Thoughts Concerning Education (Locke), 58 Sommerville, William (1692-1742), 56 Sound, 189f f Space, 418ff Spaniard in the Works (Lennon) , 321n Spectroscopy, 184, 368ff ; o f starlight, 453 Spencer, Herbert (1820-1903), 131, 286, 289 Spengler, Oswal d (1880-1936) , 230, 492 Spiegelman, Sol, 276, 348 Spinoza, Baruch (1632-77), 14 , 31, 52, 71,108,441,500 Sputnik, 2 9 St. Augustine (354-430) , 12n, 418, 463n , 501 St. Bernard, 493n Stael, Madame de (1766-1817), 71 Standard Model , 405 Stars: main sequence stars , 457; lifecycle, 456ff; red giants, 457; white dwarfs, 376, 457; synthesis of the chemical elements , 458; supernovae , 459ff; pulsars, 45 9 Steele, Richard (1672-1729) , 62,12 2 Steno, Nicolaus (1638-86), 259 STM (scanning tunneling microscope) , 136 Stoppard, Tom, 492 Strangeness, 404 Strassmann, Fritz, 146 Stravinsky, Igor (1882-1971), 490 Strindberg, August (1849-1912), 127 Strings, 410 Strong force, 404

Index

Sturgeon, William (1783-1850) , 87 Sturm und Drang movement, 71 Summa Theologiae, 31 Sumner, William Graha m (1840-1910), 131 Sun, 190 , 207, 322, 369, 429, 447ff, 457; solar wind, 445 Superconductivity, 9 9 Survival o f the Fittest, 273 , 289 Sutton, Walter Stanborough (1877-1916), 265 Swammerdam, Jan (1637-80), 26 0 Swan, Joseph Wilson (1828-1914) , 124 Swift, Jonathan (1667-1745), 62 Swift-Tuttle comet, 42 Swinburne, Algerno n Charle s (1837-1909), 286 Swinburne, James , 165 Symmetry, 885, 409 System of Synthetic Philosophy (Spencer), 289 Systema Naturae (Linnaeus), 257 Systeme de la nature (D'Holbach) , 57, 64 Szilard, Leo (1898-1964), 378 Tamberlaine (Marlowe), 113 Tartaglia, Niccola Fontana (c.1500-57) , 29 Technology, 65, 73, 74,121,122ff Tectonic plates, 443 Telegraphy, 85,123 Teleology, 337 Telegony, 288 Tennyson, Alfred Lor d (1809-92), 126, 285 Terman, Lewis (1877-1956), 313 Tetradymas (Toland) , 59 Tetraktis, 171 Thales (c.624-546 B.C.) , 135, 16 9 Theodoric (c.454-526), 175,17 6 Theologiae Christianas Principia Mathematica (Craig) , 35 Theory of Colors (Goethe), 70 Theory of the Earth (Hutton), 274 Thermodynamics, 133 ; the first law, 214; the secon d law , 222ff , 351 , 499 ; the third law, 230n Thomas, Lewis, 126 Thomas, R. S., 442 Thompson, Benjami n (Count Rumford), 210

L53L Thompson, Silvanu s Philips (1851-1916), 124 Thomson, David , 493 Thomson, Georg e Paget (1892-1975), 379 Thomson, Joseph John (1856-1940), 137ff, 153n , 158, 361 , 379 , 431 Thomson, William (see Kelvin, Lord) Timaeus (Plato), 175 Time, 218ff, 418ff ; dilation , 42 7 Tindal, Matthew (1655-1733), 59 Times (London), 55 Titian (c.1487-1575) , 256 Tocqueville, Alexis , Comte de (1805-59), 60 TOE (theories o f everything), 412 Toland, John (1670-1722), 59 Tolstoy, Count Leo (1828-1910), 30 Torture Chamber of Science (Weber) , 130 Total Eclipse (Tony Lucas), 177 Traite de mecanique celeste (Laplace), 61 Traite elementaire de chimie (Lavoisier), 119 Transposon, 30 2 Treatise Concerning the Principles of Human Knowledge (Berkeley), xvi Tritton, David, 241n Tschermak von Seysenegg, Erich (1871-1962), 264 Turing, AlanMathison (1912-54), 312 Turner, Joseph (1775-1851) , 70 Two Cultures and the Scientific Revolution (Snow), 492 Two-slit experiment; wit h light, 191 , 393; with electrons , 380 Tyndall, John (1820-93), 108 , 350 Tyson, Edward (1650-1708), 269 Uncertainty Principle , 389f f Unified Fiel d theory , 101, 441 Universal gravity , 43ff, 82,101,176, 443, 461n, 49 3 Updike, John, 408 Uranus, 448 Urey, Harold Clayton (1893-1981), 343 Ussher, Archbishop Jame s (1581-1656), 259n Utilitarianism (Mill) , 286 UV (ultra-violet) radiation, 96,18 9

