Risk and Meaning: Adversaries in Art, Science and Philosophy

Risk and Meaning

Nicolas Bouleau

Risk and Meaning Adversaries in Art, Science and Philosophy Translated by Dené Oglesby and Martin Crossley

Nicolas Bouleau Ecole des Ponts ParisTech Marne-la-Vallée, France [email protected] The publication of this book was helped by the contribution of the FONDATION DU RISQUE and the INSTITUT LOUIS BACHELIER

ISBN 978-3-642-17646-3 e-ISBN 978-3-642-17647-0 DOI 10.1007/978-3-642-17647-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011920822 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Although the best care has been devoted by the author to the research of all rights owners, he is well prepared to meet all copyright obligations pertainty about sources which could not be ascertained. Typesetting: camera-ready copy produced by author using QuarkXpress. Cover design: eStudio Calamar S.L. Cover: «Le réveil de Samson ou la terreur des Philistins» watercolors by André Devambez (1867-1944), private collection, Paris. When the hair of Samson, cut by the lascivious Dalila, grew again, Samson recovered his strength and destroyed, as revenge, the temple of Gaza devoted to god Dagôn. He died under the debris together with the king of the Philistines and all the court. The story inspired Jean-Philippe Rameau who composed an opera on a libretto of Voltaire.

Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

In the first instance, risk seems no more than a part of an essential calculus [...] This is risk in a world where much remains as ‘given’, as fate, including external nature and those forms of social life coordinated by tradition. As nature becomes permeated by industriatization and as tradition is dissolved, new type of incalculability emerge [...] managing risks which nobody really knows has become one of our main preoccupations [...] Many believe that in the age of risk there can be only one authority left, and that is science. But this is not only a complete misunderstanding of science, it is also a complete misunderstanding of the notion of risk. Ulrich Beck, Politics of Risk Society, Polity Press 1998.

Entrance : Interpretation and Paradigms, 1 I. Cicero and Divination, 13 II. Cournot’s “Philosophical Probabilities”, 29 III. Mathematical Probabilities, 47 IV. Democracy by Chance, 65 V. Gestalt, Structure, Pattern, 81 VI. The Third Dimension of Risk,109 VII. ‘Modern’ Architecture, 125 VIII. The Ideal City, 149

Risk and Meaning IX. X.

Daring the Abstract in Art, 165 Saussure or the Dread of Mathematical Probabilities, 183 XI. Jacques Monod’s Roulette, 203 XII. From Fortuitism to Animism, 225 XIII. The Slip as Fortuity and Meaning, 243 XIV. Guessing Astronomy, 259 XV. The Legitimacy of Science and Love, 273 Hints and index, 293

Entrance : Interpretation and Paradigms

2

3

When we try to understand our surroundings places, systems, situations, behaviors - we interpret the stimuli we receive. Starting with a clue, shaped by our memories and our knowledge, we construct a narrative, linking together familiar forms, and an interpretation emerges… we understand, more or less. This complex process, never completely explicit, leaves a particular impression: there is meaning. It does not matter here if this meaning is right, if we have grasped the true significance of the situation; that is another question. But already there is a first great distinction between that which shouts at us and that which says nothing to us. When we do not understand, i.e., we do not recognize anything and cannot guess what is there, the stimuli do nothing to us. Just like certain times in school!

4

5

The guiding thread of this book is the confrontation between this presence of meaning and the possibility of chance, our ultimate goal being to shed light on our tendency to adhere to scientific representations. Let's start with some well-known arguments of the epistemologist Thomas Kuhn, from which chance will be seen to play the role of a reactive agent in our philosophical experiments. Compared with classic epistemology - including the work of Karl Popper, who essentially aimed to give rules for what is and what is not in the field of science - The Structure of Scientific Revolutions1 is a revolution in itself. It presents, in effect, a radically new vision of the processes of development and dissemination of scientific knowledge. Thomas Kuhn rejects, in an extremely convincing fashion, the neopositivist philosophy based on correspondence rules (between scientific terms and experimental realities). He examines how there is meaning in science and its relation with scientific habits. In other words, he reveals the semantic and pragmatic dimension of the language used in these disciplines. His views are the basis of most contemporary epistemological work2 . The criticism sometimes leveled against him, of having somewhat concealed his debt to Gaston Bachelard, is partially justified. Bachelard's remarkable psychological analyses of the relations between the symbolic and advances in physics may seem similar to Kuhn's ideas, but they rely on a universalist, almost positivist, viewpoint and do not make any sociological reference to the scientific community that shares these meanings, which is an essential point. According to Kuhn himself, the term “paradigm” is responsible for the contradictory comments which gave rise to his book The Structure of Scientific Revolutions. A decade later, he clarified his thoughts3. His starting point is sociological: “A paradigm is what the members of a scientific community, and they alone, share. Conversely, it is their possession of a common paradigm that makes a scientific community out of a group of otherwise disparate men.” To escape this cir1. T. Kuhn, Univ. of Chicago Press, 1961. 2. In international scientific activity, one is met with a considerable number of Popperians. No matter the number of vociferous partisans, these researchers still do not know the contents of this philosophy. Moreover, the weaknesses of Popper’s epistemology does not interest them. What they want more than anything is that there exist a conclusive distinction between science and everything else. And yet, it’s exactly this point that weakens this philosophy. 3. «Second Thoughts on Paradigms» (1974), in The Essential Tension, Univ. of Chicago Press 1977.

6 cular reasoning, we could use the term “disciplinary matrix” to designate that which a scientific community shares, and the paradigms are the constituent elements of this. It may be about simple analogies or real ontological commitments4: In any case, it is about the field of meaning: an electrical circuit is seen as a stationary hydrodynamic system, a gas is thought of as a collection of microscopic billiard balls moving randomly, up to real metaphysical connections: the heat of a body is the kinetic energy of its constituent particles. In this way, we arrive from “disciplinary matrix” to the second meaning of “paradigms”: examples or generic cases. Their importance is central to understanding the theory, and the end-of-chapter exercises in scientific works are there to train students to extend these paradigms to new situations using the established theoretical language. This is done, according to Kuhn, not by following correspondence rules, but by similarity. Solving an exercise most closely resembles a child's game where we have to find the silhouette of an animal or a face hidden in a picture of a forest or of clouds. The child looks for shapes that are like those of animals or faces he knows. Once he has found them, they do not disappear into the background because the child's way of seeing has been changed 5. Kuhn developed a very interesting argument to show that this approach is not based in quantitative criteria. The raw data of experience is not sensations, he notes, but the stimuli. And these, contrary to 4. This term became widespread in America after the major article «On What There Is» where Quine introduced ontological commitments (in From a Logical Point of View 1953). 5. In the same spirit, Gérard Fourez exposed Kuhnian epistemology in a rather judicious way by taking the analogy of the game to find a legend in a comic, which had the advantage of making understood the social anchorage of interpretive materials and the plurality of solutions. Cf. G. Fourez La construction des sciences, De Boeck 1988, p 105 et seq.

7 what Descartes thought, are not in a one-to-one correlation with sensations. The same drawing can be seen as a duck or a rabbit. “Though data are the minimal elements of our individual experience, they need be shared responses to a given stimulus only within the membership of a relatively homogeneous community, whether educational, scientific, or linguistic”. The introduction of quantitative criteria stops the plasticity of the system, but this plasticity is essential to the understanding of the new by the community that shares a paradigm6. Consider, he says, a child visiting a zoo, where his father teaches him to recognize swans, geese and ducks. Phrases such as "all swans are white" may play a role in this process, but they are not essential. Instead, Johnny's education happens like this: his father points to a bird and says "Look, Johnny, it's a swan!" Soon afterwards, Johnny replies "Daddy another swan!" but he is then corrected "No, Johnny, that's a goose" etc. After a number of corrections, Johnny knows how to recognize swans, geese and ducks. Birds which previously looked alike are now separated into three distinct categories.

6. The biologist Ludwig Fleck has recently resurfaced as the concept of ‘collective thought’ is central to his epistemology [L. Fleck, Entstehung und Entwicklung einer wissenschaftlichen Tatsache (1935), Suhrkamp 1980]. In fact, he makes it play a role appreciably different than in Kuhn’s theory. The consistence of scientific knowledge resides in fine for Fleck in the law of maximum experience, experience as one says a man is experienced. One could take the image of discussions from the core of a group of mountain guides, and here would be a collective thought: knowledge non-systematized by a theory, adapted to gathered observations, and critiqued for taking into consideration new cases. From this, Fleck draws rather original consequences prefiguring the concerns – rather than the methods – of science studies. Kuhn, who is also a physicist, places much more emphasis on interpretation, which is what interests us here.

The separation criteria, though non-quantifiable, work well when he encounters fowl which clearly fit into one of the three groups, that is to say, if he stays in a community where swans, geese and ducks are common. In other words, he has learnt to attribute symbolic codes to nature without using rules or definitions and, in doing so, he has gained some knowledge of nature. This process, combined with symbolic generalization and modeling, is, for Kuhn, an adequate reconstruction of scientific knowledge. He believes that "scientists assimilate

Games where the forms are prexisting and the child simply needs to find them are less amusing and less interesting than those where the drawings are random and the child needs to properly exercise his imagination. Here random lines have been thrown on the page. One can see plenty of things in them. The epistemologist Gérard Fourez believes that this process is at the heart of scientific creation. La construction des Sciences, De Boeck 1988, and Apprivoiser l’épistémologie, De Boeck 2004.

10 and store knowledge in shared examples" and rejects the philosophical idea that describes science as qualifying representations by precise criteria.

Whether these criteria are very strict (fig 3) or very broad (fig 4), they have strict implications for any new creatures not yet examined. More vague criteria (fig. 5) are surely a wiser choice for understanding new types of bird. But a process of readjustment is necessary, determined by the new bird that has appeared (fig. 6). Kuhn emphasizes this essential plasticity in the practice of science. This process isn't limited only to physics; it is present in all the sciences and, more generally, in all representations that are candidates for scientific validation, be they intellectual intuitions, or artistic creations, illuminating, moving, or entertaining. The question we address, and which we will develop in a range of areas, was apparently first posed in a precise way by Cournot in the nineteenth century. It concerns the relation and interaction between chance and these representations. What leads us to think that an observed or perceived structure is a property relying on scientific principles, rather than a contingent configuration appearing by chance? For example, Bode's law, which gives a simple formula for the orbits of the planets7, is considered an amusing find, while climate change models, based on complicated equations from physics and economics, and giving relatively uncertain results, are considered to be completely scientific by the community of international experts. We can also approach the question from another angle. The idea that chance can produce something meaningful strikes us as completely paradoxical, yet we often talk of "pure, dumb luck". We will investigate examples where the realm of chance encroaches on the meaningful. That then puts us in a critical situation. The presence of meaning leads us suspect the unexpected. There is conflict, and curiously, our judgment in these cases is far from balanced; we have a 7. A law also declared by Titius-Bode, r=0.4 for Mercury, r=0.4+0.3x2n-2 for the planets following the number n, counting n=5 for the asteroid belt between Mars and Jupiter.

11 clear preference for meaning. As we will see in Chapter X, even the great linguist Ferdinand de Saussure couldn't make head nor tail of it. When an underlying law is suspected behind the data we gather, when we tend to believe that there is something there, a deep structure, a law; what is the nature of this tendency of ours? It is not quantifiable. Cournot insists on this point as much as Kuhn. It's to do with a belief, of a strange nature, which cannot be evaluated by a ratio of favorable cases to unfavorable cases. It is not a calculation of probabilities. Cournot, who excelled in mathematical probabilities, and who was one of the first to introduce mathematical modeling into economics, is emphatic on this point. It would be a huge mistake to introduce numbers here, which is why he introduced the term "philosophical probabilities" specially for this. They played a decisive role in his philosophy of science. These are the philosophical probabilities we are going to clarify and penetrate. They have, as one might suspect, ancient roots, but the Ancients approached these questions through their own frames of reference, linked to their ideas of religion, although Cicero's fight against the oracles, soothsayers and haruspices (Etruscan diviners) also has a strong political resonance. But it is in the modern era, in Cournot's foundational text, that the problem of philosophical probabilities is proclaimed sufficiently clearly and precisely to be able to penetrate like a wedge into the cracks in a range of philosophical ideas. They are at the heart of the very topical question of chance, which is not simply about randomness and calculation of probabilities, because it is loaded with meaning - a difference in nature that a certain reductive conception of science tries, in vain, to erase. We will trace these philosophical probabilities through art and architecture, linguistics and literature. We will not be surprised, being living and thinking beings ourselves, to see them play a central role in biology, and in the controversies surrounding Jacques Monod's book-cum-manifesto. They weave, in that area, a network of links between philosophical and moral issues, asking us to step back from our cultural and social reference points. It is therefore down to anthropology to shed some light on these problems. As for psychoanalysis, these probabilities are certainly relevant when patients speak randomly and we wish to extract and understand the meanings. Finally it is by astronomy and physics that we return to our starting point - the motive of both Cournot and Kuhn - the epistemological question of the nature of scientific knowledge.

12

Detail of Rembrandt engraving.

Cicero and Divination

14

The Sibyl predicting, Giovanni Paolo Pannini (1691-1765), Nantes, musée des beaux-arts.

15

Before the modern concept of chance could take its place, bringing many interesting philosophical questions with it, the Ancients had to extricate themselves from the idea that all observed phenomena were either the result of need or of will (of gods, demi-gods or various divinities). Cicero played a decisive role in creating a place for the idea of an "unintentional accident", a primitive form of our modern notion of chance. In doing so he had to fight a degree of religiosity, which led to him disabusing the world, in a striking parallel with the consequences of scientific and technological developments today.

16

17

Cicero positioned himself against the oracles, a group that some Greeks and Romans were already beginning to question. On any occasion people would turn to the talent of the seers who know how to interpret particular configurations, birds, liver, etc, that ordinary mortals found banal and without meaning. It is difficult for us, growing up with the Abrahamic religions, to truly grasp the intimate way that religious and civil life were intertwined in Greek civilization, or to think of earthly or abstract places, as places where divine powers operate."Every pantheon", wrote Jean-Pierre Vernant, "like that of the Greeks, supposes multiple gods, each one having his own functions, his reserved domains, his particular habits, his specific type of power [...] These multiple gods are in the world; they are part of it. They have not been created by the action of a unique God who, in so doing, marks his absolute transcendence in respect of a work where existence derives from, and depends entirely on, him. The gods are born of the world. [...] There is, then, the divine in the world, and the worldly in the divinities."1 The Ancients did not view the questions of chance and of meaning according to the same categories as we do. For them, the main distinction was between that which is necessary and that which is willed, between that which is spontaneous (automaton) and that which is intentional, willed by man or by the gods. In this respect, some wisdom is required if we are to express Aristotelian thought in today's terms. A simple translation is not enough. We need to immerse ourselves in different representations, interpretations and values. Aristotle's aim is not, as some have thought, to distinguish the three real categories of that which is necessary, that which is done for a particular goal, and that which is due to chance. Anglo-saxon editors have wisely preserved the Greek terms tychism and automaton without translating them as "chance" and "spontaneity"2. For Aristotle, nature had its purposes: "Things have a purpose from the moment they come into being, whether by the intelligence of man or by nature"3. He particularly wants to emphasize the class of phenomena where something 1. J.-P. Vernant, Mythe et religion dans la Grèce ancienne, Seuil 1990. 2. Cf. P.H. Wicksteed, F.M. Cornford, Aristotle Physics Books I-IV, Harvard Univ. Press 2005. 3. Physics, Book II Chap. V.

Aristotle, by Raphael, School of Athens, detail.

18 unforeseen happens as a result of pursuing a known goal. In this situation fortuitous spontaneity (automaton) has intervened. At the heart of this category Aristotle wants to set apart those situations that arise from the will of a sentient being endowed with free-will. That subset is the domain of tychism, an idea which one could then render perhaps as "fortune". Tychism concerns the case where someone pursuing a goal finds himself facing a situation that is either favorable or unfavorable to him, which is unrelated to the objective he seeks. It's a notion somewhere in between an actual or practical idea such as "opportunity", and an interpretation such as "loved by the gods" or "born under a good sign". The presence of a purpose is essential for Aristotle. Particularly important is this phrase from Book II, Chapter VI of Physics: "It's for this reason that neither the inanimate being, nor the brute, nor even the child, leave anything to chance (tychism) because they have no free and considered preference in their actions". In other words, the child, being governed by forces larger than him, be they the will of gods, of men, or natural, does not encounter chance, because it is not pursuing an autonomous object.4 The conflict that Cicero brought up, being different and not having been specifically addressed by Aristotle, should truly be credited as an invention of Cicero. In Aristotelian terms, it concerns the boundary or the overlap between tychism and that which has no tychism in the automaton, between the cases where circumstances make sense and the cases of pure fortune. The question has already acquired a more modern flavour. We see that Cicero's question leads us ultimately to the problem of knowing if one should consider the gods - who govern, or at least reign over, nature - as beings endowed with free will or as children! A difficult question indeed, especially, if one accepts Homer's testimony that the gods of Olympus, and the local divinities, often show humour, stubbornness and mischievousness. In his work Concerning Divination, written during the first century B.C., Cicero outlines his views in the

4. The same dilemma appears in Plutarch‘s speech “On the fortune or virtue of Alexander” where he demonstrates Alexander’s successes are not due to fortune, but to his philosophical conduct in all things.

19

The Delphic oracle, mentioned by mythical epics (of Homer and Euripides) and by historical stories (of Herodotus, Diodore, Eusèbe, Pausanias, Plutarch), was so famous that it was consulted for important decisions by people and cities from all over the ancient world well into the Roman period. Plutarch (46-126 B.C.), who was a priest of Apollo in Delphes, wrote “The divinatory trance similar to a clean slate (tabula rasa), irrational and indeterminate of its own fate, but apt to receiving the fantasies of the imagination and premonitions, grasped the future without being able to reason the moment when it detached from the present. It is put outside of itself by the combination and the disposition of the body which is in a state of change, which we call enthusiasm.” “The god who uses a prophetess to listen is like the sun which uses the moon for sight, it shows and manifests its own thoughts, only it shows them all mixed up through a mortal body and a human soul which cannot remain at rest, nor offer itself to he who renders it immobile and appeased, but even more perplexing, as a swell, in contact and in touch with the movements and passions which are in it” (Pythic Dialogs) Of the innumerable responses provided by the successive prophetesses of Delphes, only 615 are known by means of ancient authors and inscriptions (H. W. Parke, D. E. W. Wormell, The Delphic Oracle, Oxford 1956). They are often skillfully written in verse.

20 form of a dialogue with his brother Quintus, a Stoic who defends the good based on the words of the haruspices, sibyls and soothsayers. Quintus says But what? You ask, Carneades, do you, why these things so happen, or by what rules they may be understood? I confess that I do not know, but that they do so fall out I assert that you yourself see. ‘Mere accidents,’ you say. Now, really, is that so? Can anything be an ‘accident’ which bears upon itself every mark of truth? Four dice are cast and a Venus throw5 results — that is chance; but do you think it would be chance, too, if in one hundred casts you made one hundred Venus throws? [Quid quaeris, Carneades, cur haec ita fiant aut qua arte perspici possint ? Nescire me fateor, euenire autem te ipsum dico uidere. Casu, inquis. Itane uero ? Quicquam potest casu esse factum, quod omnes habet in se numeros ueritatis ? Quattuor tali iacti casu Venerium efficiunt ; num etiam centum Venerios, si quadrigentos talos ieceris, casu futuros putas ?]

Quintus's point is in the same vein as a discussion that is popular even today. It consists simply in marvelling at the fact that certain rare events actually occur here and there. We want an explanation as to why the rare can actually happen, that things outside the habitual routine do occur. As with horoscopes, astrology and fortune-telling, there is no other argument than to repeat ad libitum the fact that rare things happen in order to make the necessity of an explanation felt. The questions the Ancients asked themselves recall fundamental investigations which modern science has made us used to by offering obvious responses, such as the notion of cause. What deserves an explanation? That which is exceptional, because what is ordinary is already taken into account by current language: that animals move and reproduce is contained within the concept of animal; we'd call it "analytic" to use the eighteenth century term. Well-constructed language does not require any explanation for the habitual while, conversely, an explanation is certainly required for the unexpected. He continues: Haruspices (Etruscan diviners) divining from the entrails of a cow. Relief from the Trajan Forum (Louvre).

5. A ‘Venus’ is when each of the four dice land with a different number on its face.

21 It is possible for paints flung at random on a canvas to form the outlines of a face; but do you imagine that an accidental scattering of pigments could produce the beautiful portrait of Venus of Cos6 ? Suppose that a hog should form the letter ‘A’ on the ground with its snout; is that a reason for believing that it would write out Ennius’s poem The Andromache? «Carneades used to have a story that once in the Chian quarries, when a stone was split open, there appeared the head of the infant god Pan; I grant that the figure may have borne some resemblance to the god, but assuredly the resemblance was not such that you could ascribe the work to a Scopas. For it is undeniably true that no perfect imitation of a thing was ever made by chance. [Adspersa temere pigmenta in tabula oris liniamenta efficere possunt ; num etiam Veneris Coae pulchritudinem effici posse adspersione fortuita putas ? Sus rostro si humi A litteram impresserit, num propterea suspicari poteris Andromacham Enni ab ea posse describi ? Fingebat Carneades in Chiorum lapicidinis saxo diffisso caput exstitisse Panisci ; credo, aliquam non dissimilem figuram, sed certe non talem, ut eam factam a Scopa diceres. Sic enim se profecto res habet, ut numquam perfecte ueritatem casus imitetur.]

Cicero replied with the few arguments available in that era. He tried to show that the reality of the world is in itself quite varied and that it naturally engenders events which seem exceptional to us by the attention we bring to them. Again, when certain other events occurred as they had been foretold by diviners and I attributed the coincidence to chance, you talked a long time about chance. You said, for example, ‘For a Venus throw to result from one cast of the four dice might be due to chance; but if a hundred Venus throws resulted from one hundred casts this could not be due to chance.’ In the first place, I do not know why it could not; but I do not contest the point, for you are full of the same sort of examples — like that about the scattering of the paints and that one about the hog’s snout, and you had many other examples besides. You also mentioned that myth from Carneades about the head of Pan — as if the likeness could not have been the result of chance! And as if every block of marble did not necessarily have within it heads worthy of Praxiteles! Cicero was in the difficult position of having to show that Quintus's need for an explanation was unfounded. He obviously could not say that rare events are frequent, so he resorted to the natural fecundity of circumstance. Finally, he found a

6. This was a painting by Apelles and one of the greatest of antiquity. It was later brought to Rome by Augustus.

22 strong argument using a new dimension, bringing our intepretative capacity into play: For his masterpieces were made by chipping away the marble, not by adding anything to it; and when, after much chipping, the lineaments of a face were achieved, one then realized that the now polished and complete work had always been inside the block. Therefore, it is possible that some such figure as Carneades described did spontaneously appear in the Chian quarries. On the other hand, the story may be untrue. Again, you have often noticed clouds take the form of a lion or a hippocentaur. Therefore, it is possible for chance to imitate reality, and this you just now denied.7 [Nam cum mihi quaedam casu uiderentur sic euenire ut praedicta essent a diuinatibus, dixisti multa de casu, ut Venerium iaci posse casu quattuor talis iactis, sed quadringentis centum Venerios non posse casu consistere. Primum nescio cur non possint, sed non pugno ; abundas enim similibus. Habes et respersionem pigmentorum et rostrum suis et alia permulta. Idem Carneadem fingere dicis de capite Panisci ; quasi non potuerit id euenere casu et non in omni marmore necesse sit inesse uel Praxitelia capita ! Illa enim ipsa efficiuntur detractione, neque quicquam illuc adfertur a Praxitele ; sed cum multa sunt detracta et ad liniamenta oris peruentum est, tum intellegas illud quod iam expolitum sit, intus fuisse. Potest igitur tale aliquad etiam sua in lapicidinis Chiorum exstitisse. Sed sit hoc fictum ; quid ? In nubibus numquam animaduertisti leonis formam aut hippocentauri ? Potest igitur, quod modo negebas, ueritatem casus imitari]

And since chance can imitate truth perfectly, it follows that life, history, victories and defeats may not be the intention of anybody, which is the very heart of this controversy for Cicero8. A philosophical space opens up where there is neither necessity nor will, concerning all aspects of life and thus modifying the basis of political thought. Cicero considered himself a member of the brotherhood of Soothsayers but he didn't believe in divination, creating a difficult position for himself. Was this hypocrisy or paradox? No, he simply understood his role as Soothsayer differently: as a wise counsellor, as a coach, we might say today. While the Greeks viewed oracles as being linked to religion and often to sacrifices and initiation rituals - the oracle of Delphi had a pan-Hellenic reputation conferring a genuine role in 7. Loeb Classical Library, Harvard University Press, vol. XX, 1923; Latin text with facing English translation by W. A. Falconer. 8. This question had already been asked by Euripides: “O Zeus! What say you? Do you watch over men, or is that nothing but an illusory belief? Is it false, what we believe, that gods exist? And does chance (tyche) alone decide the fate of mortals?” Hécube, v. 488-491. Much later, the Christian apologist Lactance (260-325) would concern himself with knowing “if there exists a providence governing all things or if all things are the effect and product of chance” Institutions divines, I, 2.

Rocks at Ouessant Island. The old inhabitants believe, like Quintus Cicero’s brother, that the wind and the sea intended to sculpt a fisher wife scrutinizing the horizon.

international politics - they progressively gained currency during the Roman Republic and, later, Empire, to the point where "every Roman, when he leaves his home, when he has a plan in his head or a fear in his spirit, reacts to the sight of such and such an animal to his right or to his left: he classes them as aves (birds), auspicia (sightings of birds) or, by subsequent precision "omens of encounter" (auspicia oblativa). No matter their importance, public or private, all acts could suddenly be postponed or abandoned at any time."9 The Romans felt an ever-growing need to know the future, to the point that the specialists established themselves in society, as the Marcii family did. To calm the growing concerns, the college of Soothsayers instituted rules that the auspicia oblativa loses its effect if 1) they are not seen by anyone, 2) if no-one paid them any attention, 3) if, when seen, they are denied.10 Historians believe these rules to come from the influence of the Etruscans, who are famous for their interpretative science of divine signs that would have revealed the demon Tages and the nymph Vegoia, and that they would have passed on to their followers, along with all their "secrets". It is even said that they knew how to decipher the forms of 9. J. Bayet, Histoire politique et psychologique de la religion romaine, Payot, 195 10. Loc. cit. p. 52.

Clouds have ever been interpreted. After the war of 1870, during the time where Alsace was German, the draftsman Hansi published several patriotic books to invigorate the French feeling in Alsace. He writes : “... and it seems like squadrons of heroic troopers running from the horizon”. (Mon Village, ceux qui n’oublient pas, Floury éditeur, Paris)

rman, e. He llage,

25 lightning and the peals of thunder. Seneca paints a gripping portrait of them: Here is why we do not agree with the Etruscans, specialists in interpreting lightning. According to us, it happens because there is a collision of clouds that make an explosion of lightning. According to them, there is no reason for the collision except to provoke the explosion. Seneca, Natural Questions, II, 32 It would be hasty to think that the issue has been resolved. A touch of the ancient beliefs remain in the contemporary fervor for palm-reading and horoscopes. Does the position of the planets on the day of our birth have any significance? Is there meaning in a hand of cards? Are the lines on your palm a result of necessary ontogenetic development, or due to a random mix of blastomere cells from the embryo? Can one read from them an intention, or harmony with the world, which reveals our plans? Seneca, following Cicero, established a rationalism which has developed into an entropic process today, where beliefs are hunted down and the world is "disenchanted", or enlightened, as we often say today. That word was used as a heading by the scientist, Georges Matheron - an eminent contemporary statistician - in a book where he analyzes certain beliefs in biological Achiles and Ajax playing dice. theories with regard to the role of chance in evolution, something we'll come back to later. Rather than disabusing, does it not simply displace? Let's go back to the example of lightning: In 1938, E.V. Appleton wrote about electricity in the atmosphere: "I will go straight to the report of the theory which, I believe, is the correct one, but I should add that some specialists still do not accept it. This theory was proposed by Cambridge professor C.T.R. Wilson, the most eminent of researchers in the field of atmospheric electricity. According to it, in short, storms are responsible for maintaining the negative charge of the planet, in spite of the antagonistic influence

26 Cicero asks himself why the oracle of Delphes lost its ability to predict (Concerning Divination [De Divinatione] LVII). However, the main question is this: Why are Delphic oracles (of which I have just given you examples) not uttered at the present time and have not been for a long time? And why are they regarded with the utmost contempt? When pressed on this point, their apologists affirm that 'the long flight of time has gradually dissipated the virtue of the place whence came those subterranean exhalations which inspired the Pythian priestess to utter oracles.' One might think that they are talking about wine or brine which do indeed evaporate. But the question is about the virtue of a place — a virtue which you call not only 'natural' but even 'divine' — pray how did it evaporate? 'Given enough length of time,' you say. But what length of time could destroy a divine power? And what is as divine as a subterranean exhalation that inspires the soul with power to foresee the future — such a power that it not only sees things long before they happen, but actually foretells them in rhythmic verse? When did the virtue disappear? Was it after men began to be less credulous? By the way, Demosthenes, who lived nearly three hundred years ago, used to say even then that the Pythian priestess 'philippized,' in other words, that she was Philip's ally. He meant to infer by this expression that Philip had bribed her. Hence, we may conclude that in other instances the Delphic oracles were not entirely free of guile. But, for some inexplicable cause, those superstitious and half-cracked philosophers of yours would rather appear absurd than anything else in the world. You Stoics, instead of rejecting these incredible tales, prefer to believe that a power had gradually faded into nothingness, whereas if it ever had existed it certainly would be eternal. Loeb Classical Library, Harvard University Press, vol. XX, 1923; Latin text with facing English translation by W. A. Falconer. Cicero by Jean Antoine Houdon

27 of the air-to-ground currents"11. In other words, storms are most certainly subject to fluctuations in time and space but their overall behaviour obeys an essential law. We see that one effect of science is, in first place, to move the boundary between that which is attributed to chance and that which obeys a law that could be seen, in this account, as necessity. In these sort of ideas, there is a typically positivist position, expressed by Renan, which asserts that we are behaving scientifically whenever we attribute to chance anything that could be believed to carry some significance. "In these small exalted worlds [certain communities, such as pious Protestants, Mormons, Catholic convents], it is not rare for conversions to follow some incident where the stricken soul sees the hand of God. These incidents always have something childish about them, so the believers hide them from others; they are a secret between heaven and themselves. Chance is nothing for an unmoved or distracted soul; it is a divine sign for a devoted soul"12. On the contrary, there are certainly inspirations in the history of science which are rather similar to the conversion of St Paul. In 1752 William Stukeley, a friend of Newton, wrote: "After dining with Newton in Kensington on 15 April 1726 :The weather being warm, we went into the garden and drank tea, under shade of some apple-trees, only he and myself. Amidst other discourses, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood ...." . In 1928 Alexander Fleming discovered penicillin by accident, and so on. The question that ultimately interests us is not about knowing if the situation merits a scientific or a religious interpretation, but to try to understand how we can distinguish situations which are "interpretable" from those which simply are "just like that". More precisely, are there degrees of "interpretability", from the case of a plausible, vague impression to the case of very strong presumption? How can this gradation be thought of rationally? This brings us to Augustin Cournot, the first to shed some light on this mystery.

11. In Le progrès scientifique, Lib. F. Alcan 1938 12. Preface to La vie de Jésus.

28

Pythie or Sibyl of Delphos after Michelange Sixtin Chapel

Cournot’s ‘‘Philosophical Probabilities’’

30

31

Why do we think that nature follows certain rules? What is it that leads us to believe that there is some law at work rather than none? Cournot gave the first deep analysis of our propensity to recognize structures, an ability that is essential to scientific discovery. For him, this sort of belief is not quantifiable and has nothing to do with the calculation of probabilities. By highlighting the importance of the interpretive dimension of knowledge, he opened up a string of questions, about subjectivity, pluralism, etc., which still occupy epistemologists to this day.

32

33

Cournot has come to be known

as the person who defined chance as the encounter of two independent sequences of events. We live in the era of cut-and-paste. In many publications, and in the simplified narratives found on the internet, this is "chance according to Cournot", and so the rumour spreads. Attaching his name to this idea, unfortunately, comes at a high price, since it implies that Cournot thought about chance only in these terms. This was far from the case, as we will see. Cournot himself attributed this idea to Jean de la Placette, who he quotes explicitly: "I am persuaded that chance encompasses something real and positive, namely the coincidence of two or more events [...], each, individually, having its own cause, but their coincidence having no discernible cause" Traité des jeux de hasard, 1714. The philosophical significance of this remark has often been overstated. What is a sequence or events, and what exactly is a cause? From the moment of one encounter taking place, the subsequent possibilities branch out, and in this network everything depends on what happens at the nodes of the graph. What, then, is the independence in question? The nothing is not at all clear. In the strictest, and conceptually comfortable, framework of the contemporary theory of probabilistic statistics, determining whether or not the observed phenomena are independent requires delicate procedures which often only conclude with a broad statement "according a certain probability". If the simultaneity and proximity in question concern natural phenomena such as the historical concurrence of the appearance of flowering plants and insects, or physical phenomena such as the encounter of a planet with an asteroid, or my computer freezing at the exact moment when I am downloading a file, the accidental nature of this, i.e., its independence, is not immediately apparent, and can only be determined through some investigation. If, on the other hand, a roof tile, slowly loosening itself, finally falls on a passer-by who has just left his home as usual, the impression of independence comes evidently from the fact that, for him, it's "just a tile". We always try to accommodate anything that makes sense, and Cournot tackled this new question of understanding how and why we are inclined to think that certain things make sense.

34

Laurent de la Hyre (1606-1656), Les joueuses de dés ou la tuile [The Tile or The Dice Players] (after the book of emblems by Andrea Alciato 1492-1550). The theme of the falling tile is classic from the 16th century onwards.

35 He specifically attacked the ideas of his contemporary, the mathematician Poisson1. Adopting a position similar to that of Quintus in his dialogue with Cicero, albeit in a more modern and scholarly way, Poisson attempted to establish that a remarkable event is due to a special cause and not to chance combinations. Cournot quotes him: “If we consider,” he said, “thirty balls extracted from an urn containing equal numbers of black and white balls, then a remarkable event would be the extraction of 30 balls of the same color, 30 balls alternately black and white, or 15 balls of one color followed by 15 balls of the other color, etc. […]” By beginning here, and by supposing that we know the number of remarkable events and the number of unremarkable events, Mr. Poisson assigns the probability that the appearance of a remarkable event is not at all due to chance based on the commonly accepted rules of a posteriori probability theory.2 But, Cournot points out, the flaw in this reasoning is in the supposition that we can draw a clear distinction between the remarkable events and the unremarkable. Moreover, there is also the assumption that the so-called remarkable events are each remarkable to the same degree, and should be placed in the same class. Cournot then looked at a variant of the example of the balls in the urn, in greater detail. Suppose there is some quantity, he says, which can take values between 1 and 10,000. If one makes four observations of this quantity, and the results form a geometric progression, then one would conclude that this cannot be down to chance, and that the quantity is not behaving like a random draw from an urn containing the numbers 1 to 10,000. Moreover, the four numbers could Siméon Denis Poisson (1781-1840) form a different arithmetic pattern - they could be a sequence of squares, of cubes, of pyramid numbers, etc. The grounds for belief are linked to the simplicity of the pattern in the numbers. The more complex the pat1. Siméon Denis Poisson (1781-1840) is a major figure and highly respected adversary. He is one of the founders of the mathematical theory of the propagation of heat and an expert in the calculation of probabilities. His works, always profound, yet written in a straightforward and accessible manner, were often considered great works of art (cf. the Poisson summation formula). 2. Exposition de la théorie des chances et des probabilités, (1843), §237.

36 tern, the less room for doubt about the randomness of the process. Conversely, the simpler the pattern, the stronger the belief that it is random. The point Cournot wants to emphasize here is that this belief is not quantifiable. The following passage is of great epistemological importance. It can be seen as the first work to consider the limits of positive, mathematical science, a precursor to the crisis in the foundations of mathematics caused by Gödel's incompleteness theorems and the collapse of Hilbert's program in the early twentieth century3. Suppose that ten points on a planar surface are observed to lie on the circumference of a circle. One would immediately conclude that this coincidence cannot be down to chance, but that there must be some kind of law determining that the observed points, and any other points that we go on to observe in the same manner, have to lie on a circle. If, instead, the ten points were in slightly different positions, so that they were near to, but not exactly on, a circle, one would attribute this to experimental error rather than assume the law no longer holds [...] Instead of falling in a circle, the points could lie on an ellipse, or a parabola, or any of an infinite number of different curves [...] The probability that the observed points are behaving according to some rule would depend, then, on the perceived simplicity of the curve they lie on (or near). But any such classification of curves is unquestionably artificial [...] A parabola could be regarded, in some respects, as simpler than a circle [...] a spiral could be seen as more appropriate for expressing a law of nature, in certain situations, than an algebraic curve [...] Therefore, since any probability determined this way derives from the perceived simplicity of an observed curve, such a probability cannot possibly be expressed numerically, unlike those which result from the enumeration of favorable and unfavorable cases amongst all possible cases4. 3. Cf. N. Bouleau Philosophies des mathématiques et de la modélisation, L’Harmattan 1999, p 42 et seq. 4. Ibid. §236. Here, Cournot thinks beyond all theories of simplicity. Today, there are many such theories. Popper proposed one linked to the idea that the more simple the theory, the easier to refute it. (The Logic of Scientific Discovery, 1959, Chap. VII). The mathematician George Birkhoff, famous for a profound ergodic theory, imagined another in order to construct a theory of art, the measure of aesthetic M of one work being equal to the ratio O/C where O is “the order” present in the work and C represents its complexity. He refined these notions in his book Aesthetic Measure, Cambridge 1933.

Several architectural geometric motifs of ancient Greece were inspired by flours or shells

Philibert de l'Orme, architect of the castle of Diane de Poitiers at Anet, France, draws 18 spirals in both directions. The living nature is often less symmetric, a pine cone shows 8 spirals clockwise and 13 counterclockwise.

38 There are, then, two conceptual categories. On the one side we have quantifiable probabilities, where meaning does not intervene. Here one counts similar, enumerated cases and their combinations. On the other side we have an unquantifiable presumption of regularity, which has something to do with what statisticians today call likelihood. But it's more than that, since statistics concerns itself with the likelihood of probability laws or of certain quantifiable properties. Here we are dealing with the unquantifiable, a domain that many scientists tend to forget the existence of! It is useful to give a name to our propensity for guessing at a possible rule. It has to do with a reading, an interpretation; we could talk of a "model", a "form", or "Gestalt", keeping in mind that this faculty of recognition does not give us any certainty. Cournot wanted to emphasize the hypothetical nature of the interpretation. He suggests, in contrast to the "mathematical" notion of probability, a notion of "philosophical probability", which he expresses particularly well in the following passage: In addition to mathematical probabilities, there are probabilities which cannot be reduced to an enumeration of possibilities. These probabilities lead us to a plethora of judgments, some very important, based in our belief in the simplicity of nature's laws. We may describe these as philosophical probabilities. All rational humans have at least a vague awareness of them. In more delicate settings only a cultivated intelligence can detect them, and in some cases only a genius can. They provide the basis for a system of philosophical criticism foreseen by the most ancient scholars, which represses or reconciles skepticism and dogmatism, but which must not, under pain of strange aberrations, be allowed to enter into the domain of mathematical probabilities5. It is with that phrase that Cournot ends his book, showing how important he thought it was. Let's not forget that Cournot was also a mathematician. He was one of the pioneers - along with Jules Dupuit6 - of the introduction of mathematical thinking into the field of economics, and his mathematical research was evidently one of the things that led him to the

5. Ibid. §240. 6. Jules Dupuit (1804-1866), a civil engineer, is best known for analyzing the pricing of bridge tolls. Mathematically, he showed the existence of a toll which would bring in the most money and explained it with a cost-benefit analysis for the user. He is cited among the founders of mathematical economics by K. J. Arrow in "Discounting Climate Change Planning for an Uncertain Future" 1995.

39 notion of philosophical probabilities : But, even if geometers have no reason to concern themselves with probabilities which elude calculation, we should not conclude that such probabilities are worthless in the eyes of philosophers. Far from it, all critique of human wisdom, outside the narrow path of logical deductions, rests on them, [...] Even in geometry itself, new ideas are often found by the following the guidance of such probabilities7. In effect, the researcher is guided, in his investigations, by impressions and heuristics, which are based in probabilities that are semantic in nature. The mathematician does not work on a logical chain of formulas. Rather, he uses a meaning, or meanings, derived from past work, from other areas of science, or from the work of colleagues. So it is closely related to these philosophical probabilities. The mathematician Henri Lebesgue wrote "If I had the chance to discover, I also had the chance to fool myself into big mistakes, which in turn proved to be points of departure". He most definitely did have the chance to discover: his great accomplishment is the tool known as the Lebesgue integral which is the sort of discovery all scientists would love to make: a way of calculating areas (or "primitives") that is more general than previous methods, yet which also follows simpler rules, a double advance. As for his mistakes, the only significant one concerns the complexity of the projection of a planar set upon one of the axes, and this mistake led to some very fruitful research. In other words, intuition is both a source of discovery (philosophical probabilities) and a source of error. The account of another mathematician, Jacques Hadamard, is relevant here, since he is one of the few scholars to list some of the discoveries he could have made, had he not rushed through his research without seeing them8: “[On the question of the roles of logic and chance in research,] it seems to me, after some personal reflection, that we can gain a good understanding of the question from Poincaré's metaphor of atoms fired from a source: a metaphor I will extend to the

7. Ibid. §239. 8. Essai sur la psychologie de l’invention dans le domaine mathématique, A. Blanchard, 1959. 9. Hadamard alludes to the theses of Henri Poincaré on the role of the unconscious in mathematical discovery exposed in Science et méthode, 1908, to which he largely subscribed (cf. N. Bouleau, La règle, le compas et le divan, Seuil 2002, p 28 et seq.).

40 shooting of a hunting rifle9. We know that a good cartridge has the desired dispersion. Too great a blast radius makes it impossible to aim correctly. Too little and there is too much chance of missing the target. I perceive the circumstances to be similar in our subject. Going back to Poincaré's atoms, it may happen that our instinct launches itself very narrowly, or fairly narrowly, in a certain direction. In this case, it has the advantage that the proportion of lucky encounters among ideas will be relatively large compared with the proportion of sterile encounters; but these encounters may be insufficiently distinct. On the other hand, it could happen that the atoms are dispersed widely. In that case, the majority of the encounters will be uninteresting. However, as in a lottery, this disorder has a high value because those rare encounters that are useful are more exceptional, producing the more unusual ideas that are likely to be the most important.” That which we commonly call mathematical intuition, which allows the researcher to "foresee" the most remarkable combinations, was believed by Poincaré to receive a significant contribution from the subconscious which works like an aesthete, attaching value to configurations according to their beauty. Hadamard pushes the analysis further, showing the existence of an inexpressible thought and the role of a choice we make among the things chance happens to bring us. It is likely that Cournot was driven to the idea of philosophical probabilities by his attempts to deepen La Placette's definition of chance as the meeting of independent sequences. Even simply from a pedagogical point of view, if one takes this definition as the starting point, then independence cannot be understood in the same way as in probability calculus, namely that the probability of the conjunction of two events is the product of their individual probabilities. To avoid this vicious circle, independence must be thought of in the realm of meanings, of phenomena which have nothing to do with each other, which relate to distinct registers of interests. "A Parisian gentleman", he writes, "decides one day to visit the countryside. He takes a train to his destination. The train is involved in an accident in which the poor traveler is a victim, and a fortuitous victim, because the causes of the accident have nothing to do with his presence". The tenor of a story is not one of countable or quantifiable facts; it lies in a different realm with its own notion of likelihood. But what is the characteristic of these philosophical probabilities that keeps them separate from quantitative probabilities? Probability that comes from a sense of order and of the logic of things, and which is the true basis of most of the judgments we make, both in the loftiest questions and in the most mundane; this probability which we call philosophical probability, certainly has similarities with the mathematical probability which comes from the evaluation

41 of the chances of a favorable or unfavorable outcome. Both relate, in different ways, to the notion of chance [...] Both are apt to grow and shrink imperceptibly, without sudden changes which would lead to distinct demarcations. But the dissimilarities are no less noticeable; and it is most essential that we appreciate that philosophical probability resists all attempt at numerical evaluation. The main reason for this is that we cannot enumerate all the possible laws or all the forms of order, nor can we classify them, or grade them, in such a way as to fix, by one decision, free of all arbitrariness and expressible numerically, the characteristic of the simplicity of the laws, and the perfection of forms, and the relative importance of these characteristics. 10 Cournot's logical argument is an observation about classification: there is no natural linear order which will classify all forms. This recognizes the force of our feeling of presence. Actually, such semantic classifications can be obtained, but only by trickery: alphabetic order, "keyboard" order for Chinese dictionaries, "organic" order which groups things together by "functions" like in a catalogue of automobile parts. Nothing is clear about how our propensity to believe could be tested. Philosophical probabilities can be very strong presumptions, or minute hints: "The character of simplicity may be so striking, the number of observations be such, the approximation can fall between such strict limits, that there remains not the slightest doubt, notwithstanding the sophisticated objections that can always be made against any proof which is not strictly mathematical. In other circumstances, the probability becomes smaller, shrinking imperceptibly, conforming to the law of continuity - which is most strikingly depicted by the dimming of the light and the consequent fading of colours: different people are affected differently, without one being able to identify a precise point where certainty ends, or where indecision begins, nor the point where indecision is replaced by the opposite belief, that of ignorance about where we are from the law of the phenomenon." Going further, perhaps as a result of his mathematical experience, Cournot's thoughts turn resolutely away from psychological analysis and that which cannot be deduced from reality itself: starting from the distinction between philosophical and mathematical probabilities, he distinguishes our propensity to see order in things and our ability to recognize a logical connection. "This idea of order and of the logic of things should not be confused with the idea of the link between cause and effect: [...] It is hardly by the type of observation and by the testimonies of the consciousness, that suggest our 10. Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique (1851)

42 notions of cause and effect, that one can explain the idea we have of the order and the logic of things." For Cournot, the idea of "the order and the logic of things" is the principal source of philosophical and scientific reasoning: "This idea is the very foundation of all philosophy, the ultimate and supreme goal of all philosophical speculation, that which perfectly characterizes the philosophical spirit of curiosity, and that which gives, in varying degrees, a philosophical stamp to all work of thought, in things of taste or of imagination, as in those which are the source of scholarship and of science." If the forms, stuctures or laws that are suggested to us by philosophical probabilities are derived from reality, are they then an image of this reality? On this point Cournot seems somewhat hesitant. He recognizes first a sort of relativism, in the measure to which this faculty, which we can call aptitude for the recognition of meaning, depends on the conditions in which we find ourselves, and on the point of view from which we perceive things: "To judge that, in certain regards, our ideas conform to the reality of things, is to affirm that the true view of things is not distorted or blurred by the nature of our perceptions; but this does not mean that it is possible for us to attain absolute truth." Cournot takes an example from celestial mechanics. He notes that astronomy explains the laws of planetary motion, carefully freeing them from any effects caused by motion of the observer: nevertheless, the movements that the laws and the theory describe are still relative to the solar system, just as the movements that one observes on a ship are relative to the system formed by the ship and the bodies contained within it." He opened the door to an idea of relativism, but wanted to keep within the realm of objectivity. Here, he adopted a point of view which could be qualified as tempered Platonism: points of view are relative, but more elevated points of view can be found which surpass these individual points of view, without necessarily finding the ultimate reference point which would make us know absolute truths. And yet, it is not given to us to reach the final term of this series, to have absolutely fixed reference points in space, or the steadiness from which we would have absolute certainty [...] this is a decisive example of a well defined scheme to make us understand how we can have notions removed from any internal cause of error, or of illusion, perfectly conforming in this sense to the external reality, though not reaching absolute reality which we only know how to gradually approach.11 11. Ibid.

43 We see, in this last assertion, the principle of ultimate convergence, to which many philosophers and scientists are attached even today, analogous to that found in the work of Peirce, one of the founders of American pragmatism. In his famous article "The logic of science", Peirce postulates that on the same object of study all distinct paths used for different means of investigation will inexorably converge towards the same results12. Cournot is somewhat less positivist; since he was only trying to fully understand one thing, that our propensity to recognize structures leads us to greater understanding. So Cournot attributes a key role to these philosophical probabilities. Thus the diverse faculties, by which we acquire our knowledge of things, come under the command of a superior faculty which directs and controls them, [...] and this superior faculty is that which grasps things, pursuing reason, order, law, unity and harmony. Its means of criticism or of control are not definitive and peremptory proof, but the inductive judgment or the philosophical probability, of which the force, in some cases, is no less irresistible.13 He vigorously discounts all idea of non-transitory relativism and all idea of pluralism:

12. Charles Peirce, «Chance, Love and Logic: Illustrations of the Logic of Science», New York: Harcourt, Brace & Company, Inc., 1923, p. 56: «They may at first obtain different results, but, as each perfects his method and his processes, the results will move steadily together toward a destined center. The same holds true for all scientific research. Different minds may set out with the most antagonistic views, but the progress of investigation carries them by an exterior force to one and the same conclusion. This activity of thought by which we are carried, not to where we wish, but to a preordained goal, is similar to the way destiny operates. No modification of the point of view taken, no selection of other facts for study, no natural bent of mind even, can enable a man to escape the predestinate opinion. This great law is embodied in the conception of truth and reality.” 13. As Th. Martin pointed out, in Cournot’s mind, “to say that philosophical probabilities are subjective is clearly not to abandon them to the arbitrariness of individual judgment or to reduce philosophical reflection to a rationalization of impassioned beliefs. It means that philosophical statements can only be validated by inductions and analogies of which the number and the force certainly increase the probability, but without which this, as elevated as it may be, can be equivalent to demonstrative certainty”, "Cournot, philosophe des probabilités" in Actualité de Cournot, Th. Martin ed. Vrin 2005.

44 It can be said that this faculty which controls the others controls itself, and that in this sense it is truly autonomous, to the exclusion of all other: for, if the idea of order (such as we find in ourselves) has nothing corresponding to it outside, then it will inevitably lead to the situation where, as this idea penetrates further and further into our knowledge of the outside world, we find increasingly that everything confirms to this expectation of regularity.14 The chronology is interesting: Peirce was five years older than Nietzsche, who was 33 when Cournot died in 1877. It was only in 1881-82 that Nietzsche published The Gay Science, where he wrote: “It is the same for this belief which today satisfies so many materialistic experts who believe the world should be measurable by our tiny scales, and lie within the reach of our small thoughts; they believe in a "real world" that our tiny human minds can finally conquer [...] That there is only one legitimate interpretation of the world, where you others remain legitimately, where one cannot explore and continue to work scientifically except in your sense [...] and which does not accept anything apart from counting, calculating, weighing, seeing and grabbing, all this is but stupidity and naivety if it is not madness or idiocy [...] But I think that we are today far away at least from this ridiculous immodesty of declaring, based on our point of view, that the only valid perspectives are those from our particular angle. The world, on the contrary, has become "infinite" again: for, as much as we may ignore it, it holds an infinity of interpretations.” Not only is Cournot far from this relativism but also his aim is not one of studying the pluralism that follows naturally from the theory of probabilities: the independence or the correlation of phenomena can depend on the observer in function of the probability which governs the world, from his point of view. Such phenomena are familiar today in economics, in financial markets for example, where the trends of assets are subjective and provoke different behavior from different agents, which is why some buy and some sell15. But, as is already clear in Cournot's example of the Parisian tourist, the probability of an accident can be calculated from the point of view of the train and this will not give the same 14. Essai sur les fondements. 15. Cf. N. Bouleau, Financial Markets and Martingales, Observations on Science and Speculation, Springer, 2004.

45 number than if it is calculated from the point of view of the Parisian gentleman relative to his own way of life. Cournot's path was that of a man searching for the principles upon which a natural intersubjectivity could be founded. In his examples, a sort of common sense provides the objective basis for his philosophical probabilities, and he explicitly builds scientific knowledge upon this principle. In a way, we have returned to Thomas Kuhn's point of view, since he defined a paradigm as a representation shared by a scientific group or the scientific community, with the notable difference that Kuhn believed knowledge to be socially dependent on this fact.

46

47

Mathematical Probabilities

48

49

The mathematical theory of probability is not central to the theme of this book but, to clarify the background, it will be useful to review this theory, whose language everyone speaks, and which is now used constantly in all areas of our society touched by science. The historical path, from the first studies of games of chance, to Kolmogorov's celebrated axioms is marked by debates and controversies. Lesser known are the subjectivist theories (of Ramsey, Savage, De Finetti) which brought epistemological issues to the science of economics and posed the question of where the boundary lies between that which is "economizable" and that which must unquestionably be considered outside this category.

50

Fortune and her gamblers, title page of Abraham de Moivre’s book The Doctrine of Chances (1717).

51

This corner of the history of science

is certainly passionate and colourful, as interpretations, paradoxes and dilemmas provoked new ideas and stirred up quarrels between different groups. An abundant literature is available on the development of probability and statistics and the ways they have been used by states, economists, sociologists and pyschologists. These works being easily accessible today, I propose a general tour stopping only on some more noteworthy perspectives rather than deliver a supplementary synthesis of these works in this chapter.1. After a long period mainly concerned with probability on the philosophical and theological level, the calculation of probabilities began in the seventeenth century in studies of games of chance. From the first epistolary exchanges of Pascal, Fermat, and the abbot Mersenne it developed rapidly based on the firm and solid foundation of counting. Numerous memorable figures extended the research to new problems: A. de Moivre (1667-1754) whose treatise is entirely founded on the calculation of favorable and possible cases, Maclaurin (1698-1746), the Bernoullis: Jacques I (1654-1705), Jean I (1667-1748) and Daniel (1700-1782), whose St. Petersburg paradox foreshadowed the polemic between theoreticians in the twentieth century, and Thomas Bayes (1702-1761) whose Essay concerned the probability of causes and would be the seed of a true “philosophy” of probabilities. Abraham de Moivre

Later, questions of continuous probabilities were addressed, where one cannot actually count but only measure as one measures areas or lengths. Buffon (1707-1788) studied the needle problem and Condorcet (1743-1794) who, interested in the “probability of judgments” and the “mo1. However, we will mention the collected and taught summa of Karl Pearson (1857-1936) The History of Statistics in the 17th & 18th Centuries, 744 p., Ch. Griffin & Co, 1978 ; and Alain Desrosières The Politics of Large Numbers: A History of Statistical reasoning, Harvard University Press 2002.

52

53 tive to believe”, discovered the “paradox” of the majority vote in assemblies, which would be the starting point for Arrow’s “impossibility theorem” in economics. Legendre (1752-1833) and Gauss (1777-1855) made the connection with the least squares method. Laplace (17491827) represents a peak at the turn of the nineteenth century as mathematical techniques earned such legitimacy that they established the calculus of probabilities as a mature science, thanks to the possibility of expressing independence not only by the multiplication of probabilities of events, but by multiplying the probability laws themselves (generating functions and characteristic functions). During this classic period, as if in gestation of future debates of the twentieth century, written work constantly combined philosophical, even metaphysical, questions about the nature of chance and interest in this type of research. For example, in the middle of his treatise, after proving a theorem, de Moivre paused to dispel any misunderstandings: “Chance, as we understand it, supposes the Existence of things, and their general known Properties: for instance, a number of thrown Dice should each settle upon one or another of its Bases. After which, the Probability of an assigned Chance, that is of some particular disposition of the Dice, becomes as proper a subject of Investigation as any other quantity or Ratio can be”2. Today, we clearly need to know the probability laws of what we are studying if we are to perform any probability calculation. But in that period concepts were still settling into place, and de Moivre feared commentators who adopted the incredulous position that chance cannot be determined in any way, by definition: “But Chance, in atheist writings or discourse, is an utterly insignificant find: It imports no determination to any mode of Existence; nor indeed to Existence itself, more than to non-existence; it can neither be defined nor understood: nor can 2. The doctrine of chances, 1717, p 243 et seq. «A method of approximating the sum of the terms of the binomial (a + b)n expanded onto a series, from whence are deduced some practical rules to estimate the degree of assent which is to be given to experiment».

Johann Bernoulli and Daniel Bernoulli

54

The death of a mathematician. Originally from a protestant family, Abraham de Moivre (1667-1754) left France when he was twenty years olds, shortly after the revocation of the Edict of Nantes in 1688 for England where he had a brilliant career as a mathematician and became a close friend of Newton. De Moivre’s formula

was published in his Miscellanea analytica de seriebus et quadraturis in 1730. As De Moivre reached his eighties, he began to lose both his sight and hearing. He also began to sleep for longer and longer periods, until 20 hours a day became the standard. Yet, during the four hours he remained awake, his friends found him as keenly intellectual as ever. He remembered the smallest incidents and dictated precise replies to letters and algebraic problems. His sleep was then extended to 23 hours a day. On June 27th, 1754, the French Academy made poor reparation to the exile; they elected him a foreign associate of the Academy of Sciences, and De Moivre, blind and deaf, was still able to rejoice in this honor. The sleep continued to steal on his one hour of vitality, and on November 27th, 1754, at the age of 87, he slept the whole 24 hours and never woke again, his death being recorded as from somnolence. Such was his strange exit from life. (K. Pearson, The History of Statistics in the 17th & 18th Centuries, Ch. Griffin & Co 1978).

any Proposition concerning it be either affirmed or denied, excepting this one, ‘That it is a mere word’.” Uncertain of being able to convince a wide audience, de Moivre restricted himself to the perspective of researcher and the shared pleasure of curious and demanding minds in this community: I shall only add, That this method of reasoning may be useful applied in some other very interesting Enquiries; if not to force the Assent of others by strict Demonstration, at least to the Satisfaction of the Enquirer himself: and shall conclude this Remark with a passage of the Ars Conjectandi of Mr. James Bernoulli, Part IV. Chap. 4. where that acute and judicious Writer thus introduceth his Solution of the Problem for Assigning the Limits within which, by the repetition of Experiments, the Probability of an Event may approach indefinitely to a Probability given3 [...] This, says he, is a Problem which I am now to impart to the Publick, after having kept it by me for twenty years: new it is, and difficult; but of such excellent use, that it gives a high value and dignity to every other Branch of this Doctrine. Yet there are Writers, of a Class indeed very different from that of James Bernoulli, who insinuate as if the Doctrine of Proba3. The weak law of large numbers. Cf. for example J. Bonitzer, Philosophie du hasard, Editions sociales, p 36 and seq.

55 bilities could have no place in any serious Enquiry; and that studies of this kind, trivial and easy as they be, rather disqualify a man for reasoning on every other subject. Let the reader chuse. By the end of the nineteenth century, at the time when Henri Poincaré was teaching the calculus of probabilities (without the theory of integration) at the Sorbonne, the entire body of work of the calculus of probabilities was already near completion, and its applications were extremely numerous in physics, astronomy, insurance, and medical and demographical statistics. In the period from the seventeenth to nineteenth centuries one can already see the beginnings of ideological disputes that appeared in the twentieth century. Yet, by and large, these difficulties are considered more as curiosities, as delicate zones which must be approached with caution – as Joseph Bertrand (1822-1900) taught it regarding different ways of evaluating the law of probability from a cord to a circle following what is considered as “equiprobable” – than with radically different philosophical ideas. There is, however, one point worth highlighting here, since we will encounter it again later when we discuss Jacques Monod and his concept of genetic mutations. The passage from discrete finite situations, where equally probable cases clearly appear, to infinite ones, works if there is a symmetry or invariance imposed by the nature of the problem itself. Certain dynamical systems of classical mechanics fall into this category. Poincaré and Hopf showed that the passage is also correct for roulettelike “dissipative systems”, justifying, as a result, what all gamblers quietly admit to themselves. On the other hand, this extension can not be

56 done “naturally” for infinite discrete cases. This point deserves more attention than it is usually given. No privileged probability law exists for whole numbers or for phrases in ordinary language. To draw an angle at random has naturally evident logic; to draw a molecule at random is not as conceptually simple as one would imagine! The twentieth century, perhaps because of the prodigious mathematical developments due to Emile Borel (1871-1956), Henri Lebesgue (1875-1941) and Andreï Kolmogorov (1903-1987), who in return provoked some doubt, was one of clear oppositions between philosophies structured and constituted in a body of doctrines based on foundations, deductive principles, and specific application fields of their own. I will distinguish only two main trends: the objectivist view and the subjectivist view 4. The objectivist theory attributes to probability theory the task of describing the reality of unpredictabld phenomena by applying the laws of chance, i.e., the law of large numbers and the central limit theorem5. Thanks to these theorems, by taking averages of the observed phenomena, we estimate probability laws with increasing accuracy. These are then inferred from the frequencies of observations and appear in this respect as objective facts independent of any judgment or belief. This theory is well corroborated by the physics of emission phenomena and statistical mechanics, thanks to the huge size of the Avogadro constant.6 Critics point out, however, that this narrative is neither completely rigorous nor honest since the law of large numbers is an asymptotic law. This leaves some doubt depending on which law of probability is sought. Furthermore, this doubt is always present no matter how large the sample. The objectivists then threw them4. These may be more specifically defined as at least five “philosophies”: classical, logical—founded on the idea of propensity (K. Popper)—, frequentialist, subjectivist, cf. K. Burdzy, The Search for Certainty, World Scientific 2009. 5. In addition to these two well-known asymptotic laws, three theorems became real fields of inquiry: the law of the iterated logarithm, the ergodic theorem, and the principle of large deviations. 6. The volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas. Avogadro, Amadeo «Essai d’une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons». Journal de Physique 73: 58–76 (1811).

57 selves into the search for a precise definition of a sequence obtained “by chance”, such as the result of successive independent draws from an urn (R. Von Mises, A. Wald, A. Church, J. Ville, etc.). This objectivists’ research proved to be considerably more difficult than expected and yielded nothing until 1966 when the logician Martin Löf achieved a result which was indisputable but had no practical interest7. Despite this, the calculation of probabilities improved, convergence speeds in asymptotic laws were discovered and statistical methods perfected and multiplied, rendering the above criticism more and more theoretical. Even today, the objectivist point of view has a large following, and is the usual route taken in introductory courses on probability and statistical calculus. The subjectivist theory views the calculation of probabilities as a statement about the beliefs of each individual in the presence of unforeseen events. Certain authors (Ramsey, De Finetti, Savage) see it as the proper way to give probability calculations clear foundations that avoid contradictions. This theory could be described as the construction of a “logic of partial beliefs”8. Paradoxes, such as the St. Petersburg paradox9, are avoided by the idea that gamblers look to optimize not the expectation of their winnings but the utility of their winnings10. 7. The result of Martin Löf is that a sequence of zeros and ones is random if and only if the associated real number does not belong to any effective negligible set of the real line. Thus no sequence yielded by an algorithm may be random. Cf. Cl. Dellacherie, «Nombres au hasard» Gazette des mathématiciens Oct. 1978. 8. «The subject of our inquiry is the logic of partial belief» F. P. Ramsey, «Truth and probability» in The Foundations of Mathematics R. B. Braithwaite ed. Routledge & Kegan Paul 1931. 9. How much are you ready to pay to be allowed to participate the following game: a coin is tossed successively, you receive $2n if the first heads occurs at the nth throw? This question was asked by Nicholas Bernoulli in 1713 and discussed by Daniel Bernoulli in the Mémoires of the St Petersburg Academy. If you answer "$1000" you find yourself in the following situation: if heads appears before the tenth toss, you lose some money (at least $488); if head appears only at the tenth drawing or after, you win a greater amount. The probability that you win something is very low (0.002), but the expectation of your gain is infinite. 10. An idea already suggested by Daniel Bernoulli and Buffon who wrote “A mathematician, in his calculations, does not think of money but by its quantity, which is to say its numerical value, but the moral man must think of it in terms of the advantages and pleasures that it may procure for him” quoted by J. Bertrand Calcul des probabilités, 1888.

58 Utility functions should satisfy certain conditions which can be spelt out so that a gambler’s behavior can be coherent and rational, i.e., they are protected from losses that could be obviously exploited by another gambler. With J. Von Neumann and O. Morgenstern’s famous treatise, game theory and utility functions became a way to justify the relation between economic balances and an agent’s behavior - a considerable advance in the theory with enormous consequences. With De Finetti and Savage having studied how an agent reconsiders his beliefs in the light of his experiences, the subjective theory gave birth to what is called the Bayesian decision theory, which considers statistics starting from an a priori probability. Thus, starting from the opposite of the objectivist position, one often nevertheless ends with results which hardly depend at all on the initial probability which was chosen. This is what enables this method, which requires simpler calculations, to bear fruit. In certain cases, the insensitivity of the result to the a priori probability law can even be demonstrated as the arbitrary functions principle of Poincaré and Hopf. I do not believe that there is a real dispute between the supporters of the objective theory and those of the subjective theory except in academic encyclopedias and theses on the history of probabilities. For what is the purpose of the subjectivists? What is their epistemological contribution? They show that a calculation of probabilities “also works” to manage an individual’s affairs with the partial information which he collects about the world. The range of applications for the calculus of probabilities is thus extended. We immediately see the large advantage that economics has gained from this. Its challenge is to define economic laws, equilibriums, imbalances, trends, and anticipations from the individual behavior of agents, these agents being only assumed to manage their subjective possibilities coherently, in the same way that statistical physics bases a hypothesis on the chaotic movement of atoms. Here, the problem is more complex, but the very principle of methodological individualism is founded on the idea that each agent rationalizes enough so that, at his individual level, the subjectivist theory applies 11. In early quantum physics, Heisenberg hesitated between the closely-related terms Ungenauigkeit and Unbestimmtheit to designate the inequalities concerning the incompatibility between the accuracy of measurements of dual variables (position-speed, etc.). Though they are translated as uncertainty and indeterminacy, these two notions are quite 11. Cf. K. Arrow, «Methodological Individualism and Social Knowledge» The American Economic Review, 1994.

59

Famous page of Euler (Introductio in Analysis infinitorum 1799) where he links the series of prime numbers with the harmonic series. At that time analysis was not axiomatized as Euclidean geometry, and Euler shares with the reader an intuition essentially based on beauty. Here the series of n°273 and the product are divergent, in other words the «&c» is somewhat obscure. Gauss and Cauchy at the beginning of 19th century will improve the acuracy of the mathematical language in analysis, but a rigorous framework for probability calculus will only appear with the 20th century.

60

61

different since the first relates to subjective probabilities and the second to objective probabilities. Here, again, there is no longer any real debate - indeterminacy is the term we should use, despite deeply embedded habits 12. The boundaries of the subjectivist theory are not clear, and even some questions within these undefined boundaries remain contested. Are its principles universal enough to be applied to the psychology of all economic agents? What exactly is its relation with experience, information, and the propagation of behaviors by mimicry or by rumor? Furthermore, some choices do not seem to be made in accordance with a utility function (Maurice Allais’ paradox13) and require the conceptualization of a more abstract tool possibly depending on the agent’s propensities or aversions to risks. These controversies are the sign of dynamic research activity rather than fundamental epistemological problems. On the other hand, the subjectivist theory poses a greater philosophical question when considered from sociological and political angles. Economic agents are rarely individuals; usually they are groups of diverse powers more or less capable of collecting and processing information. This suggests that strictly individual knowledge may be relevant from a logical point of view and consistent with experimental observations. Does this mean that a dominant entity could lead all of science in the subjective direction, which would be a direction of its own creation? Or perhaps, on the contrary, must some kind of market equilibrium stabilize itself between pluralist representations so that science preserves what is expected from neutrality? It is easy to see how the sociology of the sciences is directly implied in this issue. Beyond all expectations, the twentieth century confirmed the value of setting mathematical probabilities within the framework of measure theory (also known as the 12. Cf. J.-M. Lévy-Leblond “La méprise et le mépris” Alliage, n° 35-36, 1998. 13. Cf. L. J. Savage «Allais’ paradox» in The Foundations of Statistics, Dover 1972.

62 theory of integration). This operation, when proposed by Kolmogorov in 1930, had only theoretical advantages. Kolmogorov clarified two of them: the possibility of giving a more rigorous treatment of the notion of a stochastic process, a rather abstract object which can be used to describe the Brownian movement of fine droplets in emulsions for example, and the correct general definition of the concept of conditional expectation. With the work of Wiener, Paul Lévy, and Khintchine before the war, and later Kiyosi Itô and his successors, inventions and discoveries with innumerable uses multiplied at an astonishing rate. In a way, the language proposed by Kolmogorov flourished as a tool of remarkable strength and precision, becoming what is now called stochastic calculus. It is worth clarifying the reason for this productivity: it is the boldness of the language. Bold in what sense? In the sense that this typical mathematical audacity consists of speaking about that which is only known through a sequence of approximation. First, Kolmogorov adopted the sigmaadditivity axiom, which supposes that the probabilities being studied are as consistent with series as with finite sums. This allows us to think about unknown events as limits and to handle them as if they were absolutely known; consequently, the language is more powerful. Next, for a similar reason, the spaces made by the probabilists are, like the majority of functional spaces used by twentieth century mathematicians, complete spaces where, let’s say, the convergent series converge, which allows us to manipulate their limits. The result today is so impressive that, aside from various debates about the interpretation of probabilities, the major contribution of the twentieth century will have been a language, that of stochastic calculus, which gamblers, physicists, economists, and speculators are free to use as they see fit. All this, clearly, is a far cry from philosophical ideas of probabilities. ‘Subjective probabilities’ in the above sense are quantifiable. We can do economic calculations with these probabilities. And there is the sense of a possible interpretation of reality, like those at the heart of Cournot's philosophical ideas of probability. Moreover, several authors, including the economist Keynes, note that some random situations lie outside the quantifiable domain. In political economics, it’s the role of the symbolic: the interpretations, positive or negative, that agents form of other agents, countries, cities, places of implantation, possible collaborations, etc. Fortunately, this means our affairs retain a touch of freshness, a bit of the unexpected, a taste of the non-axiomatizable creative human being. Looking back over my own life experiences, I see that all the choices I made are founded on meaning, on the significance of what is going on around me. I do not see any which could be assessable by probability, aside from specific economic choices that the financial structure imposed on me. I’m talking not only about the big decisions which direct

63 one’s life journey, but also the small things: for example, of the books in my library there are many that I’ve skimmed through often, but there are only a few I’ve read completely, each representing a choice that is absolutely non-quantifiable but which has had, nevertheless, some impact on the rest of my life. Nevertheless, we should delve deeper into the question because for some, all beliefs (including philosophical probabilities) can be handled in the framework of subjective probabilities. What exactly does this mean? It means adopting a point of view in which “individuals can quantify their beliefs, giving each a grade according to some linear classification, even if such a belief seems to fall under multiple dimensions, because they are capable of evaluating it by a monetary bet in the lottery of concrete actions in which they take part”. Such an assertion – we’ll summarize it here as “everything is quantifiable by subjective probabilities” – is impossible to prove. Certain phenomena happen only once, whether they pertain to a specific subject (first love, death, etc.) or are universal (the appearance of mammals, the proof of Golbach’s conjecture, etc.). Therefore one cannot establish this assertion by means of statistics, nor by the testimony of the people concerned since their accounts do not agree. So, it’s about a principle, and there may be advantages and disadvantages in adopting it. The advantages for economists, as we have seen, are methodological in nature. Not only does it lead them to a motivating program of research, where the laws of equilibriums or economic instabilities are rederived solely from the hypothesis that each agent

64 acts rationally, but an even greater advantage is that it pushes the borders of their discipline beyond all limits since, henceforth, at heart everything now finds itself in the field of economic reasoning. The drawbacks of this principle are felt by all those who think that some choices, certain risks are not a matter of financial negotiation and that they cannot be understood by acting as if they were14. In fact, except for economists, this principle still sheds no light on the problems in question. On the contrary, it brings additional doubts and perplexities caused - since we feel some idealogical pressure by the effort of thinking as if the principle were compulsory.

14. A typical example of a non-commercial situation where one classifies things by copying market-economic reasoning is the ranking of researchers by the system of publications in journals themselves valued, more or less, in terms of the citations of authors who publish within them. (cf. the methodology exposed by the web of science).

Democracy by Chance

66

Visite à l’atelier de Phydias, Hector Le Roux (1829-1900)

67

The Greeks assigned administrative responsibilities by a lottery system followed by a popular evaluation at the end of each term of office. Over the last thirty years or so there has been a resurgence of numerous political experiments where citizens are drawn by lots, either to establish a municipal budget, to give their opinion about a project, or to choose development principles. Society has become so complex that the knowledge of experts and decision-makers is no longer sufficient and direct interaction with the public is necessary by random selection. After two thousand years, have we returned to Athenian democracy? If so, why is the idea of drawing lots completely absent from all political literature since the nineteenth century?

68

69

In Berlin, over the last few years, a significant part of the city's budget has been given to citizens' juries for local projects. Committees were formed by drawing lots, according to categories specified by each neighborhood. Although this experiment was largely considered a success, it was not continued, because of budgetary restrictions imposed by the Berlin Senate. When French politician Ségolène Royal proposed a similar idea, in October 2006, to "clarify the way in which the elected could be held to account, at regular intervals, by a citizens' jury chosen by lots"1, there was an outcry from the right, from the center and from leftist leaders, as well as from the press and media. They spoke of popular tribunals “like those of Pol Pot or Mao Zedong” and of a certain public health committee of unhappy memory2. This violently hostile reaction, uniting professional politicians and media outlets, is all the more significant given the increasing number of such experiments around the world since the 1970s, be they for evaluating the environmental impact of projects, for triggering a larger mobilization of collective action, or simply to recognize social complexity (by opinion polls for example). Beyond the power-related criticisms, which accuse the proposal of the reciprocal anathema of "populism" and "betrayal of the elite", it seems this idea touches on a sensitive point which is intimately linked to the fact that chance obliterates ideology. In other words, by erasing the anchorage of political meanings, it prevents the expression of motivations considered fundamental to their supporters. Is a man drawn at random still a citizen since he is no longer as socialist, nor communist, nor liberal as he once was? Yet drawing lots has a long tradition in democracy. Greek cities, when not under the power of a tyrant, adopted very elaborate political institutions to bring popular opinion into judicial, administrative, and military decisions. With some variations (Athens, Milet, Pergamon, Priene, etc.), an ancient Greek city was governed by two entities: the Council, 1. Le Monde, November 18, 2006. 2. Cf. Y. Sintomer, Le pouvoir au peuple, La Découverte 2007, p. 7 et seq. A system of random selection proposed by the National Council for AIDS for the distribution of Ritonavir, in the case where there was not enough of the drug for all, had been violently rejected (Le Monde 3/1/96) under the pretext that it would pick ill people who wouldn’t benefit from the medicine.

70 the Boule, and the people’s assembly, the Ecclesia. Selected at random from each tribe, council members held office for one year. They met daily in the bouleuterion where the designated magistrates drew up proposed laws which the Ecclesia would then vote on. Those who were responsible for the law’s execution had to give explanations for it. In general, they were remunerated and could not hold office for two consecutive terms. Permanent commissions called the prytaneis sat at the center of the Boule presided over by an epistates drawn at random each day, who guarded the seal and keys of the treasury. The people’s assembly, comprising the male citizens of voting age (generally older than eighteen), met in the agora, presided over by an epistate. Anyone could speak, and votes were cast by raising a hand. The principle of random draws was the natural method of selecting people in a Greek democracy. Public officials were chosen by random draws, either through the use of an urn or the kleroterion, a device that we have some images of, but whose workings remain somewhat mysterious. Tiles, with names written on, were inserted into it and a tube and balls picked out the results, in a way that was unquestionably random, but perhaps not uniformly among the candidates.3 In any case, the presence of chance sufficed for the political purpose of this sorting method. The device had the virtue of causing a change of personnel, thus preventing the intrigues that inevitably come with any election. Ideally, Greek democracy distinguishes between the Kleroterion choosing of ideas and the choosing of men. Laws, decisions, and principles are voted on, whereas the people who vote are chosen at random. This central question of the selection of candidates is also where Plato's philosophy gets its incisiveness and originality. The system of Ideas (or Forms), true ideal entities of which we only see traces, is a way to solve this omnipresent problem of selection, be it in politics, at the Olympic games, in love, etc. 4 Plato, a determined opponent of democracy, 3. The functioning of the device had been imagined by Mogen H. Hansen La Démocratie athénienne à l’époque de Démosthène, Les Belles Lettres, 1995, cf. Y. Sintomer, op. cit. p. 43 et seq. 4. Cf. Gilles Deleuze, «Platon et le simulacre» in Logique du sens, Ed. de Minuit, 1969, p.292 et seq.

envisaged a republic based on different principles. Instead of the duality of choosing laws by vote and choosing men by chance, he proposed an Idea of justice, a justice above our partisan ideas of justice, a justice of the same scale as the city itself, which is to individual interests what the perfect geometric circle is to the crude circles that you or I may clumsily draw. The profundity and beauty of this system on a philosophical level contrasts with its practical weaknesses on a political level, as highlighted by several authors, including Karl Popper, who saw within it the roots of totalitarianism. In his analysis of the way rulers were chosen in Athens, Bernard Manin shows how the Greeks avoided the flaw random selection has of sometimes choosing incompetent indiPriene Bouleuterion viduals 5 : The system had two levels. First, the selection (for example for the designation of heliasts or nomothetes in the courts) was made between voluntary candidates. Second, every assignment of responsibility was subject to an evaluation at the end of the mandate. Therefore, public opinion felt like an important test of self-esteem for the magistrates concerned. As a result, no-one would volunteer unless they could reasonably agree to these conditions. Rotation of responsibilities and random selection arose from a clear mistrust of professionalism. As we noted when discussing Aristotle and Cicero, the drawing of lots was not thought of in the same way as today. Without going so far as to say that everyone saw it as the revelation of divine will, we must at least recognize that it was seen as not absolutely separate from an intention of the gods. This certainly fits with the idea that Jean-Pierre Vernant so insisted upon: there is no clear distinction in the Greek world between political and religious life. This uncertain, but plausible, trace of the divine in random selection gave a sufficient amount of legitimacy to those chosen, independent of 5. B. Manin Principes du gouvernement représentatif, Flammarion 1996.

any human will, to exercise their office without any worry. Similar traits are found in the Roman republic: “The random selection of the prerogative century,” wrote Bernard Manin, “made the result of its choice appear as an omen and an indication of the gods”. Moreover, the system of drawing lots continued in the governments of Medieval and Renaissance Italian Sienne, Palazzo, The good government, frescos of Ambrogio Lorenzetti cities under various forms, with the goal of preventing political (1337-1339). life from being dominated by factions which would perpetuate their power by ensuring the election of their own members. The case of Florence, a republic of which the Medicis repeatedly gained control by complex institutional games marked out by revolutions, shows, by the way in which the Medicis finally took control of all of Tuscany in 1530 in the form an hereditary dukedom, that random selection of officials, although flawed, may be the only way of guaranteeing democracy a place in society. As for the Venetian Republic, its institutions subtly combined a randomly selected committee called to appoint the candidates to the Council of Venice and the use of a secret vote to prevent the electoral campaigns that might have inflamed the factions 7. The real historical mystery of these times, insist Bernard Manin and Yves Sintomer, is the disappearance of lotdrawing from the institutions of the majority of regimes from the eighteenth and nineteenth centuries in Europe, except for special cases such as the juries of a court of law8. It is typical Sienne, Effect of the good government in the town. that Montesquieu and Jean-Jacques Rousseau devoted part of their reflections on political organization to random selection, as if that was evidently natural, while later, from the second half of the nineteenth century, no one spoke of it nor saw it as a possible institutional tool. It wasn’t until the 1970s that the idea reappeared, for rather different motives related to lifestyle and the environment, as a challenge by its users and citizens against initiatives made uncontrollable by technical innovation and profit. It is often said that a population of several million people

73 makes the practice of random selection unacceptable, but this argument does not really hold if we think of successive draws by categories exactly as the ancient Greeks and Romans did. Another objection is that the selection process is not perceived as fair unless the profiles, culture, and origins of the candidates are known by all, which is no longer clearly the case in modern societies9. But for Bernard Manin, the main reason has to do with the fact that random selection presents “this incontestable character that human will does not intervene and it cannot pass for an expression of consent. In a system of random selection, public officials are not brought to power by the will of the people they will have power over; no one brings them to power. In this sense, the draw in itself is not a procedure of legitimatizing power [...] an election, on the other hand, accomplishes two things simultaneously: it chooses those responsible, but at the same time their power is legitimatized and inspires a feeling of obligation and of engagement within those who appointed the candidates towards those who they have appointed”.10 There are other possible explanations, such as a changing view of the moral significance of chance. Following the ancient interpretation of chance, as an influence of the intentions of the gods, came the Church’s ambivalent position. It does not allow that prelates should be drawn at random, but some theologians recommend its use on the ethical level due to its fairness: “Let us suppose for example,” wrote Saint Augustine, “that you have something in surplus. It must be given to someone who doesn’t have it. But at the same time, you cannot give it to more than one person. Yet, if two people present themselves who have nothing over the other, neither out of need, nor by a friendly relation with you, nothing could be fairer than to choose by drawing lots”11. Nevertheless, divine will is not expressed by chance but by grace which the Church regards as sacred 12. Furthermore, the strengthening of the modern concept with Pascal, Fermat, and 7. The procedure developed for Doge’s election was incredibly complex with nine new successive levels (Le chef d’œuvre de 1268, according to Ladislas Konopczynski’s expression). Cf. J.-L. Boursin Les dés et les urnes Seuil 1990, p. 34 et seq. 8. From 1872 to 1905 in France and from 1831 to 1909 in Belgium, conscription relied on random selection. In Belgium, a neutral country not needing of a large army, it was possible to be replaced by paying one’s replacement, which destroyed all equality of the system which was abandoned by Léopold II under the principle argument that the strong proportion of poor in the army risked making it untrustworthy. 9. Cf. Gueniffey, Le nombre et la raison, EHESS, 1993. 10. B. Manin op. cit. Note that Manin said that the feeling of obligation is with those who vote and not with those elected! 11. Mentioned by E. Coumet « La théorie du hasard est-elle née au hasard ? » Ann. ESC n°3, May-June1970. 12. In the fifth century, Popes Celestin I and Leon I left writings confirming the designation of bishops by elected vote.

74 the Bernoullis, made the Church refine its stance on chance, regarding it as a game-like affair. In other words, it is attached to a morality far removed from serious management concerns of the modern industrial city. The eighteenth and nineteenth centuries saw the rise of the use of statistics, both at the level of information to help the State’s running and with the appearance of companies providing insurance against fire, for maritime traffic, against robbery, etc.13 Although rising premiums were still not calculated in a reliable way from the data, insurance theory progressed and its principles, at least, became clear. At the same time, Condorcet applied the calculus of probabilities to the study of voting. In a range of settings, he gave an estimation of the “grounds for belief” that good choices are obtained 14. Condorcet’s profound reflection on voting certainly contributed to the discrediting of random selection: “If choices are made at random,” he wrote, “a nation whose only laws are made by representatives elected by it undoubtedly enjoys a free constitution. Much has been done for its rights and very little done for its happiness.” Here, Condorcet introduces a new, strong argument that the conduct of affairs cannot be a random walk15, but should rely on a balancing principle. He continues, “Reduced to worrying about errors, passions and the corruption of its own representatives, a nation is forced to rely on other men, chosen equally randomly, to prevent these representatives from abusing their power. It’s not reason, virtue, or an identification of the interests of citizens and their delegates, that enables the nation to rely on them; it’s because of the balance of opposing passions, interests, and prejudices which fight against one another”16. The matter is closed. The superiority of a pluralist party system, allowing mandates with a structured content and achieving a balance of passions, is asserted. Jean-Jacques Rousseau

75 Like Montesquieu, who in turn was following Aristotle, Rousseau associated random selection with democracy and elective choice with oligarchy or aristocracy. In this debate, Rousseau drew a distinction between sovereignty, which he saw as the inalienable right of the people, and governance, which is necessary to run the country: “If one pays heed to the fact that the election of leaders is a function of government and not of sovereignty, one will see why random selection is more in the spirit of democracy, where the administration is better when its acts are fewer”. Sovereignty, for Rousseau, is an absolute concept of an immeasurable ideal: “Sovereignty cannot be represented for the same reason that it cannot be removed. It essentially consists of general will and will cannot be represented: it is either the same or it is different, there is no middle ground”. He supported his idea with excessive commentary, leaving no room for concession: “The English believe themselves to be free. They are quite mistaken. They are only free during the election of the members of Parliament. As soon as the members are elected, the public is enslaved; it is nothing. In the brief moments of their freedom, the use they make of it shows they deserve to lose it”.17 He concludes, “at the moment that a population gives itself over to representatives, it is not free, it is no longer free”. We see that Condorcet did not follow Rousseau to these extremes which, we should point out, lead him to dubious quibbles over the idea that “general will” is something clear and precise. There remained the question of how opponents could be said to be free while they were subject to laws to which they hadn’t agreed; to this Rousseau responded “The consistent will of all State members is the general will; it’s through this that they are citizens and free. When one proposes a new law to the people’s assembly, one is not asking whether or not they approve the proposition; rather one is asking whether or not it is in agreement with the general will which is theirs; by giving his vote, each one says his opinion and from the accumulation of voices the declaration of the 13. Karl Pearson designated this proliferation with the name “the boundless period” of statistics where insurance companies of every type appeared in England having their headquarters in taverns: against child abuse, for widows and orphans, and even for the chastity of spouses. (The History of Statistics in the 17th & 18th Centuries, lectures 1921-1933, Ch. Griffin & Co 1978). 14. In particular, he detailed the Borda-Condorcet Paradox concerning the voting of assemblies. Cf. R. Rashed Condorcet Mathématique et société Hermann 1974; J.-L. Boursin op. cit. p.128 et seq. 15. In mathematics, the formulatic description of a trajectory that consists of taking successive random steps. 16. Œuvres, ed. A. Condorcet, O’Connor and François Arago, in vol. 12, 1847-1849, Paris, t IX, p. 287 et seq. 17. Du contrat social, Book III.

76 general will is deduced.” A very interesting fusion is noticed here between discourse and meta-discourse: the opinion as to whether or not the motion reflects the general will is identified with the opinion of the motion itself. Today, in referendums, competitions, or opinion polls, we are accustomed to carefully distinguishing our opinion and our ideas from the majority view. The only situation where Rousseau’s position holds, curiously enough, is in financial markets where each person acts in anticipation of the balance sheet of everyone’s anticipation, which creates an instability that is often denounced, notably by Keynes. Rousseau became somewhat tangled up in the meaning of these general concepts: “Therefore, when the opinion contrary to mine prevails, this proves only that I’ve made a mistake, and that what I deemed to be the general will, wasn’t. If my individual opinion had prevailed, I would have done something other than what I had wanted, in which case I could not have been free”. This last phrase is a real pearl. It can be read over and over again; it has several meanings, all of which are far removed from ordinary rationality! A possible explanation is that Rousseau believed that we want to conform to the general will, that this is part of our personal will, and that sometimes inadvertently, by mistake or ignorance, we believe that we want something else. It’s an idea that sends shivers down your spine. But the reasoning is in the conditional tense: “if my individual opinion had prevailed”, meaning that the majority of individuals made the same mistake. Whence, then, comes the suggestion that it’s an error? The problem comes from the notion of the general will, which has taken the place of Plato’s justice, but the problem remains unresolved due to a hasty philosophical sublimation. In more modest form it is the same problem as underlies the concept of the average man, a notion proposed by early statisticians such as the Belgian Adolphe Quételet (17961874), with the aim of summarizing an entire population by a profile type, thereby neglecting the limits, variations, and frequencies of the population18. Statistical techniques have improved and the idea of a general opinion has reappeared today as opinion polls attempt to construct an image that can play the role Rousseau conceived. When done well, as they usually are today, surveys confront the elected officials with an image of social reality, sometimes better than their own impressions, thus putting them in an awkward position and risking the complete ruin of the democratic principle itself. Manin quite rightly stressed that the initiative and even the formulation of questions is done by the polling organization and thereby is an act of communication rather than an objective act of information-gathering. Usually, so-called “opinion” polls ask several questions. Some statistical manuals for human sciences say of such polls: “Precision is not affected by the number of questions asked”. If the survey is constructed well, then it is certainly true that the probability

77 law for the response to question number 7, say, does not depend on the number of questions asked but only on the sample size. However, it is equally true that if the number of questions increases, then the proportion of characteristics for which the sample is similar to the total population does not increase with the number of questions, from which it follows that many of the questions will have somewhat meaningless responses. This pitfall can be seen more clearly when the sample size is sufficiently small. If a dozen people, for example, are asked several thousand questions, then we would certainly obtain a clear idea of the characteristics of those interviewees, but we would not gain any more information about the whole population from interrogating our sample any further. In a very lively book, the mathematician John Paulos devotes a whole chapter to the problem of “too many characteristics, not enough people” by showing how quite false correlations among characteristics can be seen in a poor sample. He gives a striking example of the strange results that can arise from refining the categories 19. He imagines a person who, trying to build a reputation for himself, sends out letters to 1,024 recipients before a soccer match. In 512 of these letters he predicts that Team A will win, and in the remainder he predicts that Team B will win. After the match, he writes letters about the coming elections, sending only 512 letters, to those to whom he had sent a correct prediction about the soccer match. Again he shares two opposite predictions in equal measure. Continuing in this vein he will, in time, have a group of several people absolutely convinced that he has a remarkable gift for prophecy, and who are perhaps, in the absence of any other information, inclined to trust him once more. A new guru is born! Here, we hit the philosophical question of the qualitative survey: can the in-depth questioning of a limited population provide information that is even remotely scientific? It must be noted that the value sociologists attach to such surveys is not because they believe each individual response to be accurate, nor because of a hypothesis that the studied properties are independent. Their reasons are more interesting. In the first place, the sociologist considers individuals to be innately social in a number of their characteristics (lan18. Cf. Alain Desrosières The Politics of Large Numbers: A History of Statistical reasoning, Harvard University Press 2002, in addition, of course, the averaging between sizes linked by non-linear relations like height and weight is contradictory, which disqualifies the notion of “average representation” without further right of appeal. 19. John Alan Paulos Once upon a number, Penguin Press 1998.

78 guage, affection, communication, etc.) and that what is social strongly influences their conscience, and consequently their opinion. Marx’s famous phrase “It is not man’s conscience which determines his being, but his social being which determines his conscience” remains largely true as a methodological principle. Similarly, the sample can be used as an “indicator of its time”, as a mirror (cf. Richard Rorty’s specular man). We look, in the survey responses, not for the particularities of the individual questioned, but for the trace of social influence in his responses, the constraints he feels, and the interpretations his information suggests to him. We're looking for that which, while not conformist, we could call conformable. For this reason surveys contain questions about his reactions to new or supposed facts, as a means of detecting points of social support in his explanations. Theoreticians of the sociological method go further still: these surveys are designed to make the unconscious emerge. “Durkheim, who demands the sociologist enter the social world as if into an unknown world, credits Marx with having abandoned the illusion of transparency: ‘we believe there is much potential in the idea that social life needs to be explained, not by the impressions formed by those who participate in it, but by the deep causes which evade the conscious mind’”20. Pierre Bourdieu and his collaborators expounded a rather strong principle of the unconsciousness: “social relations cannot be reduced to mere relations between subjectivities driven by intentions or motivations because they establish themselves between conditions and social positions and, at the same time, they are more real than the subject which connects them”. The qualitative survey is a tool for revealing concepts (ideal-types according to Weber) which were hitherto unclear to the pollster. For example, some television viewers were surveyed about their choice of programs, the participants having allowed recording devices to be fitted to their television for a month. At the end of the survey there was no discernible correspondence between the choice of channels and the programs broadcast. A qualitative survey revealed that many of the viewers channel-hopped, i.e., scanned through all the channels looking for something appealing according to more varied criteria than simply the "program type", revealing these "types" to be too reductive. 20. Cf. A. Sauvy, L’opinion publique, Que sais-je PUF 1971.21. Cf. A. Röcke «Le tirage au sort dans les jurys berlinois» Politique et Société vol. 25, n°1, 2006, 13-20. 22. D. Bourg and D. Boy Conférences de citoyens, mode d’emploi éd. Ch. L. Mayer and Descartes and Cie, 2005. 23. Cf. TH. Frank, What’s the Matter with Kansas? How Conservatives Won the Heart of America, Metropolitan Books 2004.

79 A citizens' committee, then, can be thought of as a hybrid of poll and sociological survey, with the new dimension that the role of the chosen individuals goes far beyond merely answering a few questions. Experiments started in Germany and the U.S. in the 1970s and have multiplied in various countries since 1990. Their aim is always to address the rupture between the political classes and civil society, or between scientific and technological experts and ordinary citizens. We refer the reader to Yves Sintomer's work, cited above, for the full story of the flourishing of this new genre of political participation, but we need to single out the citizens' juries, chosen randomly from the electoral rolls, with the remit of addressing town-planning issues and environmental problems. The Berlin juries are among the most spectacular where, between 2001 and 2003, over 8 million euros were made available to juries chosen randomly in 17 neighborhoods of the capital, to encourage local projects21. The principle of participatory budgets used in some German communities saw the budget allocations being debated publicly among citizens chosen at random according to a representative sample which saved these assemblies from storms and disruptions caused by outspoken minority groups. The idea of deliberative polls is similar for the more general questions and a theory of these has been developed by the academic James Fishkin. The Citizens' Assembly of British Columbia was chosen at random in 2004 to prepare the text for a referendum on reform of the electoral system. In France Citizens' Conferences are often convened to address ethical or environmental problems related to technological innovations.22 As noted above, the spirit of these experiments differs greatly according to whether the random selection is made among candidates who volunteer for a role, or among individuals who are, a priori, disinterested. It has, then, a mobilizing role in the running of a city, counteracting the oft-lamented abstentionist apathy. The new mystery, posed by the reappearance of these random-selection procedures in the public realm, is their very low profile in the press and the media. The public has some sort of fear of chance, which is guilty of not acknowledging the efforts that have been made which have lead society to where it is today. Ultimately it is the fear of jeopardizing what one has if there are many who have less23. Chance touches the very heart of the concept of democracy.

80

Gestalt Structure Pattern

82

83

Cournot's ideas have been greatly developed by psychologists, art theorists, in literature and, more recently, in work on artificial intelligence. We want the reader to become reacquainted with certain of these direct and concrete phenomena through some examples. He will then become aware of the phenomenon of irreversibility in symbolic perception, which explains one of the aspects of scientific "progress". It poses then the question of the uniqueness of scientific interpretation, defended by a scholar such as Peirce near to positivism, but opposed by others such as Chomsky. We illustrate these debates with Japanese mathematical curiosities from the era of Edo, and importance of structures in physics.

85

Indeed, the most important point, or rather, the very basis of this thesis, clear and obvious for philosophers and theologians, is that there exists a power in the soul which conceives and forms the resemblances of things, which proposes and offers them to reason when it speaks and to understanding when it contemplates; that is called fantasy or imagination. Jean-François Pic de la Mirandole1

At this point we need to a step back, for the unexpected reason that a certain author, and not an unimportant one, has devoted an entire chapter to the notion of "unphilosophical probability". We refer to David Hume and his famous Treatise of human nature 2. The ideas he presents there are worth reviewing, since they form part of his conception of the imagination, a key element in his philosophy of psychology. Hume's questions about probability concern the origin of our judgments and our beliefs. He distinguishes three categories of probability that have been considered by "philosophers": those relating to chances - the chance of winning a bet, a game or something similar, those relating to causes - where, by deductive reasoning, we determine what is most likely to have caused an observed effect, and those which come from analogy - where a similarity, strong or weak, with another situation, enables us to make a judgment based on the strength of the similarity. All these kinds of probability are accepted by philosophers and allowed to be reasonable foundations of belief and opinion. But, there are others that are derived from the same principles, though they have not had the good fortune of obtaining the same sanction.3 1. Nephew and biographer of the great scientist Jean Pic de la Mirandole, De imaginatione, Venise 1501. Chap. IV. 2. A Treatise of Human Nature, Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects, 1739. 3. Ibid.

86 Hume saw these unphilosophical probabilities as cases where our judgments are dubious for less noble reasons: because we forget, for example, because an argument's strength fades with time, or because we are swayed by that which is more recent and more fresh, etc. He takes a practical point of view, one which would become a major thread of AngloSaxon philosophy from John Stuart Mill to the American Pragmatism of Peirce, Dewey and William James. The argument, which we found on any matter of fact we remember, is more or less convincing according as the fact is recent or remote; and though the difference in these degrees of evidence be not received by philosophy as solid and legitimate; [...] it is certain, this circumstance has a considerable influence on the understanding, and secretly changes the authority of the same argument, according to the different times, in which it is proposed to us.[...] A lively impression produces more assurance than a faint one; because it has more original force to communicate to the related idea, which thereby acquires a greater force and vivacity. [...] Thus a drunkard, who has seen his companion die of a debauch, is struck with that instance for some time, and dreads a like accident for himself: But as the memory of it decays away by degrees, his former security returns, and the danger seems less certain and real. [...] It is certain, that when an inference is drawn immediately from an object, without any intermediate cause or effect, the conviction is much stronger, and the persuasion more lively, than when the imagination is carried through a long chain of connected arguments, however infallible the connexion of each link may be esteemed. [...] A fourth unphilosophical species of probability is that derived from general rules, which we rashly form to ourselves, and which are the source of what we properly call prejudice. An Irishman cannot have wit, and a Frenchman cannot have solidity; for which reason, though the conversation of the former in any instance be visibly very agreeable, and of the latter very judicious, we have entertained such a prejudice against them, that they must be dunces or fops in spite of sense and reason. Human nature is very subject to errors of this kind; and perhaps this nation as much as any other.4 4. Ibid. 5. Ibid

87 As well as the role they play in reasoning, which is so dear to philosophers, memory and imagination also have a decisive role in the formation of our judgments. This is described by Hume, with neither emphasis nor idealism, as a faculty which is often automatic, produced spontaneously by use and interest: Nothing is more admirable than the readiness with which the imagination suggests its ideas and presents them at the very instant in which they become necessary or useful. [...] When we remember any past event, the idea of it flows in upon the mind in a forcible manner; whereas in the imagination the perception is faint and languid, and cannot without difficulty be preserved by the mind steddy and uniform for any considerable time.5 Hume constantly draws on the notion of the imagination, showing by examples its underlying presence in the majority of problems. As an example of human weakness, it gives him ammunition in his critique of the overly pure and theoretical views of philosophers, along with the dual notion of memory. He doesn't trust the imagination, and he draws the reader's attention to its mistakes, but its limits and automatic reflexes give him a point of support for his controversial dialogues. But Hume does not see it as the source of artistic creativity or, a fortiori, that of scientific creation.

Before going any further, let's look at some more examples.

88

At first, these graphics seem nothing but random marks, and they leave us indifferent. As Hume said: "A cause traces the way to our thought, and in a manner forces us to survey such certain objects, in such certain relations. Chance can only destroy this determination of the thought, and leave the mind in its native situation of indifference; in which, upon the absence of a cause, it is instantly re-instated." But if you turn to page 294, you will return here with meanings that cannot be erased, which will prevent you from ever again seeing this diagram the way your eyes actually perceive it.

89

Here is another similar example, albeit slightly more concealed, (cf. page 295).

90

For a child learning a language and its "correspondence" with the world, it's a constant game of choosing between beings and forms which are more or less known: look, suppose, guess. Rudyard Kipling brilliantly exploited this spontaneous ability. In his Just so Stories he hid Mister "One-Two-ThreeWhere's-your-Breakfast" among the trees near the leopard and the Ethiopian. (cf. page 296)

Certain works of arts also, either by accident or by design, present an ambiguity that is conducive to the imagination. They leave significant forms or structures surrounded in doubt, creating an effect which induces an interpretative state of mind.

91

Rembrandt's View of Omval is thought to contain, hidden in the foliage of the old tree on the left, a pair of lovers. This is more or less clear from the preliminary etches (1645) and it fits with the composition: the person standing is contemplating the landscape and the lovers need to hide themselves.

92

The engravings illustrating Jules Verne's stories delicately use the texture of the woodcut to hint, leaving the text to carry the imagination beyond what has been drawn. (Around the World in Eighty Days, Hetzel)

Is this a picture of two lovers kissing? A bride? Is she crying on her father's shoulder? Or is it two sailors, seen from behind, scanning the murky seas, with the rain glistening on their backs? (Georges Seurat 1882). In the catalog of Seurat’s works this drawing is called ‘La nourrice et l’enfant’ (The wet nurse and the child).

These examples show that if simplicity intervenes, our propensity to believe that there is something there, emphasized by Cournot, is linked more generally to meaning, with all the vagueness that goes with that. But they also reveal a decisive feature which brings into question the very nature of knowledge itself: a phenomenon of irreversibility. We are incapable of no longer seeing what we have discovered. It is impossible for us to rediscover our naivety, that neutral point of view we had when we found ourselves facing a random situation.

Therefore, there is some kind of progress in the interpretive dimension. This innocent observation is at the heart of the most profound questions: doesn't it lead us to conclude that knowledge itself is a process which advances irreversibly and univocally, dragging us away from an ancient world that we may actually have preferred, leaving us with a nostalgia for our childhood or for some golden age? On the other hand, this univocality is refuted by the plurality of interpretations. We tend to forgot this plurality, because of the force with which each particular interpretation strikes us, but it obliges us to be more detached, and to consider seduction by one sole reading of the world as a form of alienation. One may reasonably disagree with Marxism, for methodological reasons, or because of political or historical analysis. However, anyone who looks for signs, in the behavior and comments of his contemporaries, that indicate

A victory of meaning over chance, the reconstruction of a puzzle by following meanings is, for Kuhn, an analogy for the scientific process, at least for what is “normal” science where a theory exists with which one reads the met configurations (King of Rome’s5 game, Fontainebleau). 5. The son of Napoleon

Blind Tiresias, Lagrenée engraving 1775. A pitfall of interpreting is that to see other interpretations of the world, it is good not to be held captive by one point of view. Diviners and poet creatures of myths were often blind. Homer, as well as Demodokos, the aëdes of the Odyssey, were blind. The great diviner Tiresias had been rendered blind for having inadvertently seen the goddess Athena naked. In the story of the Argonauts (Apollodore, La Bibliothèque, Livre I, chap. 9, v. 20), the diviner Phinee is blind, and likewise, more recently, so is the old man Ogotemmêli who reveals the mythology of the Dogons to Marcel Griaule (Dieu d’eau, Fayard 1966). On the other hand, Saint Paul rendered the false prophet Bar Jesus blind as he didn’t see the true interpretation (Acts of the Apostles).

whether or not consciousness is affected by social conditions, will find it hard to avoid Marx's interpretation, because of its ubiquity. In this way circular reasoning infects all discussions and debates about "class", even though the concept of class needs some re-thinking today. Nevertheless, this political interpretation is also reinforced by the fact that a growing proportion of people, especially young people, have a very poor grasp - little more than a caricature - of Marxist ideas, yet obstinately proclaim the interests of their social strata. This is the only reason I can see for the continuing presence of extreme left wing parties in various elections, especially since every vote they receive is one less vote for the principal left-wing party. In the light of this, and the fact that Marx - along with the theoreticians of dialectical materialism

97 - always maintained that his doctrine was "on the side" of science and that science was "on their side", it is hardly surprising if Marx was tempted to equate this "growing interpretation", of class-consciousness, with growing knowledge. Was it emancipation from ignorance that the proletariat were pushed into, or an indoctrination towards a specific, bold understanding, with risky or even catastrophic consequences? We should also now re-consider the uniqueness of science that is so dear to positivists. In his reflections on the foundations of linguistics, Noam Chomsky investigated the linguistic abilities of a child, which must be general since the child does not know, at birth, what particular language he will learn. Chomsky refers to Charles Peirce for an explicit comparison between the interpretative gifts of a child and the nature of scientific advances: [Peirce] held that innate limitations on admissible hypotheses are a precondition for successful theory construction and that the “guessing instinct” which provides hypotheses makes use of inductive procedures only for “corrective action,” [...] He noted “How few were the guesses that men of surpassing genius had to make before they rightly guessed the laws of nature.” And, he asked, “How was it that man was ever led to entertain that true theory? You Ogotemmêli, blind keeper of the Dogon cannot say that it happened by chance, because the chances are too overwhelmmythology. ing against the single true theory ever having come into any man’s head in the twenty or thirty thousand years during which man has been a thinking animal.”6 Chomsky distanced himself from the pragmatic ideas of scientific progress that Peirce7subscribed to, believing in6. Language and Mind, Harcourt, Brace & World, 1968 7. Peirce is a typical representative of the doctrine which states that science converges on truth. The possibility of several interpretations of facts or the possibility of facts full of social determinism is totally strange to him. See his founding article “The Logic of Science”, written in French, in Revue philosophique de la France et de l’étranger, VII, 1879, 39-57, which leaves no doubt about this subject.

98 stead that "Formally speaking, acquisition of 'common-sense knowledge' - knowledge of a language, for example - is not unlike theory construction of the most abstract sort". Chomsky's thesis is that the innate has an important role. In our terms, then, biological predispositions explain how philosophical probabilities apply to the recognition of grammatical structures by a child just as well as they apply to the discovery of scientific laws. While we're talking about Peirce, it's worth noting that this very original thinker developed a whole theory of chance which he called tychism in reference to the Greek tyche. This doctrine came to change his conception of scientific knowledge as an approximation to Truth, in a very simple way: beyond the horizon of scientific knowledge is a residue of absolute chance which plays an important role in explaining why the world is the way it is. Physical laws do not govern everything to the tiniest detail. This doctrine was later taken up by William James in his pragmatist philosophy, in a somewhat different spirit of openness and tolerance to everything surprising and unexpected, in nature as much as in the religious or political views of men. The idea of tychism, which is sometimes seen as a premonition of the uncertainties in quantum mechanics, had already touched philosophers since Kant wrote8 It is absurd for man to hope [...] that one day another Newton will come who will be able to explain to us, in terms of natural laws not governed by any intention, how a simple blade of grass is produced. Kant's representation is similar to the Aristotelian way of thinking about chance, whereas Peirce does not refer to any intention, a considerable difference indeed, and one which we will meet again later when we consider chance in biology. For Peirce, the interpretative dimension - our philosophical probabilities - remains a factor in scientific discovery, and not an element of the world itself, since he defines reality as "the thing whose characteristics do not depend on the idea one may have about them". William James was more flexible in this regard and, in his quasi-ecumenical view of pluralism, he granted a place to diverse interpretations of reality without, however, going as far as the idea that science could encounter truly divergent situations where strategic or ethical choices arise.9 8. Kritik des Urteilskraft (1790) §75. 9. We will return to William James’s reasoning in more detail in Chapter XI.

99 Bifurcations in science are, in fact, possible; they have happened as a result of particular political circumstances in the past. For example, it happened to geometry during a period when Japan tightly controlled its external influences, leading to events which reveal a lot about the role of interpretation in the discovery and social respect attached: During much of the Edo period (1603-1867), Japan was almost completely cut off from the western world. Books of mathematics, if they entered Japan at all, would have been scarce. Yet, during this long period of isolation people of all social classes, from farmers to samurai, produced theorems in Euclidean geometry which are remarkably different from those produced in the west during the centuries of schism, and sometimes anticipated these theorems by many years. These theorems were not published in books, but appeared as beautifully colored drawings on wooden tablets hung under the roof in the precincts of a shrine or temple. [...] A sense of form, and an appreciation of natural beauty have always been strongly marked characteristics of the Japanese people. Consequently, it is not surprising that geometry, which attracts because of its beauty and the inevitability of the constructions and theorems, should have persuaded the diverse but equally devoted practitioners of the art that geometry was a subject fit for presentation to the gods. [...] Tablets might contain five or six theorems, almost always

100 beautifully colored. The name of the place of worship was not usually indicated, but the name and social rank of the presenter was always given. The proof of the presented theorem was rarely given. [...] The method of discovery of geometrical theorems during the Edo era, and, of course, since, seems to have relied on intense and prolonged concentration on an accurate geometrical figure. 10

The problems concern relations between distances, and vary in difficulty. On this tablette from 1852 the problem is to find the relation between the radii of the little circles (r4 r1 r22+r4 r3 r22 = r1 r2 r32+r1 r4 r32). But often the questions are deeper and can involve ellipses, spheres etc.

Votive tablet

101 One of the most famous problems is that hung in the Gion Temple in Tokyo by Tsuda Yenkyü, requiring a relation of 1,024 degrees, which was simplified by Nataka to a relation of the 46th degree. The challenges posed by these problems resemble those considered by European scholars of the seventeenth century. The historian Yoshio Mikami, a specialist in these questions, states that Japanese mathematics was not so much a science as an art.11. But is there a clear division between art and science? Today, we have abandoned the neo-positivist view in this respect. The interpretative dimension is the cornerstone of the Gestalttheorie - the theory of structures - that was developed by German philosophers at the end of the nineteenth century, which has had a tremendous influence on art and science. The principle themes, developed by Christian von Ehrenfels, then by Max Wertheimer, Wolfgang Köhler and Kurt Koffka, assert that there is an interaction between a whole and its parts in such a way that the parts are ontologically different depending on whether they are isolated or combined. This relation is situated at the level of our understanding; in our psyche, forms are understood as structures. This theory thus supports the idea that meaning - or some meaning - appears by the emergence of structures in our mind, forms being the "words" of our mental representations. Furthermore it asserts that we do not see that which is not meaningful for us. Thus in the first example of this chapter, the words "THE FEET" are invisible to begin with. In the same way, the clear-cut, 10. San Gaku, Japanese Temple Geometry Problems, Winnipeg, Canada, 1989. 11. Y. Mikami The Development of Mathematics in China and Japan, Chelsea 1910. Cf. on this subject J. P. King The Art of Mathematics, Plenum 1992.

102 clean and bright region formed by the sky in a street-scene bordered by buildings, passes unseen because it does not connect with any particular meaning, so we simply do not see it as it is. These ideas were very natural sources of inspiration for artists at the beginning of the abstract movement, notably in painting with Vassili Kandinsky and Paul Klee, but equally in all the creative visual arts. Thus Bauhaus was a school in both senses of the word. Design, like architecture, is a functional art. Form is linked to function. In the minimalist aesthetics, the form tries to express this function as strictly as possible. In other styles the form is embellished with additional cultural signifiers, referring to canons of beauty or originality. In all cases creation proposes an interpretation. The unusual relation of forms and uses creates the effect of a story, like a foreign phrase which we understand by its context. Gestalt and Gestell - key concepts in Heidegger's philosophy - are two derivatives of the verb stellen - to put. The first concerns that which is composed (put together), that which is presented as a composition of organized parts. The second has been rendered as posure, that which is put to use. Heidegger emphasized the potential of technology which is available, and which, simply by its presence, puts us in a state of active and accepted dependence that merits philosophical reflection. Heidegger's position, one hotly debated, seems to be a kind of regret that we cannot manage to dominate these technological devices to direct them towards agreed goals. To say that posure [Gestell] holds sway means that man is posed, enjoined and challenged by a power that becomes manifest in the essence of technicity - a power that man himself does not control. Thought asks no more than this: that it help us achieve this insight. Philosophy is at an end. 12 After what we have seen, we can note that the effect of irreversibility, holds for Gestalt as well as for Gestell, for different but related reasons: it concerns that which we take (Gestell) and that which we take in, or understand (Gestalt), in some sense. Even so, Heidegger's position is very ambiguous, having declared to Spiegel in 1966: I see the situation of man in the world of planetary technicity not as an inextricable and inescapable destiny, but I see the task of thought precisely in this, that within its own limits it helps man as such achieve a satisfactory relationship to the essence of technicity. National Socialism did indeed

103 go in this direction. Those people, however, were far too poorly equipped for thought to arrive at a really explicit relationship to what is happening today and has been underway for the past 300 years. What he meant by "achieve a satisfactory relationship to the essence of" technology is unclear to say the least. Today, when anthropotechnology - the genetic improvement of man, or more correctly, of certain men - have acquired the feasibility of absolute likelihood, provoking a fantastic, exuberant passion in some University communities (the transhumanist movement13) , the position of the philosopher of being converges with the most irresponsible eugenic trends. But let's get back to structures. If, in the middle of the nineteenth century, Cournot based his work on a clear distinction between philosophical probabilities and the quantitative domain, the development of computer science in the twentieth century came to modify the boundaries of these categories somewhat: pattern recognition, the recognition of forms, aims precisely to achieve a job that was hitherto psychological. Two important periods followed. After von Bertalanffy and Herbert Simon, in an excessive enthusiasm for the feats that computers were achieving, had predicted miracles (general problem solver, etc), the results became less impressive: automatic translation, speechrecognition and the recognition of handwriting were all found to be much harder than imagined. There was little grasp of the hurdles to be overcome, a false impression derived from the implicit evidence that people who understand a language find the process easy. Subsequently, for situations that are repetitive and enable an algorithm to learn (recognition of speech and writing, notably), the recognition of forms has progressively made substantial progress thanks to the methods of reorganized networks (neural networks) and random search algorithms (simulated annealing), among others. Finally this progress, far from having made the quantitative dominate where Cournot saw only the qualitative, has confirmed the importance of Gestalttheorie. Papers on artificial intelligence constantly reference it, as a typically human achievement that systematic methods need to confront themselves with. 12. Martin Heidegger, Der Spiegel 1976, tran. William Richardson. The interview was granted in 1966 on condition that it was only published posthumously. 13. Cf. collected works The New Humanists, John Brockman, ed. Barnes & Noble 2003.

105 In truth, this opposition of qualitative against quantitative has faded somewhat. Mathematics is also a qualitative science, and the notion of structure plays a huge role in it. Just before World War II, the philosopher Albert Lautman gave a remarkable analysis, showing how the ontology of the thing itself was wrong in the mathematics of his time, ideas which had a determining influence on the work of the Bourbaki group14 : It is impossible to consider a mathematical "whole" as the result of the juxtaposition of elements defined independently of all consideration of the structure of the whole of which these elements are parts. There is a link from the whole to the part, and a link from the part to the whole.15 At the end of the twentieth century the development of numerical methods of discretization for numerous problems in physics risked tipping the balance towards the quantitative. In this regard René Thom was right to insist on the importance of qualitative representations in applied questions and on the richness of mathematical language in this respect, which we showed in a particularly brilliant way in several works.16. The ideas of Gestalttheorie, those of Albert Lautman on mathematics, and those of an important person we will meet again later, Ferdinand de Saussure, were deepened and developed in a broad range of disciplines at the time of the structuralist movement, after the war: Roland Barthes in literature, Jean Piaget in pedagogy, Noam Chomsky in linguistics,

Old French sing which makes fun of overinterpreting, a typically paranoiac feature. The sentences take a new meaning by vague homophony : le coucou > casse lui le cou cancan > jette le dedans dodo > casse lui les os alleluia > faut pendre le gars and the false interpretation is threatening, I run away ...

14. A. Lautman «Essai sur les notions de structure et d’existence en mathématiques» in Essai sur l’unité des mathématiques et divers écrits (principal thesis 1937) Union générale d’édition 1977. Cf. on this subject N. Bouleau Philosophies des mathématiques et de la modélisation, l’Harmattan 1999, p. 126 et seq.15. A. Lautman op. cit. 16. R. Thom Modèles mathématiques de la morphogenèse, Interéditions 1989; Prédire n’est pas expliquer, Eshel 1991.

106

The eyes on peacock feathers dont follows the lines of the fibers. It is like a printed motif. That supposes a highly complex programmatic structure when the feathers grow.

Claude Lévi-Strauss in anthropology, Jacques Lacan in psychoanalysis, Michel Foucault - despite distancing himself from the theory - in social philosophy, and many others, showing that structural thoughts could renew methods and concepts in human sciences. Nor were these ideas absent from physics. Continuing a line of ideas from Bachelard and Thomas Kuhn, the theoretical physicist Jean Ullmo, made them a key part of the epistemology of physics. The following passage - a delightful manifesto in favor of structures - interests us mostly for the underlying conception of scientific invention: At the same time as trying to anticipate by calculation (or qualitatively) the result of new experiences, the structures suggest new types of interaction to try, based in analogy: different phenomena where one recognized (or supposed) a similar structure could be translated one into another. [...] Thus, in providing a quantitative basis for calculations, and a qualitative basis for analogies, structures are at the origin of almost all of the great developments in science. Let's recall a few examples:

the most classical is Copernicus's heliocentrism compared to the Ptolemaic theory. The structure of epicenters and of "deferents" give a good account of the contemporary astronomical laws; but Copernicus's new structure of the solar system opened the way to Kepler, Newton and modern science. Faraday needed structures to explain electrical and magnetic laws; he imagined invisible threads strung through space between charged bodies which helped Maxwell to conceive of displacement currents and enabled him to establish the electromagnetic theory. The most striking example is that of Mendeleev's periodic table; it was nothing but a gathering of laws, or, better, of patterns, and its author, being a positivist, did not plan for it to reveal an atomic structure un-

107 derlying the simple elements in chemistry. It suggested to J. Perrin and Rutherford their structure hypothesis, the miniature solar system with its electronic layers; out of which came everything in modern physics [...] To propose the hypothesis of a structure to interpret known laws is to describe a new object, to found a new explanatory theory; if it is true, as we have remarked before, that from the point of view of the acquired knowledge of science, relations are essential, and interpretations (objects, theories) are secondary and changing, - from the point of view of progress of science, the relations are just the starting point; the interpretations are the essential tool. (J. Ullmo, La pensée scientifique moderne, Flammarion 1969.) We have seen that Cournot's philosophical probabilities are distinguished from subjective probabilities by their unquantifiable character and that they provided a way of speaking of the structures of Gestalttheorie avant la lettre. But the boundary around them remains unclear. So we need a strong argument, a slogan to write on our banner, to definitively counter all temptation to reduce our interpretative talent to systematic procedures. The debates can drag on forever. A trail can be glimpsed, however, if we consider the extreme cases, the borderline behaviors. Our behaviors are not the same as those of machines. With our frequent and widespread penchant for paranoia, we can never tell if we are overinterpreting or not. In most cases one cannot say. But if a machine overinterprets, it usually interprets badly; we do not care about the state of its soul.... We will return to this side of things in Chapters XII and XIII.

108

The Third Dimension of Risk

110

111

When faced with uncertainty or when mediating in conflicts - negotiating possible compensations and reaching agreements - we tend to try to objectify risks. We ignore the subjective elements of the situation, or anything that depends on interpretation. But there is always some element which cannot be reduced to economics, and which is necessarily political in nature. A little story illustrates this better than a long proof, and it also gives us the opportunity to enjoy some of Milan Kundera's writing which gives a delicious and accurate description of this delicate topic.

112

113

With local elections approaching, the small town of Montry was unusually active. Conversation frequently turned to the elections as people tried to discern the trends without revealing their own preferences. As always, the shopkeepers agreed whole-heartedly with their customers while passing on rumors with all the usual caveats. And, of course, bets were placed. Maxime Pentier stood for election for the first time, encouraged by friends with whom he had created an independent ticket founded on strong ideas and a clear program to collectively assume responsibility in the face of uncertainty as well as thinking of long-term dangers and threats to the community. The term sustainable development would take an operational and concrete sense: local problems went beyond the town boundaries; they also concerned a basin which fed into the water supply in Montry. Jobs, factories, nature, means of communication, everything would be considered with sustainability in mind, and the choices debated through dialogue and democratic cooperation: "a reasoned and wise adventure", as his motto put it. The election campaign took place with dignity, there was nothing more to do but wait for the result of the polls. Maxime Pentier had had a rational, even rationalist, education. He had grown up in a family of radical teachers where secularism was the most highly regarded value. Access to science was considered an honor in the family. Knowledge and reason should be the foundation of judgment as that was the only way to elevate society above superstitions and partisan beliefs. John Stuart Mill, Bertrand Russell, and John Dewey were his great influences, but, considering the complexity of the modern world, Maxime went even further and intended to apply himself, through his political and economic behavior, to the most complete rationalization of ends and means. Statistics lectures he attentively listened to at university had made him understand TWO DIMENSIONS of risk: first, that which concerns the probability of an event measured as a percentage, and second, the sum of the damages for an accident or the gains for a bargain. Often repeating to himself this passage of Shakespeare from Henry IV We all that are engaged to this loss Knew that we ventured on such dangerous seas That if we wrought our life 'twas ten to one; And yet we ventured, for the gain proposed Choked the respect of likely peril fear'd,

114 Maxime Pentier was convinced that risk was a matter of probabilities and stakes, that he needed to evaluate both well if he was to obtain the best of all possible worlds. Believing that the market works to ensure that the price of goods perfectly represents their value, Maxime unhesitatingly conformed to this way of thinking. He had grown to realize that life consists of preferences. Between possessions of the same price - eight pairs of shoes and a washing machine, or a trip to Sicily - his choice was a function, more or less, of his background and previous choices: he had a utility function. This discovery contributed to the serenity he needed to maintain a harmonious professional life, where uncertain decisions could be made rationally in accordance with his personal tastes. So, after some adolescent misadventures, he decided to organize his love life rationally, choosing a companion with the help of the YourHalf.com website. This site had people from around the world, and the ease of dialogue appeared to optimize the chances of success1 . The first contacts ended in failure: they were either ugly or easy women, as he told his workmates. He needed more precise criteria, so he devised a synoptic table enabling a multidimensional analysis of his contacts based on a questionnaire that provided a list of indicators, in the same spirit as the most recent administrative and budget management procedures. He found a large number of candidates. Being prudent, after his recent experiences, he attempted to evaluate the sincerity of their remarks. How could he have known? How could he have gauged it? Any schoolboy can do experiments in the physics laboratory to test various scientific hypotheses. But man, because he has only one life to live, cannot conduct experiments to test whether to follow his passion (compassion) or not. (M. Kundera, Unbearable Lightness of Being, trans. by M. H. Heim, Harper 1984) However, “something happened” at one of his encounters. He told a woman named Marta to meet him at St. Mark’s, 1. This kind of idea, facilitated by the Internet, is not new. At the beginning of the eighteenth century, trends spread all types of relationship assurances, particularly in London society which adored club activities. For example, for a deposit of 2 Shillings, the Office of Assurance on Marriage guaranteed a gift of 37 Pounds at the time of the marriage of two of its members. The absence of precise statistics allowed the justification of the premiums that these companies made which were often exorbitant, except for a few including Lloyds founded in 1716.

115 a small chapel at the edge of Montry. Following his usual conversation he discussed mad cow disease, GMOs, nanotechnology, etc. with her. Sat together on a rock bench in the midday sunshine, besides this Romanesque chapel, they contemplated the flowers in the graveyard and the distant valley. She was politely listening to his grand theories when they both caught sight of a shrew furtively slipping into a small cranny between two rocks, sparking new life into their conversation: Shrews are small, threatened mammals ... Marta's face and silhouette were quite different to those of Maxime’s mother or sister, but she had a certain something, in her smile and they way she listened to him, that reminded him of both. "The probability of our meeting was one in a billion. "What method do you use to calculate the probability of human meetings?" "Do you happen to know of any method?" "I don't. And I regret it," I said. "It's odd, but human life has never been subjected to mathematical research. Take time, for example, I long for an experiment that would examine, by mean of electrodes attached to a human head, exactly how much of one's life a person devotes to the present, how much to memories, and how much to the future. This would let us know who a man really is in the relation to his time. What human time really is. And we could surely define three basic types of human being depending on which variety of time was dominant. But to comes back to coincidence. What can we reliably say about coincidence in life, without mathematical research? Unfortunately no existential mathematics exists as yet." "Existential mathematics. An outstanding idea," Avenarius said thoughtfully. Then he added, "In any event, whether it was a matter of one in a million or one in a billion, the meeting was absolutely improbable, and it was precisely the lack of probability that gave it value. For existential mathematics, which does not exist, would probably propose this equation: the value of coincidence equals the degree of its improbability." (M. Kundera Immortality, trans. by P. Kussi, Harper 1990.) Maxime married Marta because he felt a confirmation of his method within her. He saw the shrew as a sign, not of the supernatural, but of a shared sensibility about certain things in nature, a coincidence of interests that was objectively remarkable. When she returned to the car it was already late afternoon. And at the very same moment that she was putting

116 the key in the car door, Professor Averenius, in swimming trunks, approached the Jacuzzi where I was already sitting in the warm water being bombarded by the violent currents under the surface. That's how events are synchronised. Whenever something happens in place Z, something else is happening in place A, B, C, D, and E. "At the very moment that..." is a magic sentence in novels, a sentence that enchants us when we read The Three Musketeers, the favorite novel of Professor Avenarius, to whom I said in lieu of a greeting, "At the very moment that you stepped into the pool, the heroine of my novel finally turned the ignition key to begin her drive to Paris." "A wonderful coincidence," said Professor Avenarius, visibly pleased, and he submerged himself. "Of course, billions of such coincidences take place in the world every second. I dream of writing a big book. The Theory of Chance. The first part: chance governs coincidences; the classification of the various types of coincidences. For example 'At the very moment that Professor Avenarius stepped into the Jacuzzi and felt the warm stream of water on his back, in a public park in Chicago a yellow leaf fell off a chestnut tree.' That is a coincidence, but without any significance. In my classification of coincidence I call it mute coincidence. But imagine me saying : 'At the very moment the first yellow leaf fell in Chicago, Professor Avenarius entered the Jacuzzi to massage his back.' the sentence becomes melancholy, because we now see Professor Avenarius as a harbinger of autumn and the water in which he is submerged now seems to us salty with tears. Coincidence breathed unexpected significance into the event, and therefore I call it poetic coincidence. But I could also say what I told you when I saw you just now: 'Professor Avenarius submerged himself in the Jacuzzi at the very moment that, in the Swiss Alps, Agnès started her car.' That coincidence cannot be called poetic, because it gives no special significance to your entrance into the pool, and yet it is a very valuable kind of coincidence, which I call contrapuntal. It is like two melodies merging into one small composition. I know it from my childhood. One boy sang a song while another boy was singing a different one, and yet they went well together! But there is still one other type of coincidence: 'Professor Avenarius entered the Montparnasse Métro at the very moment a beautiful woman was standing there with a red collection box in her hand.' That is the so-called story-producing coincidence, adored by novelists." I paused after these remarks because I wanted to provoke him into telling me some details of his encounter in

117 the Métro, but he only kept twisting his back to let the pounding stream of water massage his lumbago, and he looked as if my last example had nothing to do with him. "I can't help feeling," he said, "that coincidence in man's life is not determined by the degree of probability. What I mean is that often a coincidence happens to us that is so unlikely, we cannot justify it mathematically. Recently I was walking down a totally insignificant street in a totally insignificant district of Paris when I met a woman from Hamburg whom I used to see almost daily twenty-five years ago, and then I completely lost touch with her. I took that street only because by mistake I got off the Métro one stop too soon. And she was in Paris on a three-day visit and was lost.2" (M. Kundera Immortality, trans. by P. Kussi, Harper 1990.) Anticipating the problems future generations would face, Maxime Pentier’s platform established a reasonable balance between opposing visions and interests: questions of employment and urbanization, use of water for irrigation or electricity, collective treatment or septic tanks, groves for hunting and streams for fishing. His platform made a provision for a plan of general development, which would be costly, but efficient in protecting against floods. This involved sacrificing St. Mark's chapel to make room for a reservoir that could also be used by swimmers and amateur sailors, and Maxime accepted the engineers’ arguments about the necessity of this. Maxime was a model of integrity. His logical, positive and republican education prevented him from even imagining that there might be interpretations of reality different to his own, with different estimates of the risks and differing views of what was important. The last election meeting was decisive. He presented his team and his project, explained its advantages and showed how it would preserve the interests of all for the future, thanks to wise choices based on the advice of scientific experts. He was rather satisfied with his performance for having not lost his calm, which was rather becoming of him. He reassured the voters when a participant spoke in an aggressive way, followed by others in a well of murmurs. One of these dissidents stood, unrolled a map, and declared that if one examined what the project did and did not favor, the houses on the lake and those to which access was cut off, the businesses easily served and those inconvenienced by the project, one would 2. These quotations from The Unbearable Lightness of Being and Immortality are extracts from lectures which Micheline Uzan chose and read in February 2008 during a conference on double voices about chance in the “Literasciences” seminar cycle at the Ecole Supérieure de Physique et Chimie Industrielles of Paris.

Street at Saint Claude, France. Progress and productivity was a permanent component of all political forces yet recently. Damages to environment weaken at present this positivism.

119 discover that it was a network of Maxime Pentier’s friends who benefited most through local financing. Accusations ringing out here and there in the assembly, they rose from their seats crying, “Corrupt hands are taking over the town!” Still near the microphone, Maxime Pentier stammered a few words of denial, explaining the general logic, the parties linked to the whole, the constraints of land and of timing. The hubbub did not subside. Then, a sincere argument came to him: “If I had thought only of myself, I wouldn't have sacrificed this chapel that I love,” he said. But this prompted another outcry: with his well-known atheist background, this argument looked very cynical. Maxime Pentier was defeated and his adversary made the restoration of the chapel a priority. This pleased Marta but clouded the mood in their household for some time. Fortunately, if we can say that, the following spring, a flood caused a landslide that swept away the chapel, giving some belated legitimacy to Maxime's campaign. Maxime began to think that it was the interpretations themselves which create risks. Within each interpretation, we can evaluate probabilities and damages to some extent. But between various interpretations it is impossible to conclude anything. And a new interpretation may arrive any time. Essentially, risks belong in the realm of semantics: The bowler hat was a bed through which each time Sabina saw another river flow, another semantic river: each time the same object would give rise to a new meaning, though all former meanings would resonate (like an echo, like a parade of echoes) together with the new one. (M. Kundera, Unbearable Lightness of Being, trans. by M. H. Heim, Harper 1984) In the 1920s Keynes made a famous distinction, later transcribed into economic language by Frank Knight who introduced the popular terms risk for situations where we can quantify the probabilities, and uncertainty for other situations. This distinction has been used many times in the years since then, and it undoubtedly represents an advance on the re-

120 ductive belief, still widespread among economists, that everything can be described by probabilities (even if it means placing one probability law above other probability laws). But it fails to address the subjective nature of assessing uncertainty and the role that interpretation plays in such assessments. Thus it creates vocabulary problems instead of clarifying them, because one cannot talk about risk without someone arguing that there is also uncertainty! Yet, many authors still maintain that uncertainty is only due to ignorance, to a lack of information, and that if sufficient information were available, the fog would clear and the calculation of probabilities could begin. At least the ideas of Savage, Ramsey and De Finetti about subjective probabilities took into account the fact that there are often many different interpretations of the world. Our assessment of risk always has a subjective element to it. Similarly the precautionary principle in its specific operational framework (the principle that everyone has the right to take legal action against the State) is a very imperfect and ambiguous procedure. The door between fantasy and interpretation needs to be open just enough for the symbolic to give content to the risks, but it should not open too far; we need to ensure we stay based in a positivist idea of science (facts and knowledge). It is, in fact, this ambivalence that allows such a hybrid principle to exist. But how could it be otherwise given the contradictions in a society that insists that the blacksmiths of knowledge (the researchers) ignore the way that their products will be used.

A stack of pebbles is stable or unstable depending on the curvature of the stones and the height of their gravity centers. This has been theorized by Alexander Liapounov in 19th century. This symbol was chosen by the Institute Louis Bachelier of research in Mathematical Finance in order to focuse on the control of risks.

3. Cf. namely D. Bourg "Le principe de précaution : un principe aussi mal compris que nécessaire" in R. de Borchgrave (under direction) Le philosophe et le manager. Penser autrement le manangement, De Broeck, 2006, 107-126.

121

This painting without signature is a false Canaletto. Has it a higher value as “Canaletto’s candidate” or as “true anonymous” ? Actually it is a risky object. At present its real value remains unknown, it might have been done recently by a forger, or it is indeed a painting of the 18th century, possibly a Canaletto, or a Guardi, etc. As on financial markets, risky objects are able to yield possibly more profit than objects without risk. Their value is “floating” in the field of meaning: in history, in the social uses, in the culture.

123 La Fontaine informs us failures are often attributed to misfortune and more rarely are successes attributed to luck. As far as risks are concerned, this is an initiation to relativist acknowledgement. FORTUNE AND THE BOY Beside a well, uncurb'd and deep, A schoolboy laid him down to sleep: (Such rogues can do so anywhere.) If some kind man had seen him there, He would have leap'd as if distracted; But Fortune much more wisely acted; For, passing by, she softly waked the child, Thus whispering in accents mild: 'I save your life, my little dear, And beg you not to venture here Again, for had you fallen in, I should have had to bear the sin; But I demand, in reason's name, If for your rashness I'm to blame?' With this the goddess went her way. I like her logic, I must say. There takes place nothing on this planet, But Fortune ends, whoe'er began it. In all adventures good or ill, We look to her to foot the bill. Has one a stupid, empty pate, That serves him never till too late, He clears himself by blaming Fate! La fortune et le jeune enfant (Fortune and the boy), Pierre Bouillon 1801 (Rouen).

124

‘Modern’ Architecture

126

Frank Lloyd Wright, E. J. Kaufmann house, Bear Run Pennsylvania, drawing 1936

127

Modern architecture is a break from all the styles that marked successive eras. The architect Bruno Zevi characterized modernism as being opposed to classicism, abandoning symmetry and arranging elements "randomly" instead. Chance prevents "aesthetic" reading. But where does this leave achitectural composition? What room does it leave for the architect's talent?

128

129

The unexpected shapes thrown up by a kaleidoscope fill children with wonder. Similarly adults are fascinated by the variety thrown up by cellular automatons and non-linear systems, especially when translated by computers into a multitude of graphics. But if we're expecting an actual creative act, then no automatic process of deduction, or any random draw, or simulation technique is acceptable a priori, at least not in and of itself. A more reckless commitment is expected – something more challenging to semantic meaning – a higher quest, which, in distancing itself from mechanics and chance, in the framework of its own act of defiance, attains a remarkable place, becomes a masterpiece, a point of research where one may stop because it imposes itself as a pleasant thing we can’t quite identify, but which used to be known in the day as harmony. Then along came History, complicating the issue. Perfect harmonies which sounded so nice to the ears of our ancestors, works so successful that they seemed timeless, still charm us but as overfamiliar things; the Gregorian chant became a lullaby. Nowadays, we need more dissonance to appreciate tonality, more exceptions in order to love the rule. This brings us to architecture which since olden times, and in an exemplary way during the pivotal periods of the Renaissance and the birth of modern art, is the contradictory and enigmatic place of creation at once harmonious and off the beaten track. Bruno Zevi is an architectural theorist well known in architectural schools for his work Architecture as Space1 where he insisted on the concept of architectural space at a time when architectural concerns moved from thinking only of “the forms of matter” (walls, pillars, etc.), to consider also the way things are perceived by the man-resident or the man-user. He showed how this view leads to a new interpretation of monuments of the past with a famous pedagogical analysis of “hollow spaces” at Saint Peter’s Basilica in Rome. This was part of the research which weighed on the artists of the twentieth century, who attempted to understand and define modernity, as if their epoch was the transition towards something lasting and absolute which definitively escaped the succession of historical styles; a new way which would take into account scientific development and progress, seen as universal and unequivocal. In his manifesto Towards an Architecture, Le Corbusier glorified grain silos, airplanes and “simple forms in light” with total confidence in technique and industrialization 2. 1. B. Zevi, Architecture as Space: How to Look at Architecture, Horizon Press 1957. 2. Le Corbusier, Towards an Architecture (1923), Lincoln pub. 2008.

Jugend Styl, Vienna, end-of-the-century

Secession building 1898

131 A very significant rupture came to establish an important characteristic of what would be seen as modernity. This rupture occurred precisely between the Austrian Jugendstyl and the Dutch De Stijl movements. The building “Secession” by J.M. Olbrich remained symmetrical, the café De Unie by J. J. P. Oud did not. Certain principles of classic harmony are still present in what avant-garde and end-of-the-century Vienna proposed.

De Stijl, Café De Unie, Rotterdam J. J. P. Oud 1924

132

‘Symmetry is an invariant of classicism’ : Château d’Ancy-le-Franc (1550) Sebastiano Serlio.

133 In the United States, this corresponded to the transition from Sullivan, and the Chicago School, to Frank Lloyd Wright, who progressively expressed this emancipation in his work. In doing so, he became the symbolic representative of this conception of architectural modernity.

Wright, Unity Temple Oak Park, 1906 detail.

Dudok, Hilversum Town Hall, 1924-30.

Richard Neutra, Kramer house, 1953.

134 Taking note of this evolution, in his work The Modern Language of Architecture3 Bruno Zevi wrote “Symmetry is an invariant of classicism. Therefore, dissymmetry is an invariant of the modern language”. To the question “Where should a window, a door, an object be placed outside of any symmetry?” he gave this staggering response “Anywhere.”

Mies van der Rohe, project 1924

3. B. Zevi, The Modern Language of Architecture, University of Washington Press, 1978, trans. from Il linguaggio moderno dell’architectura, Einaudi, Turin 1973

135

Permanency of the styles is a historical strength with considerable inertia, from which the modern artists attempted to escape. On the left hand side is a pedestal table of the 18th century Louis XV period. On the right hand side is a table of the 17th century before Christ made by pouring plaster in an empty space found in the dry mud covering the Minoan city Akrotiri in the South of Santorin Island due to the eruption of the volcano.

136 Yet can good architecture happen by chance? Putting that another way: is chance the only honest way of choosing a form in the residual indeterminism that is left after the functional and constructive constraints are taken into account? The paradox today, now that these problems have lost their novelty, is that chance itself is visible as such. It appears as just another choice, and one which can become as tiresome as classic styles if not more so! Or, taking the opposite view, should a good architect leave nothing to chance? For the master-builders of the Renaissance, it was certainly not about copying the ancient Greeks and Romans, but using the Greek orders - Doric, Ionic, and Corinthian - as well as their elements (pilasters, pediments, metope, and triglyphs; then caryatides from the Romans, ribbed vaults, thermal windows, etc.) to create a new language as inventive as that of poetry or theater. Jacques Herzog and Pierre De Meuron National Stadium 2007 with China Architecture Design Institute Olympic Green, Beijing,.

Jean Renaudie and Renée Gailhoustet, housing, Ivry, 1969-1975.

“Beauty will result from form and from the correspondence of the whole to the parts, between the parts themselves, and from those to the whole,” wrote Palladio, “with the result that the building appears as a whole in which each part suits the others and where all the parts are necessary to accomplish the goal” (Four Books on Architecture [Quatro Libri dell’architectura] published at the beginning of the seventeenth century in Italy). Alberti would go on to recommend giving emphasis to this language according to the meter (in the sense of poetry) of simple relations of small integers, so-called musical relations since they are based on musical harmonies.

Capella Pazzi, Brunelleschi Florence.

138 Are the likes of Brunelleschi, Palladio and Sebastiano Serlio too talented? They are imitated throughout Europe, and their creative imagination has been fixed posthumously in a standard view. Already, at the end of the seventeenth century, Claude Perrault, designer of the Louvre colonnade and Christopher Wren, architect of Saint Paul's Cathedral in London, thought about new, more nuanced ideas of beauty. Prefiguring the concerns of the Baroque, they looked for more freedom than the classical rules allowed. “There are two origins of beauty,” wrote Wren, “natural and customary. Natural beauty comes from geometry; it consists of uniformity (meaning equality) and proportion. Customary beauty is the result of our perception of objects which are ordinarily agreeable to us for other reasons, familiarity or an inclination being able to give birth to a love for things which are themselves unpleasant.” (Tracts on Architecture). Perrault shares a dual concept of beauty with Wren: he distinguished between “positive beauty” and “arbitrary beauty”. This distinction probably came from his education as a physiologist and from his work in the natural sciences where he faced the difficulties of experimentation. Perrault’s two types of beauty resemble the contrast between fact and right: “positive beauty seems to relate to the intrinsic structure of the building, whereas arbitrary beauty is more concerned with how a building works within our system of taste". Arbitrary beauty concerns what is agreeable and it concerns decoration, what is fashionable. A prodigious mastering of stereotomy is necessary to cut stone for awkward surfaces, such as those required by the audacious Baroque artists – Borromini and his emulators from Sicily and the Aus- Churches in London trian-Hungarian Empire – who dared to build churches in the form of ellipses with ribbed vaults in skew biquadrate curves and other inventions decorated with skillfully worked and delightful sculptures, such as those of Giacomo Serpotta. With such prowess in stonemasonry and stucco, the Baroque was an era in which the knowledge and skills of workers and artists, of architects and engineers were once again intertwined. The nineteenth century then gave birth to academicism and the pompous style of the Ecole des BeauxArts and the Prix de Rome, in total discord with the realities of industrial development. Here, once more, modern architecture attempted to escape from fixed references, preventing interpretative readings based on the old values of monumentality and the persistent traces of the classical canon. Christopher Wren 1632-1723.

by C

ndon

139 Chance has the virtue of erasing meaning and can be used specifically for that, as Bruno Zevi pointed out. Alas, in doing so, he engaged in a new cycle of the argument of harmony and creation. The faces of housing projects are “animated” with unexpected variations, mass housing plans of urban areas are given a pseudo-liberty, and we find ourselves once again mired in placid routine. Louis Kahn and Le Corbusier clearly turned away from this false solution. “Simple forms” – spheres, cylinders, cones – are symmetric and allow a return to the “positive beauty” of geometry. Louis Kahn would be the genius of unusual combinations of simple forms. Le Corbusier would adopt the principle of regulating lines using the golden ratio or Modulor in which the principal virtue is to keep in the no-man's-land between rules and fantasy. Though the relation itself Φ=a/b=b/(a+b) is rigid by its precise mathematics, its multiple and varied iteration creates infinite possibilities. The unexpected regains the right to be accepted, albeit in a somewhat controlled fashion, since it’s driven by the designer’s hand and judgment. A system of taste must be involved, to use Claude Perrault’s expression, but also the ability to adapt to functional and structural constraints brought about by the project. Le Corbusier’s ingenuous wonder for this tool led him to write abundantly on the subject, going almost as far as saying that the modulor guaranteed good architecture, or at least favored it. by Christopher Wren.

At this point in our discussion on chance and its importance in architecture, it’s worth stopping to consider a more profound philosophical issue concerning the architectural project itself. Like an awe-struck architecture student, we wonder what type of work this is; what is its essential nature? Is it an artistic inspiration? Or a careful deductive analysis of the site, the program and the finance available, that leads to the desired solution. Or is it something intermediary - in which case, again, we may wonder about its nature - that will lead to a hybrid that is neither free nor necessary? The most relevant parallel is to compare the architectural project with science as a process, and several factors suggest mathematics to be the most comparable discipline. First, mathematics and architecture are both born from this collective abstract cooperation that is the project of creating housing, requiring an anticipatory conceptualization of space. After a fire or other destructive event, reconstruc-

140 tion must be done from memory, without a model. The body’s measurement serves as a standard. Wooden huts or houses being smaller or larger according to individual needs, the invariant of form (the slope of the roof for example) from the outset posed homothetic problems long before Thales: geometry was part of the art of construction from the very beginning. Mathematics and architecture maintain a quasi-permanent relationship: in Egypt with the use of the 3, 4, and 5 triangle; the Greek temple and its proportions, the Roman vault, ancient Japan and the tatami algorithm, Villard de Hon-

Mason marks.

necourt’s gothic drawings and stonemason's marks engraved in the stones of cathedrals; the regulating precepts of Renaissance theorists, Gaudí’s catenary curves, simple forms, Buckminster Fuller’s geodesic domes, are but a few milestones in their common saga. In addition, the nature of mathematics itself has always had an artistic dimension. From the Greeks to the modern day, beauty has played a primitive role in the way the community appreciates new results and methods.4 The importance of an aesthetic sense in research had been pointed out by Henri Poincaré and Jacques Hadamard5 and remarkably demonstrated by F. Le Lionnais and J.P. King6 . Conversely, the beauty of nature is often seen in its mathematical patterns (shells, symmetries, etc.).7 4. We quote here the great British mathematician G. H. Hardy (1877-1947): “A mathematician, like a painter or a poet, is a maker of patterns. […] Like the patterns of the painter or the poet, the mathematician's must be beautiful […] Beauty is the first test: there is no permanent place in the world for ugly mathematics" (A Mathematician's Apology, Cambridge Univ. Press 1940). 5. Cf. Hadamard, Essai sur la psychologie de l'invention dans le domaine des mathématiques, Blanchard 1959. Also, N. Bouleau "L'inconscient mathématicien" in La règle, le compas et le divan, Seuil 2003. 6. F. Le Lionnais, "La beauté en mathématiques" in Les grands courants de la pensée mathématiques, Blanchard 1962; J. P. King, The Art of Mathematics, Plenum 1992. 7. Cf. Hermann Weyl, Symmetry, Princeton University Press 1952.

141 The most pronounced similarity between mathematics and architecture is the mathematician's constant quest for an "interesting theorem". He settles himself in a place, an area of mathematics, related to signifcant, older questions, possibly originally posed by physics. Scaffoldings are intended to disappear. So, From the point of view that only the final result matters, their form has no importance and may be left to chance. In mathematics, the idea is diputable. For some ones hesitations and attempts are interesting. Gauss would have said that no self-respecting architect leaves the scaffolding in place after completing the building. On the invention in mathematics see N. Bouleau Dialogues autour de la création mathématiques (1997), http://halshs.archives-ouvertes.fr/halshs-00346564/fr/

142 Mathematical logic objects to this quest being pursued by the use of any sort of program or safe method that is guaranteed to give results. We need to remember that the phenomena of incompleteness and undecidability - which spare nothing but the weakest theories that offer virtually no interest – arise from the fact that simple theorems may require very long proofs that cannot be shortened. That is the key to the sort of find that leads to a mathematical proof. If a knight is placed on a chessboard, it is easy to determine whether or not it can move to a specified square. It is immediately clear that, with sufficient moves, it can reach any square. But can every square be reached in an even number of moves? One can easily think of harder questions along these lines. Mathematical proofs are similar. Can we proof a given statement? For some statements the proof is easy, for others less so. In general, for any given statement, there is no algorithmic answer. A proof generally presents itself as a very complex scaffolding around the theorem that it proves. Thus what we see from mathematics is that the creative scientific act is linked to the simple result of a complex combinatorial dynamic. A general methodology for this type of research does not exist. The only way is to manipulate the statements and formulas, according to their meanings, and thereby attempt to obtain a new and simpler theorem. Consequently, the semantic aspect is decisive. The mathematician does not simply manipulate formulas; he uses a meaning handed down to him by other mathematicians, other scientists and history. Several meanings are often available. This makes intuitive representations possible which he attempts to perfect and which guide his thoughts, his attempts at construction allowing him ultimately to manage the symbols in his mathematical formulations. Following the mathematician’s example, the architect uses meanings to guide his thought, i.e., the representations and readings of issues in the arrangements he studies. By placing tracing paper on tracing paper (or screen after screen8) and by reading the variations and the sub-variations from the point of view of their usage, he revises his ideas until his plans crystallize into something solid and remarkable whose elements are in accord. The mathematician works on his research as the architect works on his project. It is not a standard scientific activity. 8. It is not certain that architecture students benefit from this advance in technology. The ease with which the software enables the perfection of their projects bogs them down. Their square monitors handicap their imaginations.

143 He focuses on sub-problems, he is very fond of meanings to guide his attempts (for example, he will interpret a positive functional as an energy); he lets himself be influenced by a sense of beauty, poorly defined though it may be; he is interested in surprising configurations. I believe that the links between mathematics and architecture should be taken seriously, much more so than is generally accepted, just as Pacioli and Alberti felt they should. It is not simply a question of geometry or whole numbers, of relations with music or the golden ratio. It concerns a more intimate solidarity that endures to this day: two exploratory activities where detailed rules - those of construction on one side and those of logic on the other - should be respected, but where the importance, nevertheless, is entirely in the meaning, the final result showing little trace of the intellectual paths that lead to it. The search may continue indefinitely. It ends when, often unexpectedly, it meets simplicity. Among innumerable solutions or near-solutions, one comes across remarkable configurations which may not fulfill the criteria any better than other configurations, but are desirable because they are simpler. We win a small victory over complexity. This is worth something. In mathematics, the most precious ideas are those which simplify things. Imaginary numbers, for example, are fully accepted despite philosophical reservations, because of the simplifications they bring to trigonometry and the study of power series. Likewise, in architecture, a simple thing has worth in and of itself. As far as architectural creation is concerned, there are two extremes: for example, the palace of Cheval the mailman9 on one side and the convent of Dominican sisters by Louis Kahn on the other. One may attribute all the dream-like imagination one wants to this original postman. Here, there is little architecture; his project has already succeeded 9. Ferdinand Cheval (1836-1924) collected stones on his daily mail routes. With these stones and a bit of mortar, he built a hap-hazard palace which still exists today as a historical monument in the Rhone Valley of France.

144 so long as he keeps to his plan. In such a case, simplicity is not sought for its own sake. Modernist and minimalist doctrines make simplicity a paragon of beauty, but there is another point: simplicity often reveals itself fortuitously while we are pursuing other goals or rules. It is hard to define what we mean by "simple". Why has so much ink been spilled over the Pazzi Chapel in Florence? The arcs, cupolas and semi-circular banners are the remarkable result of undoubtedly difficult work, a maieutic by which Brunelleschi leaves us such an exceptional combination that it has as much claim to eternity as a great theorem. When Alberti extolled the virtues of “the harmony and agreement of all the parts in such a way that nothing could be added, removed or modified without altering the whole”, he succinctly expressed the effect of necessity, which becomes attached a posteriori to a simple solution. This applies to a theorem just as well as to the Citroën DS automobile. Theorems don’t automatically appear; deductive chains are so divergent that there is always a profusion of consequences in every direction. But occasionally one finds a configuration whose simplicity suggests that it must have existed for all eternity. One comes to mind: “The points from where an ellipse subtends a right angle form a circle”. The simplicity of a theorem is, in some ways, the most valuable thing to a mathematician. Similarly, a lover of architecture recognizes the contribution of design work by the simplicity that has been plucked from an inextricable tangle of possibilities. In architecture there is also gained knowledge: the master-builders of the past studied the vaults, domes, L-shaped houses; there are “examples” we should refer back to in order to unders-

Is chance now definitively out of architecture? Is it recognized as a pseudo-solution, as dodging true conceptual work? It may be believed so since the post-modernism in the wake of Gaudi as theorized by Robert Venturi emphasizes semantics.

10. Cf. for example A. Rossi, L'architecture et la ville, L'Equerre 1981.

145 tand how to address certain architectural problems.10. Specific knowledge is also necessary to research mathematics efficiently. There is also a science of architecture, based on history as any knowledge is. It teaches the innovations of the past, techniques of today and, through criticism, introduces the cultural and social dimensions affecting the field. Is chance now definitively banished from architecture? Is it recognized as a pseudo-solution, as dodging true conceptual work? One could believe this, given the force of current post-modern semantics in the wake of Gaudí, as theorized by Robert Venturi. At the end of the twentieth century it certainly seemed that chance was dead, and that architects, having definitively surpassed modernity as Bruno Zevi understood it, knew how to play with all the available signifiers, using them knowingly. More recently, however, two major phenomena have arisen contradicting this analysis. The first major phenomenon, coming from computer science, was discovered by Frank Gehry among others. The elements of a building are not necessarily chosen from existing catalogues of construction material producers and other providers of industrial hardware. On the contrary, there is a great advantage in working with the manufacturers of construction material and abandoning a conception of industrialization based on standards. Indeed, computers allow the definition of the form and dimensions of each board, each panel, and so on, in terms that are directly usable by the machines that make them. This opens the way to

Daniel Libeskind, Jewish Museum Berlin

146 a free geometry (cf. the Guggenheim Museum in Bilbao) which is reminiscent of the freedom of forms that the introduction of reinforced concrete permitted, and which accomplished great projects, like those of the most recent towers. A similar approach was adopted by Herzog and De Meuron for the Beijing stadium. The second major phenomenon is the use of chance in its highest semantic function, which is to say nothing. With shapes, neither whiteness nor emptiness actually have this annihilating potential, because any such white is the white of a support that occupies a certain space, and emptiness is only the gap inside some containing object. The Jewish Museum of Berlin is the memorial of a drama which transcends historical references and any possible discourse. Daniel Libeskind uses the only appropriate language: that of silence. In fact, this involves a specific geometry, frozen there, which has its own questions. Are there traces of mathematics behind these appearances? Or is it ignorant chance concealing the mystery of kabbalistic principles?

147

148

Pierre Bourdieu’s face on a wall in Paris.

The Ideal City

150

151

Cities grow like some sort of plant. Some of them, including some very beautiful ones like the medina of the Maghreb, seem to have been stuck together randomly like great corals. But is it truly random? Isn’t it actually the result of strong local, historical and technological constraints? On the other hand, Greek and Roman cities were designed with rigid plans. Though the overall shape and the road and waterway networks were tightly constrained, each unit had considerable freedom, allowing the city to accommodate the unexpected and adapt itself to new things. Naples, for instance, formerly known as Neapolis - the "new city" - has kept its antique grid pattern. How can structure be given without causing rigidity? The city is a spatial translation of the rights that govern the collective and the individual. Berlin is a contemporary example of this dialectic.

152

153

Favelas - the poor neighborhoods of Rio de Janiero more or less controlled by mafia gangs - are situated on the slopes of hills organized in terraces, linked by passages, paths and stairs. Many of them have stunning views of the bay. The urban setup and the buildings are strikingly similar to the wealthy houses built on the slopes of Capri Island. Does this mean that this type of habitat, so conducive to a sense of community, would be optimal in itself and that the difficulties of cities only arise from conflicts between social classes? In both cases, access is basically reserved for pedestrians. The lack of privacy, the narrow passages, the horizontal and vertical overlapping of properties are common to both. Life among neighbors is intensely social: they meet, talk, and help each other with errands and with children. The poor suffer this state of things, captives of social conditions where choices are limited and mutual aid is the only social security. Yet, for other reasons, the same things are sought by the wealthier population of the islands of the Neapolitan Gulf. Between these two extremes are all the ancient cities, formed as a means of protection, shaped by history into natural clustered structures in which people now live as best they can. The populations of Italian hill-cities, and those of the cities perched in Sicily, are evolving. As religious practice becomes less and less common, churches are poorly maintained. Youth come and go; the buildings, loaded with meaning, do no not meet their needs. The elderly remain and are now joined by some middle class non-conformists hoping to escape their dependence on the automobile and the stress of big cities. The collective dimension is predominant in this setting. It brings with it advantages: local services, and limitations

which people accept because they seem to restore the harmony between private and public, between family unit and society. The city is like a massive coral, a polyparium which slowly proliferates and modifies itself over the course of years and centuries. Architecture may not have used chance as a way of transcending traditional references until late in recent history, but cities have always been the bearers of disorderly growth. Perched on dizzying promontories, Sicilian cities such as Modica-Alta, Erice, and Enna have been shaped by history since the dawn of time and subjected to a range of powers - Greek, Latin, Norman, Arabic, Neapolitan and Spanish - which transformed them while protecting them against ruthless bandits. Preserved neighborhoods, like the Albazin of Grenada or even the medina of the Maghreb, are testimonies of this spontaneity that has no written rules, and no apparent geometry, but leaves us marveling at such architecture without an architect that only centuries can bring about.

Above Calascibetta, near Enna, left Raguse, Sicily. Right Ghardaïa, Algeria

155 Perhaps the most fascinating examples of this are the Muslim city Ghardaïa in the Algerian M’Zab or that of Sidi Bou Saïd in Tunisia, that are unchanged in their authenticity. Aristotelian categories (cf. Chapter I) fit perfectly here: in the absence of global will, one cannot speak about chance. In fact, this kind of drawing without design obeys an infinite number of local directives which come to arrange volumes next to volumes around patios maintaining continuity of access. But while the urban vernacular form may seem flexible, adaptive and in perfect symbiosis with the lifestyle that engendered it, it can also be felt as an excessive pressure on the lifestyle that young householders aspire to. Here it is impossible to envisage a house surrounded by a garden and a privet hedge; but such a constraint might not matter. However, doesn’t the historical beauty of a city sometimes have too strong an influence on the consciences of its citizens? The contrast with new cities, based on geometric plans, is striking. The Greek colonial cities of Asia Minor, based on Hippodamus's plans, Priene, on its terrace on the hillside dominating the plain of Meander, Milet, Pergamon, Ephesus, or those of Greater Greece, Selinunt, Agrigento, were all the object of a directing plan. Avenues, purification systems, religious and political facilities and residential sectors were organized in a simple, rectangular, hierarchical geometry as if it were the most natural plan. It seems as if geometry was, for the Greeks, a human value; this idea is reinforced by the following anecdote which appears in an epigraph of The Sixth Book by the Latin architect Vitruve: “They say that the philosopher Aristide, a student of Socrates, having been saved from a shipwreck on the coast of Rhodes Island, and having perceived geometric figures drawn in the sand, said in exclamation to those around him: We’ve nothing to worry about, I see tracks made by men”.

Sidi Bou Saïd, Tunisia.

Cnossos, plan of the ancient palace (approx. 1400 A.D.) after Evans.

The Minoan palaces of Crete seemed, to the Greeks who found their ruins, to be random because their layout was so complicated. The creation of a myth as terrible as that of the Minotaur, who regularly devoured young women until defeated by Theseus with the help of Ariadne’s thread, attests to their dread before such inhumane architecture. With the Romans, the geometry arose out of military discipline. Their cities were established like camps. Victorious mercenaries were often rewarded with the right to settle, thus becoming settlers used to strategically organize space. The Roman plan has had the greatest historical influence throughout Europe. It consists of a grid built around the main thoroughfare - the decumanus maximus. A typical example can be seen in the remains of Timgad. Aigues-Mortes in France was designed according to similar principles, as Timgad were the fortified towns of Gascogne in the seventeenth and eighteenth centuries. Other solutions have also been attempted. After the earthquake of 1693 in Sicily, the city of Grammichele was reconstructed on a hexagonal plan. Another force also reworks space: history. The islets of Priene, or the elementary squares of Timgad, having been initially built to meet the tastes and needs of certain individuals, have been transformed by succeeding generations into Marciac, France

Villeréal, France

Grammichele, Sicily

157 blocks of houses. Residents have modified certain details, but the original guiding plan remains. In Pharaonic Egypt such worker cities were rigid as even the smallest cell was regulated, the very opposite of the ancient master plan which allowed the city to live and grow. Naples thrives, oblivious to its original plan as a new city - the ancient Neapolis. The same is true for Pavie. This principle of flexible regulation could be symbolized by the use of the opus incertum construction technique in some traditional pavings in rural buildings in southern Italy. These terraces are made of pebbles set randomly within regular squares that form a whole from a visual perspective. To our modern eyes, the spontaneously proliferating city seems to be the generator of an unplanned urban space, like the pseudo-random number generators used in Monte Carlo Naples

Pavie

El Amarna, worker district of the Pharaoh city Akhenaten (13th dynasty).

158

The modern city of Syracuse is still divided up into the five ancient quarters: Ortigia, Acradina, Tyche, Neapoli, and Epipoli. Tyche, the most populous part, derives its name from an ancient temple of Fortune. The cathedral, splendid baroque building, reuses for its structure the pillars of a Doric temple This ancient Temple of Athena ( built by the tyrant Gelon to celebrate the Greek victory over the Carthaginians in 480 BC - the same year that their mainland compatriots were defeating the Persians at Salamis) was made into a Christian church in 640 AD. After the 1693 earthquake - which wreaked such havoc in south eastern Sicily - the present baroque facade replaced the collapsed Norman one. Gods change, but architecture travels down the ages.

159

Noto, Sicily

methods. But, in fact, there is a microscopic quasi-determinism, arising from the forces of social, family, and religious rules. Transmitted, historicized necessities bring about the know-how and the models that perpetuate it. On the contrary, the structure-giving rules of town-planning can provide the conditions needed for true freedom and creativity in subsequent periods. This is what has happened in successful new cities. Noto, the beautiful Baroque city of Sicily, would be one of the most splendid examples of this if economic hardship had not stifled its development. The design of new cities inevitably involves a bet on the continuity of political, religious, and productive institutions. Brasilia, in spite of its rigidity, seems to have been a success thanks to its garden-cities. However its continued success is not guaranteed, because of the way its design is based so strongly on the use of cars. Already, the most remote quadras of the symmetrical axis of “the bird” are the poorest. Similar things can be said about Toulouse-le-Mirail, where 25,000 homes were built on 680 hectares in a branching pattern with a large concrete mall (the dalle) and zigzagging rows of buildNoto, right Sta Monte Virgini church, arch. Sinatra. Left San Domenico church, arch. Gagliardi.

In some towns like Roubaix, the urban blocks bounded with middle-class buildings were filled with workers housings during the industrialization. These houses inside the courtyards disappeared in the late 20th century.

ings, and an inner road to optimize social relations. Thirty years later, the town is a concentration of all the problems of a rough neighborhood; the dalle is in the process of being demolished. How can freedom be permitted without local interests and individual goals undermining all semblance of a whole and destroying symbolic landmarks? The problem of a market-led society is that the pride of the client all too often ex-

161

Toulouse le Mirail, arch. Candilis and Team X (1960-1975).

162 presses itself by superficial signs of wealth and success using a symbolism that is obsolete, if not ridiculous. This depressing phenomenon can be seen in our ordinary civil cemeteries. Everyone wants to die better than he has lived. The porcelain flowers, beveled marble, and columned chapels combine in something pathetically pretentious. The sparse dignity and simplicity of Japanese cemeteries, by contrast, is striking. How can there be structure without rigidity? In other words, what is the spatial representation of the fact that the city is a legally-constituted state, where the freedom of each individual must respect the visual tranquility and residency of all? An interesting answer to this question has been adopted in Berlin. A height-limit of 22 meters has been imposed for the entire city (in the spirit of pre-war Berlin which also made provision for an extra floor that was set back from the main facade) but exceptions are allowed, managed at each step by authorities. The result is a prodigious spectacle of contemporary architecture.

Berlin, recent projects. Französische strasse, arch. Kollhoff, Vöchting Friedrichstrasse, arch Kollhoff, Markgrafenstrasse, arch Dudler, Mohrenstrasse, arch.Stepp, Quartier Schützenstrasse, arch. Rossi, Bellmann, Böhm.

163

Berlin, plan of exceptional operations, Bundestag quartier, British embassy, arch. Wilford.

164

Daring the Abstract in Art

166

Previous page Charles Bouleau (1906-1987), gouache 1961.

167

It was chance that persuaded Kandinsky of the emotive power of abstract painting. He had failed to recognize one of his own works because it happened to be wrong way up, but found that it evoked feelings that were not there before. In the following years he hesitated between an abstract with meaning, i.e., a symbolic language, which was the path that Klee took, and a pure abstract, that worked by unknowable chance. What was Marcel Duchamp looking for with his incongruous “ready-made”s and his strange gamble where he “drew with chance”? And why did the composer Xenakis, when he wanted to escape the reflexes of tonal harmony, resort to bringing chance into the process of composing?

168

These kinds of hide-and-seek games between chance and meaning, so familiar to us now, are clearly present in every artistic creation. We will see that philosophical ideas as well as dilemmas take form in certain pivotal moments in painting and in music. The Surrealist movement is certainly the one the most influenced by the problems which interest us, but these questions appear whenever a decorative or artistic value is attributed to something other than representations1. Are Jackson Pollock’s movements of a different nature than the decorative investigations of Arabic architects? Pollock’s haphazardness is not really random; his colors follow the dynamics of the body throwing them onto the canvass. Similarly, the Alhambra’s motifs preserve a trace of combinatorial geometry despite their apparent free abundance. Is this duality designed to incite philosophic meditation? Was the exhibition of Pollock’s work in New York’s Museum of Modern Art designed to send its visitors into an imaginative daydream? Following this 1. In his philosophical research, Gilles Deleuze outlined an ideal game where chance would permanently intervene “It’s each thought which forms a sequence in time smaller than the minimum time consciously thinkable. It’s each thought which emits a unique distribution […] Therefore, the game is reserved to thought or art, where there are only victories for those who know how to play […] It is also in this way that thought and art are real, upsetting the reality, morality and economy of the world.” Logique du sens, 1. Ed. de Minuit 1969.

170 logic, we are lead to our main question: Doesn't the real content of abstract art, the source of its “effect”, reside in the fact that it is the application of Cournot’s philosophical probabilities? Consider Kandinsky’s famous painting currently at the Centre Pompidou in Paris, called Yellow, Red, Blue:

In it we can find the profile of a face with a nose, an eye, hair, and a forehead, as well as the neck of a shirt. A lamp illuminated in the head is an idea: the idea of abstract art: a combination of colors and form. The checkerboards evoke rules, the sinuous line resembles freedom, and the perspective suggests depth and a projection of the abstract towards the concrete. It’s an allegory, then, which represents “the invention of abstract art”. But if one of Kandinsky’s paintings is an evocation, a fable, then his others become invitations to search for the beginnings of mysteries, of sources of abstract thought: Kandinsky only began working abstractly after some time painting figuratively. The transition was not instanta-

171

Kandinsky Bild mit rotem Fleck 1914 Gegenklänge 1924

neous. Sometimes he went back to his former habits or transformed his own paintings by giving them a more geometric and more brightly colored turn (cf. the canvas titled Rückblick). Abstract painting appeared between 1910 and 1920, with Malevitch and Mondrian beginning almost simultaneously, and it was on this new pathway that Kandinsky established his teaching in Bauhaus until 1933. For Kandinsky, this change took the form of a revelation: he recounts that one evening, after a day of working in his studio, when it was already dusk, he noticed a canvas that made a strong impression on him, stirring up a rare pictorial emotion, with relations of colors like those he often sought. After a moment, he realized that it was one of his own paintings that, by chance, happened to be placed upside down in his studio: “The painting was imbued with a great value [...] It was one of my paintings which was leaning against the wall wrong way up”2. The next day, Kandinsky recreated the experiment to feel the same impression. But, he realized that the effect was gone; it could no longer provide a new feeling like before. He knew what had happened: meaning had fallen into its habitual ruts: “Now I understood, the object harmed my paintings […] even on the side, I would constantly recognize the objects and the fine dusk light was gone”. By this 2. Cf. Wassili Kandinsky, Regards sur le passé et autres textes : 1912-1922, ed. presented by Jean-Paul Bouillon, Hermann 1990.

172 fortuitous event, Kandinsky became aware of a new type of value that forms and colors could have if one could destroy the meanings that gave birth to them. It is as if, when a viewer first sees a painting, he is more alert as his mind is trying to recognize the object, and this state of alertness makes him more sensitive, and enables him to establish a different relation to the work, than when his mind has stopped searching for a meaning. If one ventures into abstract art after having experienced this ‘awakening’, the colors on the canvas surface are carried by forms in every possible way. The question then is to know if emotion participates in the effacement of itself and of the distance taken by the artist compared

Kandinsky Improvisation III 1909 Skizze zu Komposition IV 1911 Without title, watercolor 1916

173 to ordinary and trivial reality - the path mapped out by Cézanne and followed so skillfully by Nicolas de Staël - in which case a trace of the initial signifiers should remain so that one can measure the change, or, on the contrary, if the forms themselves can say something. That was the path taken by Paul Klee, described in his Pädagogisches Skissenbuch (1925)3, in his search for a true general semiology that would make abstract art a language of ideas, sensations and feelings. At the heart of abstract art lies the confusion of chance and purpose, of the possible, uncertain arbitrariness in which Mondrian adopted his typical position. Aren't the lines he draws so simple and pure that they must arise from some hidden mathematical constructions? It seems that he never revealed whether or not he used the golden ratio, though analysis of some of his works suggests this, but this mystery is an inherent part of the questioning that constitutes his works.

Elements of the theory of forms Paul Klee, 1925.

3. f. Paul Klee, Théorie de l’art moderne, Denoël-Gonthier 1973

3

Nicolas de Staël, Les Footballeurs 1952

In fact, the emotional freshness that Kandinsky sought is also present even if the artist uses elements that are common-place and recognizable, provided that they are placed outside of any framework that would give them context. This is the long-established Arcimboldo effect, which would also play a role in Cubist collages. Ready-mades are an extreme attempt at this use of accidental meaning as art. Objects already made, usually common industrial products such as bottleholders or pharmaceutical devices, were presented as they were or slightly retouched (“helped”). Marcel Duchamp signed around twenty of these works between 1914 and 1925. The most famous, the fountain, a ceramic urinal signed R. Mutt, was refused entry into the New York Salon of Independents in 1917.

Moholy-Nagy Watercolor 1926-30 Sketch for a Score for a Mechanized Eccentric 1925.

Mondrian Fox Trot, Lozenge Composition with Three Black Lines 1929. Opposition of lines, Red and yellow 1937

175 Duchamp’s ready-mades are considered a key stage marking the birth of contemporary art which feeds on the controversies surrounding the questioning of art itself. It should be noted that these are "any old thing", and it is this carelessness that shocks, being a denial of the creative talent of the artist. However, though they may be any old thing, they are things that already have a meaning. An excerpt from Duchamp's notes reads, “a tube and a rod which are an exact fit one inside the other each despite belonging to unrelated objects”4. A ready-made is not a section of reality actually taken at random: a rectangle cut into bodywork or into asphalt. If it were, we wouldn’t recognize any object, and there would be no clash of different sequences of meaning. The ready-made is not abstract; it remains in the field of semantics, pointing out ordinary signifiers that are very distant from those generally presented in museums. According to Duchamp, a ready-made is a reflection on art as choice, the artist choosing a theme and a style: “But it’s always a choice made by the artist. Even when you make an ordinary painting, there is always a choice: you choose your canvas, you choose the subject, you choose everything. There is no art; only choice. There [with readymades], it’s the same thing. It’s a choice of object. Instead of making it, it is already made. The choice, obviously, depends on the reasons which you choose. Here, it’s a rather difficult question to explain: instead of choosing something that pleases you or displeases you, you choose something that has no visual interest for the artist. In other words, aim for a 4. M. Duchamp, Notes, Flammarion 1999.

176 state of indifference towards this object.”5 Art as choice necessarily brought Marcel Duchamp to the question of risk and meaning.

On the background paper are printed the words infinitely repeted «moustiques domestiques demi stock» and under the title Roulette de Monte Carlo : «Emprunt de quinze mille francs 20% divisé en 30 obligations de 500 francs chacune remboursables au pair en trois ans par tirages artificiels à partir du 1er mars 1925 (loi du 29 juillet 1881)». This law, actually, is the one which forbids to past posters on public monuments, as often seen on the walls in Paris: «défense d’afficher, loi du 29 juillet 1981».

Duchamp formed an enterprise of which he was the director. 500 Franc shares were sold and the money was used for a gamble in Monte Carlo. After selling some shares, and playing for some time, he ended his efforts. Friends who had subscribed lost some money in the process, but were able to recoup any losses if they kept the share certificate - after the war these items became much sought after. But it's not the art market we are interested in. Duchamp's notes (Cf. Duchamp du signe, Flammarion 1994) show that he truly intended to place some bets: “With a small amount of capital, I tried out my combination over five days. I won regularly every day - albeit only small sums within an hour or two. I'm still perfecting the system and I expect to return to Paris with a flawless system". What was the nature of his strategy then? We can guess his strategy based on some of his comments: “The problem consists of finding the red and black figure to set against the roulette [… ] But with the right number, even a bad martingale can work, and I believe I've found the right number. You see I haven't stopped being a painter; now I draw with chance.” So it has to do with numbers, but what does it mean to draw with chance? The idea is exactly that which Cournot implemented in another way. Chance usually does not draw any remarkable patterns, or, to put that another way, the result of chance is generally not at all remarkable. If I choose a remarkable pattern of reds and blacks, then I have a good chance that the roulette wheel will not draw this pattern. For example, if I take the following series: one black, two reds, three blacks, four reds, etc., and if I 5. Marcel Duchamp parle des ready-made à Philippe Collin (1967), ed. L’échoppe 1998.

177 wait until the game starts this pattern, it won’t go very far before deviating from this pattern. So if I bet against this pattern, I will win. Similarly, if I take numbers on a roulette circle in the shape of a regular star, or any other imaginable shape, this is “drawing with chance”. The strategy is to think of combinations that make sense and bet that they won’t appear.6 But Cournot's criticism of Poisson comes into play here, because the boundary between the remarkable and the unremarkable is vague. Moreover, our dear Marcel realized this: “Having developed the martingale, I launched these bonds which should return 20% of any profits I make at roulette. Unfortunately, the system was too slow to have any practical value. Sometimes I had to wait a half-hour for the numbers to appear in a succession of reds and blacks and the weeks I spent in Monte Carlo were so boring that I quickly abandoned it, happy to pull myself away with no losses”7. Duchamp had not read Cournot; meanings are not understood through probability. The roulette marble understands nothing, thinks nothing, doesn’t avoid any figure; it has no memory! Musical pleasure is linked to habit even more strongly than the aesthetic pleasure that Perrault and Wren spoke of. Our ear hears simple relations related to physical frequencies, attached to intervals of thirds, fourths, fifths, and octaves. But well beyond that, we are conditioned by the way these harmonies are used so that, for example, we expect a tonic chord after a dominant seventh chord, etc. In some ways, our familiarity with Bach, Vivaldi, and Mozart makes us appreciate the imbalances, the expectations provoked by the dissonances of Chopin, Brahms, and Debussy. This learning process goes further: some people switch off when it comes to Poulenc, Boulez, Messiaen or Stockhausen or especially Pierre Schaeffer or Charles Ives. For them, this music is ‘any old thing’; something carelessly thrown together. If abstract 6. Jean Baudrillard thought that the game of roulette seduced the player because it denies chance. “He always calls into question the reality of chance as an objective law and he substitutes a related universe, preferential, dual, agnostic and predictable—a universe of charm in the strong sense of the word, a universe of seduction […] The magic of the players, of those who play their birth date until locating a series (the eleven came out eleven times in a row in Monte Carlo), the most subtle martingales to the lucky rabbit’s foot tucked in a vest pocket, all of that fuels the idea that chance doesn’t exist, that the world is to be taken as a network of symbolic relations…” De la séduction Ed. Galilée 1979. Duchamp’s reasoning is deeper than that. He doesn’t believe in an enchanted world. On the contrary, he emphasizes the inability of chance to provide meaning. 7. Loc. cit.

178 painting leaves the public rather indifferent, on the contrary, this same public is hardly prepared to give any time to experimental music that makes it feel like a guinea pig. Time is the dimension that is unique to music. A good memory recognizes rhythms and tunes and invariably is surprised by new figures that happen, as in a dance it doesn’t lead. Time puts improvisation at the center of musical creation. It is certainly present elsewhere, but here, it comes fully into play. It is not found as naturally in painting, with the exception of Clouzot's film about Picasso. It could have gained more acceptance if abstract art had pursued Klee's proposed language path a bit further - and if this language had worked - like the pianists and violinists of the eighteenth century took the liberty of using themes and variations of the masters for their auditions and their cadences - "variations in the register of customary beauty” as Christopher Wren put it, himself having made great use of the concept in decorating the fifty churches he built in London after the fire of 1666. For a composer like Xenakis, the problem is clearly different as it is not a question of improvisation, because this works - at least in part - with reused material. It’s musical creation that interests him. He aims to situate himself in relation not just to current music trends but to all avant-garde movements and he tries his utmost to share their aesthetic and even philosophic values.

Is the beauty of a score in relation with that of the music? A page of the opera Nabucodonosor by Verdi.

179

Art, and especially music, has a fundamental function which is to catalyze sublimation […] If a work of art succeeds in this, even for a moment, it has reached its goal. This giant truth is not made of objects, feelings, or sensations; it is beyond that, in the same way Beethoven’s Seventh Symphony is beyond music […] The first task is to erase all the inherited conventions and to exercise a basic critique of the act of thinking and the realization of these conventions […] Indeed, what does a musical work propose at the strictest level of construction? It proposes a collection of successions which should be causal. When, for simplicity, the major scale implied a hierarchy of tonal values (tonic-dominant-subdominant) which other tones orbit around, it imposed a structure, one part linear processes - melodies - and, the other part, the simultaneities - the chords - in a strongly deterministic way […] Linear polyphony destroys itself by its actual complexity […] This inherent contradiction of polyphonic music disappears when the independence of the sounds is complete.

180 Linear combinations and their polyphonic superpositions no longer working, what matters will be the average statistic of the isolated states of transformation of components at a given moment. The macroscopic effect could then be controlled by the average movement of objects chosen by us. Thus the notion of probability is introduced, implying, in this specific case, combinatorial calculation.8 We see that Xenakis is absolutely in the same position as Bruno Zevi in architecture: he looks to escape the classical canon which are expressed in music by the rules of harmony as described in the “theory of musical analysis” long taught in conservatoire classes thanks to the classic “Danhauser”9 manual, whose role in music is similar to that of “Letarouilly” and “Gromort” in architecture. Like Zevi, he considered chance as the only way to erase meaning10. Again, the question is to know whether this semantic void allows for the appearance of new meanings. By profession, artists are rather optimistic about this. Jean Cocteau reported that Picasso said, “One can write and paint whatever one may since there will always be people to make sense of it”11. 8. Iannis Xenakis, Kéleütha, Ecrits, L’Arche 1994. 9. A. Danhauser, Théorie de la musique, ed. reviewed and supplemented by Henri Rabaud, Paris 1929. 10. Jean Baudrillard, who favored the use of categorical formulas, thought that it was not chance, but ritual which erased meaning. “One does not escape meaning by disassociation, by disconnection, by leaving usual areas. One escapes it by substituting the effects of meaning with a more radical pretence, an order still more conventional […] such as the innumerable rituals of daily life which evades disorder and the order of political, historical, social meanings which are imposed on them […] Only ritual abolishes meaning.” De la séduction, op. cit. p187. Baudrillard’s idea only seems profound on the surface, but it doesn’t work, in architecture or in music. Of course, ritual dulls meaning, but its structure, no matter how poor it may be, becomes a mnemonic tool. Conventions and rituals have a past and they are found throughout the pitfalls of historical readings. Zevi and Xenakis are right about this point. 11. Cocteau Journal (1942-1945), March 23, 1942.

181

Camouflage has to be efficient in a great variety of circumstances, it uses the chance as eraser of meaning.

182

Saussure or the Dread of Mathematical Probabilities

184

185

The meaning of a phrase is related to its sequence of sounds and its enunciation. But how is this correspondence made? Does it involve a mapping from a set of terms to a set of meanings? Or is it more global - the meaning of a word depending on the context and influencing this context in return? In that case, are there situations where several meanings superimpose and intertwine with each other? Saussure found examples of this in Latin poetry, but never published his findings. Unable to establish the boundary between his semantic discoveries and a game of pure combinatory chance, he found himself at dead end. For some linguists, the problem is an epistemological one.

186

187

Ferdinand de Saussure (1857-1913) was a brilliant scholar, a specialist in Sanskrit, Lithuanian, and Indo-European languages, and a professor in Geneva and Paris at the turn of the twentieth century. He was practically unknown before World War II except among linguists. Lacan regretted Freud did not know Saussure and we will see it is also quite regrettable that Saussure did not know Freud 1. Among linguists his reputation grew quickly as a result of the remarkable originality and audacious methodology of his article “On the Primitive System of Vowels in Indo-European Languages”, published in 1878 when he was still in his twenties. In this work he postulated the existence of several archaic phonemes called “sonantic coefficients” based on a theory known as “laryngeals” in which, for the first time in this field, the approach is algebraic with opposite and relational quantities  2.  In  1906,  when  German  archeologists  discovered  a  large  number  of cuneiform tablets in Central Anatolia, the decryption of Hittite, an Indo-European language, brought new linguistic materials and provided a partial confirmation of Saussure's laryngeals, persuading many linguists of the value of his theory. Other recent works tend to confirm the interest of Saussure’s approach3. This discovery had been compared to Le Verrier ’s discovery of Neptune. Mathematical methods, or rational methods, would become as much the bearers of discoveries in linguistics as they were in natural sciences. However, the approach is structurally quite different: the entities supposed by Saussure are only present in certain Indo-European languages and some conclusions appear to remain unfounded  4. 1. Here, we extend the study “Saussure côté jardin” that I made conducted in La règle, le compas et le divan, Seuil 2002. 2. Cf. Michel Lejeune, Traité de phonétique grecque, Klincksieck, 1955, §186 p173. 3. A. Bammesberger dir., Die laryngaltheorie und die Rekonstruktion des Indogermanischen Laut- und Formensystem, Heidelberg, 198890 ; F.O. Lindenman, Introduction to the « Laryngal theorie » Oslo, 1987. 4. Cf. E. Benveniste, Origines de la formation des noms en indo-européen, Adrien-Maisonneuve 1935, p151.

188 What interests us here is Saussure’s relation to mathematics since these works from his youth (and this would be confirmed in his Course in General Linguistics) use logical and mathematical concepts such as relation, symmetry, substitution, etc. His scientific renown seems to be related to this shift in perspective in this field of human sciences of which he himself said, “No subject is more controversial; opinions are almost infinitely divided and different authors rarely make a perfect, rigorous application of their ideas”. 5 . Saussure’s Course in General Linguistics (CGL), taught between 1907 and 1911, had a great influence on linguistics, at least on some of its numerous trendsetters including Antoine Meillet, Louis Hjelmslev, Emile Benveniste and Roman Jakobson. Unearthed after World War II by Lacan, Kristeva, Barthes and others, CGL became the standard of the structuralist movement. Therein, from half a century earlier, could be found an approach which could serve as an example for all human sciences6. For this very reason, the opponents of structuralism would base their critiques on Saussure's principles7. Saussure effectively reinvigorated linguistics both conceptually and methodologically. Without neglecting the classic diachronic approach, he emphasizes the study of language as a system of a given era, which is called the language. He proposed concepts that form a general framework for particular languages. One of his fundamental ideas is that a language makes sense, not as nomenclature, but by a set of relations between its elements. Saussure rejected the traditional view - which would have been held at the time of the Port-Royal grammar, for example, and was the idea of Wittgenstein's first way - that the reference to the world could be taken for granted, and that terms can be seen as labels that can be combined according to the rules of logic. Instead, he viewed the sign - i.e., the signifier-signified pair - as something arbitrary and saw language as being constituted solely of differences. The value of each word in a language is as a relational structure. The sign is thought of as a relation in the mathematical sense of the word, that is to say as a set of pairs in 5. A detailed biography of Saussure is given by Tullio de Mauro in the appendix of the edition based on notes of students from the Course in General Linguistics, reprinted Payot 1995. 6.  E. Benveniste, Problèmes de linguistique générale, 1, 1966; 2, 1974, Gallimard; Cl. Lévi-Strauss Anthropologie structurale, Plon 1958; J. Lacan Ecrits, Seuil 1966. Here, it is also worth noting Louis Althusser, Jean Piaget, Noam Chomsky, and Michel Foucault (although he defends it), etc. 7. Cf. notably J. Derrida De la grammatologie Ed. de Minuit 1967. 

189 which the first term is the acoustic image, or the signifier, and the second, the idea, is that which the signifier wants to express, also called the signified. This relation need not  be  one-to-one,  since  languages  can have all sorts of idiosyncracies, homophones, polysemy, etc.  The two principles at the foundation of Saussure’s linguistics are the arbitrary nature of the sign and the linear nature of the signifier or acoustic image. The sign is arbitrary because the signifier-signified relation is not necessary a priori. It is unmotivated, at least before the structural relations of the language itself are taken into account: “The French word vingt (‘twenty’) is unmotivated, whereas dix-neuf (‘nineteen’) is not unmotivated to the same extent. For dix-neuf evokes the words of which it is composed, dix (‘ten’), neuf (‘nine’), vingt-neuf (‘twenty-nine’), dix-huit (‘eighteen’), soixante-dix (‘seventy’) etc.”8. But this “arbitrary nature” remains a kind of enigma or epistemological invention since we do not know where or in what space this arbitrariness operates. The sign is neither individually nor socially arbitrary; for the listener, the sign is imposed by the language and its history. A child is certainly capable of understanding several languages, but his maternal language (and possibly paternal language) will undoubtedly influence his manner of thought. In any case, it’s a freedom for which we have no way of evaluating its degree of arbitrariness. There is a type of manifesto in this: for Saussure, asserting the arbitrariness of the sign has the principal function of placing that which is linguistic straightaway under the protective wing of mathematics 9. This, in a way, is rather simplistic at its core if one compares it to Chomsky’s later works or the works of logicians such as Quine. The 8. Course in General Linguistics, published by Ch. Bailly and A. Séchehaye, 1916, trans. by Roy Harris, Open Court Publishing, 1986. Henceforth, abbreviated as CGL hereafter. 9. Also, in 1891, to support interest of the axiomatic method in mathematics, David Hilbert had this witticism “Instead of the words ‘points’, ‘rights’, and ‘surfaces’ in geometry, we should be able to say at any time without inconvenience ‘table’, ‘chair’ and ‘a glass of beer’”. Cf. N. Bouleau Philosophies des mathématiques et de la modélisation L’Harmattan p.44.

190 existence of a world of signifieds is overlooked, for example. Lacan seized the notion of the signifier, Grammatical scheme of Un coup which is at the heart of his teachde dés jamais n’abolira le hasard, ing, noticeably modifying, moreElement of analysis by Julia Kristeva, La révolution du langage over, the notion of sign. Instead of poétique, Seuil 1974. being a function from one space to  another  (the  space  of  signifieds), Lacan made it a function of a space into itself - an endomorphism to use the mathematical term - from the space of signifiers. Of course it is again not necessarily a one-to-one function. The idea of the arbitrariness of the sign, although unprovable, is quite clear10. Jean-Claude Milner suggested that in this way one could interpret Mallarmé’s famous verse Un coup de dés jamais n’abolira le hasard (A role of the dice will never do away with chance) giving it a philosophical meaning which, at the very least, was hardly evident. “It is clear,” he wrote, “that the chance he thought of was that which governs the relations of sound and of meaning. The word ‘hazard’ is derived from an Arabic word which means ‘game of dice’. Mallarmé probably knew this, so one could interpret it in the following way: the roll of dice that is deciphered in the word ‘hazard’ doesn’t negate the word ‘hazard’ itself. We can see that the chance that Mallarmé was thinking of was, in his eyes, integrally constituent of the language."11 10. Mathematicians are familiar with similar situations: if arithmetic is coherent (as everyone thinks), the non-contradiction of arithmetic is an unprovable, yet true, assertion.  11 J.-Cl. Milner, «Hasard et langage», in Le hasard aujourd’hui, Seuil 1991. This interpretation is anticipated by Michel Leiris in his 1967 preface to a collection of prose poems by Max Jacob Le cornet à dés (1923) “A book with an ambiguous title evoking limitless chance without limits under a well defined form of a still life object. This chance whose name comes from an Arabic term designating a game of dice, so that the Mallarmian axiom – which Max Jacob is not the only one to have thought of – could read: A role of the dice will never do away with the game of dice.”. Despite the discrepancy of dates, Milner charged the verse (of May 1897) with ato one with much greater weight by evoking the arbitrariness of the sign (1907)

191 Jean-Claude Milner took the analysis further, unleashing an epistemological double step which we also see in biology and which could well be a general method for developing scientific knowledge. The first step is to “realize that there is no necessity, divine or otherwise, for language to exist [and] to establish that neither is there any necessity, divine or otherwise, for it to be as it is. It’s what I would call chance.”  The second step “consists of explaining that it is as it is. When describing language as a whole, or a particular language, it remains to be shown that such and such a characteristic is explained in relation with another. Putting things in relation like this will, in the best cases, take the form of a deduction: ‘Given such and such a combination of characteristics, one may logically deduce that this and that will happen.’ There is the objective of the science of language”. However, the first of these two phases remains generally unsatisfying. “Basically, do we have an exact idea of what it means to say that a language is contingent? I’m not quite sure. Taking myself as an example: I am a speaking being and even if I make every effort, yet there will still be times in my imaginary working where my mother tongue seems necessary to me."12 Now let's turn to some lesser known works. Ferdinand de Saussure devoted many years to research of quite a different nature, albeit still linked to the study of Indo-European languages. In the period between 1906 and 1909, during preparatory reflections for the CGL, Saussure discovered anagrams of famous names (for which he coined the term hypogram) within Latin poems. When lined above the text of the poem, these anagrams evoked the names of Gods, or of key characters linked with the subject of the poem, broken into constituent syllables.Saussure's research into these hypograms fill over 140 notebooks in the University of Geneva library, so we can imagine the amount of time he must have spent on it. Was this a real discovery or imaginary? One cannot say a priori. When Jean Starobinski published a detailed analysis on it under the title Les mots sous les mots (The Words Behind the Words) (Gallimard 1971) this revelation lead to talk of “two Saussures” and “the second Saussurian revolution”.13 These handwritten notes cover: Saturnian verse (17 notebooks and one bundle of loose papers) - an ancient Latin style of poetry so named for its evocations of the time Saturn reigned in Latium, whose principal characters are Andronicus, Naevius, Ennis and Plato from the third century to the middle of the second century B.C., Virgil (19 notebooks), 12. Op. cit. 13. Cf. F. Gadet, Une science de la langue, P.U.F. 1996.

192 along with other Latin poets - Lucretius, Seneca, Horace, Ovid among others, Homer (24 notebooks), some contemporaries of Saussure who wrote poetry in Latin, and the Germanic legend of the Nibelung, where Saussure researched the original historical events in the Franc and Burgundy dynasties behind the characters and the stories. These last investigations were pursued in October 1910 during the Course, which was taught from 1907 to 1911. The hidden words can be found in different ways. One way is letter by letter as in Titus Livius (a response of the Delphic oracle addressed to the Romans, thereby reporting Apollo’s words). In the group  amplom victor ad mea templa portato Saussure finds two occurrences of APOLO: AmPLOm victOr ad mea temPLA PortatO Alternatively, working by syllables, we see, more or less, clearly that the Saturnian verse gives SCIPIO:

Taurasia Cisauna Samnio cepit Taurasia CIsauna SamnIO cePit

A further way of deciphering the text is by phonic analogy where a verse such as Mors perfecit tua ut essent gives the vowels of Cornelius in order: o e i u. This is only a glimpse of the possibilities. Saussure’s investigation based on Saturnian verses extends to almost all Latin poetry and investigates for the Greek sources of these traditions. During this extension, the discoveries evolve, perfecting and adapting themselves to the analyzed material. About Saussure's methods, we note that: the rule, which we assume the poet was following, and the body, where it is applied, are together in the process of being defined. This is made possible by the fact that the rule allows for exceptions. Ever pragmatic, at the time, Saussure spoke of “transactions”

193 since the rule is presented as the objective pursued by the poet, achieved, more or less well, in his poem. The body of Saturnian poetry is very incomplete. According to Quicherat, the verse had just one harmony: the caesura or break. For Saussure, on the contrary, the work of the poet is governed by eight rules. The first stipulates "Before anything else, embed those syllables and phonic combinations of every kind, that constitute the theme of the work, [...] For example if the theme, or a key word, is Hercolei, then use the fragments -lei- or -co- [...] He should then - the second rule - compose his piece, putting as many of these fragments as possible in the verse, for example afleicta, to suggest Hercolei, and so on." It is plausible enough, especially if we think about the harmonious principles underlying ancient architecture, that the Saturnian poets followed rules, and looked for beauty through certain canons other than those provided by meter, since their verses had no scansion. Saussure added up the discoveries and hypotheses. Consumed by the pleasure of his vast decryption project, he probably tended to underestimate the liberties the poet took in interpreting the given rules. From Jean Starobinski’s analysis of Saussure, we see clearly that Saussure’s heuristic is cumulative. There is a precise reason for that: once we have seen something, we can no longer not see it. In the course of his work, the paths he followed would, by their repeated use, turn into ruts that he would get stuck in. This is a well-known psychological phenomenon that was emphasized by the Gestalttheorie thinkers (cf. Chapter V).  Saussure’s stages of construction are marked by a very reflective choice of new terminology: the terms hypogram, anaphony, paramime, paronyme, paronomase, paraphrase, alliteration, anagram, paratext, logogram, antigram, diphone, locus princeps, syllabogram, mannequin, paramorph, partial mannequin, and complex-mannequin are specifically defined and redefined. They serve as tools to establish what physicists would call “correspondence rules” between a theory and the studied material. Saussure admitted that a voluntary method to discern the hypogram is not always possible and that this can result from an unconscious process in the work of the poet or even from an interaction between the text and Saussure’s own unconsciousness. About a passage in the Aeneid he wrote: “Afterwards I understood that it is the request my ear unconsciously received towards Hector which created the feeling of ‘something’ which had to do with the names evoked in the verse”. Although the passage did not mention Hector, the anagrams, hypograms, and anaphors of the word Hector had - by a type of subliminal reading - aroused in Saussure’s unconsciousness the idea of looking for the hidden inscription of the word Hector. This same tendency may have been present in the poet. Should we take the view that these hypograms drove Saussure into a delirious obsession, an impulsive production

194 responding to his interpretive skills of pronunciations and their variations? Some saw the Course as a way for him to avoid the descent into madness, a type of compensation where rationalization for once lead in the right direction of clear and general principles. The end of the hypogram story is quite sad. While our great linguist discovered more and more names hidden in more and more fields of literature, he remained anxious and vexed at being unable to dismiss once and for all the obvious criticism that his discoveries were simply accidental and implied by the calculation of probabilities. The progress of his investigation fueled this preoccupation to a crescendo that he was perfectly aware of: “The more the number of examples grew,” he wrote in April 1909, “the more there is place to think that it’s a natural bet on the chances that 24 letters of the alphabet should produce these coincidences semi-regularly”. He hoped to put an end to this uncertainty by writing to a contemporary author of Latin poetry. He chose Giovani Pascoli, repeated winner of the Certamen Hoeufftianum - the Royal Dutch Academy’s prize for Latin poetry. Saussure shared what he had found hidden behind his verses and asked Pascoli if he used “themes” to create his work. After a letter of initial contact to which the Latinist colleague most likely responded, a second more explicit letter from Saussure was left unanswered. Several letters from friends and rather unenthusiastic discussions lead Saussure to decide to not publish this immense work, a part of which he had already written up.  Nonetheless, these works were interesting in more than one aspect. They could even be said to be passionate. In 1967, Roman Jakobson voiced his opinion that this research deserved to be published in its entirety. The discoveries made by a linguist of Saussure's rank aren’t just random finds, they are necessarily in agreement with the ear and speech of the concerned historical people, compatible with their usage of language. We can also trust his choice of names in relation with the poem (the word-themes). I see four further reasons, of a very different order, for valuing Saussure's research.  First, at the heart of the investigation is poetry in Latin, a language in which the order of words is much freer than in English. The peasant kills the bear can be expressed as Agricola necat ursum as well as Ursum necat Agricola or still Agricola ursum necat and none of these phrases mean the bear kills the peasant. In Virgil’s famous verse Majoresque cadunt altis de montibus umbrae, the adjective majores relates to umbrae, the word furthest away. Within this poetic license, the skill of the poet to place the words in a certain order must certainly be appreciated, and all the more so in Sat-

195 urnian verse where there is no meter. All phonic effects should be perceptible and likened to the accompaniment of a melody. Regarding the inversions of letters tolerated by Saussure in the enunciation of hidden words, it is often a natural phenomenon of phonetic evolution. Saussure gives an example of evolution in Anglo-Saxon: föt > foot and, in the plural, föti > feet (CGL p110). Similarly, we know that Linear B, which only makes use of syllabic signs composed of a consonant and a vowel, wrote the Greek tripode in the form ti-ri-po-de. This plasticity of sounds, which also applies to the acoustic image, was Saussure’s preferred field. For him, letter groups are just transcriptions of sounds. The vital importance of spoken language is due to the fact that at the time of the Greeks and Romans, the most people could speak and understand even the most sophisticated use of their language, but could not read anything except by spelling it out, like an average English-speaker today reading Cyrillic. Secondly, the presence of constraints facilitates a poet’s creativity. Saussure rightly stressed: “We have the false idea of the difficulty of an anagram, which leads us to imagine that contortions of thought are necessary to satisfy it. When a word more or less coincides with a word-theme, it seems that efforts were necessary to be able to place it. But these efforts do not exist if the habitual and fundamental method of the poet consisted of deconstructing the word-theme beforehand, and letting these syllables inspire ideas and expressions […] More than one poet has sworn that rhyme doesn’t hinder, but guides and inspires him. It’s exactly the same phenomenon regarding the anagram”14. Today, the members of Oulipo15 abundantly testify to this. Reading them, one is quickly convinced that restrictive pretext becomes, for them, a reason to write. P.-M. de Biasi believed that these practices inspired by restrictions are in perfect harmony with a certain literary tradition in the spirit of Leibnizian philosophy16.  Citing Giono, he states: “If I write a story before having found the title, the story generally fails. A title is necessary because it is a sort of flag to head towards; it provides a goal - that of explaining the title”. 

14. In Starobinski, op. cit. p127. 15. Oulipo (OUvroir de LIttérature POtentielle) is a French literary movement which began before World War II, based on using strong a priori constraints. The most famous contributors are Raymond Queneau, Georges Perec, Jacques Roubaud, and François Le Lionnais. 16. P.-M. de Biasi “Hasard et littérature“ in Le hasard aujourd’hui, ss la dir.under the direction of E. Noël, Seuil 1991.

196 For the Saussure of the CGL, language intervenes “as a series of adjoining subdivisions drawn at the same time on the plan of confused ideas (A) and on that not less indeterminate plan of sounds (B)”

Among innumerable practices, these language handymen are yoked to the hypogrammatic form in Saussure’s sense: for example if the name of the hidden character is Montserrat Caballé, they propose17 Le concert de Thelonius n’a pas eu de succès. Ses détracteurs avaient organisé un douloureux chahut : Monk, c’est raté : cabale y est. [Jacques Bens] Giscard d’Estaing aimait sincèrement son premier ministre. Quelle ne fut pas sa tristesse quand il appris que celui-ci s’était ostensiblement ennuyé alors qu’il prononçait un important discours : Mon Chirac a bâillé !! [Georges Perec] The principle of the hypogram can be generalized to a suggestion of something that is not written, but is present by linguistic, phonetic or semantic links: the sentence Faire la maîtresse de la Fortune élémentaire des sages, pleine de secours is built out of common phrases from which the word roue has been removed 18.  Les illusions des aiguilles d’une montre : la peine du giratoire dénué d’une rotation double where one perceives the absence of ‘sens’ (direction, meaning) in both senses of the word.19

17. Oulipo Atlas de littérature potentielle, Gallimard 1981. 18. Faire la roue, la roue maîtresse, la roue de la Fortune, la roue de secours are. French idiomatic expressions using the word ‘roue’ (wheel). 19. Michèle Métail, « Filigranes », in Oulipo, La bibliothèque oulipienne vol 2, Ramsay1987.

197 In fact, well before Oulipo, poets exploited phonic evocation to avoid the platitude of the ‘real’ which disrupted the poetic effect. This has been judiciously analyzed by Michael Riffaterre in an article titled L’illusion référentielle20where he notes the transformations that happen in the mind of the reader between the first and the second readings of a poem. This leads us to the third, and certainly most important, argument in support of Saussure’s obscure research.  Psychoanalysis supplies numerous testimonies, which have become the material of more profound theories, that the unconsciousness deconstructs and reconstructs acoustic images. A patient recounts a dream where he is swimming in the sea and the water changes into milk and curdles. “Cheese embedded me”, he says. This strange dream is surprising for this young man, who is in love with a woman but encountering anxiety about that relationship. During the comments he says, “She's in bed with me… ” In Traumdeutung, Freud gives a great number of examples of “this chemistry (fragmentation and recombination of syllables)” and is not surprised “that within similar cases the spelling is less important than the sound of the words”21. But Saussure himself, in the rationalization that is the CGL, doesn’t take this phenomenon into account: “He thinks,” said Lacan, “that the thing that allows the signifier to be cut out is a certain correlation between the signifier 20. In Littérature et réalité, Seuil 1982. 21. L’interprétation des rêves, P.U.F. 1967, p348

198 and the signified”22, so that words underlying the words appear to him as an oddity which requires scientific proof. Jean Baudrillard thought that Saussure thus forbade himself from understanding that “the poetic is the rebellion of the language against its own laws”23. Lastly, as the fourth argument, we know today that Latin orators used rather elaborate mnemonic techniques, notably fascinating “memory palaces”. The basic idea is that in order to remember the monologues of a speech or long epic stories, one should construct a mental building composed of several rooms, each associated with parts of the text, thus enabling its reconstruction by mentally walking through this imaginary architecture. The method, attested to since ancient times by an anonymous document Rhetorica ad Herennium from the first century B.C., mentioned by Cicero in his De Oratore and by Quintillien, was still in use in the Middle Ages (Thomas Aquinas) and well into the sixteenth century (the Jesuit Matteo Ricci) 24. Many improvements to this method can be made; one can fill the rooms with objects related to the subject, or with people, etc. An obvious advantage  of such representations, compared with learning a text by heart, is that the reconstruction of a story can be done in any order according to a route as free as the imagination of the visitor of the ‘palace’. We know that in ancient times, places were closely associated with names of gods and rooms of houses were often devoted to specific deities. We are not too far then from Saussure’s intuitions. According to the legend reported by Cicero, the method itself would have been invented by a poet thanks to divine intervention.  And I heartily thank Simonides the Ceian, who is said to have been the inventor of the art of memory ; for they say, that as he was supping at Crannon in Thessaly, at the house of one Scopas, a man of estate and quality, after he had repeated a copy of verses which he had made upon him, where, in the usual practice of poets, there were a great many embellishments in compliment to Castor and Pollux, that this great man was so much of a scoundrel as to say, that he would give him but half what he had bargained to give him 22. J. Lacan, Séminaire on February 1, 1956. 23. J. Baudrillard L’échange symbolique et la mort, Gallimard 1976, chap. “L’anagramme”. 24. Cf. F. A. Yates L’art de la mémoire Gallimard 1975; D. Spence, Le palais de mémoire de Matteo Ricci, Payot 1986; M. Carruthers, Machina Memorialis. Méditation rhétorique et fabrication des images au Moyen-Age, French trans., Paris, Gallimard, 2002; and Le Livre de la Mémoire. Une étude de la mémoire dans la culture médiévale, French trans., Thorigny-sur-Creuse, Macula, 2002.

199 for the verses, and that he might apply for the rest, if he pleased, to the sons of Tyndarus, who had an equal share of the price. A little after, as the story goes, Simonides was called out to two young men, who were at the gate very earnestly desiring to see him ; it is said further, he arose, went forth, and say nobody ; that in the mean time the room where Scopas was banquetting fell, and buried him and his family in the ruins ; when his relations came to bury them, they were so crushed that they could not distinguish one body from another, till Simonides, by recollecting the distinct places where each had reposed, is said to have pointed out the particular bodies, so that each might be buried. This incident is said to have given him the hint, that order was the best enlightener of the memory ; therefore that they who employ this faculty of the understanding, ought to fix upon places, and imprint those circumstances in their mind, which they wish to retain in their memories : thus the order of places will preserve the order of facts, and the ideas of things will mark the things themselves, and by this means places may serve for wax, and ideas for characters. (Cicero, Three Dialogues upon the Character and Qualifications of an Orator, trans. by William Guthrie, Oxford 1840) If we consider it plausible that Latin poetry contains the hidden presence of names of divinities or famous figures related to the theme, the question which arises is that of Saussure’s block after so much meticulous research. Why did he absolutely need a proof? Let’s continue on to some comparisons. Freud, although motivated by a strong demand for the scientific, accumulated facts and testimonies without ever searching for sine qua non proof either of the unconscious or of this clear division between what comes from conscious and unconscious activities. Concerning artists’ work habits, proof of this unconscious creativity is rare as the ‘rules of

Hieroglyphs. Names and symbols of Gods are mixed and in continuity with the text. Temple Kôm Ombo, Toutmosis III, Ptolemaic period.

200 art’ are considered as privileged knowledge and only passed on through apprenticeships, never published. Jurgis Baltrušaïtis, a specialist of Medieval iconography, showed by a number of examples that the storiated capitals of Romanesque churches were designed with the underlying idea of the acanthus leaves of Corinthian capitals (which played the role of ‘model’ in the Saussure sense). We have not found written proof of this. Roland Barthes, to support his theory of five codes (or voices) of the text in the novel – hermeneutic, which posits the truth to be a mystery, semantic, symbolic, proairetic, relating to the action, and cultural, relating to external references – did not look to the testimonies of novelists. He is, nevertheless, in the same perplexing situation as Saussure. While analyzing Balzac’s Sarrazine he thought “Chance (but what is chance?) wants the first three lexical items (i.e., the title and the first sentence of the novel) to already give us the five great codes that would now unite all the signifieds in the text, without need to enforce, until the end, any code other than those five there, and no text which doesn’t find its place there”25 . Elsewhere, I have explained26 that the probability calculations that filled Saussure with dread were impossible to put into practice given the vagueness of the body of work, and the accepted exceptions. Evidently, the abundance of facts in ever more varied literatures of every period had been a trap for Saussure. But it did not bother Freud who pointed out the unconscious in Greek mythology, Shakespearian dramas, Leonardo da Vinci’s oeuvres, the figure of Don Juan, etc. Saussure, asking himself about his own talents in the matter, wasn’t far from recognizing that the abundance of cases was due, primarily, to the interpretative skill of the reader. Starobinski also thought that the solution to the dilemma was to assume that these rules, in the mind of the poets, were unconscious. Baudrillard thought the contrary, that it was the simplifications made in the CGL that were at fault, with the principles of differences and substitutions in praesentia and in absentia. Baudrillard maintained that language had several registers and was in perpetual rebellion against the apparent rules from which it can be freed. Verlaine asked “for music above all else” and Mallarmé that “there should always be mystery in poetry”. Clearly, had he taken Baudrillard's  point of view, Saussure would have placed abundance on his side, and, furthermore, would have restored the esteem he had for his own research work.  Beyond the respect for Saussure in relation to mathematics and the calculation of probabilities, there is the hope of preserving the beauty of his youthful method of discovery of laryngeals. It’s certainly a shame that he did not read Freud, 25. R. Barthes, S/Z, Seuil 1979. 26. La règle, le divan et le compas, op. cit.

201 but even more so that he did not read Cournot as he would have clearly understood from Cournot’s works that the meanings he sought were related to philosophical probabilities and were, therefore, absolutely unquantifiable. He had been a victim of castration by mathematics, which said to the applied positivist “that which is not quantifiable does not exist”, mathematics which he loved for its beautiful austerity and the creativity of its algebra: a double bind that is completely inhibitive (when it is not seen as such).  Today, quantitative methods in linguistics are well developed, being largely facilitated by systematic research tools made available by computer technology. We could place them on the side of the researcher in an approach similar to that of Saussure, as a tool to help the investigation, but we should not neglect the remarks of Lacan and Baudrillard. It is not about looking for hidden rules, but about finding statistical peculiarities, either qualitative or semantic, of certain bodies of work in relation to larger ones... 

202

Jacques Monod’s Roulette

204

205

The idea that evolution, of which man is one of the results, is due to mutations which occur at random, didn't only shock religious minds. Many scientists have pondered this element of chance, ultimately finding it an embarrassing point for future research. Rather than chance, in the context of a nuclear cell, it's a complex mix of thermal agitation, quantum chance and a good dose of our own simple ignorance. Unable to fulfil our reductionist amibitions, unable to give an exhaustive and definitive description of epigenesis, we express our ignorance through the vocabulary of randomness, not only at the level of cellular ontogenesis, but also for issues about biodiversity and stability of ecosystems.

206

207

Biology is a field where, for each and everyone, conflicts between chance and meaning seem to carry more serious consequences. There are numerous books that use this supposedly clear and obvious conflict to hog the stage with either political or religious doctrines. The most well-known - and quite rightly, given the strength and clarity of thought - is Jacques Monod’s Chance and Necessity which does nothing less than attempt to express science’s point of view, even if this has ethical implications. Even at the heart of the argument, the idea that DNA mutations happen at random, and constitute "nature's roulette", is not without difficulties: We say that these events are accidental, due to chance. And since they constitute the only possible source of modifications in the generic text, itself the sole repository of the organism’s hereditary structures, it necessarily follows that chance alone is at the source of every innovation, of all creation in the biosphere. Pure chance, absolutely free but blind, is at the very root of the stupendous edifice of evolution. (J. Monod, Chance and Necessity, trans. by Wainhouse 1972)

Am I, a thinking being, the result of such pure chance? Supported by the aura of the Nobel Prize, Monod’s comment has considerable philosophic impact. It demands the acceptance of a scientifically established “unbearable lightness of being”.

208 Before going on, let’s clarify our discussion with the two remarks. Firstly, the concept of the roulette is not to be understood in the strictest sense of the word. The roulette, a lottery, or more generally, a probability space, supposes a field of clearly specified possibilities and if the space of possibles possibilities is not finite, then the expression “at random” can not refer to an equal distribution. As the integers form an infinite set, “to choose an integer at random” is not a clear expression. Yet, it seems that chemical compounds, proteins, and amino acids permit an open collection of possible combinations. Therefore, the action of “nature’s roulette” must be understood as meaning “there is chance” or even “not deterministic”. This poses the question of the involvement of probability laws, the main subject of this book. Interrelations between the underlying hierarchies of an organism Paul A. Weiss “The Living System: Determinism Stratified” The Alpbach Symposium, Beacon press 1969.

“The same genotype can therefore produce a variety of phenotypes according to what had been the environment of the developing system. That means that if you base it on phenotype like natural selection does, there is an essential indetermination between this phenotype and the genotype; the relation only becomes determinant if you take the environment into account.” C. H. Waddington, “The Theory of Evolution Today” Ibid.

209 The second point is that the expression “sole repository of the organism's hereditary structures” is not exactly correct. It is a simplification that can lead to misunderstandings, especially nowadays when we talk more and more about genetic engineering. There is no species, at any stage of development, whose DNA finds itself in a free state as it is. There is always a context at the nuclear or cellular level and the ontogenetic development of an organism also happens within a biological context. For higher species, moreover, familial and social contexts impose their own transmission laws and the role at each stage is far from being perfectly understood. We designate the totality of these phenomena by the term epigenesis. But it is here we find the nuances which Monod undoubtedly thought should be glossed over, so that his message would have a greater impact on the public at large. Thus, we come to the main thesis, explained by Monod in an enlightening way: chance operates by a process at two levels. First, the “roulette” of mutations proposes new genetic variants and, second, by the teleonomic action of selection, evolution selects and keeps those which have the properties required to subsist and reproduce themselves. Monod wrote, “Still today, many distinguished minds seem to be unable to accept or even understand that, from one source of noise, selection could, by itself, sort all the music of the biosphere”1 or even “The universe was not pregnant of life, nor was the biosphere expecting men. Our number was picked in a game in Monte Carlo. What is so surprising, like a man who just won a million dollars, that we prove the strangeness of our condition?”2. In fact, it is the second level that is philosophically and epistemologically difficult to understand in terms of its consequences: does it ultimately lead to random results? Ninety years earlier, on July 3rd, 1881, Darwin wrote to his colleague W. Graham: “you have expressed my inward conviction, though far more vividly and clearly than I could have done, that the Universe is not the result of chance”. What Darwin wants to emphasize is that the circumstances, (climate, abundance or scarcity of food, presence of predators, etc.) make it so that in the fight for survival of the fittest a species either evolves or disappears. There is some causality here whose result is encapsulated by Monod in the term teleonomy. This roulette, then, is one in which certain implications. But this causality relies on the existing context consisting of the pre-existing species. Monod's thesis leaves 1. Op. cit. p135. 2. Ibid. p161.

210 open the possibility that, in this game of necessity, the rules of physics and chemistry may ensure that certain results are inevitable, no matter what random mutations occur. This is much the same way that a drop of water which falls on a massive mountain crag will ultimately end up adding to the river determined by the watershed. Or even - as another analogy - that the algorithms known as stochastic gradient, or simulated annealing, which randomly draw a point at each step and compare it to the preceding one, always end up finding the lowest point of a surface. But we do not know what other results could have occurred as we cannot redo evolution3. With genetic manipulations and anthropotechniques, however, their artificial character provides (or would provide) a quite different experience: the coexistence of natural species and species that have been modified by us, which is not at all the same. According to Monod’s presentation, nature solves an optimization problem by mutations and selection. Monod did not think that this problem had only one solution. But we have the impression that “there is” an intention of improvement. This question of epistemological retroaction, of links between causes and effects, is well put by Heisenberg: I remember a session from a colloquium devoted to Darwinian theory in its modern form called: “Unexpected Mutations and Selection”. To justify this theory, the following parallel had been evoked: The origin of the species was comparable to the origin of human tools. Thus man’s need to move across the water had led him to invent the rowing boat, and suddenly lakes and coastal waters had begun to teem with new objects. Then someone had the idea of exploiting the force of the wind by means of sails, and saling boats began to oust rowing boats [...] The process of biological selection must be envisaged in much the same way. Mutations occur by pure chance, just as quantum theory would expect them to do, and selection then eliminates most of these «natural experiments». Ony a few forms, which have proved themselves under the given circumstances, remain. 3. A. de Ricqlès clarifies this point with the example of marsupials: “However, everything is not chance […] As proof, we can give the extraordinary phenomena of convergence and resemblance which certain groups of marsupials show with certain placental groups. This means that everything is not possible: based on a ‘basic’ mammal, if this mammal must adapt itself to a certain way of life. If we want to ‘make’ a herbivore, if we want to ‘make’ a small tree-gliding mammal, if we want to ‘have’ a carnivore, any morphology, any structural type, any physiological adaptation would be possible. Marsupials, on their behalf, then have differentiated in the course of their own evolution certain types of organisms which surprisingly resemble placentals, which play the same roles in these ecosystems. Everything is not chance then. There are building constraints which exist in nature.” «Hasard et paléontologie» in Le hasard aujourd’hui, op. cit.

211 While reflecting about this comparison, it occured to me that the process of technological advance differs from Darwinian theory in one crucial respect, namely, just where Darwinian theory introduces chance. Human inventions are the result never of accident but of man’s intention and thought 4. I tried to see what would happen if the comparison were taken more seriously than the speaker would have wished, and if something like intention were associated with Darwinian mutation. But can one really speak of intentions apart from man ? [...] If we did, we would obviously be misusing the word “intention”. But prehaps we could choose a more careful formulation. We could ask whether the aim to be reached, the possibility to be realized, may not influence the course of the events. If we do that, we are almost back with quantum theory. For the wave function represents a possibility an not an actual event. In other words, the kind of accident which plays so important a role in Darwinian theory may be something very much subtler than we think, and this precisely because it agrees with the laws of quantum mechanics.5 Some comments or critiques made of Monod by other scientists indeed call for more shrewdness and caution in the analysis. The way Prigogine expresses himself on the matter of mutations is already quite different than Monod: It’s not instability but a succession of instabilities that allowed the crossover into the no man’s land between life and no life. We’ve only begun to distinguish certain stages. This view of biological order automatically leads to a much more nuanced appreciation of what the role of chance and necessity could be, to 4. This is also what Claude Lévi-Strauss thought: “In better known ethnological treaties we read that man owes knowledge of fire to the chance of lightning or brush fire; that the discovery of game accidentally roasted in these conditions revealed cooking food to him; that the invention of pottery resulted from forgetting a ball of clay in the proximity of a hearth. […] All of these operations [choice of clay, its mixture, its shape, choice of fuel, form of the hearth, length of baking] are much too numerous and complex for chance to have realized them. Each of them, taken separately, mean nothing. It’s only their imagined, intentional, sought and experimented combination which allows for success. Indubitably, chance exists, but does not produce results on its own. For about two thousand years the Occidental world knew of the existence of electricity – discovered, of course, by chance – but this chance remained fruitless until the intentional and directed efforts of Ampère’s and Faraday’s hypotheses.” (Race et histoire) 5. W. Heisenberg, Physics and Beyond, Encounters and Conversations, Harper & Row 1972, Chapter 20 «Elementary Particles and Platonic Philosophy (1961-1965).

212 use the title of the well-known work of Jacques Monod. The fluctuation that allows the system to leave the states close to thermodynamic equilibrium represents the unstable element, chance. On the other hand, the instability of the environment, the fact that this fluctuation will increase, represents a necessity. Chance and necessity cooperate instead of opposing each other.6 In contrast to Monod who posed the principles in a general conceptual language similar to that of the ancient Greeks and Romans with tyche and automaton (cf. Chapter I), Prigogine thought of the question as a physicist within the framework of the thermodynamics of open systems. Albert Jacquard is equally vexed by this overly simplistic mode of expression: I believe that Jacques Monod did us a disservice by giving the impression, following the example of Démocritus, that there was either chance or necessity and that everything depended on them. This disservice is even worse as he gave chance the image of a minor Greek god. You know, in Ancient Greece, each time that an event happened, they didn’t have to ask themselves any questions to know why it happened, they always had the response: this or that god had done it. There is a storm, well, Poseidon is angry. Lightning struck a tree, well, Zeus is angry. With such rapid, easy responses, science could hardly advance.7 Also, at the level of mutations, the meticulous analysis of by the statistician Georges Matheron concluded that amino acids statistically do not look as if they had been picked randomly8. According to experiments there is a game of selection and epigenesis, very complex both locally and globally, which leads to certain configurations occurring. 6. I. Prigogine «La thermodynamique et la vie», La Recherche n°24, June 1972. 7. A. Jacquard «Hasard et génétique des populations» in Le hasard aujourd’hui, op. cit. 8. G. Matheron, Estimer et choisir, Ecole des Mines, 1978; Estimating and Choosing, an Essay on Probability and its Practice, trans. by Hasofer, Springer 1989.

213 Matheron, a theoretician with great expertise in probabilities and statistics in a broad range of fields, went a step further and asserted that we cannot separate the chance that is due to our ignorance from that relating to the selection that is poorly understood because of the chemical, cellular, and environmental context. In other words, Matheron agreed there was chance, but a peculiar type of chance, and he even left us to understand that in very specific circumstances this can be asymptotically deterministic. We do not know everything. This could fuel the fire of creationism and the “intelligent design” trend of certain American Evangelical Protestants, but we sense that Matheron is opposed to it. He desires just the opposite effect: of making Monod’s discourse more rigorous and less empathetic. E. Schoffeniels’s critique pushes the determinist hypothesis further by recalling the physics of DNA fragments itself: To invoke chance, as Monod does, to explain the transformation of species by a game of mutation and natural selection, is certainly a classic view, but it is far from satisfying a number of biologists. Spontaneous mutation obeys the laws of physics and chemistry and our knowledge of the chemistry of DNA is at this point so rudimentary that it would be vain to make suggestions. 9 We can see a certain frustration in these scientists' criticisms. They do not accept that reality should be so easily qualified as random. Monod’s chance, for Matheron and Schoffeniels - and we see a similar position with Prigogine is felt as a “don’t go any further, it’s futile”, just like Comte’s positivist laws that were seen as limits to research. Today, the reservations expressed by Prigogine, Jacquard, Matheron, and Schoffeniels each turned out to be carriers of a deep, uncontestable truth. Re9. E. Schoffeniels, L’anti-hasard, Gauthier-Villars 1973.

214 search over the last thirty years on viruses and the transferring of genes or oligonucleotides by (poly)cationic lipid vectors shows that the chemo-physical context of genome sequences is a huge field of investigation where knowledge organizes itself into rationalizations and theories, where the image of the lottery is superseded, having lost the main part of its value. Here, again, we seem to be seeing the double step that Jean-Claude Milner highlighted, which we met in the previous chapter. The first phase: it is random, not due to any god, divinity, or the will of any being. The second phase: no randomness, or very little; relations, properties, and laws make it so that it could hardly be otherwise, the part attributable to chance diminishes. But this second phase remains incomplete so, we should emphasize, we are far from the final stage of the Hegelian dialectic: knowledge pushes out randomness, but does not eliminate it. On the question of knowing where chance now resides, quantum mechanics has radically changed the vision that we could have at the time of Laplace. In this respect, we see that Einstein’s attitude - encapsulated in his famous phrase “Gott würfelt nicht” (God doesn’t play dice) - is perfectly natural and in line with the above comments of Matheron and Schoffeniels about Monod’s views about chance. What is very surprising here is that chance plays an integral part in the laws of physics. This leads us to classifications of chance that we have not yet mentioned, but which are relevant here, so we will sketch a brief outline of them now. The word hazard comes from Arabic. We know it designated a particular game of dice in the thirteenth century when it first appeared in our language, and since then its meaning has progressively grown. Today mathematics and physics have revealed more complicated games than the dice games that came to compartmentalize this vast conceptual area. These are called dynamical systems. To be absolutely clear, we are outside the domain of Cournot’s philosophical probabilities, outside of the field of interpretative likelihoods; we are, therefore, in the realm of mathematics, of that which is quantifiable in some sense. But that does not mean that all these phenomena can be described correctly in the language of probability theory, i.e. the stochastic calculus which we mentioned in Chapter III. This is only true for some. The first family is that of asymptotically regular systems, which, exactly like roulette, have the property of evolving towards a uniform distribution. These systems had been studied by Henri Poincaré and Heinz Hopf who gave numerous examples of it among systems subject to classic mechanics with energy loss, otherwise called dissipative systems, like the marble + roulette system which finally ends up stopping itself due to friction. They satisfy a rule that Poincaré named

215 the arbitrary function principle: if there is any variation in the initial conditions, and this variation is random (but describable by a density function), then the variation in the final position will be uniform. Poincaré explains that the use of roulette is thus relevant in a casino or in the quasi-uniform distribution of small planets of the solar system on the Zodiac. Other systems, however, which have been described more recently, have an asymptotic evolution where the state approaches a singular set that is thin, like a folded curve, and which David Ruelle called a strange attractor. Examples are given by certain non-linear equations, some of them very simple. Most of these examples are contained within a larger class: that of systems which are sensitive to initial conditions - one of the greatest discoveries of the twentieth century. The variety of situations and phenomena is such that the term chaos theory is used to designate the generally delicate study of these evolutions which - even though they are purely deterministic, i.e., governed by clear transformations and without randomness from one moment to the next - present such irregular yet surprising and apparently creative paths that they seem to make use of a hidden source of randomness. Some of these systems imitate randomness very well, such as the pseudo-random number generators that are chosen for their good statistical performances. Others only satisfy certain properties of the asymptotics of chance. Aside from these two categories, however, the majority are such that we barely know enough to say anything about their evolution in the long term. This makes us philosophically aware of the fact that a system may make no direct appeal to chance, may lie inside the strict deterministic paradigm of Laplace, yet, in that system, rigorous logical implications may give an appearance of chance and prevent knowledge from sorting out the tangle of trajectories. To this, of course, we have to add quantum indeterminacy, whose nature is rather different and cannot be reduced to the preceding, in that today it is considered that hidden variables cannot account for the observed measurements. Many

216 authors think that, better even than the motion of molecules, quantum mechanics gives a perfect example of pure chance in nature. A comment by Werner Heisenberg about snowflakes nuances this point of view in an extremely interesting way: We may derive atomic laws not only from the fact that atoms arrange themselves nicely into ranks to form a solid material thing, but also the specific character of the organization, symmetry and structure of the crystal. But the individual exterior form of the crystal remains, according to the laws that we know, left to a game of chance; even if we could reconstruct it with precision identical to the exterior conditions of the crystal formation, the form of the obtained crystal would not be exactly the same. The drop of water which froze in low temperature atmosphere solidifies into a snowflake. In the absence of any exterior perturbation, the symmetry of the crystal will always be hexagonal but the individual form of the small star of snow is not determined beforehand by any natural law […] Then comes an argument in favor of another type of randomness, not quantum allowing Heisenberg to continue his analysis: In this example, even the experiment does not offer any point of reference which would allow subjecting the formation of snowflakes to forms which would be entirely determined by superior connections. Therefore, here we must believe without a doubt in the game of chance, even if we are not forced to this conclusion on the plan of principles; as we cannot positively affirm that the theoretical quantum state of the drop of water is actually known before and during the formation of the crystal. There is no restriction in favor of the recognition of chance (if we suppose the laws of quantum theory are exact) that in these examples of cases for which the theoretical quantum state is known with certainty: we can think for example of a piece of radioactive material, for which we have a certain knowledge of the fact that all the atomic nuclei are found in their basic state […] This immediately leads him to the question of meaning to which he responds in a very “philosophical” manner which should not surprise us given he is a specialist in quantum physics: Even if we believe that the growth of an individual crystal would not know how to be determined beforehand

217 and that therefore another crystal could just as well appear, the question of knowing if the chance to which the crystal is indebted to for its form is “senseless” is still, for all that, not a decided question as the formation of a crystal is a historical act which cannot be cancelled—and which can also play an important role in the connection of our life of the world, even if it had not been determined previously. For the type of connections about which we can legitimately use the word “meaning”, there may exist a link even with the events which could have otherwise also happened without any reason. This last paragraph puts a magnifying glass - with the greatest possible strength - on the border between insignificant chance and significant chance, in other words, risk. In fact, Heisenberg tells us that the snowflake’s development can legitimately be seen as belonging to the category of risks. He purposefully took the example of the snowflake, beautiful and inoffensive, to not lead us astray into the vocabulary of worries of the human condition, but he clearly refuses to accept the idea that we consider ourselves independent, without any connections, from events that could have turned out otherwise without any reason. We class as risky those situations that are sufficiently linked to us - or to some humans, we should say - to admit one or more interpretations (cf. Chapter VI). Henceforth, to take risks is to take account of interpretations of the world in our actions. This is a more fundamental acceptance of the state of things than the current acceptance of economists who simply situate themselves on the quantitative scale of variances in situations with the same expectation of gain or loss. The expressions propensity for risk or aversion to risk are employed in financial models in a very restrictive sense which encourages constant misunderstandings, as if we had absolute rules for how we behave in lotteries, independent of symbolic meanings at play. It’s too simplistic. Keynes used the profound concept of risk to compare the activities of able speculators to the true agents of the economy: Or, to change the metaphor slightly, professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment,

218 are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees. [...] [...] Investment based on genuine long-term expectation is so difficult today as to be scarcely practicable. He who attempts it must surely lead much more laborious days and run greater risks than he who tries to guess better than the crowd how the crowd will behave; and, given equal intelligence, he may make more disastrous mistakes. There is no clear evidence from experience that the investment policy which is socially advantageous coincides with that which is most profitable. It needs more intelligence to defeat the forces of time and our ignorance of the future than to beat the gun”. (John Maynard Keynes, The General Theory of Employment, Interest and Money, 1936) Ulrich Beck also establishes this idea in his analysis of risks arising from modernity and globalization. He arrives at a dichotomy similar to that of Cournot between the quantifiable and the unquantifiable by a new, sociological argument: modernization is reflexive, it modifies the values, references, and information on which the processes of innovation were founded which are being overtaken: “If you make the distinction between calculable and non-calculable threats, in the region of risk calculations, new types of incalculabilities and industrialized threats or products of decisions spread to the core of the globalization of high-risk industries, whether it be for the goal of war or for well-being.”10 Much ink has been spilled over Jacques Monod's ideas, and at the heart of all this writing we can single out the very lively position adopted by René Thom. His article, "Halte au hazard, silence au bruit” from Le Débat, July-August, 1980 n°3, is a virulent plea against the use of chance as a scientific explanation, imploring instead that we search for representations that incorporate mechanisms which seem hidden at first glance. In a querulous tone, Thom argues from the same point of view as Matheron and Schoffeniels. Their common thesis is that proposing chance as an explanation is always an ambivalent position: on the one hand, one presents a simply model whose validity is acceptable in all events as a first approximation, on the other hand, one says at the same time that this is the best possible scientific representation, 10. Ulrich Beck, Risikogesellschaft: Auf dem Weg in eine andere Moderne, Suhrkamp 1986. See also, U. Beck, A. Giddens and S. Lash, Reflexive modernization, Polity Press 1994.

219 which creates problems in most cases. For Thom, the “popular French epistemology”, represented by recent works such as Chance and Necessity by Monod, La Méthode by Morin, Entre le Cristal et la Fumée by Atlan, and La Nouvelle Alliance by Prigogine and Stengers, is characterized by underlying philosophies which “outrageously glorify chance, noise, ‘fluctuation’” and render chance responsible whether it be for the organization of the world or for the emergence of life and reason on the planet. “This fascination with chance testifies to an anti-science attitude par excellence”. In fact, the views developed by René Thom were extremely conventional: there is a continuum between the determinism of systems sensitive to initial conditions and random models. The random case is an ever unattainable extreme case. “Chance is an entirely negative, empty concept, and is therefore without scientific interest. On the contrary, determinism is an object of fascinating richness - for he who knows how to scrutinize it”. Thom adopted such a controversial view that it became a position. Even the definition of chance he gave, that “a random process is one which cannot be simulated by any mechanism, nor described by any formalism” is debatable. A reference in a footnote which refers us to Church's thesis, is completely irrelevant. Thom pretends to ignore the immense fecundity of the language of probabilities in applied or theoretical science and the splendid discoveries of stochastic calculus of the twentieth century that created a language useful to all sciences including the most rigorous physics. Effective calculability certainly doesn't create a schism between deterministic and probabilistic thought, but between a certain form of the abstract and the concrete. Here Thom is abusing the non-specialist reader. In his rather pertinent critique of the idea of “order by noise” and of the role of fluctuations as explanations of the complexity of the world, Thom emphasizes that if a spark sets off a fire, it is not that which creates a forest. He fails to mention that the same criticism can be made of his treatment of chance due to the meeting of two independent sequences. He says, in effect, that the meeting in question defines a subvariety, of codimension one, in the initial conditions of the global system. This may be so, but this subvariety is not available and, ex post, it is as tangled as the evolution, in the time direction, of a system sensitive to initial conditions. In other words, Thom deliberately overstates the extent to which we can describe the concrete systems we use. Justifiably, he emphasized the distinction between the representations we make in natural language (NL) and those in mathematical language (M) and recognized that there are situations for which we have satisfactory descriptions in natural language but for which we are unable to give an acceptable mathematical

220 description. Hence “the problem of articulation between the two formalisms (NL) and (M)”. All of epistemology is here. Alas, he does not respond to this question except with affirmations of evidence on what is scientific and what is not. The question of philosophical probabilities, of our propensity for believing the symbolic representations of science, is also passed over without comment, at least in this article. These ideas are, however, addressed elsewhere.11 It is interesting to note Thom and Matheron’s agreement on the fact that chance plays the same role as divine will. “At heart, in what way is an appeal to chance to explain evolution more scientific than an appeal to the will of a Creator? Is chance anything more than a secular substitute for divine purpose, as teleonomy is a respectable substitute for teleology?” Compare this with the conclusion of the first chapter of Matheron: “It is likely that J. Monod thought of his philosophy, before anything, like a war machine against Teilhard de Chardin. It’s what explains their relation. Monod’s chance is the brother foe of the good Father's [i.e., Teilhard de Chardin's] Omega point: his enemy, certainly, but fundamentally his brother; they are from the same family.”12 What is curious in this quarrel is that the adversary, whose main role is held by Monod, rightly presents chance as tearing us away from the spontaneous tendency of searching for an author of what happens, as a renunciation of hope of meaning. And yet the frustration of Thom and Matheron is a frustration of scientists. Each camp dismisses the reasoning of the other as a search for the divine. Among the authors who threw themselves into the task of rethinking the problem of chance in the whole of biology in the light of contemporary knowledge, we should single out the very seductive book of Alain Pavé La nécessité du hasard (EDP 2007). In conflicts between chance and meaning, it is usually meaning that progresses while chance dissipates like fog, yet many authors - including those cited above - fight to beat back the kingdom of chance. Alain Pavé is one of the rare exceptions, advancing arguments in the other direction. His main thesis is that living beings, in their evolution, are subject to random events but that "chance is not only a 11. Cf. for example Prédire n’est pas expliquer, Eshel 1991. 12. Op. cit. In Le phénomène humain (Seuil 1955) Teilhard de Chardin expresses himself thus: “By structure, the Noosphere, and more generally, the World, represents a whole, not only closed but centered. Since it contains and engenders the Consciousness, Space-Time is necessarily convergent by nature. Consequently, its excessive layers, followed in a reasonable way, should bend back somewhere forward, in a Point, we may call Omega —, which merges and integrally consumes them in itself.”

221 fact imposed from the exterior or resulting from our ignorance; it is not totally contingent but results, to a large extent, from a selection.” Alain Pavé distinguished the action of “roulettes” on different levels: The first roulette concerns modification mechanisms of the genome, the second, the distribution of parental genes in gametes of eukaryotic species. Next comes combining gene pools through fertilization, and, as the fourth, he mentions the horizontal transferring of genes by man-made hybrids which is not properly discussed as a roulette but nevertheless is often a diversification factor. The fifth roulette is the choice of sexual partner in sexed species, to which we should also add the paths of pollinating insects and the dispersion of grains by wind and animals. If we think of these mechanisms (in first approximation as Thom said) as random draws, then their presence, added at several levels in superior species, is unquestionably troubling and needs some explanation. More simply, Pavé's thesis could be restated as saying that the presence of chance is an advantage as it gives the species a sort of insurance against the unforeseen. Pavé gives numerous examples, but the epistemological question is knowing whether we could ever really establish such a thesis. A few comments on this subject: a) According to a widespread belief in some positivists and ecological circles, evolution makes things better, improving them by trial and error. Chance would be a way to optimize in any context. This is a false idea that biology doesn’t support. Transformations do not “undo” themselves once they have conquered an entire population. To go to the top of a tree, to take a simple image, a search algorithm which, to find the top of the tree, always takes the uppermost branch (improving the aptitude), could well lead, depending on the shape of the branches (the imponderables of the environment), to the end of a low branch. b) If a part of a population, with certain genetic and phenotypic characteristics, dies out, is the rest of the population “scarred” by reforming the lost genetic element or, on the contrary, does it thrive in a new direction? c) The fact that there are “roulettes” (on this point Pavé makes a convincing synthesis) is one thing. Maintaining that they are the result of a necessary evolutionary process is, then, a trivial statement if one views it as descriptive (in this sense, everything that exists is necessary). To give it real content, one must think of living organisms in a situation where there would be no roulettes, that is to say where the changes would all be necessary in a strong sense like mathe-

222 matical theorems. (Why is there a right triangle whose sides are integers in arithmetic progression: 3, 4, 5? Because it’s like that.) That doesn’t seem to forbid the principal characteristics of life. The reason for it is precisely because many combinatorial systems of strict determinism imitate this and are mistaken for random systems. d) In terms of living organisms as well as environmental configurations, the possibilities are quite open. We don’t know how to describe them and the combinations contain complete surprises for us, so we cannot get around the problem of chance here, nor of statistics, nor of averages, etc. In a certain way, the “roulettes” give no assurances beyond a bounded and delimited field of randomness, so that their presence gives only a very partial answer to questions of the stability of ecosystems composed of evolving species. For example, why are rainforests relatively stable in their extreme biodiversity? We could think that this biodiversity is a phenomenon of “invariant measure”, with regard to diverse random changes over the very long term, which would reinforce its vulnerability to current tragic deforestation. Much to our amusement, Pavé chooses the path that frightened Saussure. The mass of opinions, though not clearly demonstrative, leads to a certain agreement all the same: there is something there. We willingly follow it to one of its conclusions, one that is not of the least importance, which is that we need ways of measuring biodiversity in order to be in a better position to talk about it, so that we may better preserve it. However, we should note that - unlike Heisenberg, Keynes, and Beck - none of those authors cited here that are concerned with biology, ever envisioned philosophical chance in Cournot’s sense, although it underlies all of these affairs. Indeed, meaning and interpretations will take an ever-growing and foremost importance in the future, with immense difficulties attached to their plurality and their irreversibility which we’ve mentioned. We will come back to this point in the following chapters as we ponder the modification of human genetics.

223

224

From Fortuitism to Animism

226

227

Upstream from the category of chance is a larger philosophical category, concerned with that which comes to take a particular place among a set of values, qualities or forms. It is the fortuitous. When faced with a fortuitous event, we may ask if determinism, chance or intention is behind it. LéviStrauss thought that animism was not disdainful of determinism but, on the contrary, that the belief in a generalized determinism would be a prefigured science from this perspective. The philosophy of William James had this novel feature of accepting the links, by a sort of pansychic empathy, between the various fortuities that make the world, an idea which was recently taken up by the sociology of science in an anthropological approach which denounced the modern divide between facts and values. Do we then have the conceptual tools capable of undermining progressive positivism?

228

229 The category of the fortuitous. The word fortune predates that of chance and the concept of the fortuitous may be seen as a primitive, unfinished, or incomplete form of the concept of chance. Something - an event or a phenomenon - is fortuitous (whether produced by clear logic, mechanism, chance, or even by something we don't know about) when it comes to take a form, a place, a dimension, a character inside a set becoming one particular element rather than another. So we can say that the sun in the battle of Austerlitz was a fortuitous event, as was the discovery of penicillin by Fleming, as is the fact that ice is less dense than water, that absolute zero is -273.15°C, that Cleopatra’s nose had exactly the length it had, that the speed of light and other fundamental constants are precisely the values we’ve measured. But also the fact that the relation of the circumference of a circle to its diameter is 3.1415926535… or that the sum of the series 1 + (1/2)2 + (1/3)2 + … is equal to π2/6, or even that a triangle with sides 5, 12, 13 is right-angled. The presence of an explanation erases the fortuitous character of an event or phenomenon if there was no possibility of imagining a universe where the result would be different. Yet, in mathematics, we usually have abstract spaces where similar things organize themselves differently. The category of the fortuitous sometimes allows us to establish semantic hooks for particular configurations that are simply ‘like that’. That is to say, reference points in our customs and habits may “give” this singularity. The trick is to find a meaningful path that leads to that result. This is the basis for mnemonic devices (such as My Very Earnest Mother Just Served Us Nine Pickles to remember the order of the planets) of which a very elaborate form is the memory palace mentioned in Chapter X. We often wonder if, on the set in which a particular event appears fortuitous, a source of chance exists which could produce this precise case as a result of randomness. But this is a later, more scholarly question that should be kept separate. For example, our discussion on Monod and evolution, whether or not one agrees about the roulette, does not prevent us from saying that the appearance of dinosaurs on the planet was a fortuitous event as well as their disappearance (even if this last point may have explanations, because certain species like the horseshoe crab have remained abundant and unchanged since the Cambrian up until the current day). 1. In the foreword of his Theorie analytique des probabilités Laplace imagines a world where all positions and speeds of all molecules are known, therefore a world entirely deterministic (but he adds that such a knowledge is not available for human beings so they need to learn the probability calculus).

230 Could we imagine a world without fortuity? That would mean a world where everything is necessary and cannot be otherwise; a world without quantum mechanics, scintillation or ‘reduction of wave packets’. Would this be the world imagined by Laplace1 ? If we forget electromagnetic waves and other complications of contemporary physics, all of the molecules thought as of small particles whose movements are governed by the laws of classic mechanics would have to provide the necessary results. It would also be necessary to know the initial conditions, yet they appear to us largely fortuitous, so we have simply moved the problem back. Besides this, the universe also encompasses gravity which, conforming to Newton's laws, looks fortuitous simply by the form of the inverse square law (1/r)2 which, mathematically, could be different. There is no way to escape this sad conclusion that the world is, to a large extent, simply whatever, and that it only shows a certain coherence locally, here or there, in circumstances where, basically, it cannot be otherwise!   However, there is a way to escape this fortuitous character: By believing that everything is intentional. This idea was found long ago and takes various forms including animism. We have also seen that Greek religion was laden with such belief.

231 Animism and positivism. The belief in souls and spirits exists in numerous religions and is expressed through various practices. One way to describe them is by placing them into a historical theory of religion. This has been done by Edward B. Taylor (18321937), who saw this as a primitive form of polytheism, itself a precursor of monotheism, and James G. Frazer (18541941), who reunited countless tales and testimonies in an evolutionary perspective. We cannot help but be struck by this curious phenomenon that both scholars and thinkers had no hesitation in putting these historical and sociological data into an evolutionary hierarchy, without realizing that it was unprovable and therefore, based on pure belief. It is equally striking that, around the same time, Ernest Renan proposed an objective analysis of the history of religion but hadn’t the slightest hesitation over his irrevocable faith in Scientific Progress, poorly defined though it may have been. Clearly, nothing of this sort affected Claude Lévi-Strauss, of whom we will say a few words later. Without getting into anthropological analysis and its controversies, let us simply note how animism was interpreted, in 1895, by Gabriel Tarde, a sociologist who was used to searching for links, between cause and effect, in collective behaviors: I know well that religion, like language, is always an animation, a perpetual personification of natural phenomena. But it is important to not confuse under the same term of animism all kinds of spirits very opposite in their character, some malicious, others well-meaning, or very distinct in their origins, some human, others natural. Indeed, they do not all come from divinized ancestors or strangers, as Spencer would like to believe by a too narrow notion of animism, of primitive spirituality; they come from everywhere, from stars and clouds, from mountain tops and seas, from wild animals, from serpents, from monstrous or deformed vegetation. Yet since they are so unalike, as dissimilar should be the processes to appease or tame them […] We imagine the angst and despair which should be felt in a cold, smoke-filled cave on the rainy days of the idle caveman when, by chance, wild genius, he manages to reflect on the human condition. No matter where he looks, he only sees danger and threat of death, venomous teeth, poisoned arrows, bloody scratches; below and beyond the horizon, he considers everything an enemy, and a mortal enemy, everything, except for a few unhappy companions huddled with him in this cave and his dog, the only animal he has been able to domesticate. Perhaps the habit of seeing only predators or prey among living, visible beings would lead

232 him, by analogy, to think that all invisible beings he conceives of are cruel, hateful, vengeful. Or perhaps, conversely, shipwrecked in this ocean of inexorable and inexplicable hostilities, he would desperately cry out into the unknown for help, and, against all these animals and perverse men, poisonous plants, thundering storms, would dream, would call on a benevolent crowd of hidden protectors, who interest themselves in his lot, watch over him in this vast world, mysteriously giving him signs when danger is about to strike, and immediately sending him a bird, insect, any small meaningful thing to warn him. – Yet, in the first case, his main concern is diverting the wrath of malevolent gods, appeasing them, domesticating them, like great ma«...  domesticating malevolent gods, ... by the same processes which worked so well in charming the animals, by procuring bloody food for them regularly, by giving them something to eat which they so often eat: man himself...» (G. Tarde)

Sacrifice of Iphigenia,  Pompeian fresco.

Yet, not for this, the wind-bound navy weigh’d; Slack were their sails; and Neptune disobey’d. Some thought him loth the town should be destroy’d, Whose building had his hands divine employ’d: Not so the seer; who knew, and known foreshow’d, The virgin Phoebe, with a virgin’s blood Must first be reconcil’d: the common cause Prevail’d; and pity yielding to the laws, Fair Iphigenia the devoted maid Was, by the weeping priests, in linen-robes array’d; All mourn her fate; but no relief appear’d; The royal victim bound, the knife already rear’d: When that offended Pow’r, who caus’d their woe, Relenting ceas’d her wrath; and stop’d the coming blow. A mist before the ministers she cast, And, in the virgin’s room, a hind she plac’d. Th’ oblation slain, and Phoebe, reconcil’d, The storm was hush’d, and dimpled ocean smil’d: A favourable gale arose from shore, Which to the port desir’d, the Graecian gallies bore. Ovid Metamorphosis Book XII. Trans. by Sir S. Garth, J. Driden et al.

233 jestic elephants which are adored by taming them, and to domesticate them by the same processes which worked so well in charming the animals, by procuring bloody food for them regularly, by giving them something to eat which they so often eat: man himself, some enemy prisoner. Sacrifice is the food of the gods; the starved savage must suppose his gods are also starved. Here, still is reasoning by analogy. – In the second case, the first dilemma is interpreting the signs from favorable gods; from which is derived the dominating importance of diviners, foreshadowers and oracles. Thus, it’s sometimes the sacrificing characteristic, like in Mexico, sometimes that of the diviner, like in classic antiquity, which dominates in the high-priest. And from the high-priest, since the beginning, we must carefully distinguish the witch doctor, who, precursor not of the soothsayer but of the scientist, claims to prematurely extract nature's secrets, not to appease or guess at mysterious powers, but to make them work for him to his liking like our engineers use physical forces.2 This last phrase is rather extraordinary, written before the end of the nineteenth century, it would absolutely have its place as the epigraph of contemporary works of science studies. In a less intuitive way, through an in-depth anthropological analysis, Claude Lévi-Strauss confirmed that animism was not an absence of determinism, but rather a generalized causality. For him, like for Tarde, magic is closer to science than to religion. Categorically opposing the evolutionism of Taylor and Frazer, he wrote these famous lines: “It may however be the case that magical thought, that ‘gigantic variation on the theme of the principle of causality’ as Hubert and Mauss called it, can be distinguished from science not so much by any ignorance or contempt of determinism but by a more imperious and uncompromising demand for it which can at most be regarded as unreasonable and precipitate from the scientific point of view [...] Seen in this way, the first difference between magic and science is therefore that magic postulates a complete and all-embracing determinism. Science, on the other hand, is based on a distinction between levels: only some of these admit forms of determinism; on others the same forms of determinism are held not to apply. One can go further and think of the rigorous precision of magical thought and ritual practices as an expression of the unconscious 2. Gabriel Tarde Logique sociale (1895), Les Empêcheurs de penser en rond 1999.

234 apprehension of the truth of determinism, the mode in which scientific phenomena exist. In this view, the operations of determinism are divided and made use of in an all-embracing fashion before being known and properly applied, and magical rites and beliefs appear as so many expressions of an act of faith in a science yet to be born.” (Cl. Lévi-Strauss, The Savage Mind, trans. by J. and D. Weightman, Univ. of Chicago Press, 1966) Science operates by distinguishing levels of which only a few admit forms of determinism... We could even say that one of the fundamental ideas of positivism is to accept unexplained notions and to focus only on possible deductions, to refrain from searching for the first causes, the reasons for being, but to note only the necessary determinations everywhere we can highlight them. Positivism accepts fortuity. Auguste Comte and John Stuart Mill both thought that an impregnable epistemological position could be developed by not asking too much of science, only that it constitute the network of implications, of observed laws where we observe, and perfect them. This distrust towards generalities would be exacerbated with the neopositivism of the Vienna Circle at the beginning of the twentieth century where the ‘Allwörter’ were pursued in an attempt to base scientific language directly on experience thanks to ‘correspondence  rules’.  But  the  science  to  which Claude Lévi-Strauss made allusion is that of his time, well represented by Heisenberg’s philosophy which distinguished levels: particles and quantum physics, chemistry and phenomena of heat, organic life, then the consciousness, etc., levels which are interrelated but cannot be reduced one to another: reductionism is a useless and uncertain hypothesis.3

3. W. Heisenberg, Philosophie op. cit. p294 and seq.

235 William James. William James is a particularly interesting philosopher for us on this subject because his ideas combine the role of both chance and animism in a rather original way.  In relation to two other principal founders of American pragmatism, Charles Peirce and John Dewey, William James (1842-1910) deserves a place apart. His thinking, more open to the religious spirit, distances itself from positivism and classical rationalism. He himself defined his philosophy as “a radical empirism, a pluralism, a “tychism” representing order as being progressively conquered and always in process”.4 First of all, the writings of William James are striking for their luminosity, shedding light on the hardest questions and proposing, in all simplicity, stunning shortcuts of the most abstract theories; an evident family skill he shared with his brother, the novelist Henry James. He voluntarily braved the risk of meeting the scorn of intellectuals “and if by chance any one writes popularly and about results only,” he writes, “with his mind directly focused on the subject, it is reckoned oberflächliches Zeug and ganz unwissenschaftlich […] If we take the whole history of philosophy, the systems reduce themselves to a few main types which, under all the technical verbiage in which the ingenious intellect of man envelops them, are just so many visions, modes of feeling the whole push, and seeing the whole drift of life, forced on one by one’s total character and experience, and eventually ‘preferred’ – there is no other truthful word – as one’s best working attitude”5. William James positioned himself on the side of any and all concrete problems. His fluidity of speech and familiar tone have made some say that James was the pioneer of the category of literature today organized in bookshops under the subject “well-being and self-improvement”. It’s also been said that his work was an ultra-liberal economic logic disguised as philosophy, or that pragmatism is reduced to saying that the end justifies the means. There’s no doubt that these clichés have their origin in the ease with which James’s style swept the reader away simultaneously by argumentation and semantic plasticity. For example, in his first lecture he wrote, “Perhaps the most interesting opposition is that which results from the clash between what I lately called the sympathetic and the cynical temper […] The majority 4. A Pluralistic Universe, Hilbert lectures at Manchester College on the Present Situation in Philosophy, Longman, Green and Co, 1909; trans. from Philosophie de l’expérience, un univers pluraliste, Les empêcheurs de penser en rond 2007. The term “tychism” from tyche, chance, is taken up again by Peirce who introduced it to designate a vision of the world in constant and unpredictable transformation. 5. Loc. cit., first lesson, the types of philosophic thought.

236 of men are sympathetic, […] I therefore propose to you to disregard materialists altogether for the present, and to consider the sympathetic party alone”. It must be noted that James uses the ambiguity of the term sympathetic sometimes in the sense of likable, sometimes in the sense of being compassionate to position the materialists among the cynics. But James’s philosophy is fundamentally tolerant. Religion is admitted as a natural psychological trait which designates the ideal tendency of things as “God”. “God, in the religious life of ordinary men, is the name not of whole things, heaven forbid, but only of the ideal tendency in things, believed in as a superhuman person who calls us to co-operate in his purposes, and who furthers ours if they are worthy. He works in an external environment, has limits, and has enemies”. At first sight, this tolerance clashes with all the unitary, global, and total conceptions of the world that James systematically lambasted under the name of monism. It’s this opposition which pushed him towards pluralism. Next, he progressively created its content. For James, the world is neither dismembered nor unified; it is made of connecting parts, material, specialized scientific knowledge, “interior lives”, interacting by relations (material and empathetic) without necessarily losing their own innovating power gained by experience. Alas, ontology is only sketched by James. He insisted on the fact that the world is in an intermediary phase, moving towards a unity not yet achieved: “The world is in so far forth a pluralism of which the unity is not fully experienced as of yet […] In my own mind, such a philosophy harmonizes best with a radical pluralism, with novelty and indeterminism, morals and theism, and with ‘humanism’”.6 The effect of tolerance that empirical pragmatism induces on the views of the world creates a link between everything that happens, all doctrines, a link that William James compared to the Earth-soul of the psychologist Fechner which is a form of pan-psychism with the worry of attaching the greatest importance to experience and to stakes.7 6. «A world of pure experience» Jour. of Philosophy 1904, 533-543, et 561-570, in Radical Empiricism, Flammarion 2007. 7. Jean Wahl wrote “As well as pluralism, the theory of the will to believe, religious ideas and tychism, all of that is called on and unites combines together in James’s mind. Yet, he did not think that pluralism could explain everything and behind this pluralism, a mystic monism appeared or reappeared”. Vers le concret, Etudes d’histoire de la philosophie contemporaine, William James, Whitehead, Gabriel Marcel, (1932), Vrin 2004.

237 James’s pluralism concerns the nature of the world; its purpose is the description and the comprehension of things and of others8. The point of view is implicitly psychological. James is concerned little with sociological methods. Whereas, when he wrote A Pluralistic Universe, Durkheim and Weber having already published major works9, James preferred referring to Fechner: “the earth-soul traces relations between the contents of my mind and the contents of yours of which neither of our separate minds is conscious […] Fechner likens our individual persons on the earth unto so many senseorgans of the earth’s soul”,  like a type of general animism. He adds, “The analogies with ordinary psychology and with the facts of pathology, with those of psychical research, so called, and with those of religious experience, establish, when taken together, a decidedly formidable probability in favor of a general view of the world almost identical with Fechner's”10. The notable thing missing from this philosophy is sociology. Nowhere does it consider that our way of understanding the world and others could depend on our social class. Nor does it consider the idea that common sense could be the thinking of the dominant class. What a striking contrast between this goody-two-shoe tone and the methodological prudence of people such as Durkheim or Weber. Of all of the people of the past, the one who seemed to have most deeply influenced William James is without a doubt Martin Luther. James evokes him with very particular sensitivity: Luther would help in understanding the world by a sudden burst after a crisis of despair, a world where all is well: “Luther was the first moralist who broke with any effectiveness through the crust of all this naturalistic self-sufficiency, thinking (and possibly he was right) that Saint Paul had done it already. Religious experience of the Lutheran type brings all our naturalistic standards to bankruptcy. You are strong only by being weak, it shows. […] Sincerely to give up one’s conceit or hope of being good in one’s own right 8. Jean Wahl points out that James’s anti-monism lead him to adopt a rather polymorphous pluralism: “The world is not a ‘multiverse’, but it is also not absolutely a universe; nor is it simultaneously a ‘multiverse’ and a universe like the Hegelians say, but simply a great fact, in which the multiple and the one are in juxtaposition and succeed one another. The world cannot be formulated into a single proposition. Moreover, [James’s] pluralism would take on different forms according to whichever from form of monism he would oppose” Les philosophies pluralistes d’Angleterre et d’Amérique (1920) Les empêcheurs de penser en rond 2005, p 185. 9. Règles de la méthode sociologique (1894); Le suicide, étude sociologique (1897); Représentations individuelles et représentations collectives (1893) for by Durkheim and L’éthique protestante et l’esprit du capitalisme (1904) for by Max Weber. 10. Op. cit., Eighth Lesson Eight.

238 is the only door to the universe’s deeper reaches.”11 Thus, we come to a sort of “philosophy”: “Here is a world in which all is well, in spite of certain forms of death, indeed, because of certain forms of death—death of hope, death of strength, death of responsibility, of fear and worry, competency and desert, death of everything that paganism, naturalism, and legalism pin their faith on and tie their trust to” . In fact, James had a serious depressive crisis before turning towards philosophy12. From his manner of describing Luther, we speculate what James found in him the authorization to escape a superego, probably originating in his family, which subjected him to an uncompromising desire to do well13. One senses that James wished to make the reader share in his liberation of monism and intellectualism which by their certainty are the cause of useless suffering and can lead to despair.   Bergson described James’s pluralism in these terms: “Relations fluctuate and things are fluid. Far from that, there is this dry universe that philosophers create with well-defined, well-arranged elements, where each part is no longer only connected to another part, as experience tells us, but even, as our reason would want it, coordinated with the Whole. James’s pluralism hardly means anything else”14. Nonetheless, it’s worth adding that James’s pluralism is intimately linked to the idea of negotiation, a reconstruction of interests and of common sense on which all parts can rely on in fine: “Compromise and mediation are inseparable from the pluralistic philosophy. Only monistic dogmatism can say of any of its hypotheses, ‘It is either that or nothing; take it or leave it just as it stands’”.15 The pluralist vision of the world, in James’s sense, undoubtedly projects a different landscape onto the field of knowledge than the tree-like classifications of Francis Bacon, Condorcet, Auguste Comte or Ampère16, and, thus, distances itself from positivism. It seems William James admitted small islands and archipelagos of knowledge having little relation with larger continents of knowledge. 11. Ibid. 12. This difficult period lasted approximately from the fall of 1868 until the spring of 1870. In The Varieties of Religious Experience, London 1902, William James devoted the chapter «The sick soul» to commenting on similar testimonies of literature. 13. Note that Monism is one of the components of the philosophy of his father Henry James, cf. Jean Wahl Les Philosophies pluralistes d’Angleterre et d’Amérique (1920) op. cit. p. 50 et seq.14. «Sur le pragmatisme de William James, Vérité et Réalité» (1911) preface to James’s work,  Le pragmatisme. 15. A Pluralistic Universe, Lesson Eight. 16. A. M. Ampère, Essai sur la philosophie des sciences, Bachelier, Paris, 1834-36.

239 In fact James said very little about science or knowledge, apart from his positions on truth as utility: “Such is the large loose way in which the pragmatist interprets the word agreement. He treats it altogether practically. He lets it cover any process of conduction from a present idea to a future terminus, provided only it run prosperously. It is only thus that 'scientific' ideas, flying as they do beyond common sense, can be said to agree with their realities [...] We must find a theory that will work”.17 James did not venture anywhere on the level of conflicts of interpretation, as if they were intellectual quixotic problems, that would recede in practice. This is where his philosophy falters. His utilitarian view of truth appears quite weak as soon as we ask the question “useful for who?” Did James imagine a world without social categories, without social nets, without sects, without the poor or the rich? If we judge it according to the end of A Pluralistic Universe,which also concludes his oeuvre, his response seems to be “useful to sympathetic people” in the sense of those capable of empathy. However, if there is one thing we can attribute to psychoanalysis, it’s the proof that empathy is not remotely exempt from conflicts!  The New Gods of Neo-Jamesians. The recent revival of James’s philosophy is worth mentioning here as his ideas, somewhat adapted, provide a framework for a critique of the productivist practice of scientific research separated from popular aspirations  and reckless about the consequences of technology for natural equilibriums. To quickly summarize, we’ll designate Bruno Latour as the leader of this Neo-Jamesian school of thought, although the positions of David Bloor and Andrew Pickering also stand out significantly. Latour was one of the first anthropologists to highlight the conduct of researchers, vehemently denouncing their irresponsibility and proclaiming the urgent and serious need to find the means to “bring the sciences into democracy”. One rather curious aspect of this movement concerns the social construction of scientific facts. In almost all American universities, sociologists and graduate students use it to show that any discovery or scientific fact is, in reality, nothing more than the result of the social action of certain agents or institutions, that not only historical circumstances 17. Le pragmatisme, op. cit. p. 237. If James had confronted these ideas of the history of the sciences in more detail than just a sketch, we should have considered him as the precursor to Paul Feyerabend and his “anything goes” attitude.

240 favored this or that type of scientific or technical development – this we already knew – but that the contents of science themselves have no absolute character (as the researchers might think), and are products of the active interest of certain participants in the research and discourse surrounding them. These works, which require meticulous sociological analysis, mostly seemed to have greatly irked the colleagues in the hard sciences (rather than human and social sciences) and, in the most technologically advanced country, encouraged them to ignore these sarcasms. Perhaps a balance is thus found which stimulates biologists and physicists on the one hand while providing social sciences with subjects on the other (for which investigation techniques are professionally useful skills anyway).18 Yet the critique of positivism, revived by global capitalism and lead by Neo-Jamesians, goes further than these university posturings. Latour denounced the Great Divide put into effect by the Moderns as a decisive split between facts and values19. In order to develop a universal and objective discourse, scholars omitted their own position in nature as well as their social and cultural situation. This is the modern break artificially made between culture and nature. Modern science thereby shrugged off all its problems: the links with the non-human beings, the reflexive problems of the creation of knowledge, the historical origin of interpretations and the technical consequences on nature, etc.20. Latour then built what must be called a philosophical system in which the Great Divide is rejected in favor of a redevelopment of the concept of facts, taking into account the acceptance of new beings in the group, outlining the bases of a true political organization.21 Why has all of science, and all the contemporary ways scientists have of talking about science, been subsumed under this one modern term of Great Divide? Scientists' views about science, on the contrary, mostly align with William James's ideas at the most fundamental level. First, no such division has ever been present in human sciences, linguistics, sociology, or anthropology. Next, in mathematics, it is worth noting the celebrated texts of Henri Poincaré who insisted on the role of the subconscious and on the importance of the soul of fact22 and the position of the eminent mathematician 18. See Ian Hacking, Entre science et réalité, la construction sociale de quoi ? La Découverte 2001. 19. B. Latour, Nous n’avons jamais été modernes, essai d’anthropologie symétrique, La Découverte 1991. See also Par delà nature et culture, Ph. Descola, Gallimard 2005, Chapter 3 p 91-131. 20. B. Latour, Petite réflexion sur le culte moderne des dieux faitiches, Synthélabo Groupe 1996. 21. B. Latour, Politiques de la nature, comment faire entrer les sciences en démocratie, La Découverte, 1999. 22. Science et méthode, Flammarion 1908.

241 Hardy who stated that only beautiful mathematics endure. In physics, the Copenhagen School rules out any strict break between the observer and the observed. And in biology and medicine, very few researchers would deny any empathetic phenomenon in interpretations or in therapies. All scientists have been rather hastily put into the same box. Moreover, the philosophical instruments obtained by the fusion of concepts are blunt, vague, and ultimately, rather inoffensive tools. Here, the neo-Jamesians join with the pragmatists like Hilary Putnam and Richard Rorty who advocate the suppression of all the separations and dualities that have riddled in philosophy since the dawn of time: facts and values, determinism and indeterminism, nature and artifice, body and mind and, why not, war and peace? This gives a discourse resembling that of the Sophists, well oiled fighters who, as such, do not impress the progressive positivists. In our opinion, the true divide, the front line, is not located where Latour drew it but between the positivists-progressives - who have a monist vision of the world, which is indeed dominant today, relying on the tripod of liberalism, evolutionism, and positivism23, - and the pluralists-finitists - who firstly believe that the realization of the compact character of the planet on which we live is, precisely for evolutionary reasons, one of the most formidable stages that humanity has to overcome, and secondly that pluralism is not relativism. It’s clearly for controversial ends that positivists refuse to recognize that the big questions are open to a small number of pertinent interpretations, reflected in the number of large political parties. All of this leads to the issue of thinking of the anthropotechniques before they become faits accomplis. All the indications are that they will impose pluralism. The question is whether this pluralism will be that of a split of the human species with, initially, ‘genetically cleaned’ individuals who will not reproduce with other healthy carriers of troublesome genes, followed by other, more specialized splits. Or will it be a pluralism founded on political management extended to the technoscientific sphere allowing the democratic coexistence of one single species represented by parties encompassing values, knowledge, and techniques.24

23. The nostalgic speeches of literary intellectuals on disenchantment only fuel the arguments of positivists-progressives insofar as , indeed, insofar as the disenchantment thought of as an entropic law is only progress considered on the flip side of the coin. 24. Cf. Francis Fukuyama, Our Posthuman Future, Consequences of the Biotechnology Revolution, Profile Books 2002.

242

The Slip as Fortuity and Meaning

244

245

During psychoanalytic treatment, the patient on the couch is asked to speak freely without controlling himself, and in the things said by chance we find hidden meanings revealed to the consciousness. Freud deciphers a great number of examples in his Traumdeutung, but curiously, wanting to create a truly scientific work, he ignores his own interpretative talent in this matter. He conceals the fact that what he discovers is an interpretation and that his science is also made in that way. For the same reason, he does not consider Leonardo da Vinci a true scientist, a true researcher, but rather a man who, tormented by his sexuality since childhood, sought refuge in the fantasies of virtual machines. Freud, rather curiously, misunderstands one sentence from Leonardo, the meaning of which is clear to us today.

246

247

One of the basic ideas of psychoanalysis is that minor mistakes made while we speak or act, usually attributed to chance, are, in fact, full of meaning. We do not function as perfect lotteries: impure bias (unfairness) intervenes in what we inadvertently do and, perhaps, reveals wishes or fears that we don't want to admit. It is quite clear today that to efficiently correct mistakes, it is appropriate for logic to intervene. The spell-checker on my word-processor shows its limits because it doesn’t understand every sentence and wants to match nouns and verbs that don’t go together. In information technology, the serious problem of finding programming errors in large software, which are often due to small combinatorial mistakes (of the kind that are made when counting the posts around a field and the intervals between the posts) can only be securely resolved by returning to a higher programming language (highlevel language) close to the initial mathematical or logical reasoning. Freud’s idea is different: the mistake itself has a meaning. His approach consists of adopting a similar point of view to the ancient Greeks and Romans (before Cicero) where chance doesn’t really exist since everything was susceptible of being intentional (cf. the Aristotelian categories of  Chapter I) A fair amount of intellectual education is a prerequisite for believing in chance; primitive people and uneducated ones, and no doubt children as well, are able to assign a ground for everything that happens. Perhaps originally it was a reason on animistic lines. Even today, in some strata of our population, no one can die without having been killed by someone else — preferably by the doctor. And the regular reaction of a neurotic to the death of someone closely connected with him is to put the blame on himself for having caused the death.1 Taking the role of chance into account is initially in line with the logic of scientific objectivity; it’s an important step to which Cicero contributed. But there is no reason why there shouldn't be an equal movement of knowledge in the other direction, i.e., investigating certain phenomena that we dismiss as purely fortuitous instead of interpreting them. It’s precisely in this way that Freud begins his psychoanalysis:

1. “New Introductory Lectures on Psycho-Analysis”, trans. J. Strachey Norton & Co, 1965, p. 152.

248 I have noticed in the course of my psycho-analytical work that the psychological state of a man in an attitude of reflection is entirely different from that of a man who is observing his psychic processes. In reflection, there is a greater play of psychic activity than in the most attentive self-observation; this is shown even by the tense attitude and the wrinkled brow of the man in a state of reflection, as opposed to the mimic tranquility of the man observing himself. In both cases there must be concentrated attention, but the reflective man makes use of his critical faculties, with the result that he rejects some of the thoughts which rise into consciousness after he has become aware of them, and abruptly interrupts others, so that he does not follow the lines of thought which would otherwise open up for him; while in respect of yet other thoughts, he is able to behave in such a manner that they do not become conscious at all- that is to say, they are suppressed before they are perceived. In self-observation, on the other hand, he has but one task- that of suppressing criticism; if he succeeds in doing this, an unlimited number of thoughts enter his consciousness which would otherwise have eluded his grasp. [...] In the condition which it utilized for the analysis of dreams and pathological ideas, this activity is purposely and deliberately renounced, and the psychic energy thus saved (or some part of it) is employed in attentively tracking the undesired thoughts which now come to the surface- thoughts which retain their identity as ideas (in which the condition differs from the state of falling asleep). Undesired ideas are thus changed into desired ones.2 (Freud’s emphasis) In other words, representations received as fortuitous and meaningless appear to be the result of a process of the production of meaning. The following passage gives more detail The phenomena in question are the small faulty actions performed by both normal and neurotic people, to which as a rule no importance is attached: forgetting things that might be known and sometimes in fact are known (e.g. the occasional difficulty in recalling proper names), slips of the tongue in talking, by which we ourselves are so often affected, analogous slips of the pen and misreadings, bungling the performance of actions, losing objects or breaking them. All of these are things for which as a rule no psychological determinants 2. Die Traumdeutung, (1911) Chap. II.

249 are sought and which are allowed to pass without criticism as consequences of distraction or inattention or similar causes. [...] These small things, faulty actions and symptomatic or haphazard actions alike, are not so insignificant as people, by a sort of conspiracy of silence, are ready to suppose. They always have a meaning, which can usually be interpreted with ease and certainty from the situation in which they occur. And it turns out that once again they give expression to impulses and intentions which have to be kept back and hidden from one’s own consciousness, or that they are actually derived from the same repressed wishful impulses and complexes which we have already come to know as the creators of symptoms and the constructors of dreams.3

«This smile has called for an interpretation, and it has met with many of the most varied kinds, none of which has been satisfactory»

3. «De la psychanalyse», in Œuvres complètes 1909-1910, PUF 1993, translation from web site of St. Anselm College, Manchester, New Hampshire.

250 This research program - to find the structures, laws, and causalities behind what had been thought of as chance - is a massive extension of the ideas of Monod that Matheron and Schoffeniels had both claimed.

Freud proposed an analysis of Leonardo da Vinci’s personality based on a text where Leonardo said his mouth had been brushed by the tail of a vulture, something which would have given him a propensity to a certain type of sexuality.  Among the numerous arguments suggested, there is the presence of a hidden vulture in one of Leonardo’s paintings.4 The hidden image of the vulture had been debated by many commentators. Freud gathered the arguments together. This is in itself a very interesting point. In positive science, a single argument suffices (the proof that Saussure sought). In the field of interpretation, plentitude does no harm and even overabundance brings forth a rush of conviction. The same thing occurs in Charles Darwin’s theory of evolution: it is impossible to prove that evolution is governed by the survival of the fittest since the fittest are those that survive, but this empty theory becomes consistent by the profusion of examples. But at the end of this lengthy, eighty-page dissertation, Freud doubts his own method; he is seized by a certain hesitation. One has the impression that he wonders if he hadn’t ‘gone a bit too far’: 4. “It seems that I was always to be so deeply concerned with vultures; for I recall as one of my very earliest memories that while I was in my cradle a vulture came down to me, and opened my mouth with its tail, and struck me many times with its tail against my lips.” (Leonardo da Vinci and a Memory of his Childhood, trans. Alan Tyson) In fact, it discussed a kite in the Italian text and not a vulture, but this ‘error’ slip’ hardly detracted Freud little from his thesis.

The gray sheet on the Virgin’s legs forms the head of a bird by winding around the waist and a tail around the left arm, just slightly grazing the child’s mouth.

251 But may one not take objection to the findings of an enquiry which ascribes to accidental circumstances of his parental constellation so decisive an influence on a person’s fate — which, for example, makes Leonardo’s fate depend on his illegitimate birth and on the barrenness of his first stepmother Donna Alberia? I think one has no right to do so;5 In a reversal of the situation, Freud now puts chance on his side. He continues: If one considers chance to be unworthy of determining our fate, it is simply a relapse into the pious of the Universe which Leonardo himself was on the way to overcoming when he wrote that the sun does not move. [...] At the same time we are all too ready to forget that in fact everything to do with our life is chance, from our origin out of the meeting of spermatozoon and ovum onwards — chance which nevertheless has a share in the law and necessity of nature, and which merely lacks any connection with our wishes and illusions. The apportioning of the determining factors of our life between the ‘necessities’ of our constitution and the ‘chances’ of our childhood may still be uncertain in details; but in general it is no longer possible to doubt the importance precisely of the first years of our childhood. (idem) The article ends with a highly significant confession by Freud. He concludes with a quote from Leonardo that he considers obscure, which he didn't understand, despite the fantastic interpretative talent that he has just demonstrated by writing eighty pages based on a short piece of writing. (continuation of preceding quote) We all still show too little respect for Nature which (in the obscure words of Leonardo which recall Hamlet’s lines) ‘is full of countless causes that never enter experience’. (la natura è piena d’infinite ragioni che non furono mai in isperienza) Every one of us human beings corresponds to one of the countless experiments in which these ‘ragioni’ of nature force way into experience. (idem)

5. «Un souvenir d’enfance de Léonard de Vinci» Œuvres complètes, 1909-1910, PUF 1993. (trans. by Alan Tyson, J. Strachey ed., W. W. Norton & Co 1964)

252

253 The words that Freud found obscure, and which he uses as if they were waiting to be loaded with meaning to achieve the effect he seeks, are in fact clear to those who have visited the Leonardo da Vinci Museum in Milan 6 or looked through the drawings of Leonardo’s machines. The great engineer is alluding here to the immense variety of effects which can be used to drive machines. For reasons that can only be guessed, throughout the article Freud minimizes, or even ignores, the creative talent of Leonardo, presenting him as someone incapable of taking responsible actions, someone happier with fantastic artificial mirages. Freud probably knew that his methodology was bold in  deriving his conclusions from just a small part of the person he was analyzing. (It is true, of course, that Freud knew nothing of the Madrid Codex which was only discovered in 1974, and perhaps he did not have access to the six thousand pages of Leonardo's notebooks that have been preserved). Da Vinci's inventions: worm screws, helicopters, kites, presses, scales, machines of varying speeds, regulated gears, turbines, studies of birds in-flight, calculations of concave mirrors and devices to polish them, drawings of caustics, vaults, roofs, ideas for hydraulic and excavator machines, etc. – made more than a century before Galileo – are not realized ideas (they did not reach the developement stage, as we might say today). They are precisely causes which have not yet passed into experience. Here, abundance works against Freud. He discarded too much for his theory to be truly convincing. This ties in with his immense and dual construction: his self-analysis on one hand and, on the other, the theorization of the psyche using dream material 7. By his anxiety to create a scientific work, and the intellectual rigor he insisted on, Freud was not in a position to be able to assess his own interpretative talent, nor get any perspective on the truths he was discovering. He does not see the parallel between Leonardo and Sigmund, because he doesn’t want to see it. So the idea that Leonardo's work was scientific, that he was a true researcher, and that science is made in that way, is alien to him  8. In this same 6. Or the Da Vinci Museum in Amboise, France. 7. Cf. Didier Anzieu L’Auto-analyse de Freud et la découverte de la psychanalyse, PUF 1998. 8. S. L. Montgomery in his remarkable work The Scientific Voice, Guilford Press, 1996, shows that Freud’s language is the same as the one in use before scientific standards appeared in the second half of the 19th century. Indubitably, he considered it poorly adapted to his comments, use of statistics, experiences, detailed quotations of authors, division of his text into sections, etc. However, he is very precise in his literary language, in his descriptions and deductions and protects the reader against any hasty, vague or summarily half-hearted conclusions. 

254 vein, Lacan would take quite a different point of view. The comprehensive study of the nature of paranoia lead him to accept the role of interpretation in the creation of knowledge, and, as a result, he diverted psychoanalysis from the test of justifying itself as a science, which had become a serious burden. But, let's get back to the double movement: presence of chance and dissipation of chance. There is reluctance (a resistance Freud would say) about each of these. First, to accept chance like Cicero or Monod is to disillusioning. Even physicists regret the fact that there is not more meaning: when the Copenhagen school talked about quantum chance, Einstein and Louis de Broglie looked for hidden variables. Secondly and on the contrary, when psychoanalysis gives meaning to dreams, bourgeois society cries foul, rejecting this ‘illusion’ 9. Preaching is necessary to convince them and Freud understood the importance of establishing an international network of correspondents and associations for psychoanalysis, which dissidents such as Lacan saw as a ‘church’. Similarly for the patient, who rejects the interpretation of the material that he himself supplied, instead of welcoming these possible interpretations as enlightening realizations, he represses them and this resistance cannot be overcome except by the unusual trust known as the transfer mechanism. The dream is no longer random images or sequences of images; it has a meaning, or at least, it has some meaning. Strong links with profound effects may be noted here and there while the rest of the dream resembles a literery work, arranging the story in a likely way that also takes some account of social conventions. What does it mean to say “there is some meaning”? It means that the dream, or the spontaneous association it triggers, brings to mind something else, something more ancient, earlier in the person's history, a trace of interactions between the subject with others. “Very early on” wrote Serge Lebovici, “a baby can sense heat, cold, colors, sounds, but not much else. And this a-modal sensing expresses itself in the emotions that the child shares with those he interacts with. Very quickly, his capacity to recognize that he acts on his surroundings and can so change them, will give meaning to it all”.10 This changes the way we think about knowledge compared with nineteenth century views. When Cournot, developing the idea of philosophical probabilities, considered some examples where there is the possibility of a physical law, 9. On this subject, see the well-written text by Stefan Zweig: Freud, La guérison par l’esprit (1930), Stock 1932. 10. In Le hasard aujourd’hui, op. cit .

255 he went too quickly to an extreme case. As soon as an apparent intentionality is seen, there is a presumption of significance and possible meaning. Whether this is applicable to the objectivity and universality of scientific knowledge is another issue, which could be the object of a long procedure and of which the result could only be a general presumption. So the current case involves two subjects: the interpreter and the one whose intentions are being discerned. This means that two unconsciouses are involved. The second one is not necessarily a god. For example, let’s suppose that the forms we are trying to interpret are elements of a speech and the activities of a large industrial group, or the behavior of a branch of a sect, or even the health system of a country, so discerning whether it is by chance or intent is not only difficult but could be too cursory a Manicheism. The rules we guess, as the ideal-types of Max Weber, follow from our interpretative talent, and our assessment of their status - chance or will – depends on the degree of awareness of the concerned social institution, which in general have no familiarity with. Therefore, what is interpreted often has an ambiguous status. But what I do myself is neither out of necessity nor by chance. The creative faculty running through the individual also establishes itself as ambivalent; what I say is susceptible to interpretations I may be unaware of. “I think,” wrote Chomsky, “that certain themes have been suppressed or isolated during the scientific progress made these last centuries. For example, this worry about effortless creativity to which I’m referring truly existed for Descartes [creativity of the simple speaker knowing a language]. When he discusses the difference between a parrot, capable of reproducing speech, and a human being, in measure of pronouncing new things appropriate to the situation, and when he added that this distinct aptness indicates the limits of physics and trains us in the science of the mind to employ modern terms, I think that it refers to the type of creativity I have in mind;…” 11. Finally, scientific representations are also imagined by someone. Lacan said "knowledge has to be invented". In the same way that the unconscious appears clearly to he who becomes aware of something which is, then, no longer unconscious - "The unconscious", said Lacan, "is something that will be realized in the symbolic or, more precisely, is something which, thanks to the symbolic progress in the analysis, will have been”12 - in the same way we have difficulty recognizing these scientific interpretations for what they are, except when they are obsolete. The gods of science are the 11. Chomsky N. and Foucault M., De la Nature humaine, justice contre pouvoir (1971), L’Herne 2006. 12. Lacan, Séminaire on April 7, 1954.

256 geocentric system, phlogiston, spontaneous generation, ether, they are well visible because they have been deposed; they are symptoms of scientific activity since at one time or another they had been scientific. “First, the symptom presents itself to us in the guise of a trace […] Literally, this will never be anything more than something which, at a certain time, will have been”13. Speaking of Lacan, let us close our chapter with a quote from his last seminar in 1977, which he concludes with a quip to say that psychoanalysis also necessarily bears a reflection on science:  Life is not a tragedy, it’s a comedy and yet it’s quite curious that Freud couldn't find anything better to call it than an Oedipus complex, i.e., a tragedy. We don’t see why Freud, when he could have taken a more direct route, designated it something other than a comedy, what he had to do, what he had to do in this relation which linked the Symbolic, the Imaginary and the Real. For the imaginary to unravel, it has only to be reduced to a fantasy. What is important is that science is itself a fantasy and that the idea of an awakening is, properly speaking, unthinkable. (Lacan, Séminaire on November 15, 1977)

13. Ibid.

Le bon Toto et le Méchant Tom by Trim, illustrated by Eugène Le Moüel

257

258

Guessing Astronomy

260

261

Science may not proceed by guesswork, but it is certainly capable of predicting facts not yet observed. It was the chemist and politician Marcelin Berthelot, an ambitious and querulous character, who announced the biggest "blunder" in this subject. The question is these "laws" of nature: What is their origin? Is it some preexisting reality or an interpretation? The comparison between Bode's law about planetary orbits and the law about the hydrogen spectral series is very clear, imprecision on one side, quantum fundamentals of a grand theory on the other. But what about Laplace's law about Jupiter's moons - is that an imaginative whim or an astronomical reality? It is exactly in between the two, which can help us understand that reality is also shaped by our interpretations.

262

263

Ancient Chinese, Egyptian, and Greek civilizations associated the constellations with divinities. Certain animal or human figures indicated the directions of the sun throughout twelve lunar months, passing each year over the same celestial path, which the Greeks called the Zodiac. Belief in the influence of configurations formed by the sun, planets and the fixed stars, on nature and humans in particular, seems one of the most widespread basic convictions still in the world today. Yet, it was essentially by distancing itself from astrology that astronomy became a science, albeit using observations gathered by its predecessor. Astronomy is, consequently, a field of knowledge where practicioners are wary of interpretations. Astrophysics, however, is forced to offer many interpretations, since the objects are so distant and so complex that only very patchy information is available, so hypotheses have to be combined in order to corrobate them.

Orion constellation

264 Astronomy being but one example, the question is to know to what extent in general is science made of interpretations. The position of the chemist and politician Marcelin Berthelot is absolutely cut-and-dry: Positive science pursues neither the initial causes nor the end of things […] all features, no matter what kind, are based on observation and on experience. One principle of positive science is that no reality can be established by reasoning. The world cannot be guessed.1 Berthelot is, here, the author of one of greatest idiocies ever written on science. Of course the world can be guessed! It’s even one of the main motors of knowledge. Neptune had been guessed by Le Verrier, the “laryngeals” had been guessed by Saussure before being recognized in Hittite, the positron had been guessed by Dirac before being observed by Anderson, the interference of electrons and their diffraction were guessed by De Broglie before being observed some years later. Clearly, all of that was neither foreseen in a crystal ball nor in tealeaves. Fermat’s last theorem was announced four centuries before its complete proof. Science is essentially the scaffolding for a process of successive interpretations where the game is to make sense of a new region of complexity, whether that be material or some combination of symbols. The effect of ‘guesswork’ comes from the fact that the hypothesis is later proven. In this respect, the existence of atoms as well as microbes had been guessed. But we must acknowledge that the interpretations we abandon are of the same nature as the others, otherwise we would be able to reject them beforehand. They are relics of science, its jurisprudence. Kepler, in his long road to his three eponymous laws, first thought that the orbits of the planets could be obtained by successively inscribing in polygons (triangle, square, etc.). He then improved this scheme by considering spheres circumscribed by nested polyhedra centered on the sun. 1. In Science et philosophie, Calmann-Lévy (1886).

265 The Earth is the measure of all the other orbs. Itself circumscribed in a dodecahedron, the sphere surrounding it is that of Mars; circumscribed to the orb of Mars, a tetrahedron: the sphere surrounding it is Jupiter. Circumscribed to the orb of Jupiter, a quadrate: the surrounding sphere is Saturn. Now placed in the orb of Earth, an icosahedron: the sphere which is in line with it is Venus; placed in the orb of Venus: the sphere which is in line with Mercury. There you have the reason [for the position] of a number of planets. 2 As for what makes the planets move, he expresses himself in the following way at this period: But if we hope to bring ourselves even closer to the truth and find a commonplace equality in these relations we should accept one of the following two assertions: either the moving bodies are all the more weak the further they are from the Sun, or there is only one moving body in the center of all the orbs, that is to say the Sun, the body which most strongly moves the planets which are nearby and less so for those further away, due to the great distance and the weakening of force related to it. 3 It's worth trying to understand Kepler's motives: After discovering that the orbits were elliptical and announcing his first two laws, he devoted a large part of his Harmony of the World to extending Pythagoras's aesthetic emotion which compared the planets with the seven strings of the lyre. He drew up a truly musical theory: Saturn and Jupiter as the bass, Mars the tenor, Venus the contralto and Mercury the falsetto. It’s not until Book V, after these theories have been presented, that we finally encounter the famous third law concerning the periods of revolution. This musical theory was reworked by Father Mersenne, who, noting some slight inaccuracies with the observations, finally dealt with this problem by recommending that musicians change their habits to fit the laws of the heavens! 2. Johann Kepler Mysterium Cosmographicum, 1596, as cited by Alexandre Koyré, La révolution astronomique Hermann 1961. 3. ibid.

266

Kepler’s musical theory from the Harmonice Mundi (1619)

Treaty of Universal Harmony, F. Marin Mersenne (1627) which contains Musical Theory & Practice of Ancient and Modern Times, with the causes and effects, enriched by Reasons taken from Philosophy and Mathematics.

267 The question resolved too hastily by Berthelot can be approached in a concrete way: is, for example, Bode’s law (approx. 1770) that the radii of the orbits of the planets around the sun are given by the formula rn = 0.4 + 0.3 x 2n (using the earth's orbit as a unit) by taking n=-1 for Mercury and by counting as a planet the asteroid belt between Mars and Jupiter, is this law of the same nature as the following Rydberg-Ritz law which at the turn of the twentieth century gave the frequencies of hydrogen's spectral lines? 1/λ = Rh( (1/p)2 - (1/n)2 ) In the first case, Newtonian mechanics did not exist yet, and in the other, quantum mechanics were not yet in place. In both cases, it’s about fitting into the accuracy of instruments available. The reader would be justified in observing that this parallel isn’t complete. Already in the eighteenth century, Bode’s law was quite approximate. Thus it is more relevant to choose another law. It turned out that Laplace, a mathematician and specialist in celestial mechanics, discovered a law concerning Jupiter’s first three moons: The movements of Jupiter’s first three moons present an even more extraordinary phenomenon than the precedent which is that the average longitude of the first, minus three times that of the second, plus two times that of the third is constantly equal to two right angles. θ1(τ)−3θ2(τ)+2θ3(τ) = π (2π) Galileo had compared Jupiter’s moons to a celestial clock. With Laplace’s law, θ1(τ)−3θ2(τ)+2θ3(τ) = π its cogs are revealed. If the positions of moons 2 and 3 are known, then that of the first moon is completely determined.4 The average angular speeds also satisfy a linear relation and Laplace adds this sublime phrase directly after: There is an infinity bet against one that this equality is not at all due to chance. 5 4. Until the 17th century, ships used to work out the time - an essential part of navigation - using the positions of the moon and Jupiter’s moons. Chronometers that were sufficiently accurate and could cope with nautical motion only appeared with John Harrison’s improvments in the mid 18th century. 5. Laplace, Exposition du système du monde, 1835.

268 Here, we should remind ourselves that Laplace is also the greatest probabilist of his time. He was the first to use imaginary numbers to demonstrate the central limit theorem, and it’s not the least of his merits to be the initiator of statistical methods accurately estimating if certain measured deviations from the positions of the planets can be attributed to instrumental errors or are significant. In his memoire for the Academy concerning Jupiter’s moons, he details his reasoning: Struck by these results, I suspected that these quite approximate regularities, which the tables still nonetheless differentiate by several minutes, were rigorous and that the table differences depended on mistakes to which they were still susceptible. I thus looked in the theory for the cause of these regularities, and by going into detail, I found that the mutual attraction of the first three moons made the previous relations meticulously exact; from which I concluded that by determining with more accuracy than we had not yet made regarding the movements of these moons, and by employing a greater number and more distanced observations, these movements would approach these relations even more. I had the satisfaction of seeing this consequence of the theory confirmed by the research of Mr. de Lambre.6 At this stage, it seemed that Laplace did not have a completely rigorous argument. Great calculator that he was, he could certainly calculate the perturbations, i.e., limited series expansions that take into account forces or secondary effects. But the moons are perturbed by the oblateness of Jupiter, by the gravitational pull of the Sun and of Saturn as well as their own mutual attraction7. It seems that his thinking was intuitive and the analogy he used to make the reader understand could well be what he himself was guided by: resonance, which works in such a way that two pendulums or clocks for which the pace is just slightly off, being placed on the same support, end up having exactly the same rhythm. 8

6. Laplace, «Théorie des satellites de Jupiter», Mém. Acad. Sc. (1789-1792). 7. The relation concerns the first three of four satellites discovered by Galileo (Io, Europa, Ganymède). The movements are also disturbed by the fourth satellite Callisto and by smaller satellites (Mmore than 60 are currently known as well as a ring). 8. Laplace, Essai philosophique sur les probabilités (1825) tII, p.65.

269 To say what we should think of Laplace's law today is the easy way for a historian of science. We will return to this in a moment. However, we should note that there is more to learn, from an epistemological point of view, by staying within the limits of knowledge of that time. Laplace hardly knew the status of the discovery he had made. The presumption that guided him, based on an analogy with vibrations, and by the unlikelihood of a fortuity so simple mathematically is, typically, an application of Cournot's philosophical probabilities. His use of the expression infinity to one bet reveals that he clearly knew that he was outside the realm of quantitative evaluation of probabilities or statistical estimations of likelihood. Laplace tried hard to explain how he arrived at this discovery, being very interested in the psychological aspects of the process. He preferred to reveal everything and opposed the practice of secrecy that was common among scholars - an aspect of scientific life that has since been lost: the taste for communicating through riddles. Perhaps this way had simply been forgotten amid the concrete and operational powers which resulted from the immense progress of physics in the nineteenth century. Writing about Newton and law of universal gravitation, Laplace expressed his distaste for riddles: It’s through synthesis that Newton expounded his theory of the system of the world […] We should regret with the geometrists of his time that he had not followed, in the exposition of his discoveries, the route by which he had arrived there; and that he had suppressed the demonstrations of several results, appearing to prefer the pleasure of making his readers guess it in order to clarify it. (Exposition du système du monde, op. cit.)

270 That was the custom at the time. In 1610, it was by the following exacting anagram that Galileo ‘published’ his discovery of the phases of Venus: Haec immatura a me iam frustra leguntur : o, y which means These immature letters have already been read by me: o, y but which should make the object of a permutation so that we read Cynthiae figuras aemulatur mater amorum from which should be understood: The mother of love (Venus) imitates the figures of Cynthie (the Moon), an anagram which had not been correctly discovered by anyone before Galileo revealed the solution.9 These extremely numerous practices, linked, as Laplace said, to the pleasure of making people guess, suggest that scholars of the time considered that they shared an amateur spirit of riddles surely connected to the skills that they attributed to scientific practice itself. What, then is this law of Laplace? It concerns, effectively, a phenomenon of resonance, which is something we encounter in many situations that involve vibrations, including the most recent quantum physics, for example in the properties of certain ring laser gyroscopes used in airplane navigation systems. Today astronomers express themselves on this subject in the following way "There is nothing mysterious about Laplace's relation: the laws of celestial mechanics enforce resonances between bodies that rotate concentrically. The same relations hold between asteroids and the fourth moon is also affected by resonances. But this resonance attributed to Laplace is striking. Will it endure forever? It's not certain. Moreover, it is not exact, because 9. Cf. Fernand Hallyn « De l’anagramme au cryptogramme » in Regards sur Galilée, Actes de la journée Galilée from February 9, 2000.

271 of libration, which means adding an angle to the 180 degrees of this relation. This angle varies over time while always remaining small. It could grow indefinitely and that would destroy the phenomenon of libration around Laplace's relation: we would then have a circulation, which is another phenomenon frequently seen in celestial mechanics but which does not have the spectacular character of Laplace's relation. So there is no mystery: celestial mechanics explains all and allows us to calculate it precisely. However, we only know the values of the angles to a degree of accuracy limited by observations, which makes it difficult to predict how all this will evolve in the long term.”10

Thanks to these examples we should admit that science uses interpretations as material, a view quite different to that of classic positivism which held that science revealed a predefined truth. Consequently, the changes caused by our knowledge are not only on the level of material, systems, chemical synthesis, etc. Certain new forms of consciousness contribute to creating the real, which makes scientists more responsible as their interpretative skill must be employed. This also begs a new question about the procedures for controlling the boundaries. As well as the validation by experience, on the other side, we need to know where the limit of the interpretative lies, and how to distinguish over-interpretations. This question was posed by Umberto Eco in the context of literary analysis11. The scientific domain is, itself, based on reason. But who are the champions of reasoned interpretation? The paranoiacs. They are often cited among the great scientists, which only serves to confirm that this faculty of seeing meaning in meaningless things (the ball those children threw at my window to annoy me; the handkerchief that Othello understands as proof, etc.12)is of a similar nature to the interpretative faculties that contribute to finding fundamental representations of science. When Lacan writes "science is successful paranoia", the adjective successful should simply mean to say that from this fiction, we don't, at this moment, know how to escape, at this moment only.

10. Report by J. E. Arlot, Observatoire de Paris. 11. Umberto Eco, Interprétation et surinterprétation, PUF 1996. 12. Cf. F. Roustang Comment faire rire un paranoïaque, O. Jacob 1996.

272

The Legitimacy of Science and Love

274

275

If we allow for interpretation in the creation of knowledge, validity cannot come from experimental verification alone according to a positivist or neo-positivist view. Cournot pointed out the importance of a theory’s simplicity, but there are other factors, such as coherence with other theories, etc. But why isn’t the interpretative invention of the researcher systematically considered as subjective and socially formatted? Why does individual enlightenment pass so easily to a paradigm shared by a scientific community? Another interpretative and social phenomenon that can enlighten us on this matter is love, often legitimized because it happens “by chance”. The parallel goes further than one might think. To prove the researcher’s innocence one should play down the interpretative dimension of his activity and present science as comprised only of fortuitous discoveries of reality. On the other hand, to prove the researcher's culpability we need to recognize his interpretative skill and the cultural aspect of science, seeing research as an activity that shapes reality and its truths.

276

277 To Describe or to Understand. We have seen that Cournot was somewhat hesitant about the question of knowing whether a representation, that we have guessed and find philosophically probably, is an image of reality or not. First of all, he admits a form of relativism in so far as the aptitude for the recognition of meaning depends on the conditions of our perception and our points of comparison. Then he rejects the path of skepticism and relativism without further investigation. Cournot - like most philosophers, it must be said, even today - tackles the question of scientific truth in a Manichean fashion. Either the exterior world exists, and our imperfect knowledge gradually improves, and the resulting progress, despite the conceptual revolutions that it causes, is proof that one cannot say just anything. Or we are skeptic, relativist and think that all viewpoints are possible. What is curious in this dichotomy is that, from the times of Pyrrho through to the present day, there have been champions of the second position who are original and nonconformist, cramped by rational thought patterns, who adopt a provocative position, necessarily vague and superficial in content, of which the principal effect was to goad the others and serve as their foil. The interesting opposition is not between truth and relativism, but between monism and pluralism, which is very different. Regarding scientific knowledge, pluralism is not an abstraction without operational consistency like its caricature of relativism; it is in many respects the philosophy best suited for contemporary research problems, and a way to think of the connections between democracy, technique, and environment. From our perspective, the central role of interpretation is the basis of this reflection. For example, Noam Chomsky goes further than Cournot by reviving the Cartesian idea of second substance, at least the approach leading to it: At present, contrary to many of my colleagues, I believe that Descartes’ choice to postulate a second substance had been very scientific and not at all metaphysical. In many respects, it resembled the intellectual choice of Newton while he determined action at a distance; he penetrated into the domain of the obscure, if you will. He entered into a domain which transcended established science, and attempted to integrate it there by developing a theory in which these notions would be properly clarified and explained. Descartes acted in a similar way by defining a second substance. Of course, he failed where Newton succeeded; he showed him-

278 self incapable of throwing out the foundations of a mathematical theory of the mind.1 The case of Ernest Renan, a former seminarist turned scientist, is very interesting. A rationalist advocate of scientific and technical progress, he is in fact a religious person. Not the positivist religion of Comte or Saint Simonianism, but a vague religion completely in the spirit of William James's ideas. This is clearly reflected in the following passage: Woe also to reason in the day when it suppresses religion! Our planet, believe me, is working on a profound oeuvre. Don’t pronounce yourself recklessly on the futility of this or that part of it; don’t say that this cog must be removed which seems to do nothing but contradict the others. Nature, which endowed the animal with an infallible instinct, put nothing deceptive in humanity. From its organs you can boldly conclude its destiny. Est Deus in nobis2. False when they try to prove, determine, portray infinity; religions are correct, if I dare say it, when they affirm infinity. The most serious errors that they mix into this affirmation are nothing compared to the worth of the truth they proclaim. The simplest creature, so long as he practices the religion of the heart, is more enlightened about the reality of things than the materialist who believes in explaining everything by chance and the finite.3 That last phrase is well chosen. Indeed, what is without meaning is chance and the finite. But he who penned such a passage is also the author of La vie de Jésus and, notably, L’avenir de la science which is triumphantly positivist. Nietzsche also wrote this point in a lovely, but merciless text, which today appears with striking clarity: RENAN. – Theology is the perversion of reason by “the original sin” (from Christianity). Take as proof, Renan, who, as soon as he risked a yes or a no from a general order, struck wrong with a scrupulous regularity. For example, he wanted to narrowly unite science and nobility: but science is part of democracy, that is palpable […] Renan possessed, just like a Jesuit and a Confessor, his inventive faculty of seduction: his spirituality wasn’t lacking in this big, meek smile of a clergyman as, like all priests, he only became dangerous when 1. N. Chomsky and M. Foucault, De la Nature humaine, justice contre pouvoir (1971), L’Herne 2006 2. There is a God Inside us. 3. Preface to La vie de Jésus (1863).

279

he loved. There is no equal to him in his manner of loving what makes life dangerous… This spirit of Renan, a spirit which puts one on the edge, is yet another calamity for this poor sick France, sick in its will.4 With regard to the role of theories in understanding the world, there is an author almost totally ignored who, at a time when ideas promoted experience to the utmost, put forward some penetrating views anticipating those of Thomas Kuhn and even Paul Feyerabend: Emile Picard. An academic and professor at the Sorbonne, Picard is a mathematician to whom we owe an iterative integral method for solving differential equations which proved to be very successful, and is now designated with his name. The following are excerpts of a rare text written in 1909: The philosophy of Auguste Comte exerted a large influence on the second half of the century; we consider only the strictly scientific side of it without discussing its originality.5 Scientific truths are truths of the experimental order; we find facts by observation and experimentation and, by linking facts closer and closer to one another by immediate relations, we arrive at notions of a more general order which provide the common explanation of an immense number of individual facts. Through the indefinitely varying circumstances of these, we perceive constant relations, leading us to laws, such as, to take one example, the laws of the pressure of gas and the tensions of vapors, which were recognized after a great number of individual experiments. Comte, moreover, had no difficulty with the notion of reality; as he put it, the positive word designates reality as opposed to the fanciful. The Comtian doctrine, which does not bother itself with any careful analysis, seems assuredly simple, but singularly superficial. Comte, concerned primarily with sociology, was no scholar. He spoke, so to say, of a complete science, as shown, for example, by his unfortunate predictions about the bounds imposed on various scientific researches and his static vision of a science that he wished to see promptly definitive is unacceptable to us. Taine said at some 4. Le crépuscule des idoles (1888). Here, Without a doubt, Nietzsche certainly makes allusion to La réforme intellectuelle et morale (1871) where Renan directly concerned himself with “the honor of France”. 5. Emile Picard «De la science» in De la méthode dans les sciences, Alcan 1909.

280 point that Stuart Mill cut his own wings in order to strengthen his legs; many scholars prefer to keep some wings, and think that the fanciful plays its role in the construction of science. Comte's simplistic positivism needs to be enlarged by a more complete analysis. […] In the previous chapters we spoke about structure, interpretation, imagination, and here is a scientist who appeals to the fanciful! As for ideas – Picard employs the word ‘concepts’ – they present a type of arbitrariness: The distinctions by which we abstract certain elements in order to retain just a few of them, form one of the most basic operations we can do with our experiences, and these abstractions lead us to concepts […] Let us add that the formation of concepts has a certain degree of arbitrariness, resulting from a certain indeterminacy in the choice of elements conserved. This brings us to a very important point: the concept plays an essential role in the genesis of science and scientific knowledge tends to be achieved through concepts. The arbitrariness we mentioned earlier is present in the formation of these concepts, which reveals clearly the role in the development of science that is played by the mind working on the data of experience […] A system of concepts associated to individual laws or facts, and transformed by reasonable deductions so as to put, subject to certain hypotheses, these facts or laws into more general frameworks, constitutes a scientific theory. We have mentioned the part of arbitrariness in the formation of concepts; it is a fortiori larger still in the formation of theories. This arbitrariness principally resides in the hypotheses leading to generalization, which are the essential points of the theory. In the different sciences, the development of theories takes very different forms and is not understood by all scholars in the same way […] Generally, we demand that a theory be simple. This principle of simplicity, despite its hypothetical character, tends to produce a sentiment of certainty in us. Faced with a simple law, we believe less in the possibility of error; we can presume that the law of universal gravitation would not have had much of a future if instead of an exponent of two, it needed, as has been proposed to explain certain oddities of the movement of the planet Mercury that do not fit with observations, to substitute the number two increased by sixteen units of

281 the eighth order 6 […] We can say that at each moment we let ourselves be guided by this principle of simplicity; we thus have a first approximation of the genesis of science. Any theory bringing forth a certain number of concepts, hypotheses, experimental facts and reasoning forms an amalgam in which each part cannot easily be separated. Also, in general, no experiment can establish the truth of an element of this whole presenting a hypothetical character. 7 Quite naturally, Picard leads us to pluralism, which – once again – contains no relativism. This represents remarkable intuition on his part as the proof of multiple interpretations would not appear in mathematics until approximately 1915-1920 (with the Löwenheim-Skolem theorem), nor in physics until the dualities of quantum mechanics were discovered around the same time. It happens, then, that several theories can develop simultaneously and report the same group of phenomena. We could always make a theory agree with experiment, by modifying certain concepts or introducing additional hypotheses. But here, again, the idea of simplicity intervenes, making us reject any theory that is too complicated; this is because we don't see any use in a theory that is too difficult to work with, and perhaps also because its complexity makes it seem less pretty to us. […]The preceding generalities highlight the part our mind plays in the genesis of science and it is accurate to say that we make our own science, speculating on exterior realities only through our own concepts and theories. But these do not form a rigid framework like the forms and categories of certain idealism. An important part of scientific progress is the attainment of a more complete knowledge of objective elements, which we express by saying that science tends to become more and more objective, and this knowledge necessarily influences the formation of concepts and their classifications. It must, nevertheless, be acknowledged 6. Picard wrote during the period between Le Verrier and the theory of general relativity when the anomalies of Mercury’s perihelion remained inexplicable. 7. Specialists of epistemology promote the idea - the Duhem-Quine thesis - that experience cannot decide on an assertion, but only on a theory. It is argued in 1906 by Duhem in La théorie physique : son objet et sa structure (p303-328) and taken up again in a more formal way by W. V. O. Quine « Two dogmas of empiricism » in From a logical point of view (1953). Here, Picard renders this idea natural and intuitive.

282 that complete objectivity in science is a fantasy; our science is created by us and with our organs, in our style, and it will always be somewhat dependent on our relations with the exterior world. Also there is a strong element of illusion in those who see science as making known the mysteries of the universe. […] Scholars, at least the majority, hardly think in these conditions to find the true words of things, as Renan naively hoped in the Avenir de la science; they are no longer very sure of understanding the meaning of such expressions. In one hundred years, this text has not aged in the slightest. It is a salutary criticism of the positivism dominating the period which remains to this day, and is perhaps even reinforced. The only change which must be noted since it gives the question of description and comprehension in the sciences a completely new twist is the emergence of modeling tech-

283 niques. This has altered the balance. With Newton and gravitation, Maxwell and electromagnetism, Einstein and relativism, and quantum mechanics, the most effective way to cover and describe a great number of phenomena, was to make use of a theory - which made it so that epistemology focused on theories. Now, however, with growing precision and storage power, we are capable of archiving fortuitous data, taken by measuring the world surrounding us, which gives a framework for projections, evaluations, various projects and is very useful in practice. On one hand it seems - as has been noted by many authors - that the invention of theories has run out of steam somewhat. On the other hand, the existing theories find wider application by modeling, and that modeling has, moreover, boldly employed the same empathetic means as ordinary language to convince and defend, on occasion, the views of this economic agent or that powerful group. We arrive at a true language, with which we can say the best as well as the worst, which uses symbolism like science does, as well as clutches8, understatements and other analogies as found in political discourse for example9. Legitimate love. When speaking of love we may appear to discard our scientific concerns, but it is only an appearance. The question I briefly want to focus on now is why, as innumerable literary examples attest, a romantic encounter produces a love felt to be true if it happens by chance: After Tomas had returned from Prague to Zurich, he began to feel uneasy at the thought that his acquaintance with Tereza was the result of six improbable fortuities […] Tomas appeared to Tereza in the hotel restaurant as chance in the absolute. There he sat, poring over an open book, when suddenly he raised his eyes to her, smiled, and said, “A cognac, please.”

8. A ‘clutch’ is a term used by French linguists for something that helps the listener to understand who the speaker is and what the circumstances are. For instance, “Dear colleagues, as chairman of this ceremony, I would like to say that…” Such clutches in principle do not exist in classical scientific discourse. They are hidden, but they frequently appear in modeling. 9. On this subject, see N. Bouleau Philosophies des mathématiques et de la modélisation, L’Harmattan 1999.

284 Necessity knows no magic formulae—they are all left to chance. If a love is to be unforgettable, fortuities must immediately start fluttering down to it like birds to Francis of Assisi’s shoulders. [Milan Kundera, The Unbearable Lightness of Being, op. cit.] There are many such instances in Jane Austen’s Emma who makes light of its surprising nature after Frank Churchill meets Harriet, having come to her rescue on an English country road where a woman and boy were caught red-handed in the act of trying to rob poor Harriet. It was pure coincidence that led Frank Churchill to appear at the precise moment Harriet was in most need of help. He happened to have judged it a fine day for a walk and happened to stop at a friend's house to return a pair of scissors, delaying him so that at the precise moment he turned the bend, he arrived at the scene. Frank Churchill not only swept Harriet away from danger, but also off her feet. A une passante

Such an adventure as this,—a fine young man and a lovely young woman thrown together in such a way, could hardly fail of suggesting certain ideas to the coldest heart and the steadiest brain. So Emma thought, at least. Could a linguist, could a grammarian, could even a mathematician have seen what she did, have witnessed their appearance together, and hear their history of it, without feeling that circumstances had been at work to make them peculiarly interesting to each other? [...] It was a very extraordinary thing! Nothing of the sort had ever occurred before to any young ladies in the place, within her memory; no rencontre, no alarm of the kind;—and now it had happened to the very person, and at the very hour, when the other person was chancing to pass by to rescue her!—It certainly was very extraordinary!—And knowing, as she did, the favourable state of mind of each at this period, it struck her the more. [...] It was not possible that the occurrence should not be strongly recommending each to the other.10 10. Emma, Jane Austin, ed. by Alistair Duckworth, London, Palgrave, 2002 (p. 262).

La rue assourdissante autour de moi hurlait. Longue, mince, en grand deuil, douleur majestueuse, Une femme passa, d'une main fastueuse Soulevant, balançant le feston et l'ourlet ; Agile et noble, avec sa jambe de statue. Moi, je buvais, crispé comme un extravagant, Dans son œil, ciel livide où germe l'ouragan, La douceur qui fascine et le plaisir qui tue. Un éclair... puis la nuit ! - Fugitive beauté Dont le regard m'a fait soudainement renaître, Ne te verrai-je plus que dans l'éternité ? Ailleurs, bien loin d'ici ! trop tard ! jamais peut-être ! Car j'ignore où tu fuis, tu ne sais où je vais, Ô toi que j'eusse aimée, ô toi qui le savais ! Charles Baudelaire, Les Fleurs du Mal

285 To a Passer-By The street about me roared with a deafening sound.  Tall, slender, in heavy mourning, majestic grief,  A woman passed, with a glittering hand  Raising, swinging the hem and flounces of her skirt; Agile and graceful, her leg was like a statue’s.  Tense as in a delirium, I drank  From her eyes, pale sky where tempests germinate,  The sweetness that enthralls and the pleasure that kills.

e,

A lightning flash... then night! Fleeting beauty  By whose glance I was suddenly reborn,  Will I see you no more before eternity? Elsewhere, far, far from here! too late! never perhaps! For I know not where you fled, you know not where I go, 11 O you whom I would have loved, O you who knew it!

!

Emma learns her lesson about meddling in such complicated affairs as love: “Here have I,” said she, “actually talked poor Harriet into being very much attached to this man. [...] Oh! that I had been satisfied with persuading her not to accept young Martin. There I was quite right. That was well done of me; but there I should have stopped, and left the rest to time and chance...” (Emma, p. 108-109) We see the same idea affirmed in this quotation from Fyodor Dostoyevsky: We sometimes encounter people, even perfect strangers, who begin to interest us at first sight, somehow suddenly, all at once, before a word has been spoken.

Love, which must justify itself - whether it is inconvenient, or disturbs an apparent harmony, provoking intrigue or jealousy, or simply creCharles Baudelaire, Les Fleurs du Mal ates concern - is never assumed to be an act of deliberate will with a chosen target. No, chance did it all - that's the whole story. The lovers’ hearts cannot be held responsible in any way. In L’education sentimentale by Gustave Flaubert, the simple sight of an unknown woman, Madame Arnoux, seen by Frederic while on a boat floating down the Seine suffices to birth the passion from which the entire book is based: “Ce fut comme une apparition.” Here love is not being justified as such but, in some ways, the absence of a logical sequence of events leading to this mad but enduring love helps Flaubert to make it seem more plausible to the reader. 11. Translation by William Aggeler, The Flowers of Evil (Fresno, CA: Academy Library Guild, 1954)

286 Don Juan is the incarnation of the opposite. And it is precisely the fact that he knowingly seduces and arouses true love in the women he conquers which makes him seem monstruous. Finally Molière ends the play by making him monstrous but, except when provoked by the commander, Don Juan is, at heart, human and even charming, guilty only of not having left chance to spark affections. The same is true, at least to begin with, for the Vicomte of Valmont and the Marquise of Merteuil in Les Liaisons dangereuses.12 In the novel, the Aristotelian categories – the intentional and the unintentional – supplant our more modern classifications. Further literary analysis would undoubtedly reveal an infinity of variations and nuances. Novelists use the terms chance and fortuity interchangeably, and this flexibility is lucky. As fortune contains all specifics - if we have enough imagination to think it arbitrary - and all authors, by the maieutics of writing, strongly feel all the choices that their characters have not taken, the situations which would appear necessary from an objective viewpoint can well be described as the result of chance. A typical example is that of the social situation of Emma Bovary: All her immediate surroundings, the wearisome country, the middle-class imbeciles, the mediocrity of existence, seemed to her exceptional, a peculiar chance that had caught hold of her, while beyond stretched, as far as the eye could see, an immense land of joys and passions.13 This manner of thinking can go as far as to erase all sociological necessities. Fundamentally speaking, isn't it chance that has made me bourgeois, noble, or peasant? And in some egalitarian discourse, isn’t it by chance that I am one sex rather than another? Referring to a vague metempsychosis, we think of the individual as a largely random incarnation. Even the arranged marriages that happen in numerous countries even today - for a very large majority of the world population - can be felt as chance, chance that it be you and me, chance that it be us. We - you and me - are so alive, so full of the unexpected; our initiatives have so much charm that it’s a godsend that these traditional social rules have chosen us.

12. By Choderlos de Laclos, 1782. 13. Madame Bovary, Gustave Flaubert, 1857, trans. by Charles P. Button, 1969.

287

Mme de La Fayette, La Princesse de Clèves There was to be a Court ball at the Louvre, and she spent the whole of that day in her own room getting ready for it. When she arrived she was greatly admired, for her clothes, her jewels and her beauty. The ball opened, and while she was dancing with M. de Guise there was a stir at the entrance to the ballroom, people making way as though for somebody important. Madame de Clèves went on dancing, and while she was considering whom she should take for her next partner the King called to her to take the newcomer. She turned round and saw a man striding over benches to get to the dancing floor: at once she felt that this could be none other than M. de Nemours. The first sight of this handsome Prince, always quite startling, was made more so on this occasion by the trouble he had taken with his appearance, and equally the first sight of Madame de Clèves was amazement. M. de Nemours was so much struck by her beauty that, as she curtseyed to him, he could not conceal his admiration. They began to dance together, and as they did so a murmur of applause ran round the ballroom. The King and Queens reminded each other that these two had never met before, and thought it strange to see them dancing without knowing each other. (La Princesse de Clèves). (trans. Nancy Mitford, New Directions Publishing Corp. 1951)

288 Innocence Surprised by Love, drawing by Prud’hon. Already in Kant’s time, the chance romantic encounter was considered such an overused literary practice that to criticize the philosophy which managed to demonstrate what it wanted, Kant compares it to this easy effect: “just as novelists scare the heroine far from the story, so that a happy coincidence or chance makes her meet her lover” and to illustrate this purpose, he cites the following famous and charming verses of Virgil: Malo me Galatea petit, lasciva puella Et fugit at salices, et se cupit ante videri (Bucolic Eclogue III : Galatea threw me an apple, the crazed child, and fled toward the willows, being concerned whether she had been seen), verses which nevertheless go beyond what the Königsberg’s serious philosopher wanted make clear since they established the game of desire on the ambivalent idea of intertwining of the unintentional and the intentional.

Of course, the concept of legitimacy is inappropriate for discussing love. Psychoanalysts detect there the ingredients of transgression, of misunderstanding and projection, without one ever knowing the exact recipe. A love without pretence! Legitimacy for lovers or in relation to their social circle? The two interact, as there is something social in all of us. For Molière - excluding Don Juan - love born by chance does not upset the social order much; a happy marriage needs a shared impulse of the heart and harmonious circumstances. Poor alliances lead to either family clashes (Le Bourgeois Gentilhomme Act III Scene 12) or conjugal misfortunes14. As morals later evolved, love grew more complex with Marivaux and Beaumarchais and still more so with Feydeau, Courte14. Here is what it is to have wanted to marry a young lady! You are accommodated in every room, without you being able to take it out on anything; and the mansion keeps your hands tied. The equality of the situation at least leaves the honor of the husband free of resentment” (Georges Dandin Act I Scene 3)

289 line or Guitry. In the real world, obviously, objective sociological analysis would show that social reproduction is still important today15. Ultimately, a detailed sociological enquiry, if the necessary information were available, could explain any romantic alliance – up to an ‘equivalence’... Let’s summarize a number of points so that we can refer back to them: 1) Love acquires some legitimacy from appearing at random. 2) In any case, love is presented as random by anyone asked to explain it. 3) In reality, it is largely conditioned by social conditions and circumstances, and we can almost show that it is socially constructed. 4) This sociality may be denied and disputed endlessly. The reader sees what I am getting at! Clearly, we cannot think—without some naivety—that science today is universal. It creates knowledge that is intimately linked to the interests of the countries, economic organizations and social groups that are affected by the research, either by the orientation of the research, by industrial contracts, or by the values most prevalent in the environment of the research group. It is not universal because it is only taught in privileged places. Furthermore, science has never been universal except in the utopias of Condorcet or Wilhelm von Humboldt. We may regret this of course, but the direct consequence of this state of things is that a problem of responsibility arises. If a dam breaks, should the responsibility be assumed by the enterprise, the engineer, or his continuum mechanics professor? If GMOs make a large number of insects and birds disappear, are biology researchers responsible? Is Andreï Sakharov to be counted among those responsible for Chernobyl like Robert Oppenheimer for the atomic bomb affectionately called Little Boy? The researcher is protected because he discovers by chance. In other words, he doesn't really know what purpose his discovery will serve, nor does he aim to benefit a particular agent or institution. It's one of the reasons why, faced with growing pressure from the authorities (European, American or Japanese) to pursue applied research (industry-driven 15. Cf. Thélot, Tel Père, Tel Fils ? Position sociale et origine familiale, Bordas 1993.

290 research) with utilitarian aims, researchers defend themselves, relying on the preservation of fundamental research which is their only guarantee of innocence. It’s the element of chance that establishes the legitimacy of science. More precisely, to prove the researcher’s innocence one should play down the interpretative dimension of his activity and present science as comprised only of fortuitous discoveries of reality. On the other hand, to prove the researcher's culpability we need to recognize his interpretative skill and the cultural aspect of science, seeing research as an activity that shapes reality and its truths. Now we can understand the long-term goal of science studies, which is to adapt the arguments and judgements about responsibility, and why this is so disdained by researchers in the disciplines concerned: computing, biotechnology, nanotechnology. The analogy with love goes further: in both cases the ambivalence between the fortuitous and the intended - which corresponds to an indeterminacy between knowledge and ability - can not only endure but can, in many cases, be advantageous for anyone able to skilfully maintain this balance. Jean-Jacques Salomon, in a prescient and noted work, shows how scientists have frequently held ambiguous positions, about eugenics certainly, but also on the development of weapons, especially nuclear weapons, etc, and again now in biotechnology particularly16. U-turns are common; having contributed to the perfecting of bombs, one becomes a pacifist. To compare these situations with the games of love and chance is not necessarily naïve or innocent. On the contrary, it shows that there is something unfathomably deep in human nature ... which will cause even more serious narcissistic injuries than before if we try to overcome or sublimate it17. 16. Les Scientifiques entre savoir et pouvoir, Albin Michel 2006. 17. The archaic origin of the deresponsibilizing and disculpation by chance is perhaps to be searched for in sacrificial customs: “In societies where human sacrifice is practiced,” wrote René Girard, “orphans were the victims of choice. To sacrifice a child whose parents are alive runs the risk of alienating them. The process of victim selection is marked by careful prudence […] By sacrificing an orphan, the temptation is reduced to a minimum for the members of the community to make themselves the champions of the victim; consequently, the risk of fueling the fire is reduced. The chances of an efficient sacrifice are thus maximized. A terrible ‘sacrificial wisdom’ dictates the choice of the orphan and of drawing lots. Entrusting the selection of the victim to the free judgment of those doing the sacrificing always runs the risk of leading to disagreements. Therefore, the selection must be entrusted to chance, the role of which is not ignored by those doing the sacrificing in spontaneous meetings. […] The orphan drawn at random is a ‘ritual’ scapegoat, a substitute for the original victim who spontaneously creates unity against him and reconciles the community in his death. La route antique des hommes pervers, chap. 12, Grasset 1985.

291 Rather than list catastrophic examples, we can very easily see the ambiguities in the development of research by considering the case of anti-dope experts and professional athletes. The researchers specialize in optimal nutrition for physical effort. Evidently the best drug inspectors, to be effective, must keep abreast of the latest doping techniques. These are more or less well known and require biochemical research based on manufactured drugs. In so far as we know more than the inspectors, we are able to advise unscrupulous athletes. Who is going to win this race? In any case, good nutrition is not a clear concept. Rights and legislation are trying to catch up with the advances in knowledge. This is but one generic example. And now, today, the cynical discourse of the transhumanists is common across American universities. It is essential that we think more what is currently happening with anthropotechniques (human genetic engineering). Here we flounder completely, as traditional moral benchmarks collapse. I’ll bring up an excellent book by Francis Fukuyama already cited. “In any discussion on cloning,” he writes, “stem cell research, germ-line engineering, and the like, it is usually the professional bioethicist who can be relied on to take the most permissive position of anyone in the room.” They are similar to the researchers who want to preserve the freedom of their investigations and they are so steeped in the mystery and excitement of research that they become sterile and unable to think of other interpretations of the risks. Thinking of two interpretations at once is very difficult; accepting more is practically impossible for a single individual - only pluralism in society has shown itself capable of that. But ultimately we have to be able to handle two interpretations, because we are permanently faced with the unanswerable philosophical question of whether men and women, two animals that do not have the same chromosomes, think about the world in the same way. The Hegelian dialectic is an attempt to resolve two opposing views using the “wisdom” of historical time. In similar fashion, physics accommodates wave-particle duality in quantum mechanics, though these are truly two interpretations, each one quite clear, the marriage of which is not clear to anyone18. Pluralist parliamentary systems are superior to every philosophy in their ability to accept numerous interpretations of the world. The researcher, if he has considered the risks at all, should recognize that only plural thinking can hope to govern science. 18. On dualities, cf. J.-M. Lévy-Leblond, Aux contraires, Gallimard, 1996.

292

293

Hints

294

Reading THE FEET modifies our relation to the randomness hypothesis (cf. p 88)

295

Similarly the text «step back to reflect» which may be guessed, is certainly not fortuitous (cf. p 89)

296

Mister «One-Two-Three-Where’s-your-Breakfast» is actually a giraffe as Kipling let us understand. (cf. p 90)

297

Index

298

299 Agrigento 155 Aigues-Mortes 156 Akrotiri 135 Alberti Leon Battista 137, 143, 144 Allais Maurice 61 Ampère André-Marie 211, 238 animism 225, 231, 233 Anzieu Didier 253 Apollo 19 Arago François 75 architectural space 129 Ariadne’s thread 156 Aristotle 17, 18, 71, 75 Arrow Kenneth J. 38, 53, 58 Athens 69, 71 Atlan Henri 219 Augustus 21 automaton 17, 18, 212 Avogadro 56 Bachelard Gaston 5, 106 Bacon Francis 238 Barthes Rolland 105, 188, 200 Baudelaire 284, 285 Baudrillard 177, 180 Baudrillard Jean 177, 180, 198-201 Bauhaus 102 Bayet J. 23 Beck Ulrich 218, 222 Benveniste 187, 188 Bergson Henri 238 Berlin 69, 79, 145, 146, 151, 162, 163 Bernoullis the 53, 54, 57 Berthelot Marcelin 261, 264, 267 Bertrand Joseph 55, 57 biosphere 207

Birkhoff G. 36 Bloor David 239 Bode's law 10, 261, 267 Bonitzer J. 54 Borel Emile 56 Borromini Francesco 138 boule 70 Bouleau Ch. 166 Bouleau N. 36, 39, 44, 140, 141 Bouleuterion 70, 71 Bourbaki Nicolas 105 Bourdieu Pierre 78, 148 Bourg Dominique 78, 120 Brasilia 159 Broglie, Louis de 264 Brunelleschi Filippo 137, 138, 144 Buffon 51, 57 Burdzy K. 56 Calascibetta 154 Canaletto 121 Capri 153 Cauchy Augustin Louis 59 Cheval (postman) 143 Chomsky Noam 83, 97, 98, 105, 188, 189, 255, 277, 278 Church Alonzo 57 Cicero 11-15, 17, 18, 21-26, 35, 71, 198, 199, 247, 254 Citizens' Assembly 79 Citizens' Conferences 79 classicism 127, 132, 134 Cnossos 155 Cocteau Jean 180 Comte Auguste 213, 234, 238, 278-280 Condorcet, Nicolas de 51, 238, 289

Copenhagen School 241, 254 Copernicus 106 Cournot Antoine-Augustin 10, 11, 29, 31, 33-36, 38, 40-45, 62, 83, 95, 103, 107, 170, 176, 177, 201, 214, 218, 222, 254, 269, 275, 277 Courteline Georges 288 Darwin Charles 209, 210, 250 De Finetti Bruno 49, 57, 58, 120 de l'Orme, Philibert 37 De Meuron Pierre 136, 146 De Stijl 131 Deleuze Gilles 169 deliberative polls 79 Dellacherie Cl. 57 Delphic oracle 19, 26 democracy 65, 67, 69, 70, 72, 75, 79 Demosthenes 26 Descartes René 7, 255, 277 Desrosières A. 77 Dewey John 86, 113, 235 divination 13, 18, 22, 26 Dogon mythology. 97 Don Juan 286, 288 Duchamp Marcel 167, 174-176, 177 Dudok Willem M. 133 Duhem-Quine thesis 281 Dupuit Jules 38 Durkheim Emile 78, 237 ecclesia 70 Eco Umberto 271 economics 58, 61, 62, 63, 64 Edict of Nantes 54 Edo period 83, 99, 100 Einstein Albert 283 Emma Bovary 286

300 Ephesus 155 epigenesis 205, 209, 212 equilibrium 212 error 250 Euler Leonhard 59 Euripides 19, 22 evolution 205, 207-210, 215, 219, 220, 221 Faraday Michael 106, 211 favelas 153 Fechner Gustav 236, 237 Fermat, Pierre de 51, 264 Feydeau Georges 288 Feyerabend Paul 279 financial markets 76, 121 Flaubert Gustave 285, 286 Fleck Ludwig 7 fluctuation 212 fortuity 225, 229, 230, 234, 243 fortune 123, 196, 286 Foucault Michel 106, 255 Fourez Gérard 6, 9 Frazer James G. 233 Freud Sigmund 187, 197-200, 245, 247, 248, 250, 251, 253, 254, 256 Fukuyama Francis 241, 291 Gailhoustet Renée 136 Galileo 267, 268, 270 Gaudi 144Gauss Carl Friedrich 53, 59, 141 Gehry Frank 145 general will 75, 76 genotype 208 Gestalttheorie 38, 81, 101-103, 105, 107 Gestell 102 Girard René 290 Gödel Kurt 36

Grammichele 156 Great Divide 240 Greek cities 69 Greek democracy 70 Grenada 154 Griaule Marcel 96 Guitry Sacha 289 Hadamerd Jacques 39, 40, 140 Hansi 24 Hardy G. H. 140 Haruspices 20 Heidegger Martin 102, 103 Heisenberg Werner 58, 210, 211, 216, 217, 222, 234 Herzog Jacques 136, 146 Hilbert David 189 Hittite 187 Homer 96, 192 Hopf Heinz 55, 58 Hume David 85-88 indeterminacy 58, 61 individualism 58 intentional 211 interpretation 245, 249, 250, 254 Iphigenia 232 Itô Kiyoshi 62 Ives Charles 177 Jacquard Albert 212 Jakobson Roman 188, 194 James William 86, 98, 227, 231, 235-240, 278 Japanese mathematics 101 Jugendstyl 130, 131 Jupiter's moons 261, 267, 268 justice 71, 76 Kahn Louis 139, 143

Kandinsky Vassili 102, 167, 170-172, 174 Kant Emmanuel 98, 288 Kepler Johannes 106, 264-266 Keynes John Meynard 62, 76, 218 Khintchine A. 62 Kipling Rudyard 90, 296 Klee Paul 102, 167, 173, 178 kleroterion 70 Koffka K. 101 Köhler W. 101 Kolmogorov A. 49, 56, 62 Kristeva Julia 188, 190 Kuhn Thomas 5, 6-8, 10, 11, 45, 95, 106, 279 Kundera Milan 111, 114, 115, 117, 119 La Fontaine, Jean de 123 la Hyre, Laurent de 34 la Mirandole 85 la Placette, Jean de 33, 40 Lacan Jacques 106, 187-190, 197, 198, 201, 254-256, 271 Lagrenée Louis 96 Laplace, Pierre Simon de 53, 214, 215, 229, 230, 261, 267-271 Latour Bruno 239, 240, 241 Lautman Albert 105 Le Corbusier 129, 139 Le Lionnais François 140, 195 Le Verrier 187, 264, 281 Lebesgue Henri 39, 56 Legendre Adrien-Marie 53 Leonardo da Vinci 245, 250, 251, 253 Lévi-Strauss Claude 106, 211, 227, 231-234 Lévy Paul 61, 62 Lévy-Leblond J.-M. 61 Libeskind Daniel 145, 146

301 Löf Martin 57 love 273, 275, 283-286, 288-290 Löwenheim-Skolem 281 Luther Martin 237, 238 Malevitch 171 Manin B. 71-73, 76 Marx Karl 78, 96, 97 mason marks 140 mathematical probabilities 38, 41, 183 probabilities 47, 51-58, 61-63 Matheron Georges 25, 212-214, 218, 220 Mauss Marcel 233 Maxwell James Clerk 106, 283 meaning 216, 217, 243, 249 Medicis 72 Mendeleev 106 Mersenne 51, 266 Messiaen Olivier 177 Michelange 28 Mies van der Rohe 134 Milet 69, 155 Mill John Stuart 86, 113, 234, 280 Milner Jean-Claude 190, 191 Minoan palaces 156 Mme de La Fayette 287 modern 125, 134, 144, 210 modernism 127, 144 Moholy-Nagy Laszio 174 Moivre, Abraham de 50-54 Molière 286, 288 Mondrian Piet 171-174 Monod Jacques 11, 55, 203, 207, 209, 210-214, 218-220, 229, 250, 254 Monte Carlo 176, 177, 209 Montesquieu, Charles Louis de 72, 75

Montgomery Scott L. 253 Morgenstern O. 58 Morin Edgar 219 mutations 210, 211 Naples 151, 157 Neapolis 151, 157 necessity 207, 212 Neo-Jamesians 239 Neptune 187 Neutra Richard 133 Newton 27, 98, 106, 230, 269, 277, 283 Nicolas de Staël 173 Nietzsche Friedrich 44, 278, 279 Noto 159 Ogotemmêli 97 Oppenheimer Robert 289 oracle 19, 22, 26 Othello 271 Oud J.J.P. 131 Oulipo 195, 196, 197 Ovid 192, 232 Pacioli Luca 143 Palladio Andrea 137, 138 paradigm 5, 7 paradox 22, 51, 53, 57, 61 Pascal Blaise 51 pattern 81, 103 Paulos J. A. 77 Pavé Alain 220, 221, 222 Pazzi Capella 137, 144 Pearson 51, 54, 75 Peirce Charles 43, 44, 83, 86, 97, 98, 235 Perec Georges 195, 196 Pergamon 69, 155 Permanency of the styles 135

Perrault Claude 138, 139 Perrin Jean 107 phenotype 208 philosophical probabilities 38, 39, 40-43, 45, 269 Piaget Jean 105 Picard Emile 279, 280, 281 Picasso Pablo 178, 180 Pickering Andrew 239 planets 265 Plato 70, 76 pluralism 236-238, 277, 281, 291 Plutarch 18, 19 Poincaré Henri 39, 40, 55, 58, 140 Poisson Siméon Denis 35 Pollock Jackson 169 Popper Karl 5, 36, 56, 71 positivism 101, 227, 231, 234-238, 240, 241, 264 , 280, 282 Praxiteles 21 Priene 69, 71, 155, 156 Prigogine 211-213, 219 Princesse de Clèves 287 probability 33-36, 38-44, 212 progress 95 prytaneis 70 psychoanalysis 247, 256 Putnam 241 Pyrrho 277 Pythian priestess 26 Pythie 28 quantifiable 62, 63, 201, 214, 218 quantum mechanics 215, 216, 261, 267, 270, 281, 283, 291 Queneau Raymond 195

302 Quételet A. 76 Quine W. V. O. 6, 189, 281 Raguse 154 Ramsey Frank 49, 57, 120 ready-made 167, 175, 176 Rembrandt 91 Renaissance 129, 136, 140 Renan Ernest 27, 231, 278-282 Renaudie Jean 136 risk 109 risky object 121 Roman Republic 23 Rorty Richard 78, 241 Roubaix 160 Roubaud Jacques 195 roulette 176, 177, 203, 207-209, 214, 215, 221 Rousseau Jean-Jacques 72, 74-76 Royal Ségolène 69 Ruelle David 215 Russell Bertrand 113 Rutherford Ernest 107 Saint Augustine 73 Saint Simonianism 278 Sakharov Andreï 289 Salomon Jean-Jacques 290 San Gaku 101 Santorin 135 Saussure, Ferdinand de 11, 105, 183, 185, 187189, 191-201, 264 Savage Leonard J. 49, 57, 58, 61, 120 Schaeffer P. 177 Schoffeniels E. 213, 214, 218 science studies 290 Secession 130, 131 selection 208, 210, 213

Selinunt 155 Seneca 25 Serlio Sebastiano 132 Serpotta Giacomo 138 Seurat Georges 94 Shakespeare 113 Sibyl 28 Sicily 153-156, 158, 159 Sienne 72 Simon Herbert 103 Simonides 198, 199 Sintomer Y. 69, 70, 72, 79 slip 243, 248, 250 Socrates 155 St. Petersburg paradox 51, 57 Starobinski Jean 191, 193, 195, 200 Stengers Isabelle 219 Stockhausen 177 strange attractor 215 structure 81, 180 symmetry 127, 132, 134, 140 Syracuse 158 Tarde Gabriel 231-233 Teilhard de Chardin 220 teleonomy 209, 220 Thales 140 Thom René 105, 218-221 tile 33, 34 Timgad 156 Tiresias 96 tychism 17, 18, 98 Ullmo Jean 106, 107 Umberto Eco 271 uncertainty 58 unquantifiable 38, 201, 218

utility 57, 58, 61 Venetian Republic 72 Venturi Robert 144 Venus 20, 21 Vernant Jean-Pierre 17, 71 Verne Jules 92 Vienna Circle 234 Vinci, Leonardo da 245, 250, 251, 253 Virgil 191, 194, 288 Von Bertalanffy L. 103 Von Ehrenfels Chr. 101 Von Humboldt Willhelm 289 Von Mises R. 57 Von Neumann John 58 Wald A. 57 Weber Max 237, 255 Wertheimer M. 101 Weyl Hermann 140 Wiener Norbert 62 Wittgenstein Ludwig 188 Wren Christopher 138 Wright Frank Lloyd 133 Xenakis Iannis 167, 178, 180 Zevi Bruno 127, 129, 134, 139, 145, 180

Copyrights : RMN Réunion des Musées Nationaux, Paris. NB author personal rights. Cover: NB; p7-8, Univ. of Chicago Press; p9-10 NB; p12 Rijks Museum Amsterdam; p13 RMN; p16, 20 RMN; p21,22,23 NB; p26, 34 RMN; p37, 45, 48, 50, 51 NB; p52 Griffin & Co ltd; p55, 56, 57, 59, 60, 61, 63 NB; p65 RMN; p70, 74, 80, 81, 84, 88, 89, 90 NB; p91 Rijks Museum Amsterdam; p94, 95 RMN; p94 nb; p97 M. Griaule; p101, 104, 106, 107, 110, 114, 118, 119 NB; p120 Institut Louis Bachelier; p121 NB; p122 RMN; p125 F. Ll. Wright Memorial foundation; p130, 132, 133, 135 NB; p136 Atelier Renaudie, P. Maurer; p137, 138-139, 140, 141 NB; p145,146 Daniel Libeskind; p147, 150, 153, 154, 155, 156, 157, 158, 159, 160 NB; p162 Bauwelt-Birkhaüser; p165, 169 NB; p170, 171, 172, 173 RMN; p173 Denoël; p174 Könemann; p174 RMN; p176, 178 NB; p179 L’Arche; p180, 181, 184 NB; p190 Le Seuil; p199, 204 NB; p208 Beacon Press; p212, 213, 223, 226, 230, 234, 242, 243 NB; p249, 250 RMN; p257, 261, 266, 270, 272, 273, 282, 292, 294, 295, 296 NB.