Advances in Psychology Volume 99 Foundations of Perceptual Theory

FOUNDATIONS OF PERCEPTUAL THEORY

ADVANCES IN PSYCHOLOGY

99 Editors:

G. E. STELMACH

P. A. VROON

-

-

NORTH-HOLLAND AMSTERDAM LONDON NEW YORK TOKYO

FOUNDATIONS OF PERCEPTUAL THEORY

Edited by

SERGIO C . MASIN Department of General Psychology University of Padua Padua, Italy

1993

-

NORTH-HOLLAND AMSTERDAM LONDON NEW YORK TOKYO

NORTH-HOLLAND ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhanstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

L i b r a r y o f Congress C a t a l o g i n g - I n - P u b l i c a t i o n

Data

F o u n d a t i o n s o f p e r c e p t u a l t h e o r y ! e d i t e d by Sergio C. M a s i n . p. crn. -- ( A d v a n c e s i n p s y c h o l o g y ; 99) i n c l u d e s b i b l i o g r a p h i c a l r e f e r e n c e s and i n d e x e s . ISBN 0-444-89496-9 ( a l k . paper1 1. P e r c e p t l o n . I. M a s i n . S e r g i o C e s a r e . 11. S e r i e s : Advances 117 p s y c h o l o g y ( A m s t e r d a m . N e t h e r l a n d s ) ; 99. BF311.F667 1993 153.7--dC20 93- 1 10 1 2 CIP

ISBN: 0 444 89496 9 1993 ELSEVIER SCIENCE PUBLISHERS B.V. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic. mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science Publishers B.V., unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands

V

PREFACE Historical analysis reveals that perceptual theories and models have a relatively short life. Equally worrying is that even the most popular contemporary theories in perceptual science do not have as wide an accep tance among researchers as do some of those in other sciences. For example, what perceptual theory comes close to the near universal acceptance of the theories of quantum mechanics and relativity among physicists? Does this difficulty in perceptual science depend on the perpetuation of wrong assumptions from past theories, on an inadequate definition of perception, on the complexity of perceptual problems, or on the failure to recognize some basic theoretical principle? To understand this crisis, clearly we must examine the conceptual and philosophical foundations of our science. Performing only experiments without analyzing our conceptual roots is insufficient. Almost unanimously, perceptual scientists believe that the human brain originates perceptions. The inevitable questions that follow are: What can we know about the relationships between brain states and perceptions? How can brain models be used to understand perceptions?Should we remain satisfied with the common reductionistic approach in modern perceptual science that identifies perceptions with brain states? This present volume explores the above questions, although we can appreciate that some of them might not be definitively answered. The following is a brief description of the chapters. William Uttal examines the implications in perceptual science of the barriers that inhibit the linkage of neural, cognitive, and behavioral levels of inquiry and proposes a new behaviorism. Sergio Masin demonstrates that physics and perceptual science deal with a single reality and from this demonstration he draws a novel implication for perceptual modeling. Dennis Proffitt argues that perception is a hierarchically organized and controlled biological phenomenon and examines the implications for perceptual theories of the existence of temporal constraints in biological systems. Walter Gogel presents his theory of phenomenal visual space geometry and examines its implications for perceptual theorizing. Paolo Bozzi indicates six implicit assumptions at the base of current perceptual theories and discusses five related perceptual conundrums. Giovanni Vicario discusses the antinomy in current perceptual theorizing that neither phenomenological nor neuro-

vi

w

physiological descriptions can cover the totality of psychological facts. Nicholas Pastore points out the persistence today of an old paradox in the explanation of the appearance of objects outside our body and shows that this paradox may be the source of pseudo-explanations. James Cutting offers an analysis of the logical and empirical difficulties faced by one of the most popular metatheories of perception, the ecological approach. John Tsotsos argues that some modem perceptual theories are destined to fail-even if they predict phenomena accurately-because they may be proved to be physically unrealizable. James Townsend and Robin Thomas argue for the need of a general theory of psychological similarity and discuss its importance in perceptual theorizing. Finally, Gregory Ashby and William Lee argue that an enduring theory of perception must include the axiom that there is trial-by-trial variability in perceptual information associated with perceived objects or events. The above authors debated the merits of their contributions with discussants. At the end of each chapter, the references of the discussants are listed together with those of the respective author(s) and are marked with the discussants’ initials. In each chapter, references that are first mentioned by the author($ are unmarked. I am deeply grateful to Bill Uttal for encouragement and support in the ideation and organization of this volume, which also received valuable help from Jerry Balakrishnan, Mami Fukuda, Walt Gogel, Bill Lee, Nick Pastore, Robin Thomas, John Tsotsos, and Judy Wilson.

S. C. Masin

vii

TABLE OF CONTENTS Preface

V

List of the Authors

ix

List of the Discussants

X

W. R. Uttal Toward a new behaviorism Discussants: K. Berridge and D. N . Robinson

3

S. C. Masin Some philosophical observations on perceptual science Discussants: P. R. Killeen and G. R. Lockhead

43

D. R. Proffitt A hierarchical approach to perception Discussants: G. Hatfield and U.Neisser

75

W. C. Gogel The analysis of perceived space Discussants: L. Burigana, H. Ono, and M . T. Swanston

113

P. Bozzi On some paradoxes of current perceptual theories Discussant: R. Luccio

183

G. B. Vicario On experimental phenomenology Discussants: G. Vallortigara and M . Zanforlin

197

N. Pastore T h e "inside-outside problem" and Wolfgang Kohler Discussant: S. C. Masin

221

viii J. E. Cutting Perceptual artifacts and phenomena: Gibson’s role in the 20th century Discussant: S . C. Masin

231

J. K. Tsotsos The role of computational complexity in perceptual theory Discussant: V. S . Ramachandran

261

J. T. Townsend and R. D. Thomas On the need for a general quantitative theory of pattern similarity Discussants: V . Bruce, M . Burton, and D . LuBerge

297

F. G. Ashby and W. W. Lee Perceptual variability as a fundamental axiom of perceptual science 369 Discussants: D. H. Brainard, D.M . Ennis, and S . C . Masin

Author index

401

Subject index

411

ix

LIST OF THE AUTHORS ASHBY, F. G.-Department of Psychology, University of California, Santa Barbara, CA 93106, USA BOZZI, P.-Department of Psychology, University of Trieste, 34100 Trieste, Italy CUTTING, J. E.-Department of Psychology-Uris Hall, Cornell University, Ithaca, NY 14853, USA GOGEL, W. C.-Department of Psychology, University of California, Santa Barbara, CA 93106, USA LEE, W. W.-Department of Psychology, University of California, Santa Barbara, CA 93106, USA MASIN, S. C.-Department of General Psychology, University of Padua, 35100 Padova, Italy PASTORE, N.-Department of Psychology, Qeens College of the City University of New York, Flushing, NY 11367, USA PROFFITT, D. R.-Psychology-Gilmer Hall, University of Virginia, Charlottesville, VA 22903, USA THOMAS, R. D.-Department of Psychology, Indiana University, Bloomington, IN 47405, USA TOWNSEND, J. T.-Department of Psychology, Indiana University, Bloomington, IN 47405, USA TSOTSOS, J. K.-Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4, Canada UTTAL, W. R.-College of Engineering and Applied Sciences, Arizona State University, Tempe, AZ 85287, USA VICARIO, G. 8.-Department of General Psychology, University of Padua, 35100 Padova, Italy

X

LIST OF THE DISCUSSANTS BERRIDGE, K.-Department of Psychology, University of Michigan, Ann Arbor, MI 40104, USA BRAINARD, D. H.-Department of Psychology, University of California, Santa Barbara, CA 93106, USA BRUCE, V.-Department of Psychology, University of Stirling, Stirling, FK9 4LA, Scotland. BURIGANA, L.-Department of General Psychology, University of Padua, 35100 Padova, Italy BURTON, M.-Department of Psychology, University of Stirling, Stirling, FK9 4LA, Scotland. ENNIS, D. M.-Philip Morris Research Center, P. 0. Box 26583, Richmond, VA 23261, USA HATFIELD, G.-Department of Philosophy, University of Pennsylvania, Philadelphia, PA 19104, USA KILLEEN, P. R.-Department of Psychology, Arizona State University, Tempe, AZ 85287, USA LABERGE, D.-Department of Cognitive Sciences, University of California, Irvine, CA 92717, USA LOCKHEAD, G. R.-Department of Psychology, Duke University, Durham, NC 27706, USA LUCCIO, R.-Department of Psychology, University of Trieste, 34100 Trieste, Italy MASIN, S. C.-Department of General Psychology, University of Padua, 35100 Padova, Italy NEISSER, U.-Psychology Department, Emory University, Atlanta, GA 30322, USA ONO, H.-Psychology Department, York University, North York, ONT M3J 1P3, Canada RAMACHANDRAN, V. S.-Neurosciences Program, University of California, San Diego, CA 92093, USA ROBINSON, D. N.-Department of Psychology, Georgetown University, Washington, DC 20057, USA SWANSTON, M. T.-Dundee Institute of Technology, Bell Street, Dundee DDl IHG, UK VALLORTIGARA, G.-Institute of Philosophy, Pedagogics, and Teaching of Modern Languages, University of Udine, 33100 Udine, Italy ZANFORLIN, M.-Department of General Psychology, University of Padua, 35100 Padova, Italy

Moreover, it must be avowed that percepfion and what depends upon it cannot possibly be explained by mechanical reasons, that is, by figure and movement. S u p pose that there be a machine, the structure of which produces thinking, feeling, and perceiving; imagine this machine enlarged but preserving the same proportions, so that you could enter it as if it were a mill. This being supposed, you might visit its inside; but what would you observe there? Nothing but parts which push and move each other, and never anything that could explain perception. GOTTFRIED WILHELM VON LEIBNIZ, 1714

Dear reader or, better still, dear lady reader, recall the bright, joyful eyes with which your child beams upon you when you bring him a new toy, and then let the physicist tell you that in reality nothing emerges from these eyes; in reality their only objectively detectable function is, continually to be hit by and to receive light quanta. In reality! A strange reality! Something seems to be missing in it. ERWIN SCHRODINGER, 1959

This Page Intentionally Left Blank

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

3

TOWARD A NEW BEHAVIORISM William R . Uttaf College of Engineering and Applied Sciences Arizona State University, Tempe, Arizona

ABSTRACT This essay is a call for a modification of the basic paradigm of perceptual psychology. Based upon an earlier work (Uttal, 1990) in which I argued that neither a cognitive nor neurophysiological reductionist approach to perceptual science was likely to prove viable, the present essay carries the argument a step further. A new behaviorism is suggested that is mathematically descriptive, nonreductionist, holistic, empiricist, rationalist, and multidimensional. The meanings I attach to these terms are clarified by a short lexicon and the desired properties of the new behaviorism are spelled out.

This essay is a call for a basic revision in the paradigm of contemporary perceptual psychology. It is based upon an earlier discussion (Uttal, 1990) in which some of the barriers that prevent us from linking neural, cognitive, and behavioral levels of inquiry were examined. In the present essay, the next stage of the argument is presented; here I consider what implications such barriers have on what perceptual science can and should do. I argue that the swing of the theoretical pendulum that has oscillated, on the one hand, between recent emphases on elementalist psychobiological reductionism and inferential speculation about underlying cognitive mechanisms and, on the other, earlier positivistic views captured under the rubric of molar behaviorism, is once again about to swing from the former to the latter. To support this argument the past and present states of the foundational epistemological premises of perceptual psychology must be explored.

4

W.R W

During the last century, psychological theories have alternated between the two poles I have just briefly characterized. The nonreductionist, behavioral tradition eschews both neural and cognitive reductionism. One way to appreciate what behaviorism means and what it does not is to note that it assumes that the transforms, operations, or processes executed by both kinds of mechanisms-the cognitive ones and the neural ones-are private both to the scientist and the individual experiencing them.’ However, contrary to conventional wisdom, most behaviorists accept both of these response types to be as real as the behavioral responses that are interpersonally communicable. Jokes about the use of the word ”mind” grossly misinterpreted serious behaviorist doctrine. A radical behaviorism, like its sister epistemologies-logical positivism and logical empiricism-asserts that the only data that have utility for the student of the mind are the observed responses of an organism. To invent intervening variables or hypothetical constructs (e.g., sensations and perceptions), implied the violation of laws of mathematics or principles of parsimony and created conflicts of ”data languages.” The currently dominant alternative approaches to perceptual psychology-reductive cognitivism and neuroreductionism-assume, on the other hand, that behavioral responses can sometime illuminate the underlying mechanisms. These mechanisms may be either neurophysiological structures presumed to directly account for the generation of the observed behaviors or cognitive operators that participate in transforming information and thus selecting or shaping behaviors. Even more fundamental to the reductive approach is the idea that, in principle, observed behavior can be a window into mental processes. Nonbehaviorist science is based on the hope that our research will ultimately permit us to infer unique internal explanatory mechanisms given enough experiments and “converging” experimental evidence. It must be emphasized that there seems to be no essential disagreement between either school of thought with regard to the reality of mental processes; they differ only with regard to their attitudes towards the accessibility of underlying mechanism through input-output (i.e., behav-

Throughout this chapter I will make use of some terms that have come to have specific meaning for me, but that may create some confusion. For this reason, I believe it judicious and useful to insert a mini-lexicon at this point. The words that are particular problems are (1) Mechanism; (2) Structure; (3) Operator; (4) Process; (5) Operation; (6) Transform; and (7) State. The following meanings hold for this chapter. (1,2, and 3) Mechanism, Structure, and Operator: All of these terms refer to a component of a system that does something to information. (4, 5, and 6) Process, Operation, and Transform: All of these terms refer to what is done to the information. The general distinction is between structure and function. (7) State: This term is a little more difficult to tie down but I mean it to refer to the configuration of a mechanism, structure, operator.

T m d a New Bsllaoiorism

5

ioral, stimulus-response, psychophysical) experiments. The great modern behaviorist B.F. Skinner (1963) has said: An adequate science of behavior must consider events taking place within the skin of the organism, not as physiological mediators of behavior, but as part of behavior itself (p. 951).

and elsewhere: The relation between an analysis of behavior as such and physiology is no problem. Each of these sciences has instruments and methods appropriate to part of a behavioral episode. There are inevitable gaps in a behavioral account (p. 782).

Clearly Skinner neither rejects the physiological basis of behavior nor the monist point of view. It is only the validity of introspective reports, the vagueness of hypothetical constructs, or any presumption of intervening (internal) events that he questions as he eschews the questionable reductionism of mental constructs and physiological mechanisms from behavioral data. Other criticisms of Skinner’s behaviorism (e.g., that it was not theoretical) seem quaint in light of many of the variables that Skinner himself used in his written work. Another important modern behaviorist, Peter Killeen (1988) has clarified the falsity of this criticism as he emphasizes both Skinner’s deep theoretical intuition and his repeated use of concepts such as the ”reflex reserve” as models of the forces that drive behavior. Killeen points out that Skinner (1953) does not deny the existence of inner states, but rather places them in another scientific context: The objection to inner states is not that they do not exist, but that they are not relevant in a functional analysis (p. 35).

Skinner, therefore, was simply designating mental and physiological mechanisms to be irrelevant, not denying their reality. In this light it is clear that the essence of Skinnerian behaviorism was that theories should be formulated in the concepts, terms, and logical units (Le., the language) from the same level whence came the empirical observations. The influence of his logical positivist, operationalist philosophical heritage is apparent when viewed from this point. The father of modern American behaviorism as we know it, J. B. Watson, was clearly a materialist and a reductionist. Watson’s (1925) text of behaviorism is replete with physiological information and implied explanations. It is clear that he was, in fundamental principle, a reduction-

6

W.RW

ist, not just to physiological entities but to the physical elements themselves. Physiology was merely an intermediate step interspersed between the ultimate source of the physical forces and behavior itself. The radical behaviorist most committed to theoretical elaboration was C. L. Hull (1943). Hull proposed the development of a "hypothetical-deductive" system that was construed in the language of a single level-the observable molar behavior of the organism. Nevertheless, mysterious forces such as "drive" appear throughout his system as evidence that his behaviorism did not entirely reject inner states. Hull, therefore, also does not appear to have denied the essential physiological basis of behavior or even the influence of mental states. They were, in fact, a critical part of his hypothetical-deductive system. What the behaviorists were essentially championing was an emphasis on empirical data collection of the physically and interpersonally communicable (as opposed to data that was inferred rather than measured) and, with the exception of Hull, descriptive theory (as opposed to reductive pseudophysiology.) They argued against reductive theories, not theories in general, and against fallacious attempts to measure those responses that were, in fact, intrapersonally private. Their argument was not against mental or neurophysiological reality, but against false bridge building between behavior and imperfectly measured (or, even worse, unmeasured) internal states and mechanisms. This tactical difference between behaviorism and reductionism in either its physical, neurophysiological, or cognitive forms, however, is not a small matter. The crux of conflict between these two points of view over the accessibility of mental and physiological processes by behavioral experiments is the fundamental intellectual focus of a persistent controversy in experimental psychology and, from some perspectives, the key to understanding the history of our science. The oscillation between these two points of view has been continuous during the first century of our science. Mental and neural processes have been respectable objects of psychological inquiry or not during this century depending upon which point of view was currently in favor. Currently we are at a peak of interest in neural and cognitive reductionism. What some of us believe are fantastic claims are routinely being made. A major theme of this popular perspective is that behavioral responses directly implicate specific neural or cognitive mechanisms. The main argument of the present essay is that having now demonstrated that there are more or less formal and logical proofs that neural or cognitive reduction is not feasible (Uttal, 1990), it is appropriate to reconsider what behaviorism is and whether or not we should return to this currently unpopular approach to the study of psychology.

Toward a New Behaviorism

7

These two traditions-positivistic behaviorism, on the one hand, and reductionist psychobiology and cognitivism, on the other-had their origins in eighteenth century empiricism and seventeenth century rationalism, respectively. Each school of thought has been subsequently influenced by positive intellectual developments in other cognate sciences (evolutionary theory, neurobiology, logical positivism, computer science, etc.). However, each also responded negatively in reaction to what were perceived to be the inadequacies of the other. For the past quarter century or so, perceptual psychology, driven by the extraordinary developments in computer science and neurophysiology, has been heavily reductionist and elementalist well as mentalist. Indeed, these are the defining characteristics of the cognitivist approach to experimental psychology in general. Most of us interested in perception went along with this influential school of thought.2 The relevant modem formulation of the mind-brain perplexity-can we explain perceptual experience in terms of neural processes?-has been mainly answered by contemporary perceptual theoreticians and by neuroscientists and neural net theorists (connectionists) in the affirmative. All, in one form or another, champion a neuroreductionist approach. The nonneural corollary queryIs it possible to infer the underlying mental processes from observed behavior?-has also been affirmed in the current Zeitgeist. The reasons for the present enthusiasm for reductive explanation are several. Such a perspective is consistent with the enormous contributions that the philosophy of pragmatic materialism has made in the past century in western culture. However, I believe that the main reason behind the popularity of contemporary reductionism of cognitive processes is a universal appreciation that we have done very well indeed in analyzing how peripheral nervous system components communicate information from one part of the system to another. This indisputable success in understanding what are mainly peripheral sensory and motor communication processes has bred in perceptual psychology a powerful illusion that we are on the verge of explaining the neural representation of integrative (i.e., more central, more complex) mental processes such as perception and learning in the same way. However, I have argued (Uttal, 1981, 1988, 1990) that the communication aspects of the peripheral visual nervous system, for example, actuOne mystery of modern psychology that has not yet been answered is why the “cognitive” approach to experimental psychology has been presented as virtually a new science, i.e., cognitive science. It seems to many of us that what actually has happened is a more or less natural evolution of classic and conventional experimental psychology. The problems studied are generally the same. The addition of new techniques from computer science, neuroscience, linguistics, or a number of other modern approaches does not change the substance of the challenge faced by experimental psychologists.

8

W.R w

ally have little to say about how the activity within the enormously intricate integrative networks of neurons in the brain transform into or represent perceptual experience. We do not even know where the psychoneural equivalent of perception is localized, if indeed, this mental process has a unique and singular locus in the brain. The data are increasingly abundant that suggest that visual perception is the outcome of neural processes that are, quite to the contrary, widely distributed throughout the brain.3 At an even more detailed level, and in spite of some enthusiastic hopefulness, there is no one who has successfully provided any conceptual links or even compelling suggestions of how the activity of neurons and neuronal nets could instantiate the reported perceptual experiences even if we did know where they were. The impetus toward false reductive explanations has been further enhanced by successes in the artificial intelligence field in simulating or analogizing behavior processes. It must be recognized, to the contrary, that the many applied computer vision and Artificial Intelligence models of human form perception, however useful they may be and however well they mimic the properties of human vision, are not necessarily valid explanations or theories of human vision. Indeed, it can be argued that some models (such as “expert systems’’ and list processing languages) are a complete surrender of the hope that we can really model human mental processes. These table-lookup operations clearly do not model the way human associative thinking works, but simulate the behavior by logics and mechanisms that are beyond a doubt entirely different than those used in human cognition. It is essential that the relationship between imitation by an analogy and reduction to homologous mechanisms must be clarified and understood. While we can admire and respect the practical and useful accomplishments of this field of engineering application and development (i.e., AI), we must rid ourselves of any misconception that such engineering tools are any more likely than any other model to be valid theories of human perception. Nevertheless, perceptual psychology, just as many other forms of psychology, has profited enormously by representing itself as a reductive science. The assurance of our profession to our supporters, patrons, and to society at large has been that we are not just a descriptive science, but a reductively explanatory one. The implicit promise has been, at one time or another, that of either neural or cognitive process reductionism. This terribly ambitious pledge of our profession has, thus, been that sooner or later In particular, Van Essen, Anderson, and Felleman’s (1992) and Allman’s (1981) work, which has uncovered dozens of visual areas in the primate brain, strongly argues for a widely distributed locus for the neural mechanisms that are the psychoneural equivalents of visual experience.

T m d a New Behaviwism

9

we will be able to answer questions of underlying localization, mechanism, function, and process in terms of neural and cognitive processes. Theory in perceptual psychology, though rarely achieving the promise, is presented as reductive and explanatory in the sense that it is asserted that the underlying neural or cognitive mechanisms are being assayed, if not exposed, by psychophysical or other behavioral tests. The contrary view, that the goal of internal structure analysis is actually unobtainable and thus irrelevant, is at the foundation of the behaviorist point of view. As discussed earlier, modern behaviorism originally emerged based on psychological and philosophical arguments that argued against the accessibility of internal mechanisms. But, there is another set of more formal arguments that can be mentioned that all support a nonreductive behaviorist approach. I (Uttal, 1990) have reviewed some of the mathematical, physical, and logical arguments that contend that psychological (i.e., stimulus-response, input-output, etc.) methods are, in principle, (except in the most extraordinary cases where additional macro-anatomical evidence is available) incapable of resolving disputes between alternative theories of internal structure or mechanism. I have concluded that reductionism in perceptual science (and probably throughout the psychological domain) is most likely to be an unobtainable goal. The arguments for this conclusion are exclusively formal. That is, they did not depend upon any equivocation concerning the lack of existence of mental processes, or any philosophical speculation about reductionism. Rather they are the direct conclusions of mathematical and physical principles that have emerged in recent years that have been all but ignored by psychologists and other behavioral scientists. The arguments assert that there are provable, formal in principle difficulties in linking the inferred mechanisms with the observed behavior. These arguments come from combinatorial mathematics, the theory of chaos, physical principles such as the second law of thermodynamics, generally accepted engineering limits on black box experiments, theorem from automata theory, and Godel’s incompleteness theorem. The conclusions drawn are also based on a consideration of the fundamental nature of mathematics as a method of analogy and description rather than homology and structural analysis. The reader is referred to that chapter (Uttal, 1990) for details of these arguments. The point is that, even without introducing much less well defined ideas such as the nature of consciousness, awareness, mental experiences, or any of the other conundrums that drive much human fancy as well as serious thought, it is possible to, if not prove, at least to reasonably argue, that any attempt to develop a reductionist psychology based on behavioral measures is doomed to failure. The disappointment is that so many

10

W.RW

members of our community uncritically refuse to acknowledge the same constraints and limits on our complex and multivariate science that have been accepted in comparable situations by students of much less complex problem areas. Perceptual psychologists deal with processes that are conceptually closer to the neural mechanisms than some of the higher level cognitive processes. Yet, even at the perceptual level it seems clear that the association of process and function is an overwhelmingly difficult, if not usually impossible, task.l Accepting this difficulty, given the relative orderliness of the stimulus material, the relative simplicity of the sensory nervous system, and the more than less direct isomorphism between structure and representation in the perceptual domain, it seems even less likely that higher cognitive functions should be candidates for the kind of reductive explanations that are often implicitly and sometimes explicitly promised by contemporary c~gnitivists.~ Of course, any discussion of an issue such as the present one that opens by expressing the caveat that observed behavior or neural response may be neutral with regard to mental processes (or vice versa) immediately runs the danger of being labeled as some kind of a neodualism. It is essential for the reader to appreciate that the conclusions I draw and the recommendations I present in this chapter are not based on any kind of a dualism, either explicit or cryptic. Quite to the contrary, the conceptual foundations of my approach to perceptual science is based on a highly monistic metaphysics-that mental events are real actions of some kind of a physical (i.e., neural) substrate. This metaphysical (in the sense of the philosophical discourse that is concerned with the nature of reality) materialism, however, does not diminish the argument that an epistemological dualism (in the sense of the philosophical discourse that is concerned with how we can achieve knowledge)becomes necessary as we seek the limits on what we can know. The dichotomy between a metaphysical monism and an epistemological dualism has been referred to as theory dualism by Churchland and Sejnowski (1989). To point up the formal mathematical arguments that argue against neuroreductionism as an obtainable goal, I argue, is not to deny the materialistic basis of mental processes. It is comparable to the computer scienOnly in a few specific situations can definitive statements be made of sensory mechanisms. Anatomical facts such as our binocular viewing system or the crossover of visual signals at the chiasm are among rare situations where behavioral tests can make conclusive statements about internal structure. It is interesting to observe the evolution of thought from the simplistic neural net hypotheses of the early connectionist writings (Rumelhart, McClelland, & the PDP Research Group, 1986;McClelland, Rumelhart, & the PDP Research Group, 1986)where the nodes of a connectionst networks were explicitly neurons to the more recent view that the nodes are only “symbolic” junctions at which information is interchanged with varying weightings.

T m r d a New BehaoiwiSm

11

tists consideration of the computability of an algorithm or sohabilify of a problem. It is not equivalent to saying that the problem cannot be expressed in words, numbers, or other symbols or that the complex situation cannot exist. After all, we exist and think and, therefore, neurons in the aggregate can produce all of the wonders of thought. It is, however, an expression of the difficulty and probable impossibility of carrying out an analysis of the complex situation. In other words, along with the other theory dualists, I assert that a monist metaphysics can coexist with a dualist epistemology within the rubric of a respectable scientific enterprise. The goal of the remainder of this essay will be to explain why it should happen, why such a neobehavioral, nonreductionist approach is the scientifically most defensible position, and why perceptual psychology should take this direction in the future.

SOME DEFINITIONS Before embarking on the arguments that support my contention that it is time for the theoretical pendulum to swing back to a revised form of neobehaviorism, it is necessary to define some of the terms that I must use throughout this chapter. The same words often have different meanings to different people; precision in definition at the outset may minimize misunderstandings later.

Experimental Psychology The empirical, data driven, theory oriented science of mind constrained by the intrapersonal privacy of mental events to measurements of interpersonally communicable behavior. Some experimental psychologists are cognitivists; some are behaviorists. They differ mainly in the degree to which they believe that we can infer underlying neural and cognitive processes from behavior.

Cognitivism The most recent evolutionary stage of experimental psychology. Cognitivism is characterized by beliefs that reduction from behavior to the elements of neuronal (or neuron-like)networks and mental processes is an obtainable goal and that inner mental processes can be studied and understood by input-output methods. Cognitivism, like behaviorism, accepts the reality of mental processes and neural mechanisms, but diverges from behaviorism in supporting the premise that behavioral data can be used to specify their nature. Cognitivists are implicitly, if not explicitly, reductionists.

12

W.RW

Behaviorism A school of experimental psychology, currently out of fashion. Behaviorism is characterized by the belief that the scientific exploration of mental behavior is constrained to interpersonally communicated behaviors. Introspective reports, while also interpersonally communicable, are eschewed as being too far removed from the actual mental processes and too polluted by irrelevant processes. Most modem behaviorists, like their cognitive counterparts, accept the notion that mental processes and experiences occur and are real and that some equivalent brain state must correspond to each cognitive process and each mental state. However, they deny that behavior can be used as a means of inferring the nature of the internal events. Behaviorists prefer to keep their theories limited to the same level as their data and are implicitly, if not explicitly, anti-reductionists.

Brain State A ”brain state’’ refers to the momentary arrangement of the physical and chemical mechanisms of the biological structure called the nervous system. Brain states are, in principle, independently measurable without recourse to either overt behavior or introspective reports, although, in a practical sense, they rarely are. The particular level of brain state that seems relevant to (i.e., is the psychonarral equivalent of, mental or cognitive processes is the pattern of organization of neurons into great networks with identifiable variations in pattern. Different patterns of organization, it is assumed, are different mental states. That is, the neural state is the physical instantiation of the set of processes that results in the self aware mental entity that is the essential ”me” to each of us. The organization of the neuronal network, therefore, should be considered to be the ”proper level of inquiry” if one is interested in analyzing mental processes at the physiological level.

Mental States Mental states are internal events which, inherently, can only be “witnessed” or experienced by the individual. Their existence can be signaled to others either verbally or physically (two kinds of behavior) but there is no way of ascertaining whether their true, let alone precise nature, has been communicated. That is, they are intrapersonally private and cannot be directly examined by another person. Obviously, behavior and mental state can be disassociated; this is the basis of the profession of acting. The ability to do so also alleviates much human conflict. Mental states come in a wide variety (percepts, feelings, motives, learning, etc.). Mental states, however, are inadequately described, at

T m r d a New Bsllaoiorism

13

best, by a host of illdefined terms collectively categorized as “emotions” (e.g., rage and love) or “percepts” (e.g., red and loud). Because mental states can only be measured indirectly through behavioral measures and introspective reports, the problem of linkage between behavior and mental state is as challenging as the linkage between mental states and brain states.

Behavior Responses made by an organism that can be interpersonally collectively witnessed and reliably measured by an outside observer.

Reductive Explanation A precise statement of the particular internal mechanisms (neural, logical, or cognitive) by means of which a system carries out interpersonally observable behavioral functions.

Reduction An analysis of a system into its components. Churchland and Sejnowski (1989) define reductions ”as explanations of phenomena described by one theory in terms of phenomena described by a more basic theory.” In each case, the basic concept is the same-molar roperties are deciphered in the terms of the constituent micro elements. Obviously, there is a hierarchy of elements, each step of which is ”micro” to the one above it.

?

Description A ma thematical (or neural or computational) representation of the functions, processes, or transformations carried out by a system that maps the course of events (i.e., the behavior) of that system. Process description is carried out in a way that is separable from assumptions and facts about the specific internal mechanisms that might effect the processes. I argue that most models and theories are, at best, descriptions no greater in explanatory content than an equation fitting a curve. Therefore, formal models are neutral with regard to internaI structure. While such a curve may allow us to predict behavior, it cannot tell us anything specific about the infinity of plausible and possible analogous mechanisms that may acChurchland and Sejnowski (1989) list three dassic arguments that have been invoked against mind-brain reductionism: “Neuroscience is too h a r d ; ”multiple instantiability”; and “the intentionality of psychological states” (pp. 19-20) for which they provide three respective counter arguments: a. progress is being made; b. so what?; c. intentionality is the raison d’ttre of mind, so lets not throw it out (pp. 21 ff.). It seems to me that they miss the most important set of arguments, the mathematical and physical ones, that constrain reductionism in other sciences. These additional arguments, as noted, have been detailed in my earlier paper (Uttal, 1990).

W.RW

14

count for that behavior. There is an illusion, when dealing with complex theories that involve specific parameters or components, that we can say something about internal mechanisms. This illusion is just that, a fallacious conclusion, and does not mitigate this criticism. Even the most complex mathematical or formal theories are totally neutral with regard to internal mechanisms. (See Uttal, 1990, and elsewhere in this chapter for more on this point.)

Theory Clearly, what is meant by a theory must change in the light of these more precise descriptions of explanation and description. Theories are the heart of science in that they extrapolate beyond local data to general ideas. Theories may be microscopic or macroscopic. Thus they act as syntheses and compilations, organizing and arranging knowledge. But, if the argument I have presented is correct, they can only be process descriptions and not explanatory reductions in any situation that relies solely on behavioral data. Theories often introduce concepts such as charge, gravitation, emotions, and drives that can help to simplify and organize knowledge. When they do, however, they are describing relationships and not explaining the nature of the machinery that produces those energizing forces.

Phenomena The word phenomenon is clouded by so much excess meaning that it is important that I make clear exactly how I use it later in this chapter. To me, a phenomenon is any percept, finding, observation, functional relationship, law, or other experiential or experimental descriptor of the interpersonal responses produced by stimulus scenes. Measurements of phenomena constitute the empirical data base of experimental psychology. They are the analogs of atoms, molecules, cells, organs, animals and plants that make up the observational data base of the other biological sciences. With these definitions in hand, we can consider some suggestions for the future course of a sensible kind of perceptual psychology.

SOME THINGS TO DO Toward a New Taxonomy Experimental psychology, a new science that has developed mainly within the last century, has neglected one of the most important tasks of any science-the organization and classification of its data base. It is al-

Toward a New BslwvioriSm

15

most as if this science had been fixed at some preLinnean level of thought. Rather than organizing our discoveries into a coherent taxonomic system, modern experimental psychologists seem to behave like a huge disorganized mass of “butterfly collectors’’ rather than scientists-theorists-organizers. It is only in the rarest instances that experimental psychologists have sought out the common features of the phenomena that they have uncovered. Rather, experimental psychology is usually taught and studied as a melange of microuniverses, each of which seems unconnected to any other. This leads to great difficulty in replication of findings, so much so that the very data base of our science is often q~estionable.~ Many models of how an ideal behavioral science should progress are available to us. Linneus pioneered taxonomy for biology. Mendelleev’s periodic table played the same critical role for chemistry and ultimately led to another taxonomy, that proposed by Gell-Mann (1964) consisting of such categories as hadrons and quarks. The important thing is that, in each of these cases, it was not simply a matter of creating a pretty picture from a chaotic jumble, but rather of providing a pattern, form, or organization of the data of a science that had enormous theoretical implications for all subsequent work. The Linnean system was a necessary precursor not only for biological theories of evolution, but ultimately for all other biological studies. The periodic table led directly to the atomic theory of matter and ultimately to what we now believe to be the ultimate in our search for the basic particles of n a t u r e t h e quarks. The dual questions that we should ask are-Why did psychology not follow this same reasonable course? and What might have been if it had? The former question, it is possible to answer by noting the fact that the dimensions of psychology are so much more numerous and the interactions so much more complex that any potential order was always obscure to the latent taxonomist. But this is no excuse, because even beset by this complexity, it should have been possible to divide the field of experimental psychology into subsets that should have been amenable to some kind of systemization. Why it was not, like the other sciences, so organized remains a mystery. The second question is also very difficult to answer in specific detail, but it does Seem certain that a greater taxonomic effort might have paid In a recent extensive review of the field of form vision (Uttal, 19881, I was surprised to discover that this chaotic approach to our saence seems to even have affected the quality of the data that we depend upon for insight and knowledge. Amazingly few experimental results were solid, replicable, and permanent. Most seemed to be fragile and depend in an astonishingly delicate way on the specific conditions of the experiment or the range of the parameters investigated.Part of this is due to the complexity and power of the human percep tud system. 1 am becoming increasingly convinced, however, that much of it may be due to a lack of organization of the subject matter itself.

16

W.R Uthl

off with substantial insight into the fundamental principles of perceptual psychology as opposed to the grab bag of isolated phenomena that fills the literature in this field. Psychology has classically been explorations into "little science"-situation-specific theories, isolated experimental results, and cute, but cryptic, phenomenal demonstrations-rather than a science graced by a unified set of principles or grand unifying theory. The result of this internal fractionation has been a transitoriness of theory. It has led to a conceptual isolation among scientists in this field and seriously inhibited our effort to produce universal accounts of perceptual function. This is not surprising: If one does not know how one's work is related to that of his colleagues, how can one be expected to see the commonalties? It has only been in recent years that a few efforts towards unification have been made (Uttal, 1981; Newell, 1990) A major difficulty in taxonomy generation should also be noted. Very often, we discover that what seem to be similar paradigms may assay very different processes. (E.g.,see the work of Cheal & Lyon, 1993.) Small changes in experimental design may produce vast differences in results (i.e., phenomena in the general sense defined earlier) as we cross over, without appreciation, from assaying one process to another. Two vastly different experimental paradigms, on the other hand, may have actually been probing the same perceptual process. Strictly behavioral data, therefore, may not provide an adequate foundation for a useful taxonomy. A better alternative may be one based on theories and putative explanations. The difficulty of the taxonomic task generated by the complexity of the subject matter, notwithstanding, I am convinced that progress can be made. There is always the hope that from such a taxonomic effort might come essential integrating concepts that will lead to a breakthrough in psychology of the same import as the ones that occurred in biology and chemistry. Of course, there can be no guarantees.

A continuation of Empirical Research If taxonomy has been insufficiently emphasized, there is no question that the search for new perceptual phenomena has not. From the days of Grosseteste, through the teaching of Bacon, to the "methode" of Descartes; from Fechner's mystic psychophysics, to Wundt's Leipzig laboratory; through the many schools of psychology, both rationalist and empiricist, to today's modem conceptualization of cognitive science, the empirical quest has been continuous. This is as it should be. Ideas must be tested in experiments. We must gain knowledge, not by authority or speculation, but by test and observation. An enormously sophisticated methodology has grown up in experimental psychology that is dedicated to the

Toward a New Behaoiorism

17

fulfillment of this foundation premise. The prototypical scientist is the experimenter. The archival journal, containing empirical articles reported in a firmly prescribed and highly stylized form, is the most distinguished and prestigious outlet for one’s “scientific” activities. For many, science is nothing but controlled observation or experimentation; anything else is eschewed as not quite respectable. (Another hint about why taxonomic efforts have been held in such low repute is implicit in these statements.) From one perspective, this is as it should be. Speculation without experimentation would be sterile philosophy and a data free taxonomic effort would be pointless. However, there are some substantial changes to the contemporary experimental strategy that are necessary as our science matures and we begin to understand that it is most like the interaction and arrangement of the elements that is more important than their nature. In the past the prototype of experimental perceptual research was the psychophysical experiment in which a single stimulus dimension (S) is manipulated and a single behavioral response dimension (R)measured. Formally, this can be represented as:

All other dimensions of the stimulus were ”controlled” to the maximum extent possible. This is the embodiment of the advice given to us by Descartes in proposing his “methode.” However, if there is anything certain in perceptual science, it is our appreciation that organisms do not really function in this manner. As useful and as simplifying as the analytic “methode” is, it must now be appreciated that such an elemental, analytical approach often obscures the fact that organisms perceive on the basis of multiple cues, dimensions, and attributes. It is the interaction among and combinations of these different properties, not a mechanical and automatic response to a single dimension or attribute, that accounts not just for the richness and variety of organic behavior, but also for the extraordinary fact that we can perceive at all8 A more accurate formularization of the relationship between responses and stimuli would look like this:

It is becoming increasing evident that no single attribute can be decoded sufficiently well to avoid some kind of perceptual blindness.The emergence of perceptual “quality” seems to require comparisons of different dimensions or athibutes of the stimulus.See my discussion of this matter in Uttal (1981, ch. 11).

18

W . R Uttal

where S, tabulates the various attributes of the stimulus, SSS ,,, ... suggest the interaction of multiple attributes, M e m denotes the collective memories and experiences of the organism, Set denotes its current state, and etc. denotes a host of other variables that may influence the reSp0nSe.g

Obviously there is still ample necessity to control extraneous and irrelevant variables. However, there is also a potential richness of thought and depth of understanding in considering any perceptual phenomenon to have multidimensional, rather than unidimensional, determinants. Instead of computing correlation coefficients between a single independent variable and a single dependent variable, efforts should be made to make all contemporary experimental designs multicorrelational. Rather than plotting a twodimensional graph of obtained data, we should take advantage of modern data visualization techniques to display the joint effects of two, three, four, or even more stimulus dimensions on the behavioral response. To do so would characterize the behavior of perceiving organisms more realistically and more thoroughly than was ever possible with a simple one-to-one relation between a single stimulus variable and a single response variable. In a related vein, our entire approach to psychological experimentation has been that of analysis. That is, we have striven to take the complex stimulus apart and present it as someone might dissect a frog and then measure the simplest possible response. A formidable challenge awaits us, however, as our science evolves towards a new synthesis. As we discover how the various attributes of a visual stimulus, for example, affect a perceptual experience, is it not possible that we will also be able to suggest how the various dimensions might be reconstituted so that a full perceptual experience could be regenerated from the partial stimuli? Such an approach would have potential practical outcomes (it would be possible to design efficient communication links that passed only the necessary information to a display, for example). Even more important, however, is the potential for stimulating us to achieve new insights into the rich complexity of human perception in ways that may not even be imagined a priori.10

It should not go unacknowledged that there are limits to this multiple variable approach. Experimental designs of this sort may simply be too complicated to carry out and new paradigms for combining experimental conditions in some rational way are required. Nevertheless, Equation 2 is reality, not Equation 1. lo This is hardly unique to experimental psychology. No science can anticipate what the outcome, practical or theoretical, will be a of a fact undiscovered, a place unexplored, or an idea untested.

Toward a New BehauM-ism

19

A new Role for Theory The role of theory must also change as a new behaviorist approach to experimental psychology matures and becomes more widely accepted. The naive view that a theory can peer more deeply into the inner workings of some system than the data on which it is based must be abandoned. It seems imperative that we accept the fact that all such syntheses are at best descriptive and at worst untestable. All that really can be said is that the model and the reality exhibit a fit that is sufficiently close that one can be accepted as a description or analog of the other. Allusion to the overly optimistic expectation that we can converge on knowledge by virtue of convergent operations is probably more a fantasy than a reality. Theories based on input-output analyses alone always will permit an infinity of possible mechanisms (Moore, 1956) and require infinite numbers of experiments to resolve even simple questions of internal structure. In this light, theories of mental processes, however they may have been intended to be reductive, should come to be considered more akin to summaries and organizations of knowledge than new knowledge generating media. Formal theories of the mathematical or computational kind can be extremely powerful, of course, in their ability to predict the course of events in some system. Such formal theories also have the power to suggest ways in which a certain system may not function by highlighting the impossibility of a particular sequence of events. Theories cum process summaries also have the power to clearly describe the process transformations that can occur even if they cannot distinguish among the many possible mechanisms that might account for those transformations. Most of all, theories are summarizing and organizing tools, that help us to understand what the message is that our data is collectively asserting.'l However powerful these real roles of theory are, these capabilities do not support the wistful hope that theories are potentially reductive. What theories do well is to aIIow our imaginations to go beyond the data in the same way that metaphors and heuristics stimulate speculation. They cannot, however, be either definitive or reductive. At some basic level all theories must be inductive rather than deductive. The ability to predict subsequent steps of performance by mathematical derivations may suggest a reductive role that is actually illusory. It is especially frustrating, therefore, to observe how microscopic most theories of perception are. Virtually all of the so-called theories of perceptual phenomena describe the function of but a single phenomenon (e.g., an illusion, depth from disparity, color appearance, etc.). How much more exciting it would be if global theories of vision as a whole were more prevalent. My group has made a stab at such a global model and recently published the account of our efforts in Uttal, Bradshaw, Dayanand, Lovell, Shepherd, Kakarala, Skifsted, & Tupper (1992). An important effort in a different context is Newell's (1990) work on the SOAR system which purports to be a unified theory of cognition.

20

W.R. Uftal

Given these strengths and constraints, what then is the role of an inductive, summarizing theory. The answer to this perplexity is a simple and compelling one. Theory is the ruison d’&tre of science! It is the supreme goal of all scientific research. It is the ultimately desired contribution and the objective towards which all empirical work should be aimed. Theories are general, inclusive, and comprehensive statements of our understanding of the nature of the world we inhabit. Understanding has not always been a primary goal of behaviorism. Smith (1992) presents a very clear argument that Skinner, at least the early Skinner, was more interested in the prediction and control of behavior than understanding it. Skinner was, as Smith points out, profoundly influenced by Francis Bacon’s pragmatic (as well as experimental) approach to science. Words, of course, are only words, but Smith makes it clear that there are two possible meanings to the word “understanding.” He notes that two “ideal-types of science” exist. The contemplative ideal which seeks to understand the natural world and its causes and the technological ideal, originating with Bacon, which seeks means of controlling, making, and remaking the world (p. 216).

Experiments are merely local probes or assays that help us towards that general understanding. We conduct experiments to provide the grist for the theoretical mill; we do not concoct theories simply to provide a framework for a set of data. The essential idea is that the theory is primary; the data is secondary! “Barefooted” empiricism, devoid of synthetic summary, is a sterile and empty endeavor. Mere data collection, without reason or conclusions, is waste incarnate. Taxonomies can help by collecting, organizing, and cataloging, but even that role is secondary. The ultimate role of science is to summarize and surpass the accumulated data by stimulating general statements of understanding; in other words, to formulate transcendent theories. A theory is, at its most fundamental level, a statement of the universals for the domain of ideas with which it deals. The domain need not be all inclusive; it may itself be a microuniverse of limited extent. Nevertheless, any theory of even a restricted domain should strive for the most comprehensive statement of the nature of that domain as its ideal goal. Thus, the role of the theoretical must never be minimized or ignored if the science is to be of the first quality. The role of the individual experiment is important, of course, but it is a truism that no particular experiment is essential. Should any particular experiment not be carried out, the loss would not be great. Almost certainly another example of the same general point would subsequently become available. If no summary is cre-

Towarda New Behaviorism

21

ated of a body of individually nonessential experiments, however, the loss is profound because the goal of general understanding would not be achieved. Theories come in many guises. Traditionally experimental psychology crafted its theories out of the raw material of data summarized by descriptive statistics. Null hypotheses were generated and then tested to see if statistical differences could be detected that would allow their rejection. If the null hypothesis could be rejected the hypothesis was tentatively accepted. Such hypotheses-driven theories had a tendency to be highly circumscribed and limited to a very restricted domain of inquirysometimes to only an experiment or two. In recent years, theories and models of many different and more general kinds have evolved. Structural models have been developed that associate the behavioral and presumed mental functions with the operations of other devices. Computer programs serve as models of precepts (as well as more complex cognitive processes) and neuroanatomical mechanisms. "Flow chart" models are regularly invoked to simulate or describe cognitive processes. Mathematical models that differ greatly from the statistical ones of the past have been developed that are particularly relevant to the modeling of perceptual phenomena. Analogies drawn between mental and physical systems, a strategy that has a long history, are updated as each new technology or mathematical system emerges. Most recently, some of our colleagues have utilized concepts of chaos (e.g., Townsend, 1990; Skarda & Freeman, 1987) as models of brain and mind systems; others use the language of quantum mechanics (Bennett, Hoffman, & Prakash, 1989); and still others find that the metaphor of waves describes a wide variety of psychophysical judgments (Link, 1992). Whatever the theoretical approach, it is clear that there has been a gradual evolution over the years from micromodels to more expansive macromodels. While there is great diversity in the exact mechanics that is invoked, most interesting steps forward have tended to be more inclusive then was typical of only a few years ago. Whatever the scope; whatever the domain; the important thing is that human progress in acquiring knowledge and wisdom and solving problems depends mainly upon our theoretical achievements. The rest (i.e., the solutions to the practical problems that face us) follow automatically once basic understanding is in place.

Physiological Research In previous sections of this chapter I have spoken of the limits of inpu t-output (stimulus-response) approaches definitively defining the underlying mechanisms. In other instances (Uttal, 1988,1990), I have argued

22

W.R W

that the physiological approach (in which the %lack box” is physically opened) is itself constrained by limits of numerosity, chaotic “apparently” random organization, and thermodynamic principles. In this context, it is important to remember that none of the arguments I have presented, should be misconstrued to imply that I am suggestingany kind of a moratorium or delay in the pursuit of neurophysiological knowledge pertaining to perception. The arguments (probably unnecessary) for the pursuit of neurophysiological knowledge are strong and sufficient in their own right. First, studies that attack the chemical, biophysical, or adaptive nature of neurons, on the one hand, or information communication, integrative interactions, or even the localization of function in the large centers of the nervous system, are abundantly fascinating, useful, and elegant to justify these lines of research even if the nervous system were not the instantiation of mental processes. Neurophysiology, neuroanatomy, and neurochemistry do not have to support the goals of psychological science to justify themselves: They are substantial sciences with their own agenda and important research goals. With regard to their relationship to psychological issues, however, the role of the neurosciences is more controversial than many workers in this field may accept. I (Uttal, 1990) have argued that, in principle, behavioral data cannot be validly analyzed to physiological mechanisms and that physiological data, for reasons of equally fundamental nature, cannot be synthesized to global psychological phenomena. This is the crux of the argument that there are significant barriers that exist between the neural and the psychological research programs. How, then, do we deal with the enormous amount of neuroscientific research that is purported to be directly relevant to psychological issues? My answer to this rhetorical question is that much of the biochemical, anatomical, and physiological research is relevant, but only in a practical, applied, utilitarian manner. It is, however, essentially agnostic theoretically in the context of the mind-brain perplexity. I argue that much of this enormous body of useful and fascinating research offers very little to us in understanding the relationship between brain and mind. Some neuroscientific data is too microscopic, aimed only at the physics or chemistry of the neuronal components or even the subcellular components of these wonderful cells. Some, on the other hand, is too macroscopic only elucidating the relationship between huge chunks of the brain and behavior. The problem, to reiterate an essential point, is-What is the proper level of analysis if understanding the physiological basis of mental processes is the goal? Studies of individual neurons, their parts, and their synaptic machinery, is research carried out at too fine a level. Stud-

Toward a N m B h i m i s m

23

ies of the massive effects of a drug, of electroencephalographic signals, or of the localization of mental functions, while interesting, are attacking the problem at too gross a level to answer this question. For example, let us consider neurochemistry and explain what 1 mean by the assertion that much of neuroscience is ”atheoretical.” Although all of us can look with pride and a sense of relief at the enormous therapeutic progress that has been made with psychoactive drugs, it seems to me that this serious social need has been fulfilled with little or no theoretical significance for the mind-brain issue (other than simply reaffirming that brain states are intimately related to mental states) and with minimum contribution to a theory of how neurons encode or represent mind. We know that the introduction of these drugs into the nervous system may affect some of the great transmitter systems of the brain, inhibiting or exciting synaptic conductivity in a general way. Furthermore, we may know in detail the biochemistry of how these drugs act to reduce or enhance the synaptic process either at the individual presynaptic release site or at the postsynaptic receptor site. However, neither of these two pieces of information, the macroscopic activity of whole systems or the microscopic activity of individual neurons or synapses, speaks at the “proper” level at which mental processes are encoded in neuronal mechanisms. That proper level must be expressed in terms of the detailed organization of the neural network. In fact, we do not know how the chemical conductivity changes actually affect the ultracomplex and unknown web of neural interactions that is the essential (as opposed to the irrelevant) psychoneural basis of mental processes. Neurochemistry, as useful and interesting as it is in its own right and as psychologically active as these wonderful drugs may be, finesses the proper form of the essential mind-brain question-How does neuronal organization (not chemistry) produce mind? Thus, whereas this valuable science profoundly influences and changes the quality of human existence, the development and utilization of these drugs is a more or less successful empirical attack on the very real and tragic problem of mental aberrations, rather than one that brings great depth of understanding to the actual and specific details of how the modified activity of the neural net produces the changes in interpersonally observable behavior and intrapersonally private peace of mind. This science provides the illusion of understanding without actually contributing to answering the great question of how brains encode mind. Other neuroscientific approaches also suffer from this same difficulty-the illusion of relevance rather than real contributions to our understanding of the great mind-brain enigma; that is, they ‘may be practically useful, but at the same time, theoretically sterile in our quest for un-

24

W.R uttd

derstanding how discrete and microscopic neural events encode molar mental processes. This is the key question, not some of the others that have been offered in its place as displacement activities in the words of the ethologists. The compound evoked potentials (e.g., stimulus evoked brain potentials, electroencephalograms) as well as new techniques for literally looking inside the head (e.g., positron emission tomography, nuclear magnetic resonance imaging, x-ray tomography) are all additional examples of this kind of great practical utility, but minimum theoretical significance for the great psychobiological question. All compound potentials, even though they come from the brain, obscure the details of neuronal action by their very integrated nature. They have great utility for solving one problem-they help in localizing areas where critical functions may occur. But, they are not suitable for analysis of the neuronal net any more than the spectacular pictures produced by the exciting new noninvasive techniques for examining brain structure and localization of function. The future of neurochemical, neuroanatomical, and neurophysiological research is not in question. Research should and will continue in these fields because of their intrinsic significance and the probability of potentially important contributions in achieving their own practical and theoretical goals. On the other hand, it does seem appropriate to reinterpret what such techniques mean, what they can do successfully, and what they are forever constrained from accomplishing by their nature.

Towards a New Mathematics Mathematics is a powerful tool; indeed, it is so powerful that in the words of Cutting “it can model truth and drivel with equal ease” (1986, p. xi). However, mathematics, as I have argued previously (Uttal, 19901, is fundamentally neutral with regard to underlying mechanisms. Its formulations are capable of describing the functions of a universe of devices that all may behave the same but may all be based on totally different mechanisms. Thus we have a system of representation that is at once so powerful and so limited that it often provides an irresistible impulse to lead us astray from truth as defined by more valid indicators-the behaviorally measured phenomena themselves. It is not always appreciated that we can extrapolate from mathematical formulae to mechanisms that have no physical reality. The best illustration of this is Fourier frequency analysis-a powerful technique for analyzing complex wave forms or images into an “equivalent” series of simple orthogonal functions. The point to remember in this case is that these functions are fictions! Any waveform, regardless of how it is constructed is capable of being so analyzed. It is all too easy, however, to forget that

Toward a New Bsllaviorisn

25

this means of quantifying and representing waveforms produces fictional components and, in our forgetfulness, to reify those components as real physical entities. What these fictional components really represent is a means of quantifying the qualitative. Shape-a quality+an be represented by numbers with the Fourier approach because any waveform (with a few esoteric mathematical constraints) can be so quantified. The fictional sine waves have no physical reality, however, unlike the spectral components of a visual stimulus, which do. This is one of the problems with mathematics-its seductive tendency to have its intangible abstractions misinterpreted as tangible physical entities. There is another problem, that has also to be considered and that is the inappropriateness of many, if not most kinds of mathematics to the problem at hand-the study of the mind-brain relationship. With the exception of a very few novel and recent developments, most of our mathematics is designed to study rather simple systems. For example, most forms of analysis utilize integral and differential equations that are suitable for studying dynamic systems containing only a few parts. Descriptive statistical approaches are predominantly aimed at finding the central tendencies of sets of multiple data. Inferential statistics seeks interactions between different variables. But, in doing so,statistics obscures critical information about the details of the individual components of the data sets. Much statistical research looks like theory testing. But this is an illusion. What we actually do (if you look closely at what happens when you run a statistical test, is determine whether variables are related. This, in turn, when viewed from the perspective of a series of tests, may help to identify variables worthy of further interest. Most such ”theory testing,” therefore, is really variable identification. New approaches to analyzing neuroelectric data that utilize contemporary ideas from chaos theory (e.g., Skarda & Freeman, 1987) also produce representations and measures that indicate the global behavior of the system rather than the local properties of the neural network that are, from my point of view, probably more germane to the elicitation of mental processes. Another approach utilizes the computer as a quasi-mathematical tool. The power of the computer to simulate and model is one of the most important developments of our times. However, there is also a proclivity towards misinterpretation of what the results of a model may mean when one uses this tool. Computer architectures and programming strategies are essentially feature oriented. Programmed algorithms produced intellectual forces that exacerbated by the nature of the mathematics they represent, push us more and more towards emphasis on features rather than organizational properties of images. The reason for this is simple. We have

W. R Uttal

26

methods for manipulating local regional interactions, but there is both a computer algorithm and a mathematical shortage of methods that allow us to examine or model the broad, holistic organizational attributes of human visual perception. Yet, when one examines the basic nature of human vision-the classic demonstrations and illusions-we are repeatedly reminded of its basically holistic precedence and emphasis. Even such basic properties as color appearance seem to depend more upon the interactions of widely distributed subregions of a scene than upon the wavelength components of the contained objects. The work of the late Edwin Land (1977) in this regard reinforced this argument most emphatically. The point is that modern mathematical analysis techniques are not in general appropriate for the analysis of large scale neural networks. Our science is in great need of some significant breakthrough in mathematical technique that will be suitable for studying the broad, holistic, interactive aspects of vision that are largely obscured by the local elementalist, feature-oriented mathematics currently in favor. In spite of some arguments that such a suitable mathematics is available, it has yet to be adequately demonstrated. Of course, what I am asserting here is another property of the new psychophysics that some of us believe should emerge from a new interpretation. That additional property is based on an old approach, namely the holistic point of view of our predecessors the Gestalt psychologists. This brings us to the next major section of this essay.

THE NEW BEHAVIORISM Given the points of view expressed in the earlier sections of this chapter (which are certainly not a majority view) we must ask and answer the question-What is to be the nature of a new behavioral perceptual science? One set of answers to this question has been given by Killeen (1984). He cites the following criteria for his modern version of behaviorism which he refers to as an Emergent Behaviorism. First, of course, Killeen says that it must be “behavioral.” The important point he makes here is that the significant data must be the data of observed behavior as opposed to introspective reports or inference about hypothetical constructs, either neural or cognitive. Killeen also believes that one must not deny the existence or the causal relevance of mental events. Second, Killeen suggests that it must be inductive and, contrary to the classic Skinnerian

Toward a New Behauwrisrn

27

tradition, allow hypotheses to concern events “at another level.”12Third, Killeen champions a pragmatic standard for his new behaviorism. Here he repudiates those theory generating forces that are based upon fad, fiat, doctrine, or imitation-a repudiation that should guide all science, not just a new behaviorism. Finally, he wisely notes that his ideal of an emergent behaviorism should be “prudent with its resources but not parsimonious.” Again, I agree that this is an entirely appropriate standard for any science. Killeen sets high standards for his emergent behaviorism and, indeed, for any scientific endeavor. There are, however, some additional and somewhat more specific criteria that should in my opinion guide and constrain a new behaviorist approach to perceptual research. In the remainder of this section I shall consider these perception-specific considerations. I believe the following characteristics to be essential if experimental perceptual psychology is to continue to prosper and mature.13

A Holistic Approach Must be Emphasized We must now acknowledge that human visual perception is primarily and initially holistic in its operation. The Gestalt psychologists understood and correctly taught this principle, but their wisdom was not sustained because the computational and mathematical technology that was needed to pursue the holistic strategy was not available a half century ago. One particular reason for this failure still is with us-the appropriate mathematics to describe global relations was not then and is still not now at hand. We need some new mathematical approach and, therefore, have an enormous obligation to convince mathematicians to develop techniques better suited to studying arrangement than parts. A major effort is necessary to develop the appropriate mathematics so that some future equivalent of some ”non-Euclidean” mathematics can be utilized by some future psychological “Einstein” or “Bohr” to make much needed breakthroughs in visual theory. This step is essential if perceptual science is to enjoy the same kind of growth in understanding that has graced the physical sciences. These breakthroughs may require a softer kind of mathematics able to handle different kinds of relationships other than +, -,x, and /. It would be very useful to have available a formal symbol manipuIt is not clear to me if Killeen is accepting some kind of neuroreductionism here or if he is merely reasserting the utility and necessity of some form of postulated mental events. If the former, of course I would disagree; if the latter, of course, I agree. l 3 Some of the following material has been adapted from Uttal (1988). In rereading this material 1 realized that the comments I made there also formed the base of my final recommendations for a new behaviorism in this article. I have expanded the material in some cases and reduced it in others to reflect the evolution of my ideas from then until now.

28

W.R Uttal

lation system that could handle such object relations as ”a lot alike,” ”means the same,” or even “came from the same place.” In other words, we must develop mathematical models that concentrate on quantifying, formalizing, and describing reported perceptua1 phenomena with symbols and relations that are appropriate for this science and are not borrowed from physics or agriculture. It is mandatory that there be a conscious effort to develop techniques that emphasize the global and organizational attributes of a stimulus-form.

Realistic Limits on Theory Must be Elucidated We must determine what limits apply to the primary goal of theory building. I have dealt in a preliminary way with the idea that there are in principle barriers between models and mechanisms in Uttal (1990). But, there is an urgent need for additional efforts to determine what constraints are operating on perceptual science so that we can avoid a naive and enormous waste of theory-building energy aimed at impossible goals. That there should be limits is in no sense a condemnation of perceptual psychologists or of perceptual psychology any more than acceptance of the limits on perpetual motion or speed of light are of physics. That we should ignore clear signals that we may have gone astray is not, however, excusable. Perceptual science can be justifiably criticized for not paying sufficient attention to the logical and mathematical fundamentals before imprudently attempting demonstrably untenable neurophysiological or cognitive process reductionism. I am convinced that few more skeptical combinatorial, automata, or chaos theorists interested in the problems raised by a modern perceptual psychology would do more for the future progress of our science than an army of ”true believers” in the ultimate solubility of all our problems with traditional methods.

The Empirical Exploration of Our Scientific Domain Must be Continued The empirical psychophysical approach in which new phenomena are sought, discovered, and described must be the centerpiece of any new development in this science. This empirical effort, however, should be redirected to emphasize the global or holistic properties of stimuli rather than the local ones currently in vogue. This is the most effective means of diverting the Zeitgeist from what it is to what it should be until such time as a balance and understanding of the many forces that operate in vision can be achieved. A major modification of the paradigm of perceptual research is also called for. Too long have we been unidimensional. It now is reasonable to

Toward a New Behaowrjsm

29

carry out more complex experimental designs that acknowledge the multidimensionality of most experimental scenarios.

Description, Rather Than Neuroreduction, Must be Emphasized Reluctantly, given my persona1 scientific background, I think that we must ultimately abandon the idea that perceptual processes can be reduced to neurophysiological terms by drawing inferences from psychophysical data. Similarly, I do not believe that it will be possible to conclude from vast compilations of cellular neurophysiological data anything about mental mechanisms that is relevant to the fundamental problem of mind-brain relationships. This romantic notion, this will-of-thewisp, this dream, is almost certainly unobtainable in principle as well as in practice if combinatorial, automata, and chaos theories do turn out to be applicable to perceptual science. What we know about the metabolism and physiological functioning of individual neurons, though a distinguished intellectual and scientific accomplishment in its own right, can probably never be transformed into knowledge of how they operate collectively in the enormous networks of the brain to produce molar behavior. Of course, the neurosciences are not completely irrelevant. Considerable knowledge has been obtained about the synapse, the final common paths, and localization among many other treasured pieces of knowledge. It is specifically the unbridgable gap between microscopic cellular neurophysiology and macroscopic mental processes to which I am calling attention.

Description, Rather than Cognitive Reductionism, Must be Emphasized Equally reluctantly, I believe that an appreciation must emerge that the major goal of cognitive psychology-to determine the functional processes that are carried out by the nervous system in perception or, for that matter, in any other kind of mental activity-will always be elusive. Not only have the data been inconsistent, but so too have the conclusions drawn. These outcomes reflect the enormous adaptability of the perceiver on the one hand, and the fundamental indeterminativeness of any theory of the processes going on within what is, for any conceivable future, a closed system.

Information, Rather Than Energy, Must be Emphasized We will also have to come to appreciate that the study of perception, like all of the other cognitive processes, is an information processing science, and not an energy or matter processing one. The nature of internal codes and representations, therefore, is far more arbitrary and complex

30

W.R W

and the laws describing operations are necessarily going to appear to be far less rigid than those emerging from the study of simple physical systems such as those described by quantum mechanics or cosmology. Indeed, there is even a question arising whether or not the general concept that “laws” exist (which is operative in the simpler energy/matter dominated fields of science) may be transferred to this much more multivariate domain of perceptual processes. The new behaviorism must also take into account the twin aspects of mental processes. That is, they are both empiricist and rationalist in character with both direct and automatic processes, on the one hand, and logical and mediated processes, on the other, taking part. The century old philosophical debate between the empiricist and rationalist schools can only be resolved by a rapprochement that acknowledges that the reason there has been such a persistent debate is that both were partially correct. Thus we must acknowledge that stimuli do not lead solely and inexorably to responses by simple switching circuit-like behavior. Rather, a modern neobehaviorist perceptual science must accept the fact that there is a rational, meaningful, adaptive, utilitarian and active construction of percepts and responses by mechanisms that depend more upon the meaning of a message than its temporal or spatial geometry. In the perceptual world information, unlike matter or energy in the physical world, can actually be created. Many perceptual “illusions” illustrate the truism that we can see that which is implied as well as we can real stimuli. The work of Gaetano Kanizsa (summarized in his 1979 essay) was essential in making this point clear.

The Reality of Mental Events as Processes Must be Accepted We must accept the reality of mental processes, and the psychobiological premise that these natural processes are nothing more or less than the result of ultra-complex neurophysiological mechanisms. This point can be summed u p in two axiomatic statements, both of which are fundamental to a new behaviorist perceptual psychology. First, mental processes are real. In Killeen’s words, we must recognize the “causal relevance of mental states” (1984, p. 36). The second principle-psychobiological monism-asserts that there is nothing extraneural or separate at work during mental activity-it is nothing more nor less than one of the processes of neural activity. Furthermore, we have to appreciate the danger that is raised by the fact that complexity and numerosity themselves can exert influences that come perilously close to producing exactly the same kind of results that would appear if there were such mysterious forces as ”free will” at work.

Toward a New Behaviorism

31

As we reaffirm our commitment to psychobiological monism (without which any scientific study of perception or any other aspect of the mind would certainly perish), we must also acknowledge that the gap between the two levels of discourse-neuronal network state and mental phenomenon-may never be crossed. This requires an epistemological or methodological behaviorism in practice and a metaphysical neuroreductionism in principle. An appreciation of this theory dualism is a necessity for the progress of perceptual science. The intrapersonal privacy of perception (i.e., only we can directly experience our precepts) must also be acknowledged. A most important corollary is that we can not communicate the processes underlying these experiences (or the course of any other cognitive processes) to others. We can experience the outcome, but not the steps that led to the outcome. Many psychologists (e.g., Nisbett, 1980) have shown that introspective speculations about one’s own mental processes can be terribly misleading. This is a key reason for a behaviorist approach to perceptual science. Subjects typically do very poorly in evaluating their own performance in perceptual experiments. The intrapersonal privacy of a percept is as much a barrier to scientific analysis as is the combinatorial limit or the ”black box” constraint. The end of this line of logic is that the measurable physical response (or verbal indicator of some simple action) must be considered primary and introspective reports in which subjects are required to interpret what they think they are doing ignored.

The Primacy of Behaviorally Measured Phenomena Must be Appreciated Finally, we are going to have to accept the primacy of the phenomena in any controversy between different points of view or theories in perceptual science. That is, the final arbiter of any explanatory disagreement or controversy must be some behavioral measurement of the perceptual experience. Neurophysiology, mathematics, computational convenience, parsimony, and even some kind of simplistic plausibility are all secondary and incomplete criteria for resolving such disputes. Killeen’s plea for prudence, rather than parsimony, is echoed in these words. But, this prudence must be tempered by solid links to the measured response data. The measurable phenomena is the final outcome of a concatenation of processes and is complete in the sense that it reflects all of the relevant previous steps. Anything e l s e i d e a , introspective report, theory, formal model, neural data, or verbal explanation-that is in conflict with the final measurement of the phenomenon, in principle, requires modification or rejection. This does not mean that the nature of the perceptual can completely explain everything or even indicate to us what are the underlying

32

W. R. W

processing steps. Rather, in those cases where a conflict between observation and explanation (or any of the other estimates of intervening states) does occur, the final result-the phenomenal outcome-must be definitive. At a qualitative level the perceptual phenomenon is an excellent source of heuristics for theory building simply because it is the stuff of this science: Perceptual psychologists are primarily in business to describe and explain the psychobiological reality we call perceptual experience, not to exercise computers or to speculate about uses for the increasingly large number of anatomically or physiologically specialized neurons that are appearing at the tips of our microelectrodes.

Taxonomic Classification and Organization of the Data and Theories of our Science Must be Emphasized Finally, I repeat my conviction that there is a vast, unmet need in perceptual science for efforts to classify and organize our collective knowledge. We are urgently in need of a substantial effort to systematize our theories and findings. All too often there has been unnecessary replication or unappreciated analogous experiments carried out that ignored the identity of two processes. Not only would these rather minor problems of economics be resolved by an intelligent systemization of our science, but the relationships, similarities, and even identities of perceptual processes and phenomena, which may seem to be superficially quite different, will become evident. In sum, what I am proposing is a inathematically descriptive, nonreduct ionist, holistic, empiricist, rationalist, inulfi-dimensional, neobehaviorisin that is guided more by the relevant phenomena than by the availability and convenience of analytic tools. This neobehaviorism would be ambitious to solve the classic problems of perceptual psychology, but modest in avoiding recourse to strategies that are patently beyond the limits of this or any other science. All too much of our effort has been spent on unattainable goals in the past few decades. I believe such a strategic redirection would be a major step towards a realistic and mature scientific approach to perceptual science.

Acknowledgment. I am deeply grateful to Gustav Levine and Peter Killeen for their constructive comments that have educated and enlightened me about both typos and conceptos in an early draft of this essay. While the remaining logical problems are surely my own responsibility, the final version of this essay was much improved by their collegial interaction.

Toward a New Behaviorism

33

DISCUSSION Kent Berridge (Department of Psychology, University of Michigan, Ann Arbor, MI): Uttal makes a provocative case that we can never know the computational or neural mechanisms of behavior. Based on this limitation, he argues, psychology must change its goals to those outlined in his new behaviorism. Uttal's argument springs partly from the logical relation between the mechanism of a system and the behavior it produces. The problem, Uttal argues here and in more detail elsewhere (Uttal, 1990), is that there is no one-to-one relation between mechanism and behavior that could allow one to recognize a particular mechanism by its behavioral consequences. No matter what pattern of behavioral output is observed, or how clever or exhaustive the test, there is always more than one computational mechanism that could be invoked to explain the output. In fact, there are an infinite number of such mechanisms. Explanatory reduction of behavior to its neural mechanisms faces an additional obstacle, since lawful patterns of behavior do not necessarily imply the existence of lawful patterns among the individual molecules that form its substrate. Lawfulness at the molar level can arise out of unpredictable events at the molecular level. This imposes an absolute barrier to "bottom up" attempts to build a "neurophysics of mind." A second source is Uttal's sense of annoyance at the hubris of reductionist claims. Reductionists sometimes write, he complains, as though "we are on the verge of explaining the neural representation of ... perception and learning in the same way" that simpler peripheral processes have been explained. Such writers make an enormous act of faith, for "there is no one who has successfully provided any conceptual links or even compelling suggestions of how the activity of neurons and neuronal nets could instantiate the reported perceptual experiences." Uttal suggests new behaviorism as a solution to these problems. Its goals are different from those of reductionism. New behaviorism abstains from promises to deliver the step-by-step instructions for assembling a human mind, either out of brain molecules or out of computational software. It aims for a synthetic understanding of perception-that is, the ability to build whole perceptions from sets of parts-instead of merely an analytical one, and it promotes the development of new mathematical tools to that end. New behaviorism takes the understanding of behavior as its goal, and does not lose sight of it in a maze of neurophysiological data or computer programs. But does this goal require that psychology give up its search for mechanism and convert to the ideology and language of new behaviorism? The

W. R Uthd answer may depend on what we mean by “understanding a behavioral mechanism.” Uttal seems to require a strong sense of ”to understand:” a full comprehension of the chain of causation from brain particles to behavioral pattern, or of the precise computation that renders a cognitive process. It is this strong sense of understanding that is denied by the logical and physical constraints to which Uttal alludes. A less ambitious search for mechanism might meet with more success. Granted, an infinite number of computational programs potentially exist to explain any output, and we cannot hope to find a single solution among an infinitude of possibilities. But in the conduct of science we do not choose from an infinite number of alternatives. For better or worse, we can conceive of only a limited number of classes of computations to instantiate any psychological function. It is from this limited set of alternative hypotheses-not from the infinite set of unimagined possibilities-that we must in practice choose. Actual experiments can choose among a limited set of hypotheses if they make different predictions for the data. We can and do discard the least successful classes of hypotheses. The remaining hypothesis may not be right-indeed, if we judge it as a final and complete statement of the mechanism, it will never be right. But it will be one step closer toward the truth. Similarly in our search for neural mechanism, we may strive with success to obtain an understanding that is valuable but more limited than full molecule-to-mind causation. We can identify neural systems that are especially crucial to particular psychological functions. For example, the phenomenon of ’%blindsight”after cortical damage tells us something of importance for neural mechanisms of conscious versus unconscious perception. We can also improve our understanding of the computational properties of a neural mechanism. For example, the dissociation of visual properties (color, form, motion) into many distinct areas of the cortex, along with other evidence, argues against simple hierarchical models of visual processing that might otherwise be plausible. If space permitted, this argument could be extended to psychological functions ranging from movement to motivation to language. But who can refute Uttal’s conclusion that our understanding of psychological mechanism remains mostly gaps? The largest gap may be precisely at the level in which Uttal is most interested: the level at which neural connectivity and synaptic interactions map onto specific computational and psychological functions. For this level we know nearly nothing. And despite our desire to know more, our chance for advance is more limited at this level than at any other for lack of the necessary concep-

Toward a Nau Behaviorism

35

tual and technical tools. Perhaps this will always be true. Still, we may hope, perhaps not. To contend that it is possible to gain important insights into the computational and neural mechanisms of psychological processes is not the same as arguing that we can expect success for a complete reduction of psychological processes into such mechanisms. Uttal does psychology a service in pointing out the practical implications of these issues, and his argument against a blind faith in reductionism is persuasive. The constraints on deductive reasoning from a consequence to a cause and the physical quantum uncertainty to which he points are no doubt real, and impose asymptotic limits for future advances in understanding psychological mechanisms. But those asymptotes are still far above us, and we may climb a long way yet. Uttal: Berridge’s comments about my essay are thoughtful and, in the main, in agreement with my own thoughts. His sensitivity to the arguments I make is equaled by his astute highlighting of some of the many issues that must be confronted in any discussion of mind-brain reductionism. One of the main problems in this field is that the words that we use do not mean the same thing to everyone involved in the discussion. I think that Berridge and I do agree on most of the vocabulary we use, but his comments revive the issue of the nature of the basic questions being pursued in the neurosciences. It seems to me that all too often debates occur that are founded on the false premise that we are all talking about the same thing. Sometimes, however, it seems that we are not even talking about the same problems. There are three major theoretical questions in biopsychology, in my opinion. (1) The question of localization: Where are the processes located in the brain? This is the macro-question, the question of identifiable units that are so large that they are visible to naked eye. I must admit to have been tremendously troubled by the arrival on the scene of the PET technique in the recent decade as I thought through my essentially anti-reductionist, pro-behaviorist argument. Both of these devices have the capability to localize particular psychological functions within the working brain. This has often been offered as evidence that we are on the verge of understanding how the mechanism-the brain-is related to the function-mind. However spectacular they may be, these findings only speak to the question of localization. They do not speak to the two other great issues of brain and mind: (2) The question of representation: How are mental functions encoded at the more elemental cellular level; and (3) The question of change: What change in the representation process accounts for the dynamic changes in behavior we call learning or maturation.

36

W . R Uftal

The discovery that a particular function is located in a particular place in the brain, like the blindsight phenomenon and the segregation of visual attributes alluded to by Berridge, produces a powerful and compelling theoretical illusion that we are on the verge of answering the representation problem (2) when, in fact, we have only answered a question of localization (1).The logically prior question is-What is the essential question for the philosopher, psychologist, or physiologist who wants to know how brain “secretes” or ”is” mind? I believe that the essential question is (21, and its corollary (31, rather than (1). I also believe that whatever progress we are making in answering (1) misdirects biopsychology, our patrons, and our larger popular audience from the essential questions (2) and (3). It is a bit of scientific prestidigitation in which attention is directed from the right hand (2) to the left hand (1). In this case, the pitch is-“look closely at the left hand and you will not notice that there is no right hand.” Progress is being made in linking brain and behavior, but unfortunately it is progress in answering something other than the essential question. I see great progress in pursuing the localization issue. We are gaining an increasing amount of information from the wonderful machines that allow us to look into the brain. Neuropsychology data obtained from individuals unfortunate to have damaged brains also helps to solve (1). My argument is that this is not the key issue. The key issue is neural interconnectivity. To reiterate the fundamental argument of my essay, this is a problem whose solution is blocked not by mere practical considerations but by matters of fundamental physical, computational, and mathematical principle. Berridge and I agree that we are far from the “in principle” limits that lie ahead. I think we also agree that there is very little research that should be stopped now because of my argument. I feel strongly that there are good enough reasons to continue to support virtually all neuroscience and biopsychology research currently being pursued. I would prefer, however, that those good reasons be those that are relevant and appropriate for each of those sciences and that we not offer false promises of a future understanding that is beyond possibility. The attribution of reductive power to behavioral data is such a false promise. Daniel N. Robinson (Department of Psychology, Georgetown University, Washington, D. C.): Fortunate readers of Uttal’s chapters and books have come to expect both clarity and originality, properties amply displayed in this present chapter. There is also much subtlety, and it is for this reason that even quite clear expositions warrant a second reading and some time for reflection and consolidation.

Toward a Nau Befiavimisrn

37

Can there be a new behaviorism that is at once faithful to its pedigree and, at the same time, immune to the major challenges that successfully defeated older ones? If so, the new behaviorism must accept as a central postulate that Uttal summarizes thus: We must now acknowledge that human visual perception is primarily and initially holistic in its operations. The Gestalt psychologists understood and correctly taught this principle... (p. 27, this volume).

But in granting this, is it still a behaviorism in any useful and informing sense? In his important essay, Uttal provides both critical and constructive arguments which are best considered separately. The critical component sets out to challenge reductionism as the proper methodological or metaphysical foundation for a psychology of perception. In this, I would judge the author to be entirely successful, though he is unnecessarily tolerant in accepting certain neurocognitive programs as even qualifying as genuinely reductive. What, after all, is ”reduced when, for example, some feature of perception is shown to be reliably associated with (or even “caused” by) some feature of the nervous system? The initial ontological domainwhich contained perceptual entities and neural entities-is as prosperous and numerous after these causes or correlates have been identified as it was previously. Note that no essentially correlative program can be reductive. The reductive successes in science (e.g., defeat of the phlogiston theory of gasses) mark somefhing (e.g., phlogiston ) for eradication, not correlation. Wisely does Uttal counsel experimenters when he condemns ”mere data collection, without reason or conclusions” and identifies the “ultimate role of science” to be that of surpassing ”the accumulated data by stimulating general statements of understanding” (p. 20, this volume). If I were to cavil with any part of the critique of reductionism it would be Uttal’s willingness to exempt behaviorism. In praising behaviorists (other than Hull) for their commitment to descriptive theory rather than ”reductive pseudophysiology,” I worry that Uttal will have to remove too many from the historical rolls of behaviorism (e.g., Pavlov, Mowrer, Hebb). Moreover, the formidable challenges to any and every attempt to link ”inferred mechanisms with ... observed behavior”-challenges noted by Uttal as coming from chaos theory, thermodynamics, Godel’s theorem, etc.-were never dreamed of by textbook behaviorists. Thus, their opposition to a reductive psychobiology is not to be regarded as in any way prescient. Another significant part of Uttal’s critical argument is skepticism toward introspectionism or anything hinting at ”private” experiences. How

38

W.RW

sincere this skepticism is can only be guessed at in light of Uttal’s insistence that, The empirical psychophysical approach ... must be the centerpiece of any new development in this science (p. 28, this volume).

Space does not permit even a summary of the ”privacy” problem allegedly plaguing introspective psychology. Perhaps it is sufficient to suggest that psychophysics must be grounded in the assumption that, as regards perceptual data, the percipient has ultimate epistemological authority. That reliable indices must be found by which the percipient expresses the sensory consequences of stimulation is a methodological-not an ontological-problem. Were the perception to be public to begin with, there would be no methodological problem. Were the perceptions ineliminably “private,” no method of publicity would succeed-as Wittgenstein was at pains to argue. Finally, Uttal’s critique of what might be called the standard view includes the important distinction between research and theory based on the energetics of stimuli rather than the information transmitted and received. I will return to this pivotal consideration. Note, however, that the psychophysical research envisaged by Uttal, in light of this caveat, must be liberated from its traditional ( R = k log S) moorings. Perception is not to be understood as the outcome of switching-circuits, and ”the reality of mental events as processes must be accepted.” Thus, the psycho-physicul distinction in psychophysics must be comprehended ultimately in dialectical rather than causal terms. This leads me to consider briefly the constructive arguments developed so carefully and lucidly by Uttal. He insists upon the restoration of the “mental,” for mental processes are real and causally efficacious. But he then insists further that nothing “extraneural” is suggested by this, the processes themselves an expression of neural activity. The “intrapersonal privacy of perception” is also acknowledged, but only to warn of its misleading consequences and the need to replace subjective interpretations with verbal reports or simply actions. This yields something of a ”behaviorism,” for the primary data are public, verifiable, interpersonal, etc. What might be called the positivistic allegiances of the old behaviorism are honored. It yields, too, a ”new” behaviorism because of the room provided for causally efficacious mental processes. What is left out, however, is what one might have taken to be a corollary of the liberated psychophysics: If the fundamental feature of stimuli is information, then all relationships are topics for interpretation. That is, given Uttal’s quite commendable impatience with reductionism, radical anti-mentalism, etc., one might have expected him to find common cause with any

Toward a New Behauiorism

39

number of “post-modernists” theorists (e.g., Clifford Geerts, Kenneth Gergen, Rom H a d , Jerom Bruner) who regard the herrneneuticul dimensions of perception and action as the very basis upon which something qualifies as a percept or an action. Clearly, Uttal does not want to create a behaviorism so new that it passes for some version of phenomenology or existentialism. Nor does he want to honor positivism so faithfully as to revive Hullian nomologicaldeductive learning theories. My own sense is that in respecting the soundness of Gestalt critique of reductionism, in recognizing the centrality of psychophysics, and in appreciating that a genuinely advanced and progressive psychology of perception will be information-based, William Uttal may already qualify (as Tolman said of himself) as a ”cryptophenomenologist,” but one able to enrich the tradition by imposing longneeded rigor. Uttal: One whose arguments have been sliced by the keen intellectual razor wielded by Robinson sometimes does not appreciate what will happen “when one turns one’s head.” Nevertheless, it is always the case that he gets one’s attention and stimulates thoughtful reflection about one’s premises. The slice of the intellectual ”razor” in this case demands that one reconsider whether or not one is, of all things, a “cryptophenomenologist.” Just the expression of this word originally terrified me. All too often, in my past experience, to be a “phenomenologist” was to be beyond the pale of science. Obviously, this terror has to be exorcised, denied, or one has to accept one’s fate and, with chin held high, live with the pariah role. First, lets take a look at what is currently meant by phenomenology. Initially, we have to divorce ourselves from some of the more recent uses of the term. For example, the distinction Sartre makes between phenomenology and science is not what I am about. Nor does Heidegger‘s lofty notions of ‘%being’’bear any resemblance to the organized exploration of mental events that I considered in this volume. Rather there is an older, more classic, and, I think, purer form of phenomenology that deals with the measurable events we experience. It is phenomenology as an empirical science rather than a philosophical movement denying external reality. What are the characteristics of the classic phenomenological approach? Though many may challenge the criterion, it seems to me that it was best defined by Hamilton one hundred and fifty years ago which can be paraphrased as a descriptive approach to the study of mental events. Those mental events are the phenomena that in the case of our science become public only in the form of measurable behavior.

W.RW

40

Thus, the mental events (or for that matter and data describing their fluctuation with some physical dimension) are the objects of study in a phenomenological science. Classic phenomenologists also went on to invoke another essential attribute of their kind of psychology. They specifically eschewed reductionism. Once the perceptual scientist had described and classified a phenomenon, they asserted, the job was complete. For them, it was purely a logical argument that once we have described phenomena, we should go no further. For me, the same argument is made on the basis of new ideas from the other sciences. Phenomenologists have traditionally been accused of being insufficiently empirical. It seems to me, however, that what we truly know, and all that we can know, about perceptual phenomena, can only come from measurement and controlled experimentation. Therefore, the brand of descriptive psychology denoted as phenomenology must be as much an empirical science as any other. So, what do we have? A phenomenology of the purer, older, non-existential kind that is characterized by being empirical, descriptive, and non-reductive. A phenomenology in which mental events, that is, internal models of objects rather than the external objects themselves, are what we study. It does not matter that these models are measured only indirectly by means of behavior. That problem-the unreachable object of inquiry-is faced by astrophysics and particle physics as well as psychology. Nor does it matter that we cannot reduce them to their elements. A scientific approach to perceptual phenomena is still possible. Egad! This sounds all too much like my neobehaviorism. Robinson was right! I am a phenomenologist (and not even a very cryptic one at that)! Like the little boy who did not know that he was speaking prose all his life, I have discover that I have argued myself into a position that is indistinguishable from classic phenomenology (as opposed, certainly, to philosophical phenomenalism, a kind of quasi-, neo-idealism, or its existential corollaries). So enlightened, I join Tolman, and also, I would not be too surprised, my old friend Robinson, in this camp.

REFERENCES ALLMAN, J. (1981). Reconstructing the evolution of the brain in primates through the use of comparative neurophysiological and neuroanatomical data. In E. Armstrong & D. Falk (Eds.), Primafe brain evolution: methods and concepts (pp. 13-28). New York: Plenum. BENNETT, B. M., HOFFMAN, D. D., & PRAKASH, C. (1989). Observer mechanics. San Diego, CA: Academic Press.

Tuwurd a New Bsllavforism

41

CHEAL, M. L., & LYON, D. R. (1993). Allocation of attention in texture segregation, visual search, and location-precuing paradigms. Quarterly Journal of Experimental Psychology, in press. CHURCHLAND, P. S., & SEJNOWSKI, T. J. (1989). Neural representation and neural computation. In L. Nadel, L. A. Cooper, P. Culicover, & R. M. Harnish, (Eds.) Neural connections, Mental computation (pp. 1548). Cambridge, MA: MIT Press. CUTTING, J. E. (1986). Perception with an eye for motion. Cambridge, MA: MIT Press. GELL-MANN, M. (1964). A schematic model of baryons and mesons. Physics Letters, 8, 214-215. HULL, C. L. (1943). Principles of behavior. New York: Appleton-CenturyCrofts. KANIZSA, G. (1979). Organization in vision: Essays on Gestalt perception. New York: Praeger. KILLEEN, P. R. (1984). Emergent behaviorism. Behaviorism, 12, 25-39. KILLEEN, P. R. (1988). The reflex reserve. Journal of the Experimental Analysis of Behavior, 50, 319-331. LAND, E. H. (1977). The retinex theory of color vision. Scientific American, 237(6), 108-128. LINK, S. W. (1992). The Wave theory of difference and similarity. Hillsdale, NJ: Erlbaum. McCLELLAND, J. L., RUMELHART, D. E., & THE PDP RESEARCH GROUP (1986). Parallel distributed processing: Psychological and biological models (vol. 2). Cambridge, MA: MIT Press. MOORE, E. F. (1956) Gedanken-experiments on sequential machines. In C. E. Shannon & J. McCarthy (Eds.), Automata studies (pp. 129-153). Princeton, NJ: Princeton University Press. NEWELL, A. (1990). Unified theories of cognition. Cambridge, MA: Harvard University Press. NISBETT, R. E. (1980). Human inference: Strategies and shortcomings of social judgment. Englewood Cliffs, NJ: Prentice Hall. RUMELHART, D. E., McCLELLAND, J. L., & THE PDP RESEARCH GROUP (1986). Parallel distributed processing: Foundations (vol. 1). Cambridge, MA: MIT Press. SKARDA, C. A., & FREEMAN, W. J. (1987). How brains make chaos in order to make sense of the world. Behavioral and Brain Sciences, 10, 161-1 95. SKINNER, B. F. (1953). Science and human behavior. New York: Free Press. SKINNER, B. F. (1963). Behaviorism at fifty. Science, 140, 951-958.

42

W.R W

SKINNER, B. F. (1987). Whatever happened to psychology as the science of behavior. American Psychologist, 42, 780-786. SMITH, L. D. (1992). On prediction and control: B.F. Skinner and the technological ideal of science. American Psychologist, 47, 216-223. TOWNSEND, J. T. (1992). Chaos theory: A brief tutorial and discussion. In A. F. Healy, S. M. Kosslyn, & R. M. Shiffrin (Eds.), From learning processes to connectionist theory: Essays in honor of William K. Estes (vol. 1, pp. 65-96). Hillsdale, NJ: Erlbaum. UTTAL, W. R. (1981). A Taxonomy of Visual Processes. Hillsdale, NJ: Erlbaum. UTTAL, W. R. (1988). On seeing forms. Hillsdale, NJ: Erlbaum. UTTAL, W. R. (1990). On some two way barriers between theories and mechanisms. Perception & Psychophysics, 48, 188-203. UTTAL, W. R., BRADSHAW, G., DAYANAND, S., LOVELL, R., SHEPHERD, T., KAKARALA, R., SKIFSTED, K., & TUPPER, K. (1992). The swimmer: A n integrated computational model of a perceptual-motor system. Hillsdale, NJ: Erlbaum. VAN ESSEN, D. C., ANDERSON, C. H., & FELLEMAN, D. J. (1992). Information processing in the primate visual system: An integrated systems perspective. Science, 255,419-423. WATSON, J. B. (1925). Behaviorism. New York: Norton.

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

43

SOME PHILOSOPHICAL OBSERVATIONS ON PERCEPTUAL SCIENCE Sergio C . Masin Department of General Psychology University of Padua, Italy

ABSTRACT The view that physics and perceptual science deal with a single reality consisting of perceived worlds is here supported by a number of arguments. Within this view, the occurrence and the identity of things and their attributes in perceived worlds are recognized as basic problems for perceptual science. It is argued that predictions of these occurrences must be based on constructs. The causal theory of perception meets this requirement. It is concluded that some of the variables in perceptual models constructed within this theory should be conceived as mathematically identical to perceived attributes.

According to Avenarius and Mach, physics and perceptual science deal with a single reality (Mach, 1959). A number of arguments can be given to confirm this view (Masin, 1989). Before considering these arguments and their implications, however, let us first define a few terms. We see objects, empty spaces, shadows, lights, etc., as outside our heads. Our own body is one of the objects we see. On the other hand, we hear sounds inside and outside our body, feel sensations in and through our body, and feel emotions in us. In general, we see, hear, or feel things. Here, perceive equivalently means see, hear, or feel. At any instant, our perceived world is the set of our perceived things. Since the Latin word for thing is res and real derives from res, perceived worlds may also be called real worlds. However, as defined here, perceived things are also non-conCrete things like pains or emotions.

S. C.Masin

44

PERCEPTUAL ANTINOMIES Concrete things may elude physical laws. To see this, let us first consider the following classroom demonstration on the well-known horizontal-vertical illusion. The arrow in Figure l a indicates a hole in a 50 x 100 cm cardboard. Two rigid straight wires were prepared, which here are called the standard and vertical wires. The lengths of the standard and vertical wires were about 30 and 60 cm, respectively. The diameters of these wires were the same as that of the hole in the cardboard. As shown in Figure lb, the standard wire was placed on the cardboard parallel to its base. The middle of the standard wire covered the hole. As shown in Figure lc, the vertical wire was inserted in the hole from behind the cardboard so that part of it lay on the cardboard; the other part passed behind the cardboard, exposing a portion behind its bottom edge. Thus, the two wires on the cardboard formed an inverted T. Each student was instructed to look at the inverted T and, at the same time, to adjust the part of the vertical wire on the cardboard so that it would be seen equal in length to the standard wire. The adjustment was made by grasping the portion of the vertical wire exposed below the cardboard and sliding the vertical wire up or down through the hole. Once a subject was satisfied with his or her adjustment, the part of the vertical wire on the cardboard was cut with shears at the intersection of the standard and vertical wires. In Figure ld, an arrow indicates the cutting point. In this figure, M represents the adjusted part of the vertical wire on the cardboard. After M was cut, it was placed parallel and adjacent to the standard wire. Let N be M when M was parallel to the standard wire. Thus, M and N were the same piece of wire in the vertical ( M )or horizontal (N)positions. Figure l e shows N parallel to the standard wire. As depicted in Figure le, N was seen shorter than the standard wire (2 to 3 cm). Since M and N were the same wire, the equality of the seen lengths of M and the standard wire (Figure Id) was an illusion.' The following assertions describe two facts in this demonstration. Fact I (Figure Id). Students saw that: (a) M touched the standard wire; ( b ) the two wires were orthogonal; ( c ) the two wires had equal lengths. Fact 2 (Figure le). Students saw that: ( a ) N was adjacent to the standard wire; ( b ) the two wires were parallel; ( c ) the lengths of the two wires were unequal. To show the robustness of the experimental proof of this illusion, the above experiment was repeated with the following change. Students were first asked to adjust M so that it was seen equal in length to the standard wire. After this adjustment, they had to slowly slide the vertical wire upwards and stop when M was seen barely longer than the standard wire. As before, M was then cut and put parallel to the standard wire. The result was again that N was seen shorter than the standard wire (1 to 2 an).

Philosophical Obsenxltim

I_ 1 a

44

45

b

C

d

e

Figure 1. Successive phases in building up the device for the demonstration of the horizontal-vertical illusion. (From S. C. Masin, Analisi del mondo reale, 1989, p. 4. Copyright 1989 by LivianaIPetrini Editore. Adapted by permission.)

Since the standard wires in Facts 1 and 2 were the same wire, and since M and N were the same wire, the Assertions c are incompatible. How can this perceptual antinomy be solved? Since direct and indirect physical measures of the lengths of M or N are independent of the position or presence of the standard wire on the cardboard, any physical solution of this antinomy is necessarily incorrect. Therefore, a correct solution of the antinomy in Facts 1 and 2 must be nonphysical. In the literature, two non-physical solutions may be noted. One solution is that the length-equality of the wires in Fact 1 is unreal and the length-inequality of the same wires in Fact 2 real; the other solution that the length-equality of the wires in Fact 1 and the length-inequality of the same wires in Fact 2 are two distinct realities.

FIRST NON-PHYSICAL SOLUTION To discuss the first of these solutions, we analyze the Assertions u, b, and c. Assertions u: The objects (standard wire and M ) on the cardboard in Fact 1 are the same objects (standard wire and N)on the same cardboard in Fact 2. These objects are solid, concrete things that are real in both facts. Assertions b: In Fact 1 the objects are orthogonal; in Fact 2 they are parallel. Being seen as pairs of perceived objects, the orthogonality and parallelism are real relational properties. Assertions c: In Fact 1 the objects are equal in length; in Fact 2 they are different in length. Being seen as pairs of perceived objects, the lengthequality and length-inequality are real relational properties.

S. C. Masin

46

Figure 2. The Fraser illusion.

Thus, since the Assertions c refer to real relational length properties, and since the solution under discussion claims that the length-equality of the wires in Fact 1 is unreal, this solution implies an unreal reality. Since this implication is absurd, the solution is incorrect. This conclusion is strengthened by the fact that individuals who are unaware that a property of a perceived thing is illusory assert that this same property is real. In fact, consider the Fraser pattern in Figure 2, which was shown to students in another classroom demonstration. All students who saw this pattern for the first time described it as a set of spirals on a variegated background. All of them described the spirals as real. When the students were subsequently asked to touch one spiral in the Fraser pattern with a pencil tip and run this tip along the spiral, they were surprised at seeing the pencil tip make a circular movement. After this, the students concluded that “in reality” the Fraser pattern contained concentric circles rather than spirals. This conclusion was reached even if circles were invisible in the Fraser pattern, before and after its exploration with the pencil tip. Now, all students asserted that the real spirals they saw in the Fraser pattern were illusory. Therefore, properties of perceived things are asserted to be real even if they may be illusory.

ILLUSORY AND PHYSICAL Before examining the other non-physical solution, let us clarify what the students meant by saying that circles were “real” constituents of the Fraser pattern. For this purpose, let us analyze the facts in the following classroom demonstration. Figure 3 depicts a Necker Cube. If fixated, this ”cube” is sometimes seen oriented from left to right and sometimes from right to left. Using rigid

Philosophical Obsmtions

47

wires for the edges, a wire cube may be constructed. If fixated, this cube also is seen in one or the other of the two possible orientations. As represented in Figure 3, a wire cube was hung on a wall using a string. Each student had to walk around it through Positions 1 to 6 marked on the floor. During this walk, the students had to stare at the wire cube and report what they saw. When they did not offer information spontaneously, they were asked whether the cube rotated or remained immobile. All students reported they saw the edges of the wire cube as stationary from each different position.

;String I

I

4

3

.

I

2

Figure 3. Illustration of a wire cube hung on a wall with a string. Students walked around this cube through Positions 1 to 6. (From S. C. Masin, Analisi del mondo reafe, 1989, p. 10. Copyright 1989 by LivianaIPetrini Editore. Adapted by permission.)

This experiment was then repeated with the following modification. In Position 1, each student had now to stare at the wire cube and wait until the orientation of this cube changed. After this change occurred, the students had to keep staring at the wire cube and walk around it. During this new walk, they spontaneously reported that the wire cube rotated. This rotation was compelling and surprising. Its direction was the same as that of walking.

48

S. C. Masin

The students admitted that the rotation of the wire cube looked real, just as though someone rotated it. However, they thought that this rotation was illusory. What did it mean that the seen rotation of the wire cube was illusory and also as real as the seen rotation of an actual rotating cube? The essential difference between these rotations is the following. The illusory rotation of the wire cube had no physical effect on surrounding perceived things, while a rotation imparted by a hand could have had concomitant physical effects. It seems clear, then, that the students called the rotation of the wire cube illusory because of the absence of the effects expected from a physical rotation of a wire cube hung on a wall, such as the movement of its shadow, its skipping on the wall, the string twist, etc. This conclusion allows the following distinction between properties of perceived things. Physicists formulate laws that govern perceived things.* For example, Galileo studied the laws that govern the movement of balls rolled down an inclined plane. Physical laws allow correct predictions of properties of perceived things. However, there are numerous exceptions. For example, the illusory rotatory movement of the perceived thing wire cube is a property that eludes physical laws. Therefore, properties of perceived things may be defined as illusory properties when they lead to wrong physical predictions, and physical properties when they allow correct physical predictions. Thus, the set of properties of a perceived thing is the sum of the sets of its illusory and physical properties. Then, the real spirals in the Fraser pattern were said to be illusory because these properties could not predict the circular movement of the pencil tip. This physical movement could instead be predicted if the Fraser pattern contained circles. Therefore, the students concluded that this pattern contained circles. Using this definition of illusion, we may now see why only Fact 1 involved an illusion. Measuring length by matching things against a yardstick allows precise predictions just as the measure of the amount of crop from a cornfield. Furthermore, the measurements that are logically reducible to the application of a yardstick allow precise predictions like the time of a solar eclipse, the place where a missile falls, etc. The wire matching in Fact 2 was a length measurement operation that made this fact suitable for physical predictions. That is, if M and N were used to make physical predictions, those made with N would have turned out more accurate. Thus, the length-equality of the wires in Fact 1 was illusory because it implied wrong physical predictions, and the length-inObviously, physicists may also formulate laws that exclusively govern conceptual entities, for example, the state of matter in the big bang or in black holes.

Philosophical Obsenxztions

49

equality of the same wires in Fact 2 was physical because it implied correct physical predictions. This definition of perceptual illusion may be extended to perceived things themselves. Illusory things may then be defined as perceived things that lead to wrong physical predictions, and physical things as perceived things that allow correct physical predictions. Thus, the set of things of a perceived world is the sum of the sets of its illusory and physical things. For example, the following is a partial list of illusory things in seen worlds: holograms; things observed in magnifying instruments, mirrors, stereoscopes and similar instruments, and in movies or on television, etc.

SECOND NON-PHYSICAL SOLUTION Now let us consider the second non-physical solution of the antinomy in Facts 1 and 2, which claims that the relational-length properties in these facts are distinct realities. That is, the physical length-inequality of the wires in Fact 2 would pertain to one reality, and the illusory Iengthequality of the same wires in Fact 1 to another. Similarly, the actual physical rotation of the wire cube would pertain to one reality, and the illusory rotation of this cube to another. Finally, in the Fraser pattern, the physical circular movement of the pencil tip would pertain to one reality, and the illusory spirals to another. Therefore, Facts 1 and 2 would involve no antinomy because these facts would be incomparable. With reference to the wire cube, this distinction between two realities is unwarranted, because both an illusory and a physical rotatory movement of the wire cube are seen as properties of one and the same cube. Therefore, since the solution now discussed asserts that an illusory rotatory movement of the wire cube pertains to one reality and a physical rotatory movement of this same cube to another, this solution implies that the same seen wire cube pertains to two distinct realities. Since this implication is absurd, this solution is incorrect.

THIRD NON-PHYSICAL SOLUTION Before we examine a third non-physical solution of the antinomy in Facts 1 and 2, we must develop the definitions of identical and same. We will do it by analyzing another classroom demonstration. In this experiment, one coin (X)and one chalk (Y) were placed horizontally on a table. All students in the classroom saw these things on the

50

S. C. Musin

table. One student (hereafter, the subject) was then asked to go out and stand outside the door for a while. Then, in front of the students, the experimenter replaced X with another identical coin (X’), and Y with and another identical chalk (Y’). However, Y’ was placed vertically on the table. Subsequently, the subject was called back into the room and asked to report what had changed on the table. The subject correctly reported that the chalk was now set vertically. By saying this, the subject implicitly communicated his belief that the vertical chalk was the same chalk that was seen horizontally on the table before leaving the room. For confirmation, the subject was then asked if the room, table, and things on the table were the same room, table, and things that he saw before going out. The subject answered these questions affirmatively. Indistinguishable perceived things are identical things. Consequently, X and X were identical coins for the subject and the other students. Normally, two successive identically perceived things are asserted to be the same thing when nothing indicates that the second thing replaced the first. Consequently, X and X’ were asserted to be the same coin by the subject and different coins by the other students. Now, let us see the third non-physical solution. Earlier, we asserted that M and its standard wire in Fact 1 and N and its standard wire in Fact 2 were the same pair of wires. However, this assertion was false. In fact, if it is assumed that the identical standard wires in Facts 1 and 2 had equal seen lengths, then M and N were identical different wires, because M was equal to its standard wire in Fact 1 and N was shorter than its standard wire in Fact 2. If, instead, it is assumed that the identical standard wires in Facts 1 and 2 had different seen lengths, then these wires were different wires. Therefore, at least one of the wires in Fact 1 was different from the corresponding identical wire in Fact 2. (A possible reason why this difference is normally unreported is that absolute lengths are imprecisely retained.) With this conclusion, the Assertions c about Facts 1 (the two wires had equal lengths) and 2 (the lengths of the two wires were unequal) can now be compatible.

PERCEPTUAL EXPLANATIONS BASED ON CONSTRUCTS The following analysis indicates how to explain the difference in one or more attributes of two successive identically perceived things when the first thing has not been physically replaced with the second. Figure 4a depicts a man in our seen world who stares at an apple on a table. Figure 4b depicts this man’s seen world (cf. Mach’s figure, 1959, p.

Philqhical Obsmfions

51

19). Suppose the man is first in the dark and that the light is then turned on. Obviously, the man reports seeing the apple only after the light is turned on. It is also known that recordings of light-related events in his retinas occur after the light is turned on, and those in his brain after the light has stimulated his retinas. Therefore, there is a sequence of events that must obtain for the man to see the apple: first the light, then his retinal events, and finally his brain events. In fact, if this sequence is interrupted by turning off the light or by cutting the man‘s optic nerves, his seeing the apple is no longer reported.

Nose a

b

Figure 4. Man looking at an apple on a table, and illustration of what he sees with his left eye. (From S . C. Masin, A n a l i s i del mondo reale, 1989, pp. 42 and 44. Copyright 1989 by Liviana/Petrini Editore. Adapted by permission.)

Thus, in general, there are brain events that regularly precede or are simultaneous with the occurrence of perceived worlds. However, knowledge of these events is insufficient to explain the occurrence of perceived things. In fact, the following arguments prove that constructs are required. Figure 4a depicts our seen world in which we see a man’s nose. Figure 4b depicts this man’s seen world in which he sees his own nose. This nose is not the man’s nose we see because the seen world depicted in Figure 4b corresponds to events in the man’s brain, and that depicted in Figure 4a corresponds to events in our brain. To reiterate, since our brain and the man’s brain are separate, our seen world and the man’s seen world also are separate. Consequently, things in our seen world cannot affect things in the man’s seen world, and vice versa. Thus, in general, any correspondence between some event that we perceive as a thing occurring in the man’s brain and any thing that the man perceives as occurring in his perceived world cannot be ascribed to a direct connection between these things, because these things occur in separate

S. C. Masin

52

perceived worlds. Then, to explain the occurrence of things in perceived worlds, constructs distinct from these worlds are necessary. This conclusion accords with the following considerations. Many things and their properties occur or change spontaneously in perceived worlds. Examples are a picture appearing on a monitor screen, a clap of thunder, a sudden pain in our stomach, an out-of-the-blue panic; or the change in orientation of a reversible object, the voluntary movements of an animal, the spontaneous melting of an ice cube, etc. Clearly, the future spontaneous occurrence of something in a perceived world cannot be predicted on the basis of what there is now in that world. Therefore, constructs distinct from perceived worlds are necessary to perceptually or physically predict spontaneous occurrences in these worlds. In fact, to predict a spontaneous change in the orientation of a reversible object, perceptual scientists invented constructs such as “intrafigural forces” and neural networks; and to predict the spontaneous melting of an ice cube, physicists invented constructs such as the caloric and the change in state of water molecules. Thus, the difference in one or more attributes of two successive identically perceived things without any physical replacement of the first thing with the second is explained by assuming that each perceived attribute of these things corresponds to a different variable of a single construct, and that those variables that correspond to the changed perceived attributes had different values on the two occasions when these things were perceived.

THE CAUSAL THEORY OF PERCEPTION The causal theory of perception (cf. Ayer, 1973, p. 82) meets the requirement of using constructs for predictions of occurrences in perceived worlds. In fact, this theory suggests that the apple in Figure 4a corresponds to a construct object (made up of atoms, etc.), which reflects electromagnetic waves that reach the man’s construct retinas. Consequent photochemical reactions in these construct retinas originate electrochemical processes that cause construct events in the man’s construct brain. Finally, the seen apple would correspond to unspecified construct events in the construct brain. Constructs used in the causal theory of perception are physical. Thus, the validity of the causal theory of perception depends on the truth of its assumptions and on the validity of the physical theory. However, I do not know of any argument proving that all constructs for perceptual explanations must be physical.

Philosophical Obsmtions

53

PHYSICAL EXPLANATIONS BASED ON CONSTRUCTS The above realization that perceived things may have both illusory and physical properties allows us to conclude that illusory and physical things pertain to a single reality. We have just seen that perceptual explanations of this reality require constructs distinct from perceived things. Physical explanations of this same reality also require constructs distinct from perceived things. In fact, each of the following six arguments shows that perceived things are distinct from physical constructs (e.g., atoms, molecules, photons, waves). Argument 2 (colors). Many believe that seen objects are made up of atoms or molecules. Colors are seen in objects. Therefore, colors are situated where atoms or molecules are believed to be. It follows that atoms or molecules are colored or covered with colors. Since this conclusion is absurd and since the assertion that colors are seen in objects is true, it follows that the belief that atoms or molecules comprise seen objects is false. Argument 2 (illusory properties). The assertion that a seen wire cube is made u p of atoms is contradicted by the fact that this cube, when it is supposed to be stationary, may rotate. Similarly, the assertion that a seen Fraser pattern is made up of molecules arranged in concentric circles is contradicted by the fact that the pattern contains spirals. And the assertion that the seen M in Fact 1 is made up of atoms is contradicted by the fact that this wire, supposed to contain fewer atoms than those of the standard wire, is equal in length to the seen standard wire. Since atoms cannot simultaneously have two contradictory properties, perceived things are distinct from these physical constructs. Argument 3 (illusory things). Physical laws apply to physical things and associated physical constructs, that is, sets of atoms or photons believed to be these physical things. Of course, these laws do not apply to illusory things. For example, an apple is governed by the laws of elastic impact while its reflection in a mirror is not. Therefore, illusory things are distinct from physical constructs. Additionally, illusory things may be indistinguishable from other physical things. For example, an apple and its reflection in a disguised mirror are indistinguishable. Therefore, also physical things are distinct from physical constructs. Compared with Argument 2, Argument 3 is primitive. In fact, consider for example a wire cube and its reflection in a mirror. Some properties like the rotatory movement of the non-reflected wire cube may be illusory. Instead, all the properties of the reflected wire cube are necessarily illusory. Argument 4 (perceived magnitudes are useless for physical predictions). We perceive properties in us and in perceived things. These proper-

54

S. C. Masin

ties vary in perceived magnitude (for example, the degrees of gladness, of toothache, of redness, of loudness, etc.). If perceived things coincide with physical constructs, then some variable in mathematical-physical models should vary in perceived magnitude. This never occurs. Therefore, perceived things are distinct from physical constructs. Argument 5 (physical constructs are unperceived). Analysis of the concepts of space and time as used in physics shows that these constructs defined in terms of real numbers in a mathematical space are unperceived. For example, billions of years or light-years are unperceived. The physical concepts of speed and acceleration are defined in terms of those of space and time and therefore are also unperceived. For example, consider the speed of light, c. In dynamics, the concept of force is defined as "something" that changes the position of an object. This "something" is unperceived. For example, consider a magnetic force. The physical mass, m, of an object is defined in terms of force and acceleration. Thus, we cannot perceive m . Physical energy, e, is equivalent to m, that is, e = m$. Therefore, also e is unperceived. And so on. The theory of relativity makes it clear that the deduced mathematical-physical spacetime universe is unperceived. That is, we can perceive things in their space and time, but we cannot perceive mathematicalphysical constructs in an absolute spacetime universe. In quantum mechanics, the wave-particle dualism refers to mathematical-physical constructs that are unperceived. Elementary particles in three dimensions and superstrings in ten or more dimensions are unperceived. And so on. In conclusion, perceived things are distinct from physical constructs because constructs are unperceived. Argument 6 (the definable presence and absence of mathematicalphysical variables are irrelevant for the occurrence of properties of perceived things). If it is true that perceived magnitudes are useless to predict mathematical-physical variables (Argument 41, then it must also be true that mathematical-physical variables are useless to predict perceived magnitudes. This implication is proved by countless examples in perceptual literature. The most common of these examples concerns seen movement and rest. In machine-shops containing drills, millers, lathes, etc., people may get hurt by touching parts in rapid rotation that are seen at rest. Therefore, the definable presence of a mathematical-physical change in position of a physical construct (for example, the group of molecules believed to comprise a rapidly rotating fan-blade) may correspond to the occurrence of seen rest. Similarly, the illusory movement on a television screen proves that the definable absence of a mathematicalphysical change in position of a physical construct (for example, the group of atoms believed to be a static pixel) may correspond to the occur-

Philosophical Obsmtions

55

rence of seen movement. It follows that the definable presence and absence of a mathematical-physical change in position are irrelevant for the occurrence of seen movement or rest. Therefore, perceived things are distinct from physical constructs.

DIGRESSION The causal theory of perception involves the philosophical problem of whether constructs, derived from experimentation, are mere inventions or represent existing entities. The following analysis offers an answer to this problem. With reference to predictions about perceived worlds, four different definitions of existence may be distinguished. Definition 1 . Something exists if it is perceived. Definition 2. If not disintegrated or vanished, something exists if it was perceived. For example, we may say that the Museum of Modern Art that we saw in New York exists (if not disintegrated) because we know that if we go back to New York we may see it again. On the other hand, an emotion we had, a lightning we saw, etc., are now nonexistent because they have vanished. Definition 3. If not disintegrated, something never perceived but likely to be perceived exists if it caused something that is or was perceived. For example, we may say that a specific new animal exists (if not disintegrated) if we see or saw its picture. Definition 4. A construct derived from something that is or was perceived corresponds to one or more entities that exist or existed. For example, we may say that the construct Julius Caesar derived from history books and from seeing effigies of an emperor corresponds to a man that existed; that the construct caloric derived from physical experiments and from feeling thermic changes in objects corresponds to an entity that exists; or that the construct positron derived from physical theory and from seeing traces in bubble chambers corresponds to entities that exist. Clearly, the probability that what exists is perceived is 100% for Definition 1, progressively lower for Definitions 2 and 3, and 0% for Definition 4. Theoretical predictions are independent of whether the entities supposed to be represented by constructs are asserted to exist or not to exist (Eddington, 1939). Therefore, the problem of whether constructs are mere inventions or represent existing entities is theoretically irrelevant if exist is understood in the sense of Definition 4, and is theoretically misstated if

S. C.Masin

56

this verb is understood in the senses of Definitions 1 to 3, which apply only to perceived or perceivable things? Before we end this digression, it may be interesting to discuss briefly whether things persist when they are no longer perceived. As mentioned in Definition 2 above, there are transitory perceived things like feelings, sounds, lights, etc., that are believed not to persist after they have vanished. On the other hand, there are permanent perceived things like solid objects, liquids, etc. that are believed to persist (if not disintegrated) after they have ceased being in the perceived world.

Figure 5. Example of three different degrees of transparency.

Our belief in the persistence of past permanent perceived things involves two problems. One concerns the reasons why we have this belief (Michotte, 1962). The other concerns the reasons why past permanent perceived things may occur again in future perceived worlds in agreement with physical >laws.This second problem is metaphysical.

FOUR KINDS OF PERCEPTUAL PREDICTION So far, we have seen that physics and perceptual science deal with a single reality consisting of perceived worlds; that perceptual explanations of this reality must be based on constructs; and that the causal theory of perception meets this requirement.

In physics, this problem is brought up in the analysis of the philosophical foundations of quantum mechanics (Jammer, 1974). The above Eddington’s (1939) remark that theoretical predictions are independent of whether or not the entities supposed to be represented by constructs are asserted to exist or not to exist applies to both the quantum mechanical and the traditional physical approaches because both use constructs.

57 This theory may be symbolized as follows:

0->s-

>Br=PW,

with 0 the object, S the sense-organ, BY the brain, P W the perceived world, the arrows the causal sequence of events, and the correspondence sign the correspondence between PW and some unspecified event in Br. Within this theory, the following four kinds of perceptual prediction are then possible: predictions of variables in PW from variables in 0, in S, in Br, or in PW itself. The following are examples of these possibilities. Each example concerns the same perceived attribute, namely, the degree of transparency (& of a transparent surface. Figure 5 illustrates three different 6s of an achromatic disk on a two-part achromatic background.

The filter model The Metelli (1974) filter model of transparency illustrates how Gcan be predicted from a variable in 0. A filter may be imagined as a piece of thin transparent plastic with an immense number of microscopic holes. The light arriving to the retinas from this filter may then be imagined to be a mixture of the light reflected by the filter and the light coming from the background through the microscopic holes. The reflectance of a surface is the ratio of the light intensity measured with a photometer directed toward this surface, to the light intensity measured with a photometer placed on this surface and directed toward the light source. Let us suppose that the reflectance of a gray filter is a and that of its gray background 6. A gray opaque surface on the same background and in the same illumination condition as those of this filter may be selected so that the gray of this surface matches that of this filter. According to Talbot's law, the reflectance of this selected surface is c=

+ (I-d 6,

(1)

with

where rn is the overall area of the reflecting part of the filter, and n that of its microscopic holes. The filter model of transparency applies as follows. Figure 6a shows a bistable pattern in which the black disk is Seen transparent on the white disk or, alternatively, the white disk is seen transparent on the black

S. C.Masin

58

b

a

Figure 6. Two overlapping transparent disks on a variegated background and their parts indicated by letters.

disk. The letters in Figure 6b indicate the parts of this pattern. Let x , y, and z be the reflectances of these parts X, Y,and Z, respectively. The gray of the part where the disks are superimposed may be assumed to correspond to a filter, with reflectance x when the white disk is seen in front and with reflectance z when the black disk is seen in front. Talbot’s law states that

y=ax+(l-dz.

(3)

a = (y-z) / (x-z),

(4)

This equation yields and

According to the filter model, when the black disk is seen in front the degree of transparency where the disks are superimposed is & =U(a),and when the white disk is seen in front it is S, =U(l-a), with U being an unknown monotonic function.

A retinal model A retinal model for 6 may also be developed. When the light reflected by each part X, Y, or Z of the pattern in Figure 6a stimulates the retinas, retinal photosensitive substances are bleached. According to Hecht’s theory, the mathematical relation be-

Philosophical Obseruations

59

tween the intensity, I, of reflected light and the concentration, r, of consequent bleaching products is

with h, p , and q being constants, and t the concentration of photosensitive substances after dark adaptation (Lewis, 1960, p. 480). Experimental data agree with Expression 6 for p = 9 = 1 (Cornsweet, 1962). Therefore,

Let r,, ry, and r, be the concentrations of bleaching products due to the lights with intensities I,, Iy, and I, reflected by X, Y, and Z, respectively. It may be hypothesized that

ry=erx+ (l-drZ,

(8)

with E being a weight coefficient (Masin, 1976). Consequently,

and 1-E = [(I

+ h1.J Uz-Iy)l / [(I + My) UX-IJI.

(10)

When h tends to 0, E tends to a? Then, for a fixed value for h, Sb = V ( d with V being an unknown monotonic function?

A brain model A brain model for S may also be developed. The occurrence of seen things requires retinal contours (Krauskopf, 1963). Seen transparency occurs when retinal contours indirectly “activate” proper brain constructs. Suppose these constructs become “activated In fact, given the definition of reflectance, Expression 4 may be rewritten in terms of intensities of reflected light because the intensities of incident light on the parts X,Y, and Z are the same. Clearly, the filter and retinal models of transparency can be tested properly only if U and V are specified. Kozaki, Masin, Fukuda, and Kozaki (1991) have shown that 6 varies with the illumination level. This implies that some parameter of these functions varies with the illumination level or that, if a single U or V exists, it is inappropriate to express perceptual models of transparency in terms of reflectances or intensities of reflected light.

S. C. Masin

60

when the differences between the reflectances associated with their retinal contours decrease below a threshold. Suppose also that the magnitude of an unspecified variable, corresponding to 6 in these constructs, increases from 0 to k as these differences decrease from this threshold to 0. Thus, let these variables for the retinal contours corresponding to X and Y and to Y and Z (Figure 6) have the magnitudes SXy and SYz,respectively. It has been proposed that, when the white disk in Figure 6a is seen in front, the overall degree of transparency where the disks are superimposed is

with u=

4. / ay+4-3.

(12)

where Axy and Ayz are the magnitudes of variables representing the lightness differences between X and Y and between Y and Z, respectively (Masin, 1991). Similarly, when the black disk is seen in front, the degree of transparency where the disks are superimposed is

& = u isxy+ (1-U)Sl + (1-u) [(k-$J + us],

(13)

where s is a constant representing the higher degree of transparency of dark transparent surfaces (Tudor-Hart, 1928).

The splitting model The Metelli (1985) splitting model of transparency illustrates how 6 can be predicted from visual variables. When the pattern in Figure 6a is analytically viewed, three adjacent parts X, Y, and Z are seen. Let gy be the gray color of Y. When the same pattern is normally viewed, two overlapping disks are seen. Let gx be the gray color of one disk and gz that of the other disk in the region where these disks are superimposed. Metelli (1985) proposed that with a normal viewing attitude gy splits so that

with P being a weight coefficient. When the black disk is seen in front, the degree of transparency where the disks are superimposed is

Philosophical Obswrxltions

61 (15)

and, when the white disk is seen in front, it is 1-P = (8x-gy) / tgx--gz).

(16)

The following is another example of perceptual predictions based exclusively on perceptual variables. In phenomenal geometry, the amount of seen motion of an object is

with K being the perceived lateral motion of the head, D the seen distance of the object, and $ the change in the seen direction of the object relative to the head (Gogel, 19901.

CONCLUSION In this essay, two basic points have been stressed: physics and perceptual science deal with a single reality consisting of perceived worlds (Mach, 1959) and, as in physics, perceptual science must use constructs to explain this reality. This second point is strengthened by the following analysis of Kohler’s (1960, p. 22) assertion that the structural properties of perceived things coincide with those of their direct brain correlates. Examples of structural properties are the continuity of perceived things and their segregation from their backgrounds (Kohler, 1938, p. 217). If perceived things and their direct brain correlates share structural properties, then these things and correlates should reasonably share other properties as well, for example color. If this were true, then some brain part would be colored. Kohler (1938, p. 194) seemed aware of this absurdity because he suggested that chemical reactions are the direct brain correlates of colors and, at the same time, incongruously negated that colors coincide with these correlates. This analysis shows that asserting that perceived things coincide with their direct brain correlates leads to absurdities or incongruities. To reiterate, since things in a person’s perceived world cannot coincide with any possible thing we perceive in this person’s brain, perceptual explanations must be based on constructs distinct from perceived attributes. How then can constructs predict distinct perceived attributes? As seen before, the difference in one or more attributes of two successive identically perceived things is explained by assuming that each attribute

S. C. Masin

62

of these things corresponds to a different variable of a single construct. The principle of parsimony further suggests that the variables of a construct that correspond to perceived attributes are related to these same attributes by the identity function. That is, these variables should be conceived us if they are perceived attributes. Then, according to this view, perceptual models based on constructs can have both variables mathematically identical to the corresponding perceived attributes and variables without any perceived counterpart. So conceived, perceptual models can meaningfully explain connections among distinct perceived attributes6 As a simple example, consider the Anderson (1970; Masin & Crestoni, 1988) model of the size-heaviness connection, which can be described as follows. When an object is lifted without being seen, its heaviness (77) is

17= w,

(18)

where w is a variable of a construct. When the same object is seen while being lifted, its heaviness (17’) is

where D is a coefficient varying in the real interval [0,1), and w* is a variable pertaining to the same construct that has w as a variable. This w*depends on the seen size of the object and has no perceived counterpart. The connection between heaviness ( q or q’)and seen size is then explained by the interaction of w*with w (= q ) . As a more complex example, consider the above brain model of transparency in which the dependent variable (6, or & ) and part of the inde3 Sy.) ~ ~are conceived as mathematipendent variables of a construct ( ~ and cally identical to the corresponding degrees of seen transparency. According to the present view, all variables in perceptual models that refer only to perceived things (like Expressions 15, 16, or 17) must represent at the same time attributes of perceived things and the mathematically identical variables of some construct. Similarly, part of the variables in perceptual models that refer only to constructs (like Expressions In different theoretical contexts, these connections have been called perceptual interdependences (Koffka, 1935, p. 298), interactions (Gogel, 1973), couplings (Hochberg, 1974), or linkages (McConkie & Farber, 1979). Examples of perceptual connections are reviewed by Gogel (1973). Other examples are given by Expressions 15 and 16 for seen transparency, Expression 17 for seen motion, the connection of heaviness with seen size (Charpentier, 1891; Anderson, 1970), and the connection of lightness with seen spatial orientation (Mach, 1959; Gilchirst, 1977).

Philosophiazl O k m t i o m

63

11, 13, or 19) must represent at the same time variables of constructs and some mathematically identical perceived attribute.

Acknowledgment. I thank Nicholas Pastore, Jerald D. Balakrishnan, and an anonymous reader for useful comments.

DISCUSSION Peter R. Killeen (Department of Psychology, Arizona State University, Tempe, AZ): Masin reviews numerous instances of veridical and illusory perception which ground his thesis: “Perceived things may have both illusory and physical properties [which] allows us to conclude that illusory and physical things pertain to a single reality” (p. 53). He then proceeds through a series of logical arguments showing that perceptions must be different from the things perceived; yet we may assert a correlation between them by four kinds of perceptual predictions, and thus infer an ongoing reality which anchors the perceptions. This reality he refers to as a “construct,” and argues that ”each perceived attribute of [different impressions of the same object] corresponds to a different variable of a single construct” (p. 52). One cannot read Masin’s essay without being reminded of the parallels it holds to the position of the great physiologist Helmholtz. Helmholtz recognized that there are many ”illusory” aspects in every act of perception (e.g., the double images that are ubiquitous in vision except near the focal point), and held that “we are not in the habit of observing our sensations accurately, except as far as they are useful in enabling us to recognize external objects” (1925, p. 6). Helmholtz believed that it was through the many “experiments” we perform with arbitrary starting conditions (in modem parlance, randomized designs), that let us recognize which perceptions are both enduring and correlated with other sense modalities (such as Masin’s example of tracing a pattern by hand), and which therefore calibrate both our brain connections, and our assumptions about entities in the real world. One of my questions for Masin is why he gives priority to the tactual sensations (as, he asserts “The real [sic] spirals in the Fraser pattern were said to be illusory because these properties could not predict the circular movement of the pencil tip” (p. 48); why not: ”the circles were illusory because tracing could not predict the spiral image?”). “The characteristic properties of natural objects... do not denote something that is peculiar to the individual object by itself, but invariably imply some relation to a second object (including our organs of sense)’’ (Helmholtz, 1925, p. 21). It is this set of interactions that Masin refers to

64

S. C. Musin

as the single construct, the single reality, with instantiations of it corresponding to different values of some of its parameters (e.g., the proximity of one line to another affecting a reported length). Furthermore, this reality is condensed out of a multitude of experiences: The “idea of a single individual body [such as a table] is, therefore, in fact a conception (Begriff) which grasps and includes an infinite number of single, successive apperceptions, that can all be deduced from it” (Helmholtz, 1925, p. 23). Normal perception involves the fabrication of hypothetical constructs (e.g., tables) that are useful in typical interactions with the environment. If we keep spilling the milk on an illusory table, we will soon recategorize the sensations that led to the inference of a table. If the world is turned upside down (whether by a psychologist’s lenses or by other means) all of the sensory evidence will eventually force us to the most parsimonious reinterpretation of the sensations-a righting of the visual percept (or an inverting of all other percepts!). Veridical perception constitutes an energy minimum, a state with the fewest ad hoc assumptions necessary to account for and extrapolate the percepts. In straining to make out an object under dim illumination “Suddenly it dawns on us what it is, and immediately, under the influence of the correct comprehension, the correct perceptual image also is developed in its full intensity. Then we are unable to revert to the previous imperfect apperception’’ (Helmholtz, 1925, p. 12). Because perception constitutes an energy minimum, it is usually stable; once sensations are categorized, it requires much additional energy, often provided by the stress of unfulfilled predictions (about visual projections, tactual experience, or other types of spilled milk) to recategorize them. But sometimes we oscillate between two minima (as in the case of the Necker Cube) and sometimes we can be forced from one minimum to another-with conviction, as when we move from d to e in Figure l-or with disbelief, as when we trace the ”circle” in Figure 2. What is ”reality”-the things against which our sensations are calibrated, or the set of those plus our perception of them? Helmholtz chooses the former, Masin the latter. But here the distinction is, I believe, merely a choice of definition, as both authors seem to concur closely in their analysis. Perhaps a mathematical metaphor will help. Consider the complex number z=a+ib, which may be represented as a point with an x-coordinate of a and a ycoordinate, on the imaginary axis i, of b. The x-coordinate corresponds to a state of nature, the imaginary coordinate to our perception of it. It is the complex number z which Masin takes as his ”single reality,” whereas Helmholtz refers separately to the ”external world” (a) and our perception of it (b).Note that there is no necessary correspondence between a and b, either of which can take any value unconstrained by the other. “Every image is similar to its object in one respect, and dissimilar in

Philosophical O b s m t i m

65

all others” (Helmholtz, 1925, p. 24). ”Properties of perceived things may be defined as illusory properties when they lead to wrong physical predictions, and physical properties when they allow correct physical predictions” (Masin, this volume, p. 48); but I do not like calling the latter physical properties; I would prefer “consensus” properties. In bare sensations the projection of the real variable a onto the imaginary axis is unconstrained by the value of a! Ganzfelds fade to nothing and “If objects had simply been passed in review before our eyes by some foreign force without our being able to do anything about them, probably we should never have found our way about amid such an optical phantasmagoria” (Helmholtz, 1925, p. 31): It is the ability to experiment on objects, turning them over and registering multiple controlled sensations that permits us to achieve parsimony in representation through profligacy in stimulation. Out of the many correlated sensations of multiple inspections we generate a set of impressions for which a simplifying construct (e.g., table) provides an energy minimum, both for the extended set of inspections and for the original snapshot. Our perceptual education eventually blinds us to the uncorrelated (illusory) aspects. This energy minimum that constitutes the construct may only be a local minimum: “It is a mistake, therefore, to try to find preestablished harmony between the laws of thought and those of nature, an identity between nature and mind, or whatever we may call it. A system of signs may be more or less perfect and convenient” (Helmholtz, 1925, p. 24). We can navigate through a world equally well with an inverted or ”un’linverted retinahenses. The complex conjugate a+ib and a-ib provide equally useful projections of the world onto our imagination; it is only when these representations are stressed by antinomies, such as those reviewed by Masin, that we may be forced to choose-or to reinterpret the context. We know that selection of the “physical properties” from the many “illusory properties” requires many observations of intercorrelations to achieve a global energy minimum. From many percepts, one concept. Masin and Helmholtz provide similar approaches to the physical and phenomenal. From their correlated perceptions, we achieve one conception of reality.

Masin: Philosophical realism is the view that besides our perceived worlds there is another world, which exists whether or not someone perceives it. This view is widespread among scientists. For example, an eminen t psychologist states that We all find it easy to accept the fact that simple stimulus dimensions, such as energy, time, frequency, length, and other such, are dimensions of a physically real world. We also feel comfortable stating that

S. C. W i n

66

these exist independently of a perceiver. At least I hope not many of us are concerned about that old saw so frequently used in introductory psychology textbooks, the one about the bell ringing in the desert with nobody to hear it, or is it the tree falling in the forest? At any rate, the question is whether sound exists. Of course physical sound exists, and we have available all sorts of physical operations to demonstrate its existence. There simply was no perception of sound. The extreme subjectivistic idea that reality can only be in a perception and not in the world outside clearly is utterly untenable to a psychologist with an information-processing point of view: There must be information before we can ask how it is processed (Garner, 1974, pp. 180-181).

Eminent physicists hold the same view: Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves (Einstein, Podolsky, & Rosen, 1935, p. 777).

As Killeen notes, Helmholtz (1925) referred separately to the ”external w o r l d and our perception of it. External world is what Garner called the “physically real w o r l d and Einstein the “objective reality.” Why do we all, like Helmholtz, need to refer to the “external world?” Russell (1914) showed that our idea that other people have perceived worlds (minds, in his terminology) is an unproved hypothesis. On the other hand, he noted, since its falsity is also unproved, and since it may explain people’s behaviors (e.g., a man quickly crosses the street because he sees a car coming fast), it may be taken as an assumption. Additionally, this assumption is indispensable to avoid solipsism. Thus, when we asserted that “Figure 4a depicts o u r seen world in which we see a man’s nose, [and] Figure 4b depicts this man’s seen world in which he sees his own nose,“ we implicitly assumed that the man seeing his nose had a seen world. While we accept that we and other people have separate perceived worlds, we also note that these worlds are coordinated. Coordinated means that when physical things in our perceived world change, the corresponding physical things in other people’s hypothetical perceived worlds also change. Russell (1914) argued that both our perceived things and those in other people’s hypothetical perceived worlds are the primitive data for our reasonings. Therefore, the “external world” is a hypothetical world that we need to explain the coordination of our physical

Philosophical Obsmtions

67

things with those in other people’s hypothetical perceived worlds. (Of course, the “external world” may also serve to explain the coordination of the different aspects of a physical thing in a single perceived world, as for example when a single physical table is seen from different perspectives.) Is the assumption ”there is an external world” indispensable? The answer is negative. In their famous paper, Einstein et al. (1935) argued that the description of physical reality given by a wave function in quantum mechanics is incomplete. They based their argument on their realistic view and on the assumption that there is no action-at-a-distance in nature. However, Bell (1964) showed that local theories (i.e., theories admitting no action-at-a-distance) and quantum mechanics lead to observably different predictions, and that local theories may be tested experimentally against quantum mechanics. After a review of such tests, Clauser and Shimony (1978) concluded that Because of the evidence in favor of quantum mechanics from the experiments based upon Bell’s theorem, we are forced either to abandon ... a realistic view of the physical world (perhaps an unheard tree falling in the forest makes no sound after all) or else to accept some kind of action-at-a-distance (p. 1921).

Thus, the assumption ”there is an external world” is dispensable. Of course, hypothetical constructs are obligatory to explain perceived worlds and their coordination. As in quantum mechanics, these constructs may rightly ignore the “objective reality.’’ Therefore, for the above reasonings, Helmholtz’s realistic view that the “external world” is perceived by someone is unwarranted. Besides the clarification concerning Helmholtz, Killeen also asks why I seem to give priority to the tactual sensation in the discussion of the Fraser pattern (Figure 2). My answer is that a subject who first says that the spirals in this pattern are real, may subsequently say that the same spirals are illusory even if the subject‘s tactual sense is not involved as, for example, when the subject sees another individual tracing the spirals. The spirals in Figure 2 are illusory because they lead to wrong physical predictions. In fact, the prediction that the cutting of Figure 2 along one spiral produces a physical helical piece of paper is contradicted by the fact that the resulting physical piece of paper is a disk.

Gregory R. Lockhead (Department of Psychology, Duke University, Durham, NC):Masin says that Physics and Perceptual Science both combine analyzed parts of the environment in order to produce constructs that identify a single perceived world. However, as Masin’s data show, con-

68

S. C. Masin

structs that have been considered to date are not always identical. To interpret the differences, Masin invokes a causal theory of perception in which physical constructs are mathematically identical to [hypothesized] perceived attributes and says that the "Constructs used in the causal theory of perception are physical... However, I do not know of any argument proving that all constructs for perceptual explanation must be physical" (p. 52), thus suggesting that his interpretation may not be testable. Here, I suggest other interpretations of his three studies in an attempt to further understand the important problem that he has addressed. Masin says that the data from his studies of the horizontal-vertical, Fraser, and Necker illusions support his definitions that "Illusory things may be defined as perceived things that lead to wrong physical predictions, and physical things as perceived things that allow correct physical predictions. Thus, the set of things in a perceived world is the sum of the sets of its illusory and physical things" (p. 49). To evaluate these definitions, it is necessary to know what the "correct physical prediction" is in each studied instance. Consider the Fraser illusion. If you extrapolate and connect the wide white lines, the physical result is the set of concentric circles that people report when the figure is traced with a pencil. However, if you extrapolate and connect the narrow black lines within those white lines, the physical result is the spiral that people report when the figure is examined visually. This means that both answers are physically correct and which one people report depends on the measure they use. What seems possible to account for the result is that high spatial frequency lines are dominant for vision while low spatial frequency lines are dominant for touch. Since both answers are physically correct, this might change Masin's original question to another interesting question: 'Why is touch dominant over vision when there is conflict between the measures?" While both answers to the Fraser figure are physically correct, neither considered answer to a line-drawn Necker Cube (Masin's Figure 3) is physically correct. The line drawing is physically two-dimensional and is perfectly ambiguous regarding which of two possible 3-dimensional objects might have been projected onto the plane. Masin disambiguates this usual Necker stimulus by making a wire cube which has 3-dimensional information and for which, therefore, a physically correct solution does exist. But existence alone is not sufficient to disambiguate the figure for the observers; they need a measure of that information. For example, were the wire cube viewed monocularly (which Masin did not ask his observers to do but which makes the point more quickly) in front of a uniform background, and observers did not move their heads such that there is no mo-

Philosophical Obsmtions

69

tion parallax, then the physically 3-dimensional cube is perceptually identical to the 2-dimensional line drawing. This is because these are the same things on the retina. If the observer then walked around the wire cube, the movement would add motion parallax and the cube would be seen as it really is. Masin’s report of his data suggests that the wire cube tended to be seen ”correctly” when his observers initially looked at it. This is probably because there was some motion parallax and stereoscopic information; the observers had both eyes open and they were free to move their heads. When the observers then walked around the cube, the information added by this movement facilitated their initial, correct perception and cube was seen to be stable. It did not ”flip.” However, Masin further reports that when observers were instructed to stare at the cube until it reversed, just like the line drawing, and then walk, the cube flipped during the walk. This is expected since walking provided motion parallax information such that the cube was then seen veridically. Masin concludes from his data that “Therefore, perceived things are distinct from physical constructs” (p. 55). At one level this is trite; of course the apple is not in the head and what is in the head is made of different stuff than what is on the table. Since the materials are different, the perceptual and physical constructs are necessarily distinct. But this is not the intended level of Masin‘s inquiry, which I might state as “What perceptual measures predict what physical measures?” This focuses on asking what measures are needed. Since the wire cube is perceptually ambiguous without perceptual information about its depth, perceived depth information is needed to predict any physical depth measure. This also works the other way around. The cube is physically ambiguous if only its X and Y coordinates are known. Without Z coordinate measures, physical science must report a two dimensional figure. Thus, in order to predict from either domain to the other, it is necessary to know what information both measurement systems use and to know what information each is given. Concerning the information needed by the two systems, Masin’s study of the horizontal-vertical illusion allows the guess that perceptual systems need features in context, rather than features abstracted from the context as are measured by physical devices. For example, consider what the effect would be of adding context to the horizontal-vertical illusion figure and repeating Masin’s study. This could reverse the usual result such that now the perceptual measure is ”physically correct’’ and the physical measure is not. To show this, take photographs of a person at two different distances in an ordinary environment, and use both people and a ruler to compare her height in the two photos. The two perceptual measures

S. C.Masin

will be similar and physically correct but the two physical measures will differ. This is because the two systems do different things. The ruler measures abstracted features while perceptual systems measure objects in environments (Lockhead, 1992). This suggests that in order to answer Masin’s question of how perceptual measures predict physical measures, we first need to know what dimensions, features, and measures are used by perception and by physics, and we need to know what information is available to each measuring system.

Masin: In his discussion of my definition of illusory things as ”perceived things that lead to wrong physical predictions,’’ Lockhead observes that part of the analytically seen elements in the Fraser pattern may be connected to form circles, while other parts may be connected to form spirals. He calls these connections “physical results.” However, disconnected imagined or perceived elements can only be connected in our imagination or in our perceived world, respectively. When they are connected in our imagination, the resulting thing is an imaginary thing. When they are connected in our perceived world, the resulting thing is an illusory thing. For example, a dotted line is an illusory thing. Therefore, Lockhead’s circles and spirals are imaginary or illusory things, not physical things. Lockhead also proposes the interesting view that ”... perceptual systems measure objects in environments.” See also Lockhead (1992). However, one needs to explain what is “measured by the perceptual system. For example, we could ask what is “measured” when an individual reports seeing spirals in the Fraser pattern. As I just mentioned, an analysis of this pattern reveals only imaginary or illusory circles and spirals. Therefore, the reported spirals can only be ”measures” of these imaginary or illusory spirals. If this conclusion is correct, then Lockhead needs to explain in turn what is “measured” by these imaginary or illusory spirals. Lockhead: In his reply to my commentary, Masin says that it is an illusion when elements are connected in perception, that “a dotted line is an illusory thing.” However, people report the same broken line as complete or as having an exaggerated gap depending on the situation or context (Pomerantz & Lockhead, 1991, pp. 2-5). This makes it difficult to know if this should be called illusory or imaginary or real or biased or something else. It also emphasizes the fact that more than the object of interest must be appraised. Context must also be considered. Masin said that “properties of perceived things may be defined as illusory properties when they lead to wrong physical predictions, and physi-

Philosophical Obsaxziim

71

cal properties when they allow correct physical predictions" (p. 48). Concerning this definition, consider the appearances of a piece of blank paper and of a desk with objects on it. Studies based on stabilized retinal images indicate that the retina only has information about the edges of the piece of paper and the region between these edges is somehow "filled in" by perception. Reports of a desk with objects on it such that not all of the desk top can be seen similarly indicate that the desk top is "filled in." The desk and the paper are both correctly reported as whole. According to Masin's definition concerning properties, this means that physical properties are perceived. The reason is that correct physical predictions were made. However, this conflicts with his other definition, that these perceptions are illusory because connections had to be made. To avoid such difficulties, it is at least necessary to define "physical" and to know what information is available to the observer. Physically, the Fraser figure is a collection of interrupted markings on paper. It is neither circles nor a spiral. What the figure is reported to be by observers depends on whether the wide white marks are selected and completed by tracing with a pencil or finger, thus producing circles, or the angled lines are selected and connected by eye, thus producing a spiral. Perception uses what ever information is available in order to estimate what is "out there." The information is never complete, the object itself never gets inside the head and perception must always guess. Sometimes there is conflict between information sets, particularly in two-dimensional artificial worlds which provide only restricted data, and the system must choose between the visual "spiral" and tactual "circles." Such outcomes lead Masin to posit imaginary and perceived worlds that are combined. An alternative perspective is to consider perception as a system that evolved to predict important aspects of the ordinary environment. To accomplish this, it measures whatever (usually) provides a correct physical prediction in the three-dimensional world. In this view, elements are not abstracted and then connected in imagination or perception to complete a figure. Instead, completion is part of the initial perceptual process that allows, for example, a rabbit in the woods to immediately be seen as whole, rather than as elements interrupted by the brush. It is not yet clear which of these two perspectives might be more productive for understanding perception.

REFERENCES ANDERSON, N. H. (1970). Averaging model applied to the size-weight illusion. Perception 19Psychophysics, 8, 1-4.

72

S. C. Masin

AYER, A. J. (1973). The central questions of philosophy. London: Penguin Books. BELL, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics, 1, 195-200. CHARPENTIER, A. (1891). Analyse experimentale de quelques elements de la sensation de poids. Archives de Physiologie Normal et Pathologique, 3, 122-135. CLAUSER, J. F., & SHIMONY, A. (1978). Bell’s theorem: experimental tests and implications. Reports on Progress in Physics, 1978, 41, 18811927. CORNSWEET, T. N. (1962). Changes in the appearance of stimuli of very high luminance. Psychological Review, 69, 257-273. EDDINGTON, A. S. (1939). Philosophy of physical science. Cambridge: Cambridge University Press. EINSTEIN, A., PODOLSKY, B., & ROSEN, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777-780. GARNER, W. R. (1974). The processing of information and structure. Potomac, M D Erlbaum. GILCHIRST, A. (1977). Perceived lightness depends on perceived spatial arrangement. Science, 195,185-187. GOGEL, W. C. (1973). The organization of perceived space. I. Perceptual interactions. Psychologische Forschung, 36, 195-221. GOGEL, W. C. (1990). A theory of phenomenal geometry and its applications. Perception 19Psychophysics, 48, 105-123. HELMHOLTZ, H. v. (1925). Treatise on physiological optics. New York: Optical Society of America. (Translated from the 3rd German edition, 1911. Reprinted by Dover, 1962.) [PRK] HOCHBERG, J. (1974). Higher-order stimuli and inter-response coupling in the perception of the visual world. In R. B. MacLeod & H. L. Pick (Eds.), Perception: Essays in Honor of 1. I. Gibson (pp. 17-39). Ithaca, NY: Cornell University Press. JAMMER, M. (1974). The philosophy of quantum mechanics. New York: Wiley. KOHLER, W. (1938). The place of values in a world of facts. New York: Liveright. KOHLER, W. (1960). The mind-body problem. In S. Hook (Ed.), Dimensions of mind (pp. 3-23). New York New York University Press. KOFFKA, K. (1935). Principles of Gestalt Psychology. New York: Harcourt, Brace.

Philosophical Obsmfions

73

KOZAKI, T., MASIN, S. C., FUKUDA, M., & KOZAKI, A. (1991). The effect of illumination on achromatic transparency. Hiyoshi Reviezu of Natural Sciences (Keio University), 10, 19-26. KRAUSKOPF, J. (1963). Effect of retinal image stabilization on the appearance of heterochromatic targets. ]ournu1 of the Optical Society of America, 53, 741-744. LEWIS, D. (1960). Quantitative methods in psychology. New York: McGraw-Hill. LOCKHEAD, G. R. (1992) Psychophysical scaling: Judgments of attributes or objects? Behavioral and Brain Sciences, 15, 543-601. [GRLI MACH, E. (1959). The analysis of sensations and the relation of the physical to the psychical. New York: Dover. (Translated by C. W. Williams, 1897, from the 1st German edition, 1885, and revised and supplemented from the 5th German edition, 1906, by S. Waterlow.) MASIN, S. C. (1976). Transparency as a chromatic scission phenomenon and photoreceptor theory. Italian Journal of Psychology, 3, 405-413. MASIN, S. C. (1989). Analisi del mondo reale. Padova: Liviana. MASIN, S. C. (1991). A weighted-average model of achromatic transparency. Perception & Psychophysics, 49, 563-571. MASIN, S. C., & CRESTONI, L. (1988). Experimental demonstration of the sensory basis of the size-weight illusion. Perception 6 Psychophysics, 44, 309-312. McCONKIE, A. B., & FARBER, J. M. (1979). Relation between perceived depth and perceived motion in uniform flow fields. Journal of Experimental Psychology: Human Perception and Performance, 5, 501-508. METELLI, F. (1974). The perception of transparency. Scientific American, 230 (4), 90-98. METELLI, F. (1985). Stimulation and perception of transparency. Psychological Research, 47, 185-202. MICHOTTE, A. (Ed.) (1962). Causalite', permanence et re'alite' phknotrzknales. Paris: Beatrice-Nauwelaerts. POMERANTZ ,J. R., & LOCKHEAD, G. R. (1991). Perception of structure: an overview. In G. R. Lockhead & J. R. Pomerantz, The perception of structure (pp. 1-20). Washington, DC: American Psychological Association. [GRL] RUSSELL, B. (1914). Our knowledge of the external world. London: Allen & Unwin. TUDOR-HART, B. (1928). Studies in transparency, form, and color. Psychologische Forschung, 10, 255-298.

This Page Intentionally Left Blank

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

75

A HIERARCHICAL APPROACH TO PERCEPTION Dennis R. Proffitt Department of Psychology University of Virginia, Charlottesville, Virginia

ABSTRACT Perception is a biological phenomenon and, as such, it is hierarchically organized and controlled. Research on biological systems requires a consideration of three levels of analysis: (1) the focal level of interest, (2) its initiating conditions, and (3) its boundary conditions. The information that flows into a focal level defines its initiating conditions. Light, for example, is an initiating condition for a photoreceptor. The response of a focal level to its initiating conditions can be discovered by studying the short-run behavior of the system in controlled contexts. In everyday contexts, the information flowing into a focal level is also constrained, prior to its reception, by boundary conditions imposed by the internal and external environment in which the focal level exists. The ways of life, experience, and current purposes of an organism place restrictions on how the available information will be sampled. Such boundary conditions are historically determined and can only be understood by examining the long-run behavior of the system in naturally occurring contexts.

Perception is an achievement of a biological system and, as such, is governed by historical processes operating at different time scales. The structure and functioning of biological systems are not the product of an ahistorical plan. From the level of D N A functioning to that of manipulating symbolic patterns, biological functioning is controlled by historical influences. This is because biological systems are not planned but rather are formed and controlled by hierarchical constraints-residing both within and outside of the organism-that are applied or withheld con-

D.RProfFff

76

tingent upon development and changing circumstances. DNA, for example, is not a formula for an organism, nor is a nervous system a formula for meaningful perceptual experiences. Both have their roles to play, but these roles are enacted within unplanned historical contexts. This essay is comprised of two parts. The first presents a general discussion of the temporal constraints acting in hierarchical biological systems. The second part develops the implications of these temporal considerations for interpreting research in perception.

TEMPORAL CONSTRAINTS ON BIOLOGICAL SYSTEMS The term system is defined below in the context of a simple physical system. Please keep in mind, however, that this term is neutral with respect to the domain of entities being described. The entities organized within a system could be physical, biological, logical, moral, or what have you. On the other hand, an important contrast is developed in the transition from physical to biological systems. Biological systems-including perceptual systems-exist within historical contexts, whereas physical systems are ahistorical.

Temporal Considerations in Physical Systems Systems are ensembles having characteristics that cannot be fully accounted for by describing the properties of their component parts. A description of a system must also include an account of some of the relationships that exist between its components. An ensemble possessing no constituent relationships that affect its behavior is an aggregate, not a system. A machine is a system, a disassembled machine is not. Consider a mechanical system consisting of only two components: two masses located some distance apart and occupying an otherwise empty universe. The behavior of this system is determined by the resulting gravitational field which is a function of three variables: (1) the gravitational field associated with the first mass, (2) that associated with the second, and (3) the distance between the centers of mass for the two objects. Notice here that a relevant variable-the distance between the two objects-is obviously not a property of either object, but of the relationship between them. What makes this ensemble a system is the relevance of this constituent relationship to its overall behavior. Now, it seems to me that the Gestalt dictum that a percept is different from the sum of its parts (Rubin, 1927), is equivalent to asserting that it is a system, not a collection. As with percepts, mechanical systems, organisms, ecologies, and societies are all construed as being systems for pre-

Hierarchy in P e r c e p h

77

cisely the reason that they cannot be adequately described through an enumeration and analysis of their components. Returning to the two-object universe, there is only one way in which time is relevant to this simplest of mechanical systems. The gravitational constant is, itself, an acceleration, meaning that time is one of its dimensions. This use of time is ahistorical; no particular passage of time is denoted. The laws of physics define a present in which history does not exist. On the other hand, biological systems exist within, and are controlled by, historical contexts.

Temporal Considerations in Biological Systems Consider now a neuron as an example of a biological system. A neuron is an ensemble of structurally distinct components that interact with each other in a variety of ways. The functioning of this cell is dependent upon the state of each of its constituents and their mutual interactions. A neuron’s functioning is also affected by its proximal environment and by its history. The history of a cell determines that it is a neuron and how it will function. That is, historical influences are responsible for the structure of the cell and its immediate operating characteristics. The structure of a cell is the result of differentiation. Its functioning is tuned by adaptation and modulation. Differentiation. Every cell in an organism has exactly the same genetic material. The DNA in a toe nail cell is no different from that in a neuron. It is the history of the interactions between a cell’s DNA and its environment that determines the cell’s structure. Cell differentiation begins soon after the first cell division of the fertilized ovum (de Pomerai, 1985). Though in the initial stages of cell division, the cells are similar in structure and function, their locations provide the antecedent conditions for differentiation. Once differentiation has begun, the DNA in individual cells behaves differently in accordance with its location. The composition of the cell’s cytoplasm differs as a function of its biochemical neighborhood. Information passed from the cell’s cytoplasm to its genes blocks and unblocks sites on the genes making the production of some proteins possible, via RNA mediation, but not others. It is estimated that for specialized cells, between 95 and 99% of the DNA is turned off (Bonner, 1973). An example will illustrate these relations concretely. A cell’s D N A must be controlled in order for it to produce only those RNA enzymes a p propriate to its location in the organism. In loose terms, the cell needs to “know” where it is. The cell is informed about its location by substances passed into it from its surroundings or by making ”tests” (Bonner, 1973).For

78

D.R prOff

example, potato cells test for whether they are on the surface or interior of the potato by producing an alcohol substance that evaporates at the surface but builds up in the interior. The presence of a high concentration of this substance turns off the D N A responsible for making the proteins of the epidermis (Laties, 1963). If a patch of epidermis is cut off of a potato, then the alcohol in those cells now residing at the surface will be evaporated, the D N A for epidermis production will be turned back on, and a new skin will be grown. In sum, genes control the production of organic substances and are, in turn, controlled by them. Genes are not blueprints for whole organisms, rather they are templates for creating a variety of R N A and their associated proteins. In fact, an organism’s D N A possess potential that is never expressed in that organism. If placed in the appropriate environment, an organism’s D N A is capable of producing proteins that are not typically found in the species. For example, the D N A of a chicken can produce tooth enamel if placed in the right environment (Kollar & Fisher, 1980). More generally, the complexity of species is uncorrelated with the amount or complexity of their genes (Sparrow, Price, & Underbrink, 1972; Raff & Kaufman, 1983). Simple organisms may have complex genes. The greater diversity of cells found in more complex organisms is not due to their having more complex genes, rather it is due to the manner in which their genes have been controlled over development. As the development of tooth enamel from chicken D N A illustrates, the structure and function of a cell arises from the interaction of genes and their environment. D N A is turned on and off due to historical circumstances which emerge in the long-run behavior of the system. Thus, a neuron is what it is, not only because of its D N A , but also because of its developmental history. Had the cell been placed in a different location within the organism, then it would be a different sort of cell. Being formed by historical forces acting over the early development of the organism, the neuron possesses structural characteristics that are tuned by the short-term influences of adaptation and modulation that better relate it to its immediate environment and function. Adaptation and modulation. First, let us consider a few aspects of how the short-term history of a neuron can influence its operating characteristics, and for this purpose, discuss a visual receptor cell viewed in isolation. The activity of this cell is influenced by the magnitude and wavelength of light that it collects and by its level of adaptation. Adaptation is a function of the cell’s previous history with light over a time range of about one half hour or less (Chapanis, 1947). At any level of adaptation, visual receptor cells (cones) maintain a sensitivity to changes in light intensity over a range of about 3.5 log units of amplitude (Normann &

Hierarchy in Perct?ptwn

79

Werblin, 1974). The cells adapt to the prevailing luminance and change their adaptive state with luminance changes over their sensitivity range. As exemplified in the receptor cell, adaptation is a property of all biological systems. Biological systems adapt over time to the parameters of energies in their environment; thus, adaptation is a historical concept. The activity of any biological system is a function of both its recent past and immediate conditions. In addition, the receptivity of all neurons, including receptors, is influenced by neuromodulators that alter their intrinsic properties. Neuromodulators are substances that alter the excitability of neurons by modifying the properties of their ion channels (Kaczmarek & Levitan, 1987). By changing the receptivity of receptors and the neural integration weights on neural connections, neuromodulation allows a single neural network to serve a plurality of functions (Harris-Warrick & Marder, 1991). Thus, the response of neuron to a quantity of energy depends upon the long-run molar behavior of the system of which it is a part. In sum, all neurons are tuned to their environment and function through adaptation and modulation. Thus, the manner in which a given neuron responds to its initiating conditions is, in part, a function of the history of the cell over different scales of time.

Biological Systems are Hierarchical All biological systems are hierarchically organized and controlled (Grene, 1987). Cells exist within tissues, tissues within organs, organs within organisms, and organisms within communities and ecosystems. At every level of analysis, biological systems are comprised of lower level subsystems and are contained within higher level suprasystems. The interaction among levels is both horizontal and vertical, meaning that entities at the same level interact with each other and with those at higher and lower levels. In order to describe the behavior of a biological system, it is necessary to consider three levels of analysis. The focal level of interest, and those above and below it. Influences affecting the focal level from below are called initiating conditions and those affecting its behavior from above are called boundary conditions (Salthe, 1985). The application of initiating conditions is immediate, meaning that it occurs in the context of the present state of the focal level. Boundary conditions, on the other hand, always influence the behavior of the focal level in a historical fashion. The role of time within this tripartite analysis is illustrated by again discussing the functioning of a receptor neuron. Viewed as the focal level, a receptor neuron changes its state as a function of two initiating conditions: light and neuromodulating substances. In

80

D.R proftitt

this sense, information flows into the receptor from lower levels as the accommodation of light and neuromodulation is accomplished by subsystems of the cell. An account of how changes in the focal level are caused by initiating conditions can be accomplished without reference to history. As discussed above, the history of adaptation and modulation of the receptor cell, itself, is relevant to focal level activity; however, initiating conditions are applied in an ahistorical manner onto this background state. In general, three things go into formulae showing how initiating conditions affect focal level behaviors: (1) the current activity and receptivity state of the focal level, (2) the change in the initiating conditions, and (3) a transform function specifying the manner in which (2) causes a change in (1). Time may be a parameter of one of the variables in the equation; however, history is relevant only as it affects the current operating characteristics of the focal level. Unlike initiating conditions, boundary conditions are, themselves, temporally specific constraints. The coordinated activity of exploring the environment by the whole visual system places boundary constraints on the functioning of the focal level receptor. Consider that the magnitude and wavelength of light impinging on a receptor at one instant in time may have been selected by higher level decision processes acting upon earlier samples of light transduced by this and other receptors. For example, if the focal receptor cell is in the fovea, then the structure of light impinging upon it and surrounding receptors may have been first detected by more peripheral receptors and, following central nervous system (CNS) analysis, the system may have decided that this pattern was deserving of a more careful look. Eye movements are guided by intent and by the history of visual experience over some time span. Similarly, the application of neuromodulating substances is controlled by historical influences on the higher level systems responsible for organizing molar behaviors. Boundary conditions are always temporally specific. In the case of a receptor cell, the CNS places constraints on the receptor’s initiating conditions by selecting its inputs and modulating its receptivity in accord with prior circumstances and present and future goals. In this case, it is still only the initiating conditions that are directly affecting the focal level receptor cell; however, the boundary conditions of the larger system have a pervasive role in selecting these inputs. It is important to recognize that the logic that governs the relationship between boundary conditions and a focal level is not reducible to the logic of the focal level, itself (Polanyi, 1968). To paraphrase one of Polanyi’s examples, consider the letters in the text that you are reading. These letters, construed as a focal level, are comprised of ink; however, their shape is not reducible to the structure of that ink, but rather depends

Hierarchy in Perception

81

on phonology and its realization in orthography. The ordering of the letters is, likewise, not dependent on orthography, but rather on language specific phonological restrictions and on morphology and syntax. Finally these linguistic boundary conditions are further constrained by the idiosyncrasies of my style and by the ideas that I intend to communicate. In summary, biological systems are hierarchically controlled. A description of their behavior requires a specification of three levels of analysis: initiating conditions, focal level, and boundary conditions. The manner in which initiating conditions affect the behavior of focal levels can be described in mechanistic terms and is ahistorical. The constraints placed on focal levels by boundary conditions are historically modulated. The language appropriate for describing boundary conditions is not the language appropriate for describing the influence of initiating conditions on focal levels. Boundary conditions do, in fact, act on focal levels through their appropriate initiating conditions; however, they do so by reducing the degrees of freedom on the initiating conditions that impinge on focal levels over time. That is, boundary conditions place constraints on the information flowing into focal levels by imposing structure on their inputs. The form of this structure can only be described in a language appropriate for describing the functioning of the relevant suprasystem, and the application and removal of boundary condition constraints is influenced by the history of that suprasystem. Within the range of meaningful levels of analysis, every system serves as an initiating condition for systems of a higher level and sets boundary conditions for those of a lower level.

The Decomposability of Biological Systems A useful strategy in investigating complex systems is to decompose them into their component parts and determine how each component responds to its initiating conditions independent of the boundary conditions set by the larger system of which they are a part. So, for example, it is possible to discover everything that there is to know about the functioning of a receptor cell’s response to its initiating conditions without being at all concerned about boundary condition influences. A receptor cell responds in the same way to light regardless of whether the particular parameters of light incident on its pigments are unanticipated or were selected by its suprasystem. This sort of reductionism has been practiced with such great success in the biological sciences as to make one wonder whether there is really anything that cannot be discovered through an employment of this strategy. The reductionist strategy is a fully adequate means to find out certain things about a system, but not others. If one’s interest is in describing how a focal level responds to its initiating conditions, then the reductionist

82

D. R PrOfFtt

strategy is the paradigm of choice. On the other hand, if one wants to know how the focal level relates to its suprasystem, then reductionism falls short due to the irreducibility of history. Reductionism can describe what each subsystem is capable of doing, but not what it actually does during ongoing coordinated behavior. Now, it might be argued that reductionism could be applied at all relevant levels of a complex system, and that in this manner the functioning of a whole system could be adequately described. So, for example, one could begin with the lowest levels of the visual system and work up. First, the receptors’ response to light could be described and then, applying the techniques of electrophysiology to ever ascending levels, the hierarchical structure of the visual system could be revealed. The problem with this approach is that it excludes the influence of boundary conditions on each focal level under study. Note that almost all electrophysiological investigations of vision have been conducted on anesthetized animals. To assume that the findings of such research-in which highly restricted visual stimulation is projected into the eyes of insensible animals-an be generalized without qualification to situations in which the animals are conscious and freely moving, is to assume that the nervous system’s functional organization is static and unaffected by the current intent, experience, and coordinated activities of the organism. As has been discussed, we know that this is not so. Neuromodulation, for example, changes neuronal receptivity patterns so as to allow a given network to serve a plurality of molar functions. Neuronal receptivity depends upon what the organism is doing. The initiating conditions for every focal level are structured by influences acting in the history of its suprasystem. In this manner, boundary conditions serve to coordinate the activities of a system’s components. To elaborate on this point, I return to a discussion of the functioning of DNA. An organism’s D N A is a template for the production of R N A and, through its mediation, of proteins. It is conceivable that one could enumerate all of the proteins that could be produced by the D N A of an organism. That is, the potential response of this D N A to all possible initiating conditions could be obtained. Such a description would provide a description of what the D N A could do, but not of what it actually does within the context of an organism’s cell. A s was previously discussed, most of a specialized cell’s D N A is turned off by the boundary conditions of its context. The behavior of D N A is controlled by initiating conditions specific to the environment in which its cell resides. By way of analogy, consider a piano. It is quite straightforward to determine how each key responds to its initiating conditions-those being the forces applied by the pianist’s fingers-and to specify the parameters

Hierarchy in Per@

83

of sound that result. Such an analysis could yield an exhaustive description of what the piano can do; however, it falls considerably short of providing a description of the keyboard’s functions in the playing of music. Within any particular tonal key, some keys will be played but not others, moreover certain keys can be played at the same time, but other pairings are excluded. The initiating conditions for the keyboard are constrained by the boundary conditions imposed by tonal structure, by the particular form of the composition being played, and by the current temporal position within that composition. The keyboard is not a formula for music, D N A is not a formula for an organism, and a nervous system is not a formula for meaningful experience. Viewed as focal levels, each is affected by initiating conditions that are structured by boundary conditions imposed by the suprasystem in which they reside. Boundary conditions restrict the degrees of freedom for the initiating conditions acting on a focal level. In this manner a system places constraints on the operations of its components, constraints that are not operative when its components are observed in isolation. Because boundary conditions are historical, their application may not be immediately evident when a system is initially activated. This issue has been elaborated by Simon (1973; 1981, ch. 7), who noted that hierarchical systems are nearly decomposable; the short-run behavior of a component is approximately independent of other components, whereas its long-run behavior is not. I can think of no better example to illustrate this idea than that provided by classical conditioning. It seems reasonable to conceive of an organism’s auditory and digestive systems as being modular, implying that one could study the functioning of one system without regard for the functioning of the other. Over the short-run these systems do, in fact, appear to be modular; however, as Pavlov (1927) demonstrated, if a tone is repeatedly paired with the presentation of food, then the tone will come to elicit a digestive system response in apparent anticipation of the food. In this manner, the activities of the auditory and digestive systems become coordinated through the history of their associated activation.

The Potential of Biological Systems is Given Limited Expression As discussed above, the potential of DNA to produce proteins is not realized in any cell, nor is it realized in the aggregate behavior of all of the cells of an organism. Recall that the size and complexity of the D N A in organisms’ genomes is uncorrelated with the complexity of species, and that a particular organism’s D N A is capable of producing proteins not normally found in the species. Most of an organism’s DNA is turned off.

84

D. R ProfFtt

Individual organisms possess a potential that is given limited expression as a function of three variables: (1) their intrinsic genetic potential, (2) environmental influences within and outside of the organism, and (3) the interaction between (1)and (2) over the developmental history of the organism (Gottlieb, 1992). A s was previously discussed, organisms develop through a process of differentiation in which DNA controls and is controlled by its cytoplasmic environment. This reciprocal control between DNA and its cytoplasm is constrained by boundary conditions imposed by the tissue in which the cell resides. These boundary conditions constrain the degrees of freedom of DNA/cytoplasm interactions by turning DNA off and on. Since most of an organism’s DNA is turned off, its potential is not fully expressed in individual phenotypes. It is possible that hidden in the unexpressed DNA of our cells are templates for producing the RNA enzymes associated with all of the proteins required to produce the vanished tissues of our hereditary ancestors (Gottlieb, 1992). Moreover, it is also possible that the movement of organisms into novel environments may result in the turning on of previously blocked DNA and that new phenotypic forms can thereby emerge without prior genetic mutation (Gottlieb, 1992). Speculation aside, it is certain that a description of how DNA functions within an organism falls far short of being a complete account of how it could function if unconstrained by its natural environment.

Interim Summary In the first part of the essay, I attempted to provide a brief sketch of some important aspects of biological functioning. The primary notion that I want to emphasize is that biological systems are constrained by historical influences operating at different time scales. Biological systems are organized and controlled hierarchically. Any given focal level is influenced from below by initiating conditions and from above by boundary conditions. The latter are historically modulated and place constraints on the structure of the focal level’s initiating conditions. The activity of focal levels caused by initiating conditions can be reduced to mechanistic descriptions. The constraints placed on initiating conditions by boundary conditions cannot be so reduced. Boundary conditions derive their form from the logic of a focal level’s suprasystem, and thus, their structure cannot be reduced to that of the focal level. In addition, boundary conditions are controlled by historical influences that cannot be reduced to mechanistic formulae. Information flows into a focal level through energies acting on its constituent parts. The structure of these energies is constrained, prior to its reception at the focal level, by boundary conditions imposed from above.

Hierurcly in Per-

85

Thus, the information arriving at a focal level is organized by the history and logic of its suprasystem. In this sense, the information flowing into a focal level already has meaning relative to the larger system that sets its boundary conditions. Implications of this analysis for perceptual theory are developed in the next part of this essay. The central notion that I hope to establish is that the nervous system is no more a formula for meaningful experience than is D N A a formula for an organism. In both cases, intrinsic and extrinsic influences combine in hierarchical organizations having developmental histories. Such systems require analyses that specify the contribution of both initiating and boundary conditions on focal level functioning. In this regard, I emphasize that the input arriving at any stage in perceptual processing has been organized by processes originating in both lower and higher stages. In everyday contexts, the input to the perceptual system is constrained by the environment and by the organism’s meaningfully guided exploration of it.

PERCEPTION VIEWED AS AN ACHIEVEMENT OF A BIOLOGICAL SYSTEM Few debates in the perceptual literature have generated more heat than that between those who argue for ecological validity in perceptual research and those who demand mechanistic precision. The source of this conflict, and the reason it has failed to reach a resolution, is that ecological validity requires that the system be allowed to function under its natural, historically-occurring boundary conditions, whereas mechanistic precision can best be achieved through an ahistorical reductionist paradigm. In essence the debate is about whether inquiry should be focussed upon the short- or the long-run behavior of the system. As discussed below, neither analysis alone is sufficient.

Ecological Validity To my mind, the best articulation of the ecological position in perception research is found in Gibson’s (1979) book, The Ecological Approach to Visual Perception. There, Gibson showed how the environment and perceiver are reciprocally involved in every aspect of naturally occurring ambulatory perception. For Gibson, perception is an awareness of affordances, affordances being the organism-relative value of surfaces and entities in the environment. Consider an example. Suppose that you have before you a nail and a piece of wood, and that it is your intent to drive the nail into the wood. There is no hammer

86

D.R proffitt

available for your use. What are you to do? Look about you and you will find something that will suffice as a hammer. You could use this book, although it is not likely to stand up well to the process. As I engage in this make-believe search myself, I notice that the metal base of my desk lamp is easily detachable from the rest of the lamp, and that it would serve the hammer function fairly well. The important point in this demonstration is that the environmental properties that are perceived at any moment in time are dependent upon the behavioral repertoire and intentions of the perceiver. If I am not looking for something that could function as a hammer, I will not perceive this affordance in my lamp’s base. The affordance is there, but it will not be noticed. The potential affordances of an object are indefinite in number; those that are actually perceived at any moment depend upon the perceiver’s desires. The perceiver’s behavioral repertoire and intentions are boundary conditions on perceptual processing. What will serve me as a hammer is constrained not only by the mechanical demands of the situation, but also by my size, strength, and morphology. My car would make a great hammer if only I could pick it up. As I looked about my office, I sought something of a size that could be grasped in my hands and of a material that would stand up to repeated impacts with the nail. In emphasizing the mutuality between the perceiver and the environment, Gibson was stressing the role of boundary conditions in perception. The initiating conditions for perception are constrained by the boundary conditions inherent to the ways of life of the perceiver. One pervasive aspect of these boundary conditions is that perception is typically exploratory; usually we are looking for certain things, but not others. Neisser (1976) stressed this point when proposing that perception functioned as a cycle in which the current structure of awareness guides the exploration of the environment and is, in turn, modified by what is found. When perception is viewed within an ecological context, it is seen to be temporally specific. The long-run behavior of the system is a ”stream of consciousness” (James, 18901, any moment of which derives its meaning from the history of the environment-perceiver system. Perceptions are controlled by historically modulated circumstances, development, and desires, each of these three terms having an ecological meaning that embodies a mutuality between the organism and its environment. To me, most of Gibson’s ecological approach to perception has the ring of truth to it, and yet it is far from being altogether satisfying. Most of what I know about perception from reading the empirical literature makes little or no contact with this theory. The primary reason for this is that most empirical work is focussed on the short-run behavior of the per-

Hierarchy in Perqtim

87

ceptual system, whereas ecological theory is about its long-run functioning. As was discussed in the first part of this essay, the short-run behavior of a biological system can be effectively reduced to the structure and functioning of its components, whereas its long-run behavior cannot. An affordance has value, and thus, is not a property of the entities derived from any decomposition of perception. Values are not to be found in surfaces, light, eyes, or nervous systems. Values are irreducible properties of long-run perceptual experiences. They exist in the mutuality between the organism and its environment, and it is within this system that the meaning of values resides. For me, it is difficult to write about values; I have little insight into their nature and their role in perceptual processing is rarely discussed by perceptual scientists. However, it seems to me self-evident that all of our perceptual experience conforms to systems of values. From the mundane observation that something looks “good” to eat to the aesthetic appreciation of a work of art, experience has valuative meanings. The value systems that are evident in experience serve as boundary conditions for the perceptual exploration of the environment. Just as music is not a property of pianos, but rather serves as a boundary condition for their meaningful playing, so too values place boundary conditions on the components of perceptual processing without being properties of these components, themselves. What makes ecological theory unsatisfying is the enormous gulf between the vague vocabulary appropriate for its analysis, and the precise descriptions found in investigations of lower level perceptual mechanisms. The study of perceptual mechanisms is reductionistic, ahistorical, precise, and optimistic. There is no-well posed question in this domain that cannot be answered up to the resolution of the available technology. This is a luxury not afforded by ecological research for the simple reason that natural history cannot be controlled. I return to this point after discussing a few aspects of the mechanistic approach to perception.

Mechanistic Adequacy What makes the mechanistic study of biological systems possible is that the short-run behavior of any focal level is completely determined by its initiating conditions, its current operating characteristics, and the transformations that relate these two classes of variables to focal level activity. In order to understand a system in these terms, the system must be isolated from all influences on its behavior that cannot be controlled in the experimental context. This isolation can be absolute-meaning that there are no effective variables acting on the system other than those being manipulated by the experimenter-or it can be statistical-meaning that uncontrolled conditions are permitted to contribute to the variability

88

D.R ProfFtt

in the system’s behavior but not to its correlated response to the manipulated variables. Whereas the ecological approach to perception emphasizes the role of boundary conditions, mechanistic approaches attempt to minimize their influence. The adequacy of mechanistic methodologies, in fact, depends upon the elimination of boundary condition influences on the focal level of analysis. Consider an example of the reductionist/mechanistic approach. Johansson (1973) demonstrated that people can identify the human form when observing movies showing only the motions of 13 points of light attached to the joints and head of actors’ bodies. From this finding, he was justified in concluding that the human form can be identified on the basis of motion information alone. There are, of course, very good reasons for using point-lights. Had Johansson simply shown movies of ambulatory actors, no one would have been impressed since people can identify the human form on the basis of a variety of available static pictorial cues. The motivation for using moving points of light is that almost all static configural information is eliminated in these displays. In addition to presenting displays with reduced information, subjects in these experiments were given no instructions that would allow them to form an expectation about what would be shown to them. In this manner, Johansson controlled for the naturally occurring boundary conditions that are in place when real people are encountered in everyday situations. There is a way in which studies such as Johansson’s can be accommodated by an ecological approach. Ecological considerations promote investigations of perceptual achievements that people are thought to perform in everyday circumstances. Thus, most perception researchers assume that the perception of three-dimensional form from motion information is a naturally occurring perceptual feat. Demonstrating that people can, in fact, perceive form from motion requires the sort of controlled experiment that Johansson conducted. On the other hand, ecological considerations cast doubts about the generalizability of other empirical findings when it is not obvious that the phenomenon under study actually occurs in any ecologically-valid context. Consider, as an example, the perception of subjective contours (Kanizsa, 1976). This phenomenon is observed in drawings in which the corners but not the intermediating edges of simple shapes are presented. Not only are illusory contours seen, but the apparent brightness of the interior of the shapes is misperceived as being different from that of their apparent backgrounds. To my knowledge, I have never seen a subjective contour in any situation other than perception demonstrations. Is it an ecologically valid phenomenon? I certainly do not know. The only way to answer such a question is to have a more precise understanding of the natural boundary conditions occurring in everyday perception.

Hierarchy in Perceptiun

89

If the boundary conditions for natural perception are ignored completely, then we will develop a science of what the perceptual system can do but not of what it, in fact, does. Just as DNA can cause an abundance of proteins never found in the cells of its species to be produced, so too our perceptual system can evoke experiences that never occur in our everyday life. Whether the focus is biological or perceptual, all that is required to reveal the system’s potential capacities is the placing of the system of regard in the right sort of unnatural environment. This approach, however, has shortcomings. In order to avoid collecting innumerable uninterpretable facts about what the perceptual system can do over the short-run, it is important to develop an understanding of its long-run behavior. In turn, the long-run behavior of a system can only be understood in a precise mechanistic way by studying its short-run behavior. Currently, there are a few integrative theories that attempt to relate empirical findings to systematic views of overall perceptual functioning; regrettably, however, all are completely mechanistic and ahistorical. I do not view Gibson’s approach as an exception because it makes insufficient contact with the empirical literature to be considered as an integrative theory. Probably the most influential integrative account today is that provided in Marr’s (1982) book, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. A virtue of Marr’s account is that perceptual processing is described as being hierarchically organized. Unfortunately, the flow of information in his account is unidirectional, being from the lowest level to the highest. Higher levels do not set boundary conditions for lower levels, and history has no role to play in restricting the degrees of freedom of initiating conditions operative at each focal level. The debate over ecological validity versus mechanistic adequacy is, in essence, a debate over the time span over which the system of regard should be studied. In other words, it is about whether or not history should be allowed to play its role in the behavior under investigation. Oddly enough, this debate has rekindled most recently in the field of memory research, where one might assume that the role of history could not have ever been excluded. In fact, Ebbinghaus (1964/1885), who initiated the experimental study of memory, realized correctly that the mechanisms of memory could not be adequately studied without minimizing the boundary constraints on the initiating conditions to the memory system. To this end, he created nonsense syllables as the materials to be remembered. Later, Bartlett (1932) criticized Ebbinghaus’s procedures for their lack of ecological validity. Bartlett argued correctly that it is the purpose of the perceptual system to find meaning, and that the manner in which material is remembered depends upon the history and interests of

90

D.R proffitr

the individual. This debate has resurfaced on a number of occasions, most recently in an article by Neisser (1978) who, in promoting the ecological position, asserted that: "If X is an interesting or socially significant aspect of memory, then psychologists have hardly ever studied X" (p. 4). Banaji and Crowder (1989) took umbrage to Neisser's remarks and extolled the virtues of control and precision in memory research focussed on mechanistic processes. The conflict here, as between Ebbinghaus and Bartlett, is about whether or not history should be included in memory research. The resolution to this debate may lie in recognizing that research on the long-run behavior of a system need not be viewed as inconsistent with that on short-run mechanistic processing. If one is interested in the shortrun behavior of the system, then history is best excluded. There is much to be learned from studying short-run behaviors, but ecological validity is rarely achieved. If long-run behavior is also of interest, then history is a central concern. There is much that we can learn from history, but mechanistic adequacy is not to be expected. History cannot be controlled, and thus, long-run behavior cannot be captured in mechanistic descriptions. A closer examination of this reconciliation is in order.

I'op-Down Influences are Applied in a Bottom-Up Fashion In the perception literature, it is common to refer to the influences of .nowledge and expectations on perceptual processing as consisting of topdown effects, whereas the ascending flow of information originating in recP--*mactivity is said to be bottom-up. I would substitute for these two tckL those of boundary and initiating conditions for two reasons. First, givtil the hierarchical structure of the perceptual system, the activity of one level sets boundary conditions on those below it while providing the initiating conditions for those at higher levels. The terminology of bottom-up and top-down does not accommodate well the reciprocal nature of hierarchical control. Second, top-down influences, in fact, function in a bottom-up manner. Nothing can directly affect a focal level other than its initiating conditions. Boundary conditions influence focal levels through their inputs. Every level within a system functions only in accordance with the mechanistic laws specific to its level. A piano key sets into motion the same series of events regardless of whether it is pressed during the playing of a musical composition or during the random fingerings of a novice. Likewise, a neuron responds to its initiating conditions in a mechanistic fashion that is not cognizant of the functioning of its suprasystem. Boundary conditions constrain the degrees of freedom of the initiating conditions acting on a focal level in accordance with laws specific to the suprasystem. In so doing, they do not alter the mechanistic laws of the

Hierarchy in Pereptbtz

91

lower level (Polanyi, 1968). Boundary conditions manifest their effects by constraining what the focal level does, not by changing what it is capable of doing should these constraints be removed. Consider as a focal level the activity of a neuron. Its initiating conditions consist of excitatory and inhibitory effects received from other neurons and influences on its receptivity caused by neuromodulation substances. Neuromodulation is a product of the cell’s suprasystem activity, but its direct influence is to change the cell’s operating characteristics. Information can flow into a cell from all levels via excitation and inhibition by other cells. That is, a neuron may receive information from cells at lower, higher, or the same level in the hierarchy. Boundary conditions can affect the behavior of all three. Cells at a lower or at the same level may pass on information that had been selected by the suprasystem. Obviously, information flowing into a cell from higher levels has been structured by laws of the relevant suprasystem. The direction of information flowing into a cell is manifestly multidirectional only from the perspective of the macrosystem. From the perspective of the focal level, all inputs are alike. There is nothing about the initiating conditions produced by ascending fibers to distinguish them from those originating from descending ones. It is for this reason that the response of a neuron to its initiating conditions can be reduced to mechanistic formulae. On the other hand, the pattern of this neuron’s activity over time cannot be reduced to the same formulae that describe its response to its initiating conditions, because the neuron’s long-run activity is influenced by the immediate environment and by the functioning of the organism. This is another instance of the temporal specificity of biological functioning; the short-run behavior of a biological system is decomposable, whereas its long-run behavior is not. The perceptual system functions over the long-run in a coordinated manner by constraining its inputs and modulating the activity of its components. In this sense, bottom-up and topdown processes are controlled by both the same and different laws. All bottom-up processes are reducible to the mechanisms responsible for the short-run response of relevant focal levels to their initiating conditions. Top-down processes directly affect focal levels through their initiating conditions, and thus, their application can be reduced to the same mechanisms as are effective in bottom-up processing. On the other hand, top-down processes constrain the inputs to focal levels over time in a manner that implies the meaning structures, purposes, and history of the suprasystem. In summary, the short-run behavior of any focal level within the perceptual system is reducible to mechanistic description. The long-run behavior of the system will be en-

92

D. R proffitt

tirely consistent with the mechanistic laws of its short run-behavior but it is not reducible to it.

Hierarchical Explanation In the second part to this essay, I have provided a sketch of a hierarchical point of view to perceptual functioning. The hierarchical perspective promotes analyses of both long- and short-run behaviors, that is, of both boundary and initiating condition influences on focal level functioning. Moreover, it requires an appreciation for the hierarchical nesting of focal levels within suprasystems. Further, I have attempted to show that the conflict between ecological and mechanistic approaches to perception is, in fact, about whether perception should be studied in historical or ahistorical contexts. It seems to me that neither approach is intrinsically in conflict with the other, but rather that the two approaches ought to complement each other since neither is, by itself, sufficient. Current integrative approaches, for example Marr (19821, represent the hierarchical organization but not the multidirectional hierarchical control of perceptual functioning. In Marr’s model, the initiating conditions acting on each focal level are transformed and passed up to the next level. Thus, an image’s intensities are registered, edges are found, surfaces are identified, their orientations are represented, and so forth, respectively. The influence of boundary conditions on focal levels is completely absent in this and all other information processing models with which I am familiar. What is missing is the manner in which the intent and meaning systems of the suprasystem constrain the inputs to each focal level. Often top-down processes are proposed as being influential; however, their application is, typically, proposed to occur on the final products of bottomu p processing. A hierarchical point of view suggests, instead, that the application of top-down processes-boundary conditions-occurs in the manifest organization of inputs to a focal level, not as an additional operation on its output. Consider the word superiority effect. Cattell (1886) demonstrated that a letter is more easily processed when it occurs in the context of a familiar word. For example, the minimal time required to recognize a familiar written word is far less than the sum of the times needed to identify each of its individual letters in isolation (cf. Wheeler, 1970). The word superiority effect demonstrates that a word’s meaningfulness serves as a boundary condition for the identification of the letters of which it is comprised. In reading, it is obvious that top-down semantic influences are applied before orthographic analyses are completed. The focal levels responsible for letter identification benefit from a reduction in the degrees of freedom of their inputs that morphology supplies.

Hierurchy in Percqtion

93

The processes involved in identifying letters during reading are misrepresented when studied solely in a controlled context in which only isolated letters are presented. Letter identification is much harder in the controlled context than in the naturally occurring one in which meaning is pervasive. Likewise, any perceptual competence is facilitated by the boundary conditions imposed by the intent and meaning structures of the relevant suprasystem. It is a goal of ecological research to define the structure of these meaning systems. The nature of meaningful experience is a product of our human ways of life, the circumstances we encounter, and the history of this interaction. Meaningful experience cannot be reduced to our nervous system for the same reason that our nervous system cannot be reduced to its DNA. Neither is a formula for its own functioning within an ecologically valid context. Reductionist analyses can inform us about what a biological system is capable of doing in isolation and over the short-run. It cannot provide a satisfactory account of the historical developments that give the system its coordinated functioning and meaning. Ultimately, a theory of meaningful perceptual experience will have to address issues of human values and their role in constraining the initiating conditions to everyday perception. At present, we are far from knowing how to approach such an analysis. However, I think that we are more prudent scientists when we understand what we can and cannot do with reductionist analyses. A hierarchical approach to perception promotes a pursuit of mechanistic reductionism complemented by an analysis of the natural history of meaningful existence.

DISCUSSION Gary Hatfield (Department of Philosophy, University of Pennsylvania, Philadelphia, PA): Proffitt contends that historical factors should play a central explanatory role in perceptual theory. His emphasis on the historical conditioning of perceptual systems contrasts with the ahistorical, mechanistic bent of much recent work in perception. In my view, Proffitt does not go far enough. Historical factors are even more fundamental to perceptual theory than he suggests. Proffitt distinguishes between mechanical systems and biological systems. Mechanical systems can be analyzed in terms of their current physical state without attending to their developmental histories or even their recent interaction with the environment. Biological systems are determined by historical contexts. The structure of the system is determined by its interaction with its environment during development the same D N A

94

D.R proftiff

produces different proteins and cell structures in different cytoplasmic contexts. The current properties of a system are subject to adaptation and modulation by environmental influences: photopigments become adapted to the intensity of ambient light. This distinction between mechanical and biological systems is conjoined to a systems-hierarchical analysis of biological and psychological entities. A given object of analysis (the “focal level” of a system) is influenced by ”initiating conditions” and by “boundary constraints” (see Salthe, 1985). Proffitt maintains that the entities in psychological systems that respond to initiating conditions, such as receptors in a perceptual system, are subject to ahistorical, mechanical (physical-chemical) analysis. Appeal to boundary conditions is needed, however, to understand the operation of the larger system into which the initiating conditions feed. Thus, although the momentary response of a receptor can be understood by its current chemical state, this state (and hence the adaptation level of the sensory system) can best be explained by examining the receptor’s recent history of exposure to light; similarly, the receptivity of a sensory system may be influenced by the desires and beliefs of the cognitive agent in which it is embedded. Proffitt quite plausibly applies his biological/mechanical distinction to the debate between the “ecological” and “mechanistic” (his label) approaches to perception. The ecological approach takes into account the historical circumstances of perception: the perceiver’s behavioral repertoire (conditioned by its developmental history) and current intentions and desires (modulated by its recent history). The perceptual scientist, according to this approach, must examine the organism as it interacts with its environment over time. Proffitt cites Gibson (1979) as a chief adherent of the ecological approach. Marr’s (1982) appeal to ”assumptions” about the structure of visual environments also incorporates aspects of this approach (see Hatfield, 1988, 1990). The mechanistic approach, by contrast, focuses on the mechanical properties of perceptual systems in isolation from the environment. As Proffitt illustrates with his piano analogy, mechanistic analysis of the mechanisms of perception is intended to yield an abstract characterization of the ”possibilities” latent in the system. In determining the possibilities, one simply treats a piece of “the system” as a thing with many unknown properties, and then seeks to discover these properties by tweaking the thing one way and then another, and noting the response. In essence, one seeks to determine empirically an input-output function for a particular system component, in isolation from its developmental history or recent environmental contacts. According to Proffitt, mechanistic analysis can yield ”everything there is to know about the functioning of a receptor cell’s response” without any concern with boundary conditions. The

Hiwarchy in Perczpbbn

95

mechanistic approach provides, Proffitt contends, a successful case of the reduction of a component of a biological system to its physical and chemical embodiment. He places much of the current laboratory research in perception under the mechanistic rubric. Proffitt’s analysis is accurate and insightful as far as it goes. However, I think that perceptual systems are historical entities in an even more radical sense than he indicates. His discussions of the temporal conditioning of biological and perceptual systems focus on ontogenesis and shortterm physiological adaptation; they do not include evolutionary adaptation. But evolutionary adaptation provides an additional set of historical boundary conditions (in Proffitt’s terms). Proffitt’s analysis of ontogenesis and adaptation begins with some D N A taken as a given, or with a given physically-described receptor cell. Evolutionary explanations, by contrast, can show why D N A with a particular structure is present in the gene pool, or at least why perceptual systems with a certain morphology are present in a particular environment. They chart the long-term modulation and adaptation of the system by and to the environment. Perhaps surprisingly, historical, evolutionary considerations also guide the also I legedly ahistorical, mechanistic analysis of perceptual systems-r shall argue. According to Proffitt, standard laboratory work in perceptual psychology engages in an ahistorical search for input-output mappings. This description accords with a conception of psychology as the search for the structure of cognitive and perceptual mechanisms, independent of their relation to an environmental context. I agree with Proffitt that this conception fits much contemporary work. It has been articulated in philosophical reconstructions of psychology that emphasize a “narrow” construal of psychological states (Fodor, 1980) or that adopt a ”syntactic” theory of mind (Stich, 1983). Nonetheless, I believe that all concerned have failed to see that the notion of determining an input-output function by tweaking “the system” already presupposes what philosophers call an individuation of that system into functional components. (“To individuate” is to delimit a given entity from among others; in systematic theoretical contexts, it entails providing a principled basis for including some of the matter in a particular space-time region as part of an entity and other as not, or of including some of the alterations of the entity as its proper activities, and others as not.) And this individuation, I maintain, presupposes a conception of the biological or psychological function of the system in questionone that is tacitly imported into the experimental design in the selection of independent variables and that guides the very choice of a particular piece of the system for concerted tweaking.

%

D.R proffitt

The notion of biological or psychological function that guides individuation is not equivalent to input-output function. It is historical and evolutionary. A given ”system” in an organism produces many effects, some of which investigators intuitively consider to be relevant, and others which they ignore. Thus, the heart not only pumps blood, but it also makes heart sounds. Physiologists consider the pumping of blood to be the primary function of the heart (Parmley & Talbot, 1979). On what is this judgment based? According to the etiological analysis of function statements (Neander, 1991; Wright, 1973), it is based on the belief that the heart evolved because it pumps blood, not because it makes noise. (Indeed, the organ has the “possibility” of making noise without pumping blood, by hitting the chest, though in historical time it could do so only momentarily.) The judgment that the heart is a pump carries with it a conjecture about the role this organ plays in the economy of a larger physiological system. And conjectures about its proper role are, on this analysis, conjectures about the evolutionary effects of the organ across phylogenetic development (but cf. Cummins, 1975, for a conflicting analysis). The biological and psychological function of the vertebrate visual system presumably is to receive and process information about the spatial and reflective structure of the ambient environment for the purposes of self-orientation, motion guidance, and detection of neighboring items of interest (Gibson, 1966, ch. 9). Functional analysis of the system underwrites the individuation of component structures such as the lens, the photoreceptive retinal screen, and the visual pathway. Once functionally individuated, the components can be subjected to mechanistic analysis. But this analysis is not random. It is guided by a prior conception of the functional role of the component. To see that this is so, take the example of a receptor cell. At first blush, such a cell would seem to be an ideal candidate for complete reduction to its physical-chemical constituents, and consequently for ahistorical, mechanistic analysis. One can infer the input-output functions of the various kinds of receptor cells in the retina (rods and three types of cones) through behavioral, photometric, and chemical studies; one can even plot the regeneration curves of receptor dyes, thus determining the abstract set of ”possibilities” that yield a specific state of adaptation when a receptor is subjected to an historically concrete course of light stimulation. Consider for a moment what this endeavor presupposes. First, consider the focus on light as the agent of tweaking, rather than electrical or thermal or chemical agents. This choice reflects the investigator’s tacit knowledge that the receptor cells in question are part of a light-sensitive system, and that their (bio-)function is to respond to light energy (perhaps within a specific spectral range). Indeed, the very notion of receptor

Hierarchy in Perception

97

itself is not an ahistorical, mechanical concept. It is already functional. The notion that a discrete portion of the space-time continuum in a given retina should be treated as the point of focal interest already presupposes a decomposition of the retina into biologically and psychologically relevant entities. And these entities are individuated by appeal not only to their ontogenesis from some particular D N A , but also by appeal to the specialization of their function in evolutionary time. Indeed, germ cells with D N A can undergo a wide variety of transformations depending on their physical-chemical context; but psychologists usually are interested in the morphological structures (including mechanisms of perception) that result when D N A has developed in ecologically typical contexts. The fact that human D N A normally yields sighted organisms is no accident, but reflects a long historical process of selection for visual ability (among others). Even purely behavioral studies that chart psychophysical responses presuppose a functional analysis. Experimenters attend to some aspects of the overall behavior of subjects in a perception experiment (finger presses, perhaps) and not to others. They assume that these focal behaviors are mediated by the relevant sensory system. Usually, they also assume that they know the basic discriminative abilities of the system (e.g., sensitivity to light, color, and spatial structure), so that they may now focus on more subtle aspects of perception. Of course, when clean data are obtained, these assumptions seem quite reasonable; but they are nonetheless assumptions for that. Such assumptions suggest that experimenters do not approach the perceptual system as if it were a mysterious bit of physically and chemically described matter whose properties must be charted, but rather they treat it as an organized, functionally-characterized component in a psychological system. The same point can be carried over to Proffitt's piano analogy: the fact that the "possibilities" are determined by striking the keys, rather than burning or freezing or dropping the object, already suggests that the piano is being regarded under a functional description that identifies the keys as important functional components and that marks striking the keys as functionally relevant "initiating conditions." Adopting an evolutionary stance and using evolutionary considerations to guide the functional individuation of system components does not violate Proffitt's important dictum that D N A is not a recipe for an organism, etc. Indeed, the expression of D N A requires cytoplasmic conditions. Normal development of an animal requires extrafetal stabilities prior to birth, and subsequently (after birth) an environment that falls within certain extremes of heat and cold, that is aquatic or arid (depending on the species), etc. Far from simply being boundary conditions on ontogenetic de-

98

D. R Pn$tf

velopment, these environmental stabilities-and changes that occur in them-provide boundary conditions that work at the level of the development of morphological types within a species and across species. In Proffitt's own terms, there are global temporal boundary conditions on the development of organismic structures and systems that should be included in the study of perception. Gibson (1966, ch. 9) included such factors in his conception of perceptual science. Outside psychology, investigators who study the environmental biology of vision have long attended to such factors (Autrum, 1979; Lythgoe, 1979; Munz & McFarland, 1977). The development of light-sensitive cells and of visual systems has a long evolutionary history. One historical boundary condition on this evolution has been the presence of light. The light sensitivity of most organisms is restricted to a narrow band of the electromagnetic spectrum, known as the visual range. This portion of the spectrum is not intrinsically "visual," but presumably became the visual range because it penetrated sea water, where the earliest sighted organisms arose (Lythgoe, 1979). Additional historical stabilities, as well as histories of the mutation range of early visual cones, may explain the development of our trichromatic color system (Goldsmith, 1990; Munz & McFarland, 1977). Indeed, the analysis of color as a representational kind may depend on historically-based ascriptions of function (Hatfield, 1992). Binocular single vision and stereopsis provide further examples of visual abilities with long evolutionary histories (Polyak, 1957, ch. 13, sec. 3; Walls, 1942, ch. 10, sec. D). This history has been conditioned by the presence of cohesive middle-sized objects in the environment. Evolutionarily stable environment/perceiver relations may also provide a key to analyzing some higher perceptual achievements, including basic forms of object recognition (Hatfield, 1988, 1991; Shapiro, 1992). To Proffitt's historical dyad of ontogenetic tuning and recent environmental modulation, I have suggested adding a third historical dimension: evolutionary adaptation to the environment. Tacit knowledge of this third element is already presupposed in the usual psychophysical experiments that focus on specific dimensions of the ambient environment, such as light in the case of visual psychophysics. Just as Proffitt exposed developmental and temporally local historical factors, I think that these evolutionary historical factors should be brought into plain view in perceptual theory. Ulric Neisser (Psychology Department, Emory University, Atlanta, GA): In a very stimulating contribution to this volume, Dennis Proffitt ar-

gues that biological (and psychological) systems must be understood from above as well as from below. I use "above" and "below''-instead of

Hierarchy in Percqtwn

99

”boundary conditions” /“initiating conditions”-to emphasize the link between Proffitt’s enterprise and that of the Gestalt psychologists, who were perhaps the first to take these issues seriously. In his loving eulogy of Max Wertheimer (the founder of Gestalt psychology), Wolfgang Kohler noted that Science... deals with facts and situations of two different kinds. A first type may rightly be regarded as consisting of components which are mutually independent ... But there are situations of a second type. A situation of this type does not consist of components ... its parts exhibit characteristics which they owe to their position within the larger entity... With an expression that Wertheimer liked to use: situations of the first type allow of an interpretation “from below,” an interpretation that starts with components, joins such components, and then arrives at the situations themselves. In situations of the second type this procedure is inadmissible. They have to be interpreted “from above,” because with this type it is a situation as a whole which determines the behavior of its parts (Kohler, 1944, p.143).

Nowadays situations of Kohler’s second type are called ”systems,” and it is no longer radical to note that the properties of parts often derive from the structure of the system as a whole. Like Wertheimer and Kohler, Proffitt insists that this principle holds especially for biological systems, which always require an understanding ”from above.” Also like them, he believes that the meaningfulness of perceptual experience-and by extension, the role of value in the determination of behavior generally-an only be understood from that perspective (cf. Kohler, 1938). There is yet another similarity: like his Gestalt predecessors, Proffitt takes the study of perception as the natural starting point for the investigation of issues like these. A s a longtime Gestalt sympathizer, I myself share all three of those assumptions; that may be why I find his argument so attractive. Nevertheless, this is no mere rehash of old claims. Proffitt’s argument is far more sophisticated than Kohler’s. For one thing, he insists that full understanding of biological systems requires analysis from below and above. The analysis from below, in terms of “initiating conditions,” is independent of history and context. Light falling on a photoreceptor cell, for example, initiates a particular train of chemical and electrical changes. A complete science of vision must necessarily include an account of such initiating conditions and their effects. In fact, we are close to having that particular account today: problems involving initiating conditions often have clear-cut solutions. Analyses from above, in contrast, are much more difficult. To fully understand the cell’s activity at a given moment, we would need to know how it got to be where it is and to do what it does. Its

100

D. R proffitt

history, in this sense, includes the course of its development in relation to neighboring cells as well as its DNA. Even more important, we would need to know why the cell was illuminated in just that way at just that moment. But this will always depend on “boundary conditions” that demand higher levels of analysis: on the environmental situation, the viewer’s eye movements, the reasons for those eye movements, etc. Boundary condition problems are so difficult that Proffitt sometimes (but not always, as we shall see) regards them as virtually insoluble. A second way in which Proffitt’s argument supersedes Kohler’s is in his emphasis on hierarchy. What is a unit in one analysis becomes the context for smaller units in another: there are levels within levels within levels, and all must be understood from above as well as from below. The Gestalt psychologists occasionally acknowledged the occurrence of hierarchical structure (as in the case of induced motion: Duncker, 19291, but as a rule they hoped that one level of analysis would be enough. This is particularly clear in their peculiar assumption that the whole brain-r at least large parts of it-could be treated as an undifferentiated “volume conductor” in which internal structure was relatively unimportant. We know now that the very opposite is true: that there are exquisitely detailed structures, with clear functional significance, at many levels of analysis. There is still another way in which Proffitt goes beyond Gestalt psychology. Writing in 1992 instead of 1922, he has a whole new set of muddles and misconceptions to refute. He does so beautifully; in some ways, this is the most impressive part of the chapter. Unfortunately, it is as common today as in Kohler‘s time to hear that everything in human nature will soon be explained from below. In this vein DNA is said to be a plan for the structure of the mature organism; any non-neural account of perception or action is characterized as essentially superficial; all psychological categories are thought to be temporary expedients, soon to be replaced by concepts from neuroscience. Proffitt is at pains to refute arguments like these. In a compelling analogy, he observes that DNA is no more a plan for the organism than a piano is a plan for a sonata. (What actually happens, in either case, depends on the boundary conditions that prevail on given occasions.) In fact, neuroscience alone can never tell us why any particular behavior occurs. What happens is always a lawful consequence of initiating conditions, but those conditions are what they are only because the historical and environmental boundary conditions are what they are. Because analysis must proceed both from above and from below, the debate between partisans of mechanistic adequacy and ecological validity is never over. Proffitt notes, in passing, that this debate has recently surfaced in the study of memory. In that domain, he takes the statesmanlike

Hierarchy in Perceptwn

101

position that both lines of inquiry have much to contribute. ”The resolution to this debate may lie in recognizing that research on the long-run behavior of a system need not be viewed as inconsistent with that on short-run mechanistic processing” (p. 90). In other words, ecological and traditional approaches to the study of memory are complementary wings of a single scientific enterprise. I certainly agree with that position (Neisser, 1991; Neisser & Winograd, 1989). In adopting it, however, Proffitt implicitly concedes that a science of boundary conditions is possible after all. In contemporary cognitive science, the role once played by the Gestalt psychologists is now being filled by the ”Gibsonians”-the ecologicallyoriented successors of J. J. Gibson (1966, 1979). It is they who insist that perception must be understood from above-indeed, at a more inclusive level than Wertheimer ever imagined. Gibson’s analysis did not begin with the retinal image, or even the brain, but with the whole animal embedded in and acting on the environment. Certain kinds of structured information are available in that environment: for example, the optic array and its changes over time as the animal moves about. Among the things specified by that information (along with the shapes and positions of objects) are certain ”affordances”-possibilities for action by the animal in question. According to Gibson, these affordances are the basis of perceived meaning and value. Ecological psychologists believe that the concept of affordance is fundamental for the understanding of perception. Proffitt understands these arguments very well, and even offersa good summary of Gibson’s views. They have, he says, “the ring of truth.” On that basis, he could easily have argued that the ecological and reductionistic approaches to perception, both valid, are more or less complementary (as he did in the case of memory). Oddly, however, he does not choose to do so. Instead he finds the ecological approach intrinsically unsatisfying; there is an ”... enormous gulf between the vague vocabulary appropriate for its analysis and the precise descriptions found in investigations of lower level mechanisms” (p. 87). According to Proffitt, ecological questions cannot be precisely answered at all, ”... for the simple reason that natural history cannot be controlled” (ibid.). That conclusion seems unduly pessimistic. Recent ecological research on many topics has been characterized by mathematically tractable models and high levels of precision: consider the perception of affordances (e.g., W. Warren, 1984), the information structure of optic flow (e.g., R. Warren & Wertheim, 1990), or haptic perception (e.g., Solomon & Turvey, 1988). For a particularly interesting set of examples, consider Proffitt‘s own studies of biological motion (Cutting, Proffitt, & Kozlowski, 1978) or wheel rotation (Proffitt, Kaiser, & Whelan, 1990). To me, these elegant studies

102

D.R proHitt

seem to fall directly in the ecological tradition. But Proffitt does not think of them that way; on the contrary, he cites Johansson’s related studies of biological motion as prime examples of the ”reductionist/mechanistic approach” (p. 88)! This characterization leaves me simply puzzled. It is true, of course, that discussions of higher-level structures can be discouragingly vague. That criticism was often and appropriately leveled at the Gestalt psychologists, and it applies as well to many of their successors. While it does not fit J. J. Gibson, who always defined his terms with particular care, it may indeed be appropriate to some of his sympathizers-myself, for example. My rather loose notion of a “perceptual cycle” (Neisser, 1976) is perhaps a case in point. (I was pleased to see that Proffitt finds it useful nevertheless.) Unfortunately, vagueness is not easy to avoid when one is trying to develop new ideas. That principle even applies to some of the ideas developed in Proffitt‘s own essay. Consider, for example, the notion of “hierarchy” that is central to his argument. Proffitt explicates “hierarchy” with a number of concrete examples. It is not clear, however, what these examples have in common. To see the problem, consider the following cases. (1) Biological structures: cells, tissues, organs, organisms, ecosystems (p. 79). This is a hierarchy of composition: organs are made up of tissues which are made up of cells, etc. 2) Causal histories: photons interact with photochemicals in a receptor neuron, the neuron fires, the whole sequence is conditioned by the eye movements involved in the animal’s visual exploration of its environment (p. 80). This is a hierarchy of explanation, of different causes analyzed over different time scales and different object sizes. 3) “The ascending flow of information originating in receptor activity” (p. 90). Here the hierarchy must be something like: rods & cones, ganglion cells, cells in the lateral geniculate body, cells in VZ, etc. This may be intended as a hierarchy of successive activation, though (as Proffitt is well aware) the real sequence of neural activity runs downward and sideways as well as upwards. 4) Linguistic units: printed letters, phonology, orthography, syntax, intended meaning (pp. 80-81). This is a hierarchy of constraints, not of causes. 5) Time scales: Proffitt seems to argue that initiating conditions operate more or less instantaneously, while boundary conditions are “historically modulated” (p. 81). But since what is boundary for one analysis may be focal for another, this cannot be an all-or-none matter. Perhaps, then, each level just has longer time constants than the

Hierarchy in Perception

103

levels below it. But this seems unlikely: why shouldn’t there be slow processes at the cellular level? These five cases invoke very different senses of hierarchy. As far as I can see, they do not map onto each other in any direct way. Proffitt himself may see further than I do; if so, some clarification would help. Pending that clarification, it is hard to know whether “hierarchy” is just a useful heuristic or the germ of a precisely defined scientific concept. But either way, Proffitt’s arguments have taken us a real step forward. The relation between higher and lower level theories is one of the most interesting and difficult scientific problems of our time, not only in the study of perception but in many other areas as well. If Proffitt has not provided a final resolution of that problem here, he has at least established boundary conditions within which more specific discussions can be initiated.

Proffitt: I am most grateful for and pleased by the commentaries that Hatfield and Neisser provided. Both essays reflect fair and insightful readings of my contribution, and point out clear limitations in my exposition. A common thread in both commentaries is their concern for what guides the scientist engaged in perceptual research. In responding to each commentary, I will focus on this common theme. Hatfield states that in discussing the role of historical influences in perceptual functioning, I did not go far enough. In particular, he notes that I failed to take into account evolutionary considerations. I admit that the role of evolution was not adequately discussed in my essay and agree completely with Hatfield that evolutionary considerations ought to be included within a hierarchical approach to perception. My decision not to discuss evolutionary processes was not meant to imply that I thought them to be irrelevant. In fact, an important inspiration in my writing of this essay was provided by hearing Gilbert Gottlieb speak on his new ideas about evolutionary theory and later by reading his book, lndividiial Development & Evolution (Gottlieb, 1992). One of the problems with discussing evolution is that current theory is a good deal different than what most psychologists believe it to be. That is, our profession is not especially well schooled in evolutionary theorycertainly, I am no expert-and a discussion of evolutionary considerations would have necessitated a more extensive treatment than that which I provided in describing DNA functioning. I will return to this issue shortly. A focus of Hatfield’s commentary was to show that evolutionary considerations implicitly guide the research endeavors of even the most ahistorical, mechanistically minded of researchers. He correctly points out that any focal level of study is individuated, meaning that it is set

104

D.R profistt

apart from other entities and assumed to have certain properties that are relevant to its functioning. Hatfield asserts that the sorts of functions ascribed to these enti ties typically reflect evolutionary considerations. Thus, he notes, we all assume that the primary function of the heart is to pump blood as opposed to making “heart sounds.” In choosing to study the blood-pumping functions of the heart, as opposed to those associated with its audible throbbing, the scientist is making implicit assumptions about what are the functionally relevant aspects a heart’s behavior, and thus, are worthy of study. I like very much this and Hatfield’s other examples of how researchers are guided to study certain aspects of systems and not others. In particular, I think that they illustrate well the bottom-up nature of boundary condition influences. We assume that it is the function of photoreceptors to transduce light, and so we study how they perform this function. What we look for in a system is guided by what we believe its function to be. This is another example of how boundary conditions function: Top-down influences act to constrain the information flowing into a focal level. The focal level, in this case, is the research endeavor, itself. In deciding what is relevant to a system’s functioning, the scientist constrains his or her investigation to a small subset of the system’s possibilities. I do have a quibble, however, with Hatfield’s essay. While I agree with Hatfield that researchers are guided by implicit assumptions, I do not believe that those possessed by researchers of visual perception are well captured by evoking the theory of evolution. As mentioned above, typically our knowledge of evolutionary theory is not well-developed. I agree that researchers are guided by implicit ecological or evolutionary assumptions to study certain aspects of a system to the exclusion of others; however, these assumptions are better described as reflecting the shared knowledge, or folk wisdom, of the research community, not as being based upon evolutionary theory as a biologist conceives of it. Everyone believes that it is the business of photoreceptors to respond to light as opposed to air-borne chemicals, sound waves, and so forth. This belief is not based on evolutionary considerations. That something in the eye is sensitive to light was known long before evolutionary theory came on the scene. In suggesting that researchers are guided more by agreements shared within their professional group than by evolutionary theory, I am not promoting this state of affairs. I agree with Hatfield that evolutionary considerations ought to play an important role in a hierarchical approach to perception. I think that they do not do so currently. Neisser raised three issues in his commentary. First, he pointed out the Gestalt heritage of many of the ideas presented in my essay. He also dis-

Hierarchy in Percephon

105

cussed differences, and most importantly, noted that Gestalt theory was not hierarchical. Second, he lamented what he perceived to be my lack of sympathy for Gibson’s ecological approach to perception. Finally, he commented on a lack of precision in my use of the term, hierarchy. In overview to my reply, I agree that Gestalt and Gibsonian ideas are pervasive in many of notions that I expressed. I am enormously sympathetic with these approaches, do not want to see them discarded, but do believe that they can be improved upon. In particular, like Gestalt theory, Gibson’s approach is almost entirely devoid of hierarchical considerations. Finally, I mean for hierarchy to encompass each of the five different kinds of examples that Neisser noted, and will attempt to more precisely define my use of the term before returning to a discussion of hierarchy in ecological theory. The term, hierarchy, refers to the kinds of organizations that can be described with tree diagrams. At all but the highest and lowest levels of a hierarchical system, elements are composed of lower-level entities and are constituents of one’s at higher-levels. An analysis of any element within a hierarchical system requires attention to what is within it as well as to what it is within. Biological systems fall within a particular class of hierarchies that are called control hierarchies. Control hierarchies differ from purely structural ones in that their higher levels exert specific constraints on the activities of the lower levels (Pattee, 1973). Chinese boxes are a frequently used example of a purely structural hierarchy (Grobstein, 1965; Simon, 1973).They consist of a number of boxes of graded sizes, each nested one within the other. Such an arrangement is hierarchical but not hierarchically controlled. A s an example of a control hierarchy, consider the functioning of DNA. The enzymes that it is capable of producing depend upon both the DNA’s composition and the manner in which it is controlled by its cell’s location within the organism. This constraining influence of higher levels on lower ones is the hallmark of control hierarchies. The term, boundary conditions, is used to describe these influences. Control hierarchies consist of a vertical organization of levels, each of which is best described within a particular scale of size and time. In essence, lower levels are small and fast, whereas higher levels are large and slow. The structure and function of photoreceptors, for example, are measured at scales of size and time that would be completely inappropriate for describing the boundary conditions that affect the purposeful eye movements that affect the photoreceptors’ inputs. Neisser’s list of my different uses of hierarchy reflects differences in the content, size, or duration for control hierarchies. In reply, I have attempted to make clear that the term, hierarchy, refers to a particular

106

D.R ProfFtt

kind of organization and is neutral with respect to content. Moreover, hierarchies are comprised of levels differing in the size and time scale appropriate for their description. For these reasons, hierarchical organization can be imputed for systems spanning a range from DNA to societal patterns of action. Returning to Neisser’s comments on my critique of Gibson’s ecological approach, I wish to make three points. First, Gibson’s theory is the best ecological approach to perception that we have got and I value it enormously. Be that as it may, my second point is that it does not make sufficient contact with the literature on perception, and thus, it could be improved. Finally, its greatest failing is its lack of hierarchical structure. I had intended that my essay would show a parallelism between the debates about mechanistic and ecological approaches in memory and perception. If I was more statesmanlike in my treatment of memory research, then it was only because it is easy to be statesmanlike when discussing a debate about which one has no stake. Let me state clearly that I believe that both mechanistic and ecological approaches are necessary in these and all other biological domains of inquiry. Within the field of perception, I think that Gibson’s approach is the best ecological position available today. I find it to be insightful, profound, and provocative. In my essay, I was not proposing that Gibson’s approach be rejected, but rather that it has room for improvement. Gibson’s approach does not serve to integrate or interpret most of the existing literature in visual perception. The research described in Gibson’s books and that conducted by adherents to his position comprise a small subset of work conducted in the visual perception field. Much of the work inspired by the ecological approach is excellent; however, it seems to me that there is also much excellent work not similarly inspired. A case in point is Johansson’s event perception studies. Neisser was puzzled that I described Johansson’s point-light studies as being reductionistic. In response, surely reducing the available visual information for detecting the human form down to a display of 13 moving points of light must qualify as being a reduced experiment. All controlled experiments are reductionistic. What makes Johansson’s experiment seemingly compatible with the ecological approach is that it was directed toward assessing a visual competency that people exhibit in everyday situations-the recognition of three-dimensional forms from motion information. However, Gibson, himself, did not think so. Gibson (1977) stated that

...[Johansson] seems to suppose that since a physical event can be analyzed into the motions of physical elements, its optical counterpart can be analyzed into the motions of optical elements. If he does suppose

Hierarchy in Percqtwn

107

this, I do not agree. Johansson’s analysis will work for what might be called a flat event seen from the front, or a transparent event, with the essential parts of the machine or the man always projected in the array. It will work for the motions and collisions in a frontal plane of objects like billiard balls. But it will not work for an ordinary event where one part goes out of sight behind another part and then comes back into sight again. I want to study the perception of ordinary events (p. 163).

Gibson felt that object motions are always accompanied by a local disturbance of optical structure-a deletion and accretion of visually specified texture-and since this information was absent in Johansson’s experiments, he felt them to be ecologically invalid. Gibson’s argument for direct perception is based on the assertion that a theory of perception can be obtained from an ecologically appropriate analysis of ambient optical structure as received by a moving point of observation. It is an account that recognizes only one focal level. Initiating conditions consist of optical, not retinal flow, and the boundary conditions are the ways of life of the individual organism. Because of its lack of hierarchical structure, the theory is silent about the ecological validity of research that is focussed upon lower- and higher-level processes. The approach cannot guide or interpret research on what is going on inside of the organism, nor on how culture provides boundary conditions on everyday perception. Thus, the ecological approach provides little guidance for research spanning the range from investigations of pre-attentive processes to those that seek to address how we linguistically label the surfaces that we detect. Returning to the primary issue raised in my reply to Hatfield, consider the following question: What provides the boundary conditions for current perceptual research? In discussing Ha tfield’s commentary, I argued that it was not the theory of evolution that served this function. In response to Neisser, I argued that Gestalt and Gibsonian approaches do not suffice either. Evolutionary theory is not deeply understood by most visual researchers and Gestalt and Gibsonian approaches are not integrative theories that can guide and interpret research across the variety of hierarchical levels that comprise the visual system. As Hatfield pointed out, ecological considerations provide boundary conditions for visual research whether scientists are aware of them or not. Ecological approaches to perception can stand improvement. An appreciation of hierarchy would be a start.

D.R proffitt

108

REFERENCES AUTRUM, H. (1979). Introduction. In H. Autrum (Ed.), Handbook of sensory physiology: Comparative physiology and evolution of vision in invertebrates (vol. VII/6A, pp. 1-22). New York Springer. [GHI BANAJI, M. R., & CROWDER, R. G. (1989). The bankruptcy of everyday memory. American Psychologist, 44, 1185-1193. BARTLETT, F. C. (1932). Remembering: A study in experimental and social psychology. London: Cambridge University Press. BONNER, J. (1973). Hierarchical control programs in biological development. In H. H. Pattee (Ed.), Hierarchy theory: The challenge of complex systems (pp. 49-70). New York: Braziller. CATTELL, J. M. (1886). The inertia of the eye and brain. Brain, 8, 295-312. CHAPANIS, A. (1947). The dark adaptation of the color anomalous measured with lights of different hues. Journal of General Physiology, 30, 423-437. CUMMINS, R. (1975). Functional analysis. Iournal of Philosophy, 72, 741765. [GHI CUTTING, J. E., PROFFITT, D. R., & KOZLOWSKI, L. T. (1978). A biomechanical invariant for gait perception. Journal of experimental psychology: Human perception and performance, 4, 356-372. [UNI DE POMERAI, D. (1985). From gene to animal. Cambridge: Cambridge University Press. DUNCKER, K. (1929). Uber induzierte bewegung. Psychologische Forschung, 12, 180-259. [UNI EBBINGHAUS, H. (1964). Memory. New York: Dover. (Translated from the 1st German edition, 1885) FODOR, J. A. (1980). Methodological solipsism considered as a research strategy in cognitive psychology. Behavior and Brain Sciences, 3, 63109. [CHI GIBSON, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton-Mifflin. [GH/UNl GIBSON, J. J. (1977). On the analysis of change in the optic array. Scandinavian Journal of Psychology, 18, 161-163. GIBSON, J. J. (1979). The ecological approach to visual perception. Boston: Houghton-Mifflin. GOLDSMITH, T. H. (1990). Optimization, constraint, and history in the evolution of eyes. Quarterly Review of Biology, 65, 281-322. [GHI GOTTLIEB, G. (3992). Individual development & evolution: The genesis of novel behavior. Oxford: Oxford University Press. GRENE, M. (1987). Hierarchies in biology. American Scientist, 75, 50451 0.

Hierurchy in Perception

109

GROBSTEIN, C. (1965). Strategy of life. San Francisco: Freeman. HARRIS-WARRICK, R. M., & MARDER, E. (1991). Modulation of neural networks for behavior. Annual Review of Neuroscience, 14, 39-57. HATFIELD, G. (1988). Representation and content in some (actual) theories of perception. Studies in History and Philosophy of Science, 19, 175-214. [GH] HATFIELD, G. (1990). Gibsonian representations and connectionist symbol processing: Prospects for unification. Psychological Research, 52, 243252. [GH] HATFIELD, G. (1991). Representation in perception and cognition: Connectionist affordances. In W. Ramsey, D. Rumelhart, & S. Stich (Eds.), Philosophy and connectionist theory (pp. 163-195). Hillsdale, NJ: Erlbarn. [GH] HATFIELD, G. (1992). Color perception and neural encoding: Does metameric matching entail a loss of information? In D. Hull & M. Forbes (Eds.), PSA 1992 (vol. 1, pp. 492-504). East Lansing, MI: Philosophy of Science Association. [GHI JAMES, W. (1890). The principles of psychology. New York: Holt. JOHANSSON, G. (1973). Visual perception of biological motion and a model for its analysis. Perception 6 Psychophysics, 14, 201-211. KACZMAREK, L. K., & LEVITAN, I. B. (1987). Neuromodulation. New York: Oxford University Press. KANIZSA, G. (1976). Subjective contours. Scientific American, 234(4), 4852. KOHLER, W. (1938). The place of value in a worZd of facts. New York: Liveright. [UN] KOHLER, W. (1944). Max Wertheimer, 1880-1943. Psychological Review, 51,142-146. [UN] KOLLAR, E. J., & FISHER, C. (1980) Tooth induction in chick epithelium: Expression of quiescent genes for enamel synthesis. Science, 207,993-995. LATIES, G. (1963). Control of respiratory quality and magnitude during development. In B. Wright (Ed.), Control mechanisms in respiration and fermentation (pp. 129-155). New York: Ronald Press. LYTHGOE, J. N. (1979). The ecology of vision. Oxford: Oxford University Press. [GHI MARR, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. San Francisco: Freeman. MUNZ, F. W., & MCFARLAND, W. N. (1977). Evolutionary adaptation of fishes to the photic environment. In F. Crescitelli (Ed.), Handbook of sensory physiology: The visual system in vertebrates (vol. VII/5, pp. 193-274). New York: Springer. [GHI

110

D.R

NEANDER, K. (1991). Functions as selected effects: The conceptual analyst's defense. Philosophy of Science, 58, 168-184. [GHI NEISSER, U. (1976). Cognition and reality: Principles and implications of cognitive psychology. San Francisco: Freeman NEISSER, U. (1978). Memory: What are the important questions? In M. M. Gruneberg, P. E. Morris, & R. N. Sykes (Eds.), Practical aspects of mernory (pp. 3-24). London: Academic Press. NEISSER, U. (1991). A case of misplaced nostalgia. American psychologist, 46, 34-36. [UN] NEISSER, U., & WINOGRAD, E. (Eds.) (1988). Remembering reconsidered: Ecological and traditional approaches to the study of mernory. New York: Cambridge University Press. [UNI NORMA", R. A., & WERBLIN, F. S. (1974). Control of retinal sensitivity. I. Light and dark adaptation of vertebrate rods and cones. Journal of General Physiology, 63, 37-61. PARMLEY, W. W. & TALBOT, L. (1979). Heart as a pump. In R. M. Berne (Ed.), Handbook of physiology: The cardiovascular system: The heart (vol. I I / l , pp. 429-460). Bethesda, MD: American Physiological Society. [GHI PATTEE, H. H. (1973). The physical basis and origin of hierarchical control. In H. H. Pattee (Ed.), Hierarchy theory: The challenge of complex s y s t e m (pp. 71-108). New York: Braziller. PAVLOV, I. P. (1927). Conditioned reflexes. New York: Oxford University Press. POLANYI, M. (1968). Life's irreducible structure. Science, 160, 1308-1312. POLYAK, S. (1957). The vertebrate visual system. Chicago: University of Chicago Press. [GHI PROFFITT, D. R., KAISER, M. K. & WHELAN, S. M. (1990). Understanding wheel dynamics. Cognitive Psychology, 22, 342-373. [UNI RAFF, R. A., & KAUFMAN, T. C. (1983). Embryos, genes, and evolution. New York: Macmillan. RUBIN, E. (1927). Visuell wahrgenommene wirkliche Bewegungen. Zeitschrift fur Psychologie, 103, 384-392. SALTHE, S. N. (1985). Evolving hierarchical systems: Their structure and representation. New York: Columbia University Press. SHAPIRO, L. (1992). Darwin and disjunction: Foraging theory and univocal assignments of content. In D. Hull & M. Forbes (Eds.), PSA 2992 (vol. 1, pp. 469-480). East Lansing, MI: Philosophy of Science Association. [GHI SIMON, H. A. (1973). The organization of complex systems. In H. H. Pattee (Ed.), Hierarchy theory: The challenge of complex systems (pp. 127). New York: Braziller.

Hierarchy in Perception

111

SIMON, H. A. (1981). The sciences of the artificial, Second Edition. Cambridge, MA: MIT Press. SOLOMON, H. Y., & TURVEY, M. T. (1988). Haptically perceiving the distances reachable with hand-held objects. Journal of experimental psychology: Human perception and performance, 14, 404-427. [UNI SPARROW, A. H., PRICE, H. J., & UNDERBRINK, A. G. (1972). A survey of DNA content per cell and per chromosome of prokaryotic and eukaryotic organisms: Some evolutionary considerations. Brookhaven Symposium on Biology, 23, 451-494. STICH, S. (1983). From folk psychology to cognitive science: The case against belief. Cambridge, MA: MIT Press/Bradford Books. [GH] WALLS, G. L. (1942). The vertebrate eye and its adaptive radiation. Bloomfield Hills, MI: Cranbrook Institute of Science. [GH] WARREN, W. H., Jr. (1984). Perceiving affordances: Visual guidance of stair climbing. Journal of experimental psychology: Human perception and performance, 10, 683-703. [UNI WARREN, R., & WERTHEIM, A. H. (Eds.) (1990). Perception and control of self-motion. Hillsdale, NJ: Erlbaum. [UN] WHEELER, D. D. (1970). Processes in word recognition. Cognitive Psychology, 1, 59-85. WRIGHT, L. (1973). Functions. Philosophical Review, 82, 139-168. [GHI

This Page Intentionally Left Blank

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

113

THE ANALYSIS OF PERCEIVED SPACE Walter C. Gogel Department of Psychology University of California, Santa Barbara, California

ABSTRACT This essay discusses the evidence for, the application of, and the theoretical implications of the theory of phenomenal geometry. This theory proposes that the perception of the location or change in location of stimuli depends upon the simultaneous effect of three variables: perceived distance, perceived direction, and the observer’s perception of his or her own motion or stationariness. Together, these basic percepts then specify derived perceptions of size, shape, orientation, and motion. Evidence for this theory is found in its ability to explain a variety of veridically perceived and illusory phenomena and to express the underlying processes in perceptual equations, which differ from psychophysical equations by consisting only of perceptual terms. This theory also has explanatory parsimony because the perceptual consequences for derived perceptions from particular values of the basic variables are the same regardless of how these particular basic values are determined. Finally, this theory provides an explanation in terms of essentially sensory information as an alternative to interpretations of many perceptual phenomena in terms of higher-order processes such as expectations, compensations, and cognition.

This essay will discuss a theory of phenomenal visual geometry and some of its theoretical implications. According to this theory, the location of a stimulus point in perceived three-dimensional space is determined by three basic variables or factors. These are 1) the observer’s perception of the direction of a stimulus point from himself or herself or the change in this perceived direction, 2) the perceived egocentric distance of

114

w.c.G q f i

the stimulus point from the observer or the change in this perceived distance, and 3) the observer’s perception of his or her own position or change in position as the head is stationary or is moved. It is assumed that these three basic factors contribute to the perceived location (whether accurate or illusory) of each stimulus point in apparent three-dimensional space. Numbers of such stimulus points at different perceived spatial positions specify the derived characteristics of perceived size, shape, orientation, position, and motion of the stimulus. This theory will be discussed particularly in relation to the derived perceptions of lateral and sagittal motion of the stimulus as viewed from a moving or stationary head.

THE PERCEPTION OF LATERAL MOTION OR EXTENSION IN A FRONTOPARALLEL PLANE AS VIEWED FROM A LATERALLY MOVING OR STATIONARY HEAD Instances of the application of the three basic variables to frontoparallel motions or extensions are shown in Figure 1. The outline (open) representations of stimulus objects (open circles or open rectangles) and primed notation in Figure 1, or in subsequent diagrams, identify perceived characteristics, and the filled (solid) representations and unprimed notation indicate physical characteristics of the stimulus. In Figure la, the head is represented as moving laterally left (and right) through a perceived distance K‘ while viewing a physically and perceptually stationary point of light (the solid circle) located at a physical distance D,. If the perceived distance of the point is greater than its physical distance, D ’f > D,, the point will appear to move, W’f, in a direction opposite to the perceived motion of the head. Or if the perceived distance of the point is less than its physical distance, D’, < D,, the point will appear to move, W’n, in the same direction as the perceived motion of the head. The phenomenon illustrated in Figure l a is called apparent concomitant motion since it is apparent (in this case illusory) motion concomitant with the perceived motion of the head. As is illustrated in Figure la, the three basic variables of phenomenal geometry, perceived direction, perceived distance, and perceived head motion, are consistent in that together they specify a single position of a stimulus point in perceived three-dimensional space. The successive values of these three variables throughout the head motion thereupon specify the derived (illusory or non-illusory) perceptions of stimulus motion. When investigating the effects of different values of perceived egocentric distance, D ’ in the situation of Figure la, it often is assumed for convenience that K’ = K and @’ = @ in order to avoid measuring K‘ and @’.But

klalysis of Perceizd Syace

115

I\

/I

CI

c

b

Figure 1. As is illustrated in Figures I b and lc, respectively, the apparent size-distance [S' = ZD' tan(O'/2)1 and the apparent motion-distance invariance hypothesis [M' = 2D' tan(b'/Z)l are predicted from the head motion paradigm [W' = K' - ZD' tan(of/2)] shown in Figure la, in this case for the condition in which I$'= 6'. (From "A theory of phenomenal geometry and its applications" by W. C. Gogel, 1990, Perception t? Psychoyhysics, 48, p. 106. Copyright 1990 by the Psychonomic Society. Reprinted by permission.) '

these assumptions are not required by the theory of phenomenal geometry. Instead, variations in any of the three basic perceptions regardless of whether they are veridical or not will produce variations in perceived concomitant motion, W', as is indicated by the following equation from the geometry of Figure la:

It is characteristic of Equation 1 and indeed of all the equations of phenomenal geometry, including Equation 1, that they can be expressed in terms of perceptual variables and do not require a mixture of perceptual

116

w.c.Gqd

and physical variables, as occur in psychophysical equations. In Equation 1, if K' is zero then,

which, except for the minus sign, is equivalent to the equation for the size-distance invariance hypothesis (Gilinsky, 1951; Kilpatrick & Ittelson, 1953; Schlosberg, 1950) which can be expressed as

where W' in Equation 2 is replaced by S' in Equation 3, the perceived width of the stimulus object, and 4' in Equation 2 is replaced by 6', the perceived visual angle subtended by the width of the stimulus object. The size-distance invariance hypothesis ( S D I H ) usually is written with the physical variable 8 rather than the perceptual variable 8'. However, in agreement with the theory of phenomenal geometry and the suggestions by McCready (1965,1985,1986) and Gogel and Da Silva (1987a) the 8' notation, indicating perceived not necessarily physical visual angle, is used. Figure l b illustrates the case of the SDIH known as Emmert's law (see Kilpatrick & Ittelson, 1953) in which 8' is constant as D' is changed from D', to D'f. Given that the perceived size, S', at D , in Figure l b equals the perceived head motion, K ', in Figure la, it is clear from comparing the diagrams of Figure l a and l b that one diagram can be transformed to the other if the perceived head motion K' is changed from that shown in Figure l a to K' = 0 in Figure lb, with the change in the directions between the head and stimulus object the same in Figures l a and lb. Figure l c is similar to Figure l b except that the stimulus is a point that is perceived to move an amount, m ', through the same perceived distance as S ' of Figure l b (and K' of Figure la). Again, Figure l a is transformed to Figure l c if the physically moving head in Figure l a is perceived as stationary with 4' in Figure l a equal to 6' in Figure lc. Figure l c is an example of what can be called the motion-distance invariance hypothesis ( M D I H ) analogous to the SDIH. An equation expressing the MDIH in perceptual terms is

Evidence for the validity of the MDIH is found in research by Rock, Hill, and Fineman (1968) and by Wist, Diener, and Dichgans (1976).Since 6' and D' in Figures l b and l c are equal to 4' and D' in Figure la, it follows that

Analysis of Perceizwd Space

117

All three situations of Figure 1 are an application of the theory of phenomenal geometry and represent the same basic phenomena thus providing an example of the generality of the theory. There is considerable evidence consistent with Figure l a which supports the importance of perceived egocentric distance, D ’, in determining the perception of the lateral motion of the stimulus concomitant with a lateral motion of the head. This has been shown for oculomotor cues (Gogel, 1977,1981,1982; Gogel, Loomis, Newman, & Sharkey, 1985; Gogel & Tietz, 1977,1979; MacCracken, Gogel, & Blum, 1980) for the cue of relative motion parallax (Gogel & Tietz, 1979) and for the specific distance tendency and equidistance tendency (Gogel, 1979; Gogel & Tietz, 1973).’ There also is evidence in three studies regarding a positive relation between the apparent concomitant motion of Figure l a and the SDIH of Figure l b (Gogel, 1979; Gogel et al., 1985; Gogel & Tietz, 19791, again using oculomotor cues or binocular disparity to localize the test object in perceived distance. This evidence is discussed in Gogel (1990, pp. 108-109). The theory of phenomenal geometry asserts that all three of the basic perceptual variables, D’, $’ or O’, and K‘, are of equal importance in the perceptual localization of stimulus points in three-dimensional space. Although D’ can readily be modified without changing the value of $’ or K‘, special conditions must be used in order to avoid modifying $’ as K‘ is changed or K’ as @’ is changed. Diagrams suggested for accomplishing this are shown in Figure 2 which also illustrates the concept of the pivot point, p, and the pivot distance, DPa.The pivot point is the point in space through which successive perceived directions from the observer to the stimulus object pass as the head moves laterally. As shown in Figure 2, for example, the pivot distance D, is defined by the ratio of the perceptions K’ / [2 tan($’/2)1. Thus Equation 1 expressed in terms of W’, D‘, and the perceptual ratio D, becomes

W=K(l-D’/D+.

(6)

Equation 6 is sometimes called the apparent distance/pivot distance hypothesis. If it is assumed that K’ = K and @’ = $, it follows that the pivot point is at the distance of the physical stimulus point if the stimulus point is physically stationary as is illustrated in Figures 2a and 2b. Or if the stimulus point physically moves in the same direction as the head (as is shown in Figure 2c) or opposite to the direction of head motion, the pivot distance will be greater or less, respectively, than the physical dis-

’

In Table 1 of the study by Gogel (1982) the headings (not the data) of the two columns at the far right of the table should be interchanged. The order of these headings should be CD=25, C D 4 0 .

w.c.Gag$

118

a

C w’= 0

Figure 2. Top-view drawings illustrating procedures for measuring the effect on perceived concomitant motion, W’, of changes in K’ with D’ and $’ constant (compare Drawings 2a and 2b) or in measuring the effect on W’ of changes in I$’ with D’ and K’ constant (compare Drawings 2b and 2c).

tance of the stimulus. A procedure for measuring the effect of K’ on W’ independent of both $’ and D’ is demonstrated in the comparison of Figures 2a and 2b. In these two drawings $’ and D’ are the same and only K‘ is vaned, producing a predicted change in W’ from -Wa to -W’,/2. Also, a procedure for measuring the effect of $’ on W‘ independent of both K’ and D ’is found in the comparison of Figures 2b and 2c. In this case K‘ and D’ are the same in these two figures, and only 9’ is varied producing a predicted change in W’ from -W’,/2 to W’=O.

MEASURING PERCEIVED EGOCENTRIC DISTANCE, D‘, USING A LATERAL MOTION OF THE HEAD The perceived motion, W’, resulting from viewing a stimulus as the head is moved laterally (Figure la), to be called the lateral head motion

Analysis of Perceived Spce

119

W;

Figure 3. Drawings illustrating the vector addition of perceived horizontal motion, W’, and perceived vertical motion, MI, concomitant with a perceived horizontal motion, K’, of the head, so as to determine the perceived tilt, a’,of the apparent path of motion of the test point. (Modified from “A comparison of oculomotor and motion parallax cues of egocentric distance” by W. C. Gogel and J. D. Tietz, 1979, Vision Research, 19, p. 1162. Copyright 1979 by Pergammon Press. Adapted by permission.)

procedure, has been used to measure the perception of egocentric distance, D’. Assuming that K’ = K and $’ = $ and measuring W’, the D‘ of the stimulus can be computed using Equation 1. The value of W’ in this case can be obtained by the observer adjusting by touch the lateral separation of two unseen rods to duplicate the magnitude of perceived motion, W’, of the stimulus. This method of measuring W’ is called the hand adjustment procedure. The measurement of W’ by the hand adjustment procedure and the computation of D’ from this adjustment has been used in several studies (Gogel, 1982; Gogel et al., 1985; Gogel & Tietz, 1992b). Several variations on the measurement of D’ using the head motion procedure have been applied. All are called indirect procedures because the task is not to respond directly to D‘, but instead it is to respond to W’ which is then applied in the computation of D ’. One such variation is shown in Figure 3. Figure 3a represents a situation similar to that shown in Figure la, A physically stationary stimulus

W. c.Gag$

120

point, if perceived at D ) > D,appears to move, W), opposite to the direction of the head motion. If perceived at D', c D,the stimulus point appears to move, W',, in the same direction as the head motion. In Figure 3b, however, the stimulus point moves vertically as the head moves laterally. In this case, the error in perceived distance again results in a lateral component of illusory motion, W) or W',, which occurs simultaneously with a component of perceived vertical motion, M' or M',. As indicated, the size of M' increases as the perceived distance o the stimulus point increases in agreement with Emmerfs Law. The sum of the horizontal and vertical perceived vectors in Figure 3b produces a perceived tilt, a) or a'n, of the perceived path of the stimulus motion. This perceived tilt can be measured by a tactile adjustment of the tilt of a comparison rod. Using this perceived tilt D ' f and D', can be calculated as is shown in Gogel & Tietz (1977). Additional studies in which this has been used are Gogel (1982) and Gogel & Tietz (1979). A third variation of the head motion procedure to measure D' can be illustrated in principle by Figure 2c in which the pivot distance, D,, as determined by K' and @' is adjusted in distance until W' = 0. The physical lateral motion of the stimulus concomitant with the lateral motion of the head that is needed in order to achieve the null criterion can be used to compute the D' of the stimulus object as is shown, for example, in Gogel & Tietz (1979). This null adjustment procedure avoids the need to use a comparison object for measuring W', and it can be applied to the kind of situation shown either in Figures 3a or 3b. In the latter case the null criterion is the adjustment of the stimulus to appear to move vertically (a' = 90 deg). The null adjustment involving either case has been used in a number of additional studies (Gogel, 1976, 1977, 1979, 1981, 1982; Gogel & Tietz, 1979; MacCracken et al., 1980). In the above applications of the lateral head motion procedure to the measurement of D' of the stimulus, it often is assumed, either implicitly or explicitly, that K' = K and 4' = @.However, two studies (Gogel, 1982, Figure 3; Gogel & Tietz, 1979, Experiment 3) provide some evidence for the validity of one or both of these assumptions in experiments in which only one or several cues of the distance of the stimulus are available. But even if these assumptions in particular instances are not satisfied, @' as well as K' often remain constant during changes in distance cues of the stimulus as long as D, in addition to K remains constant. Thus, even if some unmeasured (and thus unknown) differences between K' and K or between I$' and I$ do occur, the head motion procedure can show with considerable sensitivity that changes in the perceived distance, D',for a constant physical distance, D, of the stimulus occur as the cue distance of the object is changed.

f

Analysis of Perm'& Space

121

MEASURING THE EFFECT OF COGNITION ON PERCEPTION The lateral head motion procedure provides an indirect measure of D'. It is called indirect because the observer's response is to a perceived motion, w', from which D' is computed by the experimenter using the phenomenal geometry. This procedure is considered to avoid the intrusion into the measure of perceived distance of cognitive or other non-perceptual processes that can occur if a direct measure of perceived egocentric distance such as a verbal report of perceived distance had been used (Gogel, 1990). An illustration of a possible intrusion of cognitive processes into a response to perceived distance is found in a study of the familiar size cue to perceived distance (Gogel, 1976). The perceived distance of several familiar objects presented under otherwise reduced conditions was measured in two ways. One was by means of the head motion procedure, and the other was by obtaining verbal reports of perceived distance. It was found in several experiments that although the verbal reports of perceived distance differed substantially as a function of the distance simulated by the familiar objects, this result was greatly reduced when D' was obtained from the head motion procedure, using the null criterion of W' = 0. That this reduction was not the result of some lack of sensitivity of the head motion procedure was shown in a control experiment (Experiment 5). In this experiment clear changes in D' from the head motion procedure were obtained from the relative size cue of distance produced by successive presentations of the sume familiar object of different retinal size. But, according to the perceived distance measures using the head motion procedure, familiar size is only a very weak cue to perceived egocentric distance. A considerably stronger relation between perceived egocentric distance and simulated distance from familiar size was obtained from the verbal reports of perceived distance. Verbal reports of the perceived size of the familiar objects also were obtained. From these reports it was found, in agreement with previous studies (Gogel, 1969a; Gogel & Newton, 1969) that under these reduced conditions of observation the familiar objects frequently were reported to be non-normal in size. This is attributed to what is called the specific distance tendency ( S D T ) . This is the tendency for an object with only partially effective cues of distance to appear displaced from its physical distance toward a perceived distance of about 2 or 3 meters from the observer (Gogel, 1969b). If familiar size is at best a weak cue of distance the stimulus object will tend to be displaced perceptually from its simulated distance toward the distance defined by the SDT. At this modified perceived distance it will be perceived as smaller or larger than its familiar size depending upon whether the simulated distance is farther or nearer, respectively, than the distance of the SDT.

w.c.Gqd

122

That is, the familiar object will appear off-sized. There is evidence (Carbon, 1960, 1977) that the perceived size of a familiar object is expected to be inversely related to the distance at which it is perceived. Thus, if the object appears smaller or larger than normal it will be judged (cognitively) to be at a larger or smaller distance, respectively, than the distance at which it is perceived. The result is that the verbal report is cognitively modified to indicate a greater effect of familiar size on perceived egocentric distance than actually is present. The validity of this interpretation has been supported by several subsequent studies (Gogel, 1981; Gogel & Da Silva, 1987b; Predebon, 1992); nor is this interpretation necessarily limited to objects having familiar sizes (Gogel, 1990). The issue of familiar size as a cue to distance is important because it is the only distance cue that by definition requires experience, and because it is one of the few cases which, if valid, would extend the perception of egocentric distance to far portions of the visual field. However, there is a still larger problem the solution to which indirect measures of distance provided by phenomenal geometry can contribute. This is the problem of defining the conditions under which cognitive processes can modify perceptions (Fodor, 1985; Kanizsa, 1979, ch. 1; Swanston & Gogel, 1986). Using the lateral head motion procedure, it has been concluded that cognitive processes do not modify perceived distance as a result of casual suggestion (Gogel, 1981), or even post-hypnotic suggestion (MacCracken et al., 1980). Also, as discussed above, the learned (cognitive) cue of familiar size has only a very limited effect on perceived distance, whereas offsized judgments may have a large role in producing the change in perceived depth experienced with optical expansion or contraction (Swanston & Gogel, 1986). An extended discussion of these effects can be found in Gogel (1990).

APPLICATION OF PHENOMENAL GEOMETRY TO STIMULI EXTENDED IN DEPTH The perception of stimuli extended in depth can be analyzed by considering that the perceived location of each stimulus point is specified by the same three variables of perceived distance, perceived direction, and perceived head position or motion as were used for a single point in Figure la. This is illustrated in Figure 4a in which the two end points, e and f , of a stimulus extended in depth are viewed as the head moves laterally left and right between Positions 1 and 2. Because of misleading cues of depth the stimulus e,f is perceived as reversed in depth, e’,f’. As a consequence of this error in depth perception, the stimulus will appear to rotate through

Analysis of Perm'ved S p e

2

a

123

1

b

Figure 4. Top-view drawings illustrating the perceived angle, P', between changes in the apparent orientation of an object e,f as a result of viewing the object at the illusory orientations ellfVland elzflz. In Figure 4a, the object is physically stationary and is viewed while the head is moved through a perceived lateral distance K'. In Figure 4b, the head is physically stationary and the object is moved laterally through a perceived distance equal to K' in Figure 4a. It is likely, under these conditions, that p' in the situations represented by Figures 4a and 4b are not significantly different. (From "A theory of phenomenal geometry and its applications" by W. C. Gogel, 1990, Perception t3 Psychophysics, 48, p. 112. Copyright 1990 by the Psychonomic Society. Reprinted by permission.)

an angle p' as the head is moved laterally. In Figure 4b the head is physically and perceptually stationary. The stimulus with the same depth error in Figure 4b as in Figure 4a is moved left and right through the same distance as the head moved in Figure 4a. Here also the stimulus will appear to rotate through an angle p', given the conditions illustrated in the figure. Consistent with phenomenal geometry, the perceived rotation, p',

124

w. c.Gqd

is expected to be the same in the two situations. At least this is the case if D‘, $’, and K’ for a point such as Point e is the same whether Point e is presented alone or is presented simultaneously with Point f and whether the head or point is physically moved. Thus, for example, if the cue of relative motion parallax were effective in changing the perceived depth between e and f i n Figure 4a but not in the situation of Figure 4b, the magnitude of p‘ would not be expected to be identical in the two situations. It is the value of the three basic variables of phenomenal geometry as they apply to each point that specifies the perceived motion, W’, of that point regardless of how or by what cues each of the three factors are determined. This was examined in three experiments (Gogel & Tietz, 1992a). In Experiments 1 and 2 (illustrated in Figures 4a and 4b, respectively) binocular disparity using polarizing filters was used to produce errors in the perceived depth of the stimulus. Each experiment had a dynamic and a static condition. For Experiment 1 (see Figure 4a), in the dynamic condition, judgments of perceived tilt e’lf’l and e ’ j ’ 2 of the stimulus at each of the extreme head positions occurred during continuous left and right motions of the head while viewing the stimulus. In the static condition the perceived tilts were again measured at each of the extreme head positions but without any head motions, that is, without any opportunity to view the stimulus except at the extreme right or left positions of the head. In Experiment 2 (see Figure 4b) dynamic and static judgments were also obtained but in this case at the extreme right or left position of the stimulus with the head always stationary. The dynamic judgments were obtained at the extreme positions of the moving stimulus during viewing of the continuously moving stimulus. The static judgments were obtained at the extreme right or left position of the stimulus with no opportunity to see the stimulus during the motion of the stimulus. None of the values of p’ resulting from the sum of the two perceived tilts (one counterclockwise and the other clockwise) were significantly different either between Experiments 1 and 2 or between the conditions of static and dynamic viewing. Similar results between static and dynamic viewing were obtained in Experiment 3 in which an illusory perspective (a trapezoidal window) was used to produce the errors in perceived depth in a situation similar in principle to Figure 4a. Clearly, head motions were not needed to obtain these results, and, therefore, concepts of compensation for head motion (Wallach, 1985, 1987) or reasoning-like processes (Rock, 1983) are not needed for the explanation of these phenomena. The three basic variables of phenomenal geometry provide a complete explanation, and the results suggest that the three perceptual variables can be applied individually to each point of a configuration. The latter conclusion is supported also by an experiment by Gogel et al. (1985).

Analysis of Perceived Space

125

Phys i ca I

Apparent

b

Figure 5. The effect of a perceptual reversal of the depth of a face mask (Figure 5a) on the illusory rotation, p', of the mask concomitant with a lateral motion of the head (Figure 5b). Similar effects are obtained if the head is stationary and the mask is moved (similar to Figure 4b) or the mask is stationary while viewed with a moving head (similar to Figure 4a). The perceptions can be explained by the correct perception of the directions to the parts of the mask, the correct perception of the observer's own motion, and the illusory perception of depth within the mask. (From "A theory of phenomenal geometry and its applications" by w. C. Gogel, 1990, Perception b Psychophysics, 48, p. 113. Copyright 1990 by the Psychonomic Society. Reprinted by permission.)

The analysis used in the discussion of Figure 4 also can be applied in principle to a variety of situations involving the illusory motions of stimuli extended in depth. It should be noted that the principles involved in the illustrations of illusory motion, position, or extent whether of points (Figures l a and lc) or of extended objects (Figure 4) and whether the objects or observer or both are physically stationary or physically moving are meant to apply equally to non-illusory situations. One advantage of

126

W. C.Gqd

considering the perceptions and processes involved in such illusory situations is that the resulting analysis reveals the processes occurring in situations in which the perception is veridical as well as illusory. Two illusory situations with extended objects as stimuli are shown in Figures 5 and 6. Figure 5 represents a transparent face mask which is physically pointing away from the observer but appears, when monocularly observed, to be pointing toward the observer. This produces errors in the perceived depth between the parts of the mask as is shown in Figure 5a. Choosing the nose and upper forehead as the parts of the mask between which the perceived depth is analyzed geometrically, Figure 5b illustrates in the same manner as Figure 4a that an illusory perceived rotation, p', will occur as the head is moved laterally. An illusory rotation of the mask also will be seen if the observer is stationary and the mask is physically moved laterally, or if the mask is physically slanted in depth toward or away from the observer. In addition, if the mask is physically rotated around a stationary vertical axis it will appear to a stationary observer to rotate in the opposite direction. All of these phenomena will be greatly reduced or will disappear if the mask is perceived at its physical depth orientation which usually occurs when the mask is viewed binocularly. The disappearance of the illusory motion when the depth within the mask is perceived correctly suggests that K' and 4' were at least approximately veridical in the situation represented by Figure 5, assuming that K' and @' are not significantly modified by the change from monocular to binocular viewing. If K' and 4' were not perceived correctly, removing the error in perceived depth would not eliminate all illusory motion, that is, W >and/or W', would not become essentially zero. Figure 6 illustrates the phenomenon of an illusory direction of rotation of an Ames' trapezoidal window. The drawing is a top view of the physical (solid lines and filled circles) and perceived (dashed lines and open circles) orientations of the window at the terminal positions of its physical and perceived rotation. Because of the perspective cues, the small end, nl or n2, of the window although physically nearer to the observer than the large end, fl orf2, appears to be more distant than the large end throughout the rotation. As shown by the direction of the arrows between Positions 1 and 2, the perceived direction of rotation, although physically counterclockwise, is perceptually clockwise. The explanation of this illusion according to the "best bet" hypothesis of transactional theory (Ames, 1952) is in terms of two factors. One is the illusory perception of the depth orientation of the window. The other is the decrease in the overall angular size of the window (a1> a2 in Figure 6) as the window rotates counterclockwise. According to the best bet hypothesis, the observer's logical conclusion from these two factors is that the window must

Analysis OfPerceived Spzce

127

Figure 6. A top-view drawing illustrating a perceived rotation of an example of an Ames's trapezoidal window in a direction opposite to that of its physical rotation. This illusory direction of rotation is consistent with the correct perception of the relative directions of the parts of the window but an incorrect perception of their relative distances as produced by the illusory perspective of the window. The solid circles and nonprimed notations represent the physical positions of the two ends of the window as the window physically rotates counterclockwise from n l f l to n2f2. The open circles and primed notations represent the apparent positions of the two ends of the window, which is perceived to rotate clockwise from n'lf'l to n'zf'z. The physical visual angles subtended by the window are a1 at n l f l and a2 at nzfz. (From "A theory of phenomenal geometry and its applications" by W. C. Gogel, 1990, Perception & Psychophysics, 48, p. 111. Copyright 1990 by the Psychonomic Society. Reprinted by permission.)

be rotating clockwise. However from the theory of phenomenal geometry perceptual logic is not needed. The perceived rotation is explained by the error in perceived depth between the small and large ends, the constant

128

w. c.Qgd

veridical perception of the observer as stationary, and the veridical perception of the changes in perceived directions to the ends of the window. Although many of the phenomena associated with Figures 1 through 6 are discussed in terms of errors in perceived depth or distance (and, very likely in other phenomena, can be discussed in terms of errors in self position or perceived direction) the reference to errors in perception is not necessary for the explanation in terms of phenomenal geometry. Perception provides the observer with spatial information that guides behavior. However, in the absence of contrary information, visual or otherwise, there are no perceptual processes that signal errors of the perception. In each situation shown in the figures, the same perceptions could be achieved by replacing the illusions with physical events equivalent to the illusory motion with these physical events correctly perceived. For example, in Figure l a the perceived illusory lateral motions, W’, are equal to what would be experienced if physical motions identical in their physical sizes to the illusory motions were substituted for the illusory motions and were correctly perceived. As other examples, in Figures 5 and 6, the perceived illusory rotations are equivalent to what would be experienced if physical rotations of the same amounts as the illusory rotations were correctly perceived. Situations that may differ physically but are identical perceptually can be called perceptually equivalent configurations. Perceptually equivalent configurations are also equivalent in terms of the three basic factors of phenomenal geometry. Consistent with the conclusion regarding perceptually equivalent configurations is the expectation that illusory motions produced by perceptual errors in one or more of the basic factors of phenomenal geometry can not be distinguished by the observer from real motions, and related to this is the fact that perceptions from real and illusory motions can vector together. The first of these expectations is supported by a study (Peterson & Shyi, 1988) using a three-dimensional wire frame cube. Phenomena occur with such a cube similar to those observed with an inverted face mask (Figure 5). When the cube, rotating physically around a vertical axis, spontaneously reverses in perceived depth, it appears to rotate in a direction opposite to its physical rotation. It was found in the Peterson and Shyi (1988) study that the observers were unable to distinguish between the illusory and real rotation. Evidence for the vectorial addition of real and illusory motion of a stimulus point is found in the study by Gogel and Tietz (1977). Additional demonstrations consistent with phenomenal geometry as noted by Gogel (1990) are those associated with a Mach folded card, the perceived motion of a stereokinetic display as the head is moved, and the well known phenomenon of the perceived ”rocking” of a flat picture which is perceived in depth as a stereogram and viewed as

Analysis OfPerceived Spce

129

the head is moved laterally. It is also suggested (Gogel, 1990) that the theory of phenomenal geometry has implications for the changes in the perceived orientation in depth of pictured objects designed to look threedimensional and viewed with a laterally moving head or from different positions. The explanation here would in principle be similar to that discussed in relation to the inverted mask (Figure 5).

THE PERCEPTION OF SAGITTAL MOTION VIEWED WITH A STATIONARY OR SAGITTALLY MOVING HEAD As a stimulus object moves sagittally toward or away from a physically stationary observer, the changing distance between the object and the observer will be perceived, assuming that effective visual cues of the changing egocentric distance are available. Identical visual cues of changing distance between the observer and object will be produced by keeping the object physically stationary at its farthest distance and having the observer physically move toward or away from the object through the same sagittal distance as that previously used when the object moved. In order for the observer to perceive the object as moving and himself or herself as stationary in the former case and the object as stationary while he or she moves sagittally in the latter case, the observer must have proprioceptive or other information regarding his or her own stationariness or motion, respectively. Thus, information as to whether the self is stationary or is moving when the observer is presented with visual cues of changing egocentric distance is important if the observer is to correctly attribute the change in egocentric cues to object or self-motion or to some combination of both. This taking into account of self-motion either completely or partially is called compensation, and, as was mentioned with respect to Figure 4, it is considered to occur for frontoparallel as well as sagittal motions of the head (Wallach, 1985, 1987; Wallach & Flaherty, 1975; Wallach, Stanton, & Becker, 1974). A case of complete compensation for head motion which results in a veridical perception of the physically stationary stimulus object is illustrated in Figure 7. As suggested by the above discussion, two situations need to be distinguished in analyzing the compensation process using sagittal motion. In one of these, labelled Situation A, the head is stationary and the stimulus object moves sagittally toward or away from the head. In the other, labelled Situation B, the head moves sagittally and the stimulus object is either stationary or also moves sagittally. In Figure 7 and the remaining diagrams of sagittal motion only the case of the stationary stimulus object in Situation B will be diagrammed. The arbitrary units shown in Figure 7 in-

w.c.Gogei

130

Situation A

Situation B I

D;=D,=

16 3-

Figure 7. A hypothetical illustration useful in the analysis of the factors involved in the perception of the sagittal motion of a stimulus object (a point of light) toward or away from a physically (and perceptually) stationary observer (Situation A) or, the physical (and perceived) motion of the head toward or away from the physically stationary stimulus object (Situation B). The primed notation and open circles represent perceived characteristics (D', d'h, and dtg) of the egocentric distance of the object, the motion of the head, and the stimulus motion. The non-primed notation and the solid circles represent the same physical characteristics. The metric values are for comparison only indicating, for example, that D'f-D',, is the same in Situations A and B. As indicated, the distances and motions are assumed in Situations A and B to be perceived correctly. In that case, the perceived (and physical) egocentric change Dqf-DIn indicated in Situation A is canceled by the perceived motion of the head d'h. This cancellation in Situation B is expressed by the equation d'h- (D'f-D',,) = dtg, where dVg=O.Errors in the perception of d'hor D'f-D',,are expected to produce an error in dIgin Situation B as is shown in Figures 8 and 9.

dicate the distances and motions of the physical (solid circles) and perceived (open circles) stimulus object. In Situation A of Figure 7 the object

Analysis of Perceived S p e

131

moves physically, D f D , , and perceptually, D ’ r D,’ toward the physically and perceptually stationary observer with D ] = Dfand D’, = D,. In Situation B of Figure 7, the head of the observer moves physically, dh, and perceptually, d ’h, toward the physically and perceptually stationary object through the same distance as the stimulus object moved in Situation A. In this figure all the perceptions of distance and motion are veridical and compensation for head motion is said to be complete. In order to produce the same change in the cues of egocentric motion in depth, DrD,, in Situations A and B when the stimulus object in Situation B is physically stationary, and the head of the observer in Situation A is physically stationary, it is required that the physical sagittal motion of the head, dh, in Situation B equals the physical sagittal motion of the stimulus object in Situation A. When this occurs it can be assumed that the perceived egocentric motion, D’rD’,, will also be the same in Situations A and B. If this requirement is met, Situations A and B are said to be matched situations. That is, they are matched in D‘rD’,. It follows in matched situations that the measurement of D’,-D’n in Situation A can be applied as a measure of D‘fD’, in Situation B. The use of matched situations is not limited to the case in which the stimulus object in Situation B is physically stationary. It also includes the case in which both the head and stimulus object move sagittally relative to each other. In this latter case, however, it is required that the D r D , , in Situation A includes the total D r D , provided by the sum (aggregate) of the physical sagittal motion of both the head and stimulus object in Situation B. In Figure 7, the perceived egocentric distance of the stimulus object at its nearest perceived egocentric distance, D’,, is the same in Situations A and B. However, the position of the stimulus object at D’, in geographic (surrounding) space as distinct from egocentric space is not the same in Situations A and B. As the head moves forward in Situation B the perceived position of the object is carried forward with the head (a motion in tandem with the perceived motion of the head) while simultaneously the perceived egocentric distance between observer and object is decreasing until the perceived distance, D’,, is reached. It can be concluded from Figure 7 that in Situation B there are two visual vectors of perceived motion of the same size but opposite in direction with respect to the stimulus. One is the perceived change in egocentric distance, D ’ y D ,’ which if the observer were stationary as in Situation A, would result in the object being perceived as moving toward the observer as D’ decreased. The other is a perceived motion in tandem with the observer’s motion in Situation B that would move the object, if the decreasing D’ were not present, in the same direction as the perceived motion, d’h, of the head. This tandem motion will be labelled d’t. The algebraic addition of these two visual per-

132

w. c.Gag$

ceived motions occurring simultaneously in opposite directions in the case of Figure 7, Situation B, results in the physically stationary stimulus object in Situation B being perceived as stationary (d’8 = 0). Generalizing this analysis of Figure 7, there are two hypotheses that are required for predicting the perceived geographic sagittal motion or stationariness of a physically stationary or physically moving stimulus object viewed using a sagittal motion of the head. One hypothesis (Hypothesis 1) is that ”...the change in the perceived egocentric distance between the object and observer is the same for the same change in visual cues, regardless of whether the change is produced by the motion of the observer, the motion of the stimulus object, or the combined motions of b o t h (Gogel, 1992b, p. 90). This hypothesis is expected to apply whenever Situations A and B are matched. The second hypothesis (Hypothesis 2) “...states that the perceived egocentric distance D’ of the stimulus from the observer, at any instant during the head motion must be measured from the perceived, not the physical, position of the head in geographic space, regardless of whether the perceived and physical positions differ” (Gogel, 1992b, p. 91). For example, if the moving head of the observer were perceived by the observer to be stationary (d’h = 0) in Situation B, for whatever reason this happens, it would be predicted from Hypothesis 2 that the perception of object motion, d’8, in Situation B would be identical to d ’8 in Situation A in which the head was both physically and perceptually stationary. The major determiner of the perceived tandem motion, d’t, is d’h. If d‘h = d’t as is assumed in Figure 7, Situation B, it follows that

where d’, is the perceived (geographic) motion or stationariness of the stimulus object relative to the stationary surround. More generally, as will be discussed, Equation 8 should be written as

which applies whether or not d’t is identical to d‘h. According to Equation 9, the determiner of the perceived geographic sagittal motion, d’8, of the stimulus object in Situation B is the difference between d’t and D’TD’~. If this difference is zero, a physically stationary stimulus object in Situation B is expected to be perceived as stationary (d \ = 0). If this difference

Analysis 0fPermiVed S p c e

133

is unequal, for whatever reason, the physically stationary stimulus object, according to this analysis, is expected to appear to move. As will be discussed, Figures 8 and 9 illustrate situations in which a physically stationary stimulus has a perceived motion, d'g, in Situation B that is opposite to or is in the same direction as the head motion, respectively, as a result of inequalities between d'h and D ',-D',, under the assumption that d't

= d'h.

The application of Equation 9 (and of Equations 7 and 8) is not restricted to the special case of Situation B in which the stimulus object is physically stationary. It is also expected to apply to conditions in which both the head and object are physically moving sagittally in Situation B. This is expected as long as matched Situations A and B are achieved in which the physical egocentric sagittal motion of the stimulus object in Situation A is the total of the physical head and stimulus object motion used in Situation B. Matching D r D , in Situations A and B by making dh in Situation B, in in Situation A which the stimulus object is stationary, equal to 0,-D,, does not insure that d ' h or d't and D'f-D', will be equal in Situation B. It does, however, insure that D',-D',, will be the same in the two situations thereby permitting D',-D', in Situation B to be measured by measuring D',-D', in Situation A. Thus, all the factors as measured in Situation A that can influence D'rD',, without equally influencing d'h or d't also are factors that can modify d' in Situation B as predicted from Equations 8 or 9. The expected result of this inequality is that a physically stationary stimulus object in Situation B, rather than appearing stationary, would appear to move sagittally (d'g # 0). In addition, factors that modify the perception of head motion, d 'h, without equally modifying the perceived change in egocentric distance, D',-DX, also would remove the equality between d'h or d ' t and D ' y D ' , and also would result in a physically stationary stimulus object appearing to move concomitantly with the sagittal motion of the head. Consider first some factors that are likely to change D',-D',, in Situations A and B without changing d'h or d't in Situation B. One such factor is the increasingly larger perceived depth produced by a constant cue difference, for example, a change in convergence or in motion parallax, if the stimulus is perceived to be at an increasing distance from the observer (Gogel, 1964, 1977; Ono & Comerford, 1977; Ono, Rivest, & Ono, 1986; Rivest, Ono, & Saida, 1989; Wallach & Zuckerman, 1963). The mathematical expression for this relation in perceptual terms can be called the perceptual inverse square law. On the other hand if the same physical depth (not the same cue difference) is simulated to appear at increasingly greater distances from the observer,a decreasing effectiveness of the depth

w.C.Gag$

134

Observer Physically and Apparently Stationary

A df

I<

Apparent Egocentric (D'f - D'") Motion of Object = 133

I

Starting Position of Physical Motion Toward Observer

0 0

-D,= 36-1 --0',=52--1

D;= 185-1 D f = 125

-I

Physical Motion of Object -I-1nitia1 Error = 60

(Df Dn ) = 89 ~

Physical (dh) and Apparent (d'h Motion of Observer = 89

Position of Physically Stationary Object I

4-

I

0

D f = 125

E

0

0

I-Do,=~~-I D,

36 -I

-

D;= 185-1 Initial D' -I Error = 60 I+

dig= -44 4

Apparent Geographic Motion of Object

Figure 8. In Situation A, a stimulus object (a point of light) moves physically (the solid circles) between Df and D, but moves perceptually (the open circles) between D'f and D', toward a physically and perceptually stationary observer. In Situation B, the stimulus object is physically stationary at its far position, and the observer's head moves sagittally through the same physical distance as the stimulus moved i n Situation A. The overestimation of the perceived distances of the stimulus, as measured in Situation A, results in the physically stationary stimulus object in Situation B appearing to move geographically toward the observer as the observer moves toward the stimulus object.

cue due to its decreasing cue magnitude might result in a decrease in D ' r D', relative to the constant simulation of DrD,. Also, a perceived depth

Analysis of Perm'ved Space

135

might be smaller than a physical depth because of the presence of conflicting cues of distance. For example, in laboratory studies of changes in perceived distance caused by changes in convergence, the perceived depth might be reduced as a consequence of viewing the stimulus with a constant accommodation. The contribution of d't in Equation 9 also can be changed without changing D'rD',,. The perceived sagittal head motion, d'h, which is the principle determiner of d't is usually the result of vestibular/kinesthetic information associated with the head motion. The magnitude of the perceived head motion, d'h, for a number of reasons might differ from the physical head motion, dh, and, thus, the magnitude of d'f also would be likely to vary for the same D ' f D ' , , in Situation B. Also, in order for d'h to contribute to d'g of the stimulus object in Situation B, d'h must be translated into the visual vector d 'f before it can be combined algebraically with D'rD',,. This transfer from d'h to d't may be incomplete. For example, the transfer may change to some degree as a function of the distance of the stimulus from the observer. These and other factors may modify the difference between d'f and D'fD',, in Situation B. However, regardless of how the changes in either d't or D',-D',, are accomplished, the analysis asserts that this difference represents the significant determiner of the perception of the sagittal motion or stationariness of the stimulus object in Situation B regardless of whether this perception is veridical or differs from the physical or simulated motion of the stimulus. Figure 8 illustrates an instance in which D'f-D',, in the matching Situations A and B exceeds dft, where d't is assumed to equal d'h. In Figure 8, Situation A, the observer is physically stationary and the stimulus object (solid circle) physically moves sagittally toward (or away from) the physically and perceptually stationary observer through the changing physical egocentric distance, Df-D,,. If the far distance of the stimulus is perceptually at D 'p where D 'f > D f , the object will appear to move, D D',,, through a distance (between the open circles) greater than the physical distance, D f D , , (consistent with the perceptual version of the inverse square law). In Situation B, the object is physically stationary at D f and the head moves, dh, toward the object through the same physical distance, DrD,,, as in Situation A. Assuming that the observer's perception, d ' h , of his or her head motion is correct and that the identical cues of changing egocentric distance are equally effective in Situations A and B, the physically stationary object will appear to move through an apparent geographic sagittal motion, d'g, in Situation B, opposite to the direction of the perceived head motion. It will be noted in Situation B of Figure 8 that Equations 7 and 8 are consistent with the diagrammed results. That is, again d'h+D',, = D ' P ~ 'and ~ again d i = d'h - (D'fD',).The tandemmo-

'r

w.c.Qd

136

Observer Physically and Apparently Stationary

Starting Position of Physical Motion Toward Observer

f 0 -D ' p 36 -I

1-

0

0

D,= 52 -I

D;= 125 ( D ' ~- D,; )

II

D f = 185-1

-Error

Initial D' = 60

Physical Motion of Object (Dr - D, ) = 133

K

Bd

I

Apparent Egocentric Motion of Object = 89

I

' 0

Physical (d h ) and Apparent (dlh) IMotion of Observer = 133

D'f = 125

I

-I

Position of Physically Stationary Object

04 I I-

0

I

0

dn 36-1 5

D f = 185

I I-

I+

I-dIg=

Dn= 52

-I

Initial D' + Error = 60

44-

Apparent Geographic Motion of Object

Figure 9. In Situation A, a stimulus object (a point of light) moves physically (the solid circles) between Df and D, but moves perceptually (the open circles) between D'f and D', toward a physically and perceptually stationary observer. In Situation B, the stimulus object is physically stationary at its far position, and the head moves sagittally through the same physical distance as the stimulus moved in Situation A. The underestimation of the perceived distances of the stimulus, as measured in Situation A, results in the physically stationary stimulus in Situation B appearing to move geographically away from the observer as the observer moves toward the object.

Analysis of Perceived Space

137

tion in Situation B of Figure 8 for convenience is assumed to be equal to the perceived (and physical) head motion and, in geographic space, the effect of the tandem motion is opposite in direction to the changing perceived egocentric motion, D ‘ f D ’,. However, since D ’,-D ,’ exceeds d ’h (and d ’t), a component of perceived geographic motion of the physically stationary stimulus object remains to produce the perception of the geographic motion, d’8, of the physically stationary stimulus in a direction opposite to that of the perceived head motion. Figure 9 in a manner generally similar to that of Figure 8 illustrates the case in which d’h (and d’t) is greater than D’fD’n in Situation B and as a result the physically stationary stimulus in Situation B appears to move in geographic sagittal space. Again Situations A and B are matched for equality in D f D , and in D’fD’,, although D ‘ f D ’ , is less than D f D , in both situations. As the head moves sagittally toward or away from the physically stationary stimulus, because D ‘ f D ,’ < d ’t, a portion of the tandem component of motion that exceeds the perceived motion from D’f D’, remains to produce the perception of geographic motion, d’g, in the same direction as the perceived motion of the head. The diagrammed results are consistent with Equations 7 and 8 and, assuming for convenience that d’t = d‘h, they are consistent with Equation 9, with the sign of d’8 determined by its direction relative to the direction of the perceived motion of the head. In a study by Gogel and Tietz (1992b), some aspects of the above analysis of the perception of sagittal motion were examined in four experiments. The purpose of Experiment 1 was to test whether perceiving a stationary stimulus object as more distant than its physical distance would result in it appearing to move sagittally in Situation B in a direction opposite to that of the head motion. This is the result expected from the conditions illustrated in Figure 8. The error in perceived distance was generated by the specific distance tendency ( S D T ) which, even though partially effective cues of the distance of the stimulus object are available, causes the perceived distance of the stimulus object to appear displaced from its physical distance toward a perceived distance of about two or three meters from the observer (Gogel & Tietz, 1973). Thus, the perceived distance of the object (a point of light) viewed binocularly in an otherwise dark environment was expected to appear at a distance that was some compromise between its physical distance and two or three meters. In support of the result expected from Figure 8, as the head was moved sagittally in Situation B toward and away from the physically stationary object, the object appeared to move in geographic space opposite to the head motion. That an appreciable error in the perceived egocentric distance of the stimulus object was indeed present was determined by mea-

138

w.c.Gcgd

suring the perceived egocentric distance using the lateral head motion procedure. In addition, in this and the remaining experiments of this study two variables of perceived sagittal motion were measured. One was the value of D’,-D’, as it occurred in Situation A and was assumed to apply also to the matched D y D , conditions of Situation B. The other was the value of d’8 (the perceived geographic motion of the stimulus) in Situation 8. Both of these were measured by the observer adjusting by touch the sagittal separation between two unseen posts to duplicate D‘rD’,, and d’8. From these results the compensation for head motion in Situation B could be calculated. The compensation was quite limited with average values of 47% and 16% of the physical motion of the head for two different stimulus distances. In two other experiments in the same study (Experiments 2 and 31, matched Situations A and B again were used and a point of light, again the stimulus object, was presented under otherwise reduced conditions using binocular observation. In these two experiments, in Situation B, the point of light as well as the observer’s head moved sagittally toward and away from each other in opposite directions. If the compensation were complete the difference between the perceived sagittal motion of the stimulus in Situations A and B should equal the physical motion of the head. Clearly from the measures of D ’ f D ’ , in Situation A and d’, in Situation B, compensation was far from complete, averaging 19% and 25% of the physical head motion in the two experiments. In Experiment 4 in the study by Gogel and Tietz (1992b), the cues of distance were much less reduced than in the other three experiments. A nubbly pile carpet covered the portion of the visual alley within which the stimulus (again a point of light) was located or moved. The alley and stimulus object were viewed binocularly. Thus cues of binocular disparity were available between the stimulus object and the parts of the alley, and perspective and binocular disparity were present to determine the perceived extension of the alley in which the stimulus object was located and often appeared to move. Nine motion conditions were used in the matched Situations A and B. These were classified in terms of three types of geographic movement in Situation B. The geographic sagittal motion of the stimulus object simulated in Situation B was in a direction opposite to that of the motion of the head for Type I, was zero motion (stationary) for Type 11, or was motion in the same direction as that of the head for Type 111. The average perceived sagittal motion, d’8, of the stimulus object in Situation B was very similar to the simulated (expected) motion in Type I, somewhat negative (a perceived motion slightly opposite to the head motion) in Type I1 and less than the simulated motion in Type 111. The

Analysis of Perceived S p c e

139

amount of compensation averaged over all nine conditions was 80%of the physical motion of the head. The results from these four experiments together with the geometric analysis of perceived sagittal motion suggest several conclusions. One conclusion, supported by Experiment 1, is that errors in perceived egocentric distance can modify the essential relation between d’t and D ’ f D ’ , to produce an illusory geographic motion, d’g, of the stimulus object in Situation B. Another is that the compensation for the physical head motion is considerably smaller under rather reduced conditions of distance cues (Experiments 1,2, and 3) as compared with the compensation obtained under more full conditions of distance cues (Experiments 4). There are several possible reasons for this. It may be that under partially reduced conditions d ’ h is much less than d h resulting in d’h producing a small d’t. Or, d ’ h might be substantial, but the transfer of the d ‘h to d ’t is greatly reduced. Or, it might be that even though d’h and d‘t are large, the weight given d ’ t is less relative to that given D’,-D’, by the visual system. If this last reason, which receives some support from the Type I1 and 111 results of Experiment 4 is valid, a weighting constant, H , would need to be added to Equation 9 such that d’g = Hd’t - (D’fD’J.

(10)

This value of H can be computed from d ’8, d ’t, and D’,-D*,. In the study by Gogel and Tietz (1992b) D’fD‘, was measured in Situation A and d ; was measured in Situation B. Another situation to be labelled Situation C, in which d’t is measured, also is needed and is shown in Figure 10. Figure 10 provides an illustration of the situations for measuring the variables D ’,D’, in Situation A, and d’t in Situation C so as to apply these values to an understanding of the perceived geographic motion, of the physically stationary stimulus object in Situation B. In this particular illustration it is assumed, for convenience only, that d f t = d ‘ h in Situations C and B. It is not assumed (or required) that either d ’ h or d’t must equal d h . The perceived motion of the stimulus object in Situation C (the tandem effect) must use the same distance cues used in Situations A and B, but in Situation C these cues are constant. Suppose, for example, that in Situation A or B, 0)-D’,, resulted solely from changing oculomotor cues produced by the physical motions of either the head or the stimulus object. The same oculomotor cues but now unchanging must be provided in Situation C to yoke the stimulus object to the head motion with the physical distance between head and object remaining constant. If the values of D’rD’,, d’t, and d ‘8 are measured in Situations A, C, and B, respectively, by the ob-

w. c.Gq5$

140

server‘s sagittal adjustment of measuring posts, the value of H can be calculated applying Equation 10 where

H = [d; + (DkD’,J]/ d ’ p

(11)

In the example of Figure 10, H = [-20 + (80-50)] / 10 = 1. It is consistent with the results of the above four experiments, particularly under conditions of rather reduced cues of distance, that H > 1. If indeed it is found that H f 1 this implies, for the conditions used, that the value of d’t measured in Situation C is not the effective value of d’t present in Situation B. In that case a different weight is given by the visual system in Situation B to d ’ t as compared to D’rD‘,,. Additional research is needed in which d ’ t , D’fD’,,, d’g, and d ’ h are each measured to determine whether the smaller contribution of d’t to d‘g that occurs in Situation B as conditions are more reduced is the result of small values of d ‘h despite substantial values of d h , a loss in the transfer of effects from d ’h to d ’ t , or a differential weighting of d ’t and D ’ r D’, .

THE CONCEPT OF COMPENSATIONFOR HEAD MOTION IN THE PERCEPTION OF THE SAGITTAL MOTION OF OBJECTS In all of the figures illustrating the perception of object motion or position (whether illusory or veridical), associated with a lateral or sagittal motion of the head, the physical variables indicated in the figures can be disregarded in explaining the perceptions of object motions (W’or d’g). For example, in Figures 7 through 10, it is required that d h in Situation B equals D f D , in Situation A. This is to insure that D’rD’,, will be the same in Situations A and B for the condition in Situation B in which the stimulus was physically stationary. In these cases, it is the equality of D’fD’,, in Situations A and B, that is important in the analysis of d ’g and not the physical conditions by which this equality is achieved. As another example, in Figure 7 a physically stationary stimulus object appears stationary in Situation B because d’h by the production of d’t has an effect on d’g in a direction opposite and equal to that from D’fD’,,. However, again it does not matter what physical conditions are involved in achieving this equality. For instance, if d ’h < dh, and proportionally if D ’ r D ‘ , c D y D , such that the equality remains unchanged, the perception of the stationariness of the stimulus object also would remain. Thus, it cannot be said that compensation can be defined simply as the taking into account of the physical motion of the head. It might be more meaningful to state that the visual system compensates for the perceived rather than

Analysis of Perceived S p c e

141 Df - D, = 20

-l

D,,= 0 4Df =

Phys. f,n

60+1 0

n

-dh= 20+>

B

Phys. f

0

n

0

.

f

f

D f = 60D,= 40 -

Phys. n

4 4 4 Perc. f Perc. n

D' - 50 1 G - D ; = d',= 10

f,n

0

0

dg= 0

f

g=-20

Figure 10. Side-view drawings illustrating the situations (Situations A and C ) necessary for the analysis of the perception of geographic sagittal motion, d'g, in Situation B. In this figure, dIt (the tandem effect) is assumed to equal d'h (the observer's perception of self motion). If this assumption is made, dlt, as measured in Situation C, minus D'f-D',, as measured in Situation A, equals d'g, the perceived geographic motion of the physically stationary stimulus (see Equation 9). The constant physical and perceived tandem distance is somewhat arbitrarily chosen as the average of Df and D, and the average of D'fand D',, respectively, as found in Situations A and B. It will be noted that Situations C and B illustrate the case in which d'h is less than the physical head motion, dh ,(where d'h = 10 and dh = 20). This is consistent with the hypothesis (Hypothesis 2) that it is the perceived, not the physical, head motion that is important in this analysis.

w.c.Gqgd

142

the physical motion of the head. However, if Equation 9 or 10 is valid the important factor in compensation is not d'h per se but rather the effective d't as it compares to D'rD'.. According to the theory of perceived sagittal motion proposed here the concept of compensation for head motion can be described by the resolution of two vectors (d't and D'rD'.) that are often (but not always) opposite in direction in their influence on the perceived motion of the stimulus object in Situation B (Gogel, 1992b, p. 91). The visual vector d't is the result of the transfer of the proprioceptive/vestibular information regarding sagittal head motion to a component of visual stimulus motion yoked at a constant distance from the moving head. This component as measured in Situation C is in tandem with the motion of the head because of the constant (static) cue or cues of egocentric distance between the head and object. One possible reason for the visual system giving greater weight to D ' r D ' . than to d't (if this occurs) is that D'rD'. is produced by changing (dynamic) information whereas d't is derived from static (unchanging) egocentric visual information. At least under the relatively reduced cues of distance such as were present in Experiments 1,2, and 3 of Gogel and Tietz (1992b) dynamic visual cues of changing distance are apt to be more effective than static visual cues of a constant distance resulting in the lesser weight given d't relative to D'rD',,. This process of integrating d ' t and D'rD',, into a single perception of the geographic motion, d > of the object, is likely to be similar to the process by which the visual system integrates conflicting cues from diverse sources of information, for example, the perception of distance from several distance cues each of which by itself would produce a different perception of distance. An instance of this would be the case in which a change in the convergence of the eyes to an increased distance is opposed by a constant or oppositely changing cue of accommodation. This interpretation of the compensation for head motion in the perception of sagittal motion avoids an interpretation that requires any processes or concepts (e.g., cognitive processes) more complex than those normally associated with the integration of different sources of visual information.

IMPLICATIONS OF PHENOMENAL GEOMETRY FOR RESEARCH IN VISUAL PERCEPTION Internal Consistency in Phenomenal Geometry According to the above discussion, the perceptual system, as reflected in three-dimensional phenomenal geometry, in the absence of contradictory information, cannot distinguish between illusions and physical real-

Analysis of Perceived S p e

143

ity. However, if the factors of K’, $’, and D’, at any instant, together specify the perceived spatial characteristics of a stimulus in three-dimensional space, it follows that this specification, even though sometimes resulting in illusions, is internally consistent, therefore specifying stimuli that are physically possible. For example, in Figure 4a, the perceived illusory rotation, p’, of the stimulus configuration can be duplicated by an object physically rotating through the physical angle p that is veridically perceived. However, it is sometimes found that a physical representation of a perceptual interrelation is not always possible. The usual equation for the SDIH in which 8 not 8’ is used and in which a constant of proportionality is added is

S‘/ W’=Ptrm(8/2).

(12)

It is not unusual to find that P f 1 must be inserted in Equation 12 in order to produce the equality between the left and right side of the equation (Foley, 1968, 1972; Gogel, 1990). In that case, the perceived size, S’, of the stimulus object at the perceived distance, D’, does not subtend the visual angle 8. This is illustrated in the two lower drawings of Figure 11. Figure 11 represents a situation in which the observer has been asked to indicate, R, the perceived size of a stimulus, its perceived distance, and, for the purpose of possibly achieving a complete phenomenal equation, its perceived visual angle (or perhaps the assumption is made that 8, = 0’). If it is supposed that all of the responses, R, are indeed measures of perceptions then Figure 1la indicates internal perceptual consistency where P in Equation 12 equals one, but Figures l l b and l l c do not, where P is greater or less than one, respectively. If such inconsistencies between perceptions do occur in the SDIH or in other situations involving phenomenal geometry, how are they to be understood? There are two explanations which would perhaps suggest that results such as those shown in Figures l l b and l l c need not be accepted as indicating internal inconsistencies. One is that if 8’ is substituted in Equation 12 for 8, as is advocated by McCready (1965, 1985, 19861, the seeming inconsistency could disappear because 8’ could differ appropriately from 8. A second explanation is that the intrinsic geometry of the visually perceived space is non-Euclidean (Foley, 1965, 1972, 1991). In this case, if the appropriate non-Euclidean geometry were used perhaps the internal inconsistency would disappear. A third possibility, but one which does not necessarily restore the consistency between the perceptual interrelations, is that cognitive processes have intruded to modify the perceptual interrelations as distinct from only modifying the responses. This third possibility receives some support from a study by Swanston and Gogel (1986). A luminous line presented monocularly on a

w. C.Gpi

144

b

\ 3

C

3

SR

DR

I

I

I

'I

Figure 11. Drawings contrasting internal consistency (Figure l l a ) and a lack of internal consistency (Figure I l b and l l c ) in the observer's reports, R, of the visual angle, OR, the distance, DR, and the size, SR, of the stimulus object. Unlike the situation of Figure Ila, in Figures 1lb and l l c the reported size of the stimulus is too large or too small, respectively, to be consistent with the reported visual angle of the stimulus at its reported distance. (From "A theory of phenomenal geometry and its applications" by W. C . Gogel, 1990, Perception t? Psychophysics, 48, p. 116. Copyright 1990 by the Psychonomic Society. Reprinted by permission.)

monitor in an otherwise dark room expanded or contracted to simulate a motion in depth toward or away from the observer. The perceived length of the line was measured by the frontoparallel separation of posts, and the depth of the perceived motion was measured by the sagittal separation of posts. The result was that the ratio of the perceived length of the line at its farthest and nearest simulated distance was approximately the same as the ratio of the change in its physical length on the display monitor, whereas the measured perceived depth of motion was substantial. The SDIH would have predicted from the perception of changing size that the perceived depth would be approximately zero. That the ob-

Analysis of Perm'ved Space

145

tained depth from the expansion or contraction was indeed perceived depth was verified by applying the head motion procedure to measure the perceived distance of the stimulus at the end positions of its simulated motion. The effect on the perceived depth is interpreted as due to perceiving the stimulus as increasingly off-sized during an expansion or contraction. The results of this study suggest that a cognitive (off-sized) process produced the inconsistencies in the perceptual interrelations and thus caused the failure of the SDZH to predict the results. As is indicated by the research discussed previously, the perceptual interrelations involved in phenomenal geometry are usually internally consistent, thereby permitting the perceptual interrelations to be represented by a physical model. Exceptions in which this consistency does not occur might identify opportunities for studying the intrusion of learned and/or other cognitive influences into the perceptual processes involved in the perceptual interrelations of phenomenal geometry.

Cue Equivalence in Phenomenal Geometry A characteristic of phenomenal geometry in addition to its usual internal consistency is that particular values of the basic variables of perceived distance, perceived direction, and the perception of self motion or stationariness will have the same effect on the derived perceptions of the size, shape, motion, and orientation of stimuli regardless of the kind or number of sources of information or cues determining these basic perceptual values. This has been called cue equivalence or cue substitution (Gogel, 1990). Cue equivalence results in metameres in visual spatial perception similar to those in color vision. For example, in Equation 1, the effect of a particular change in D' upon W' (for a constant K' and $') will be identical regardless of whether the change in D' is produced by changes in binocular disparity or by the cue of perspective. The classes of evidence supporting this cue equivalence are discussed by Gogel (1984, 1990). Cue equivalence has the important effect of making phenomenal geometry very parsimonious in its application in that it allows the three basic perceptual variables of phenomenal geometry to have the same predictable effects on the derived perceptions regardless of the kind or complexity of the factors producing the particular values of the basic variables. Cue equivalence permits perception to become the final common pathway through which the effects of a variety of cues and other perceptual influences are funneled.

Indirect Measures and Phenomenal Geometry. Any of the perceptual interrelations found in phenomenal geometry can be used to measure any of the three basic variables of this geometry. For

146

w.c.Gas$

example, obtained measures of W' could be used, keeping @' and D' constant, to measure K ' in Equation 1. Most of the applications of indirect measures considered so far have been concerned with the measurement of D' because this is a variable that can be manipulated readily and is important in a number of other perceptual interrelations such as the SDIH. Different methods of producing indirect measures of D ' have limitations which the use of another indirect method might avoid. The head motion procedure is restricted to measuring perceived distances not exceeding perhaps four meters from the observer because of limitations on the size of the base K ' provided by a lateral motion of the head. A method called triangulation by pointing using a larger base has been developed (Fukusima, Loomis, & Da Silva, 1991; Loomis & Da Silva, 1989; Loomis, Da Silva, Fujita, & Fukusima, 1992, Experiment 3). In this procedure the observer views a stationary stimulus perhaps six meters distant and then with eyes closed walks along a previously seen straight path displaced from the initial direction to the stimulus while continuing to point with the arm to the direction of the stimulus object. The distance of the measured intersections of the directions of pointing specify the perceived distance of the stimulus. In principle this method is similar to using 9' in Figure 2c to locate the pivot distance at the perceived distance of the stimulus object with K' provided by the distance walked during the measurement. Another possible method which is presently being experimentally evaluated is illustrated in Figure 12 and is described in the figure caption. This method, to be called the method of perceptual alignment, has an adjustable base which for a given perceived distance of the stimulus can be varied by changing the position of the stationary member of the two measurement posts. Possibly this method will avoid a limitation of both the head motion procedure and the triangulation by pointing method. This limitation is that the measurement of D' requires appreciable time to complete. The time required is at least several seconds for the head motion procedure and still longer for the triangulation by pointing procedure. In measuring, for example, the near and far terminal positions of an optical expansion or contraction which moves repetitively toward and away from the observer, a procedure is useful such as that shown in Figure 12 in which the adjustment can be made and checked very quickly at successive perceived arrivals of the stimulus at the terminal distances. It should be noted, however, that also there is an important advantage offered by the head motion procedures over the other two procedures. In the triangulation by pointing procedure and the perceptual alignment procedure, it is possible for the observers to provide a measurement of distance that satisfies a cognitive rather than a perceptual criterion by pointing to or aligning the measurement posts to a distance other than the

Analysis of Perceizmi S p c e

147

Target Stimulus

In Darkness

Figure 12. A schematic drawing illustrating a method of measuring the perceived egocentric distance, D', of a stimulus by the procedure called perceptual alignment. In this procedure two measuring posts, one of which is physically stationary and the other moveable, are presented to the right or left of the observer on the alley floor. The stimulus object is located directly in front of the observer in darkness beyond the alley floor. The observer's task is to adjust the nearer moveable post until the two posts and the vertical center line of the stimulus all appear to be on a straight line. From the angle formed between the observer's straightahead direction and the alignment of the posts, the perceived distance, D', of the stimulus target can be calculated by the experimenter.

distance perceived. In the case of the head motion procedure, even an experienced observer would find it very difficult to adjust the response to W' (from which D ' is to be calculated) to achieve any criterion other than the perceived extent of W'. Perhaps one of the oldest indirect methods of measuring D ' is by means of S' in the SDIH. This method and the head motion procedure has been compared in two studies (Gogel, 1979; Gogel et al., 1985). A1though consistent differences in the measurements from the two methods were obtained the results were positively correlated. The problem of measuring D' and the separation of cognitive and perceptual effects have been serious concerns for investigations of the perception of three-dimensional space. The development and use of measures provided

148

w. c.GgEi

by the perceptual interrelations found in phenomenal geometry can contribute to the solution of these problems.

How Common Are Errors in Perceived Distance? The main reason for introducing errors in perceived distance in most of the experiments or figures discussed in this essay is that the analysis of the processes involved in perceiving lateral, rotational, or sagittal motion or stationariness in the stimulus was facilitated. It is claimed that this analysis applies equally well to veridical or illusory perceptions. The analysis is additionally important, however, if it is also the case that substantial errors in the perception of depth or distance occur in a variety of three-dimensional situations. Two questions need to be considered here. 1) Under what conditions are errors in distance or depth cues apt to occur, and 2) in which of these conditions will substantial illusions of motion occur as a consequence of observer motion. Distance or depth errors are apt to occur in distant portions of the visual field because cues of depth are attenuated or are below threshold and therefore are unable to support the perception of depth between distant objects at different distances. For example, distant mountains appear closer to nearer portions of the visual field than they are physically. This tendency for distant objects at different distances to appear more equidistant than they are physically is a general tendency that occurs as distance information is reduced. It is called the equidistance tendency (Gogel, 1965). Illusory motions of objects either lateral or sagittal are not apt to occur for objects at far distances unless the motions of the observer or the errors in perceived depth between the physically stationary objects is quite large. At near distances from the observer, the gradients of distance on the ground or floor surface unlike those at far distances can provide effective cues to veridical distance. However, these gradients, perhaps within several meters from the observer, often are directionally quite far below the level of the observer’s eyes, and, for the upper portion of somewhat isolated objects such as a lamp or the top of a chair, essentially only oculomotor cues may be available to determine its perceived distance. That oculomotor cues for isolated objects are effective, but often not completely so, is seen in Experiments I, 2, and 3 of the study on the perception of sagittal motion by Gogel and Tietz (1992b). For example, in Situation A, Experiments 2 and 3, the simulated binocularly observed sagittal motion of the point of light was 90.8 cm, whereas the average perceived motion as measured by the sagittal adjustment of the posts was 24.7 and 25.3 cm, respectively in the two experiments. Thus, it seems likely that the tops of physically stationary, vertically extended, objects at relatively near dis-

Analysis of Perceid Space

149

tances from the observer might appear to move as the head is moved either laterally or sagittally. Such illusory motions tend to be augmented when an object other than the object being considered is fixated. This is expected from an experiment by Wist and Summons (1976) in which it was found that an attended test object was displaced perceptually toward the perceived distance of a fixated object. Additional evidence for this effect of fixation was obtained in a study by Gogel and Tietz (1977) in which W’ of a monocularly observed point of light was modified in the expected direction by the distance of the object fixated. Illusory motion produced in this manner by fixation also can be observed by fixating a nearby physically stationary finger while attending to a more distant physically stationary object as the head is moved laterally. The attended object will appear to move in the same direction as the head. If the object previously attended now becomes the fixated object, the now attended finger will appear to move in a direction opposite to that of the head. There are two possible explanations of these illusory motions of the attended object. One is that the perceived motion of this object is explained by the motion on the retina as determined by the distance of fixation. The other consistent with the point of view expressed in this essay is that the perceived distance of the attended object becomes more like the perceived distance of the fixated object thus producing an illusory perceived motion W’ in the same direction as or in the opposite direction to the head motion, as illustrated in Figure la. An experiment by Gogel (1980) in agreement, in principle, with the second explanation used binocular disparity to change the perceived slant of a physically stationary object with its top physically more distant than its bottom. The illusory perceived slant which was simulated to be in error by binocular disparity was either in the direction of the physical slant or opposite to the direction of the physical slant. The stimulus on the retina, which was specified by the physical slant, was always the same regardless of the perceived slant of the stimulus. The perceived rotation, p’, of the stimulus, however, as predicted, changed direction as the perceived direction of the slant was the same or was opposite to the physical slant despite the fact that the direction of the motion on the retina remained constant. Both the unchanged retinal motion and the changes in the perception of depth were essential for the results obtained. A hypothetical additional example of a similar phenomenon is shown in Figure 13. From this figure it is evident that different motion perceptions can occur from the same motion of the retinal image. The motion on the retina always is important for the perception of motion but its contribution must be understood in the context of the basic factors of phenomenal geometry. Perceived motion is proportional to retinal motion only if stimuli at different

w.c.Gcgd

150

Retinal Stimulus at Head Position 1

Retinal Stimulus at Head Position 