534

Index Vaccination, 333 Venus, the planet, 344 ; the goddess, 446 Vesalius, Andreas (1514-64), 255 Vestiges of the Natural History of Creation (Chambers), 285n Victoria, Queen (1819-1901), 94, 130, 266 Villard, Paul (1860-1934), 188 Virchow, Rudolf (1821-1902), 261 Virtual particles, 392 ; virtual photon , 392 Virtuoso (Shadwell), 251, 260 Viruses, 321 Vital force, 268 , 320f f VLA, very large array, 451 Volland, Sophie (1716-84), 65n, 75 Volta, Alessandro (1745-1827), 84ff , 123,127, 156 Voltaic pile, 68,85, 89, 157 Voltaire, Frangois-Marie Arouet (1694-1778), 15, 25, 49n, 52 , 53, 55ff , 60, 62ff, 74 , 77, 236, 445, 486 Volterra's equations, 24 4 Wachtershauer, Gunther, 346 Walker, Arthur, 464 Wallace, Alfred Russe l (1823-1913), 27lff, 28 9 Walsh, Dennis, 43 1 Walsh, Don, 180 Walton, Ernest , 152 War and Peace (Tolstoy), 30 Water Babies (Kingsley), 284 Waterston, John James (1811-83), 204 Watson, James, 105, 292 , 317, 493 Watt, James (1736-1819), 61 Waves, 185ff; transverse, 185 ; longitudinal, 186 ; velocity , 186ff ; frequency, 187ff ; electromagneti c waves, 188ff ; soun d waves , 189 ; intensity, 189 ; interference, 190 ; diffraction, 19 3 Wave packets, 197 , 390 Wavefunctions, 371ff ; collaps e of, 383f f Way of All Flesh (Butler), 28 5 Webb, Beatrice (1858-1943), 121 Webb, Sidney (1859-1947), 291 Weber, Ernst von, 130 Weber Max Maria von, 125

Weinberg, Steven, 408, 496 Weismann, August (1834-1914), 288 Weizmann, Chaim (1874-1952), 208 Wells, H. G. (1866-1946), 291 Wheeler, John, 473 Whether the Earth has Undergone an Alteration of its Axial Rotation (Kant), 274 Whewell, William (1794-1866) , 18, 90, 128 Whiston, William (1667-1752) , 443 Whitehead, Alfred (1861-1947) , 177, 465, 501 Whizen, Bruce, 307 Wickramasinghe, Chandra, 34 1 Wigner, Eugene, 387 Wilberforce, Samue l (1805-73), 283 Wilberforce, William (1759-1833) , 133 Wilkins, Maurice, 292 Will, 276ff, 28 5 William o f Ockham (c.1285-1349), 25, 169 Willis, Thomas (1621-75) , 9 Wilson, Robert Woodrow, 469 Wittgenstein Ludwi g (1889-1951), 21, 500,504,509

Wohler, Friedrich (1800-82) , 261n, 320 Women's rights, 76,14 8 Wordsworth, William (1770-1850) , 72ff , 77,177,486 Wren, Christopher (1632-1723), 115 Wright, Kit, 493 Wright, Thomas (1711-86) , 452 Wulf, Theodor, 40 1 X-rays, 96, 124,189, 301,460, 461, 487 X-ray crystallography, 193, 29 2 Yeats, William Butle r (1865-1939), 413 Young, Thomas (1773-1829) , 191ff, 363 , 394 Z-boson, 408 Zeno (5t h cent. B.C.) , 53 Zero-point energy , 206 ; of vacuum, 391 Zola, Emile (1840-1902), 127,133, 449 Zweig, Georg, 403 Zwicky, Fritz, 432, 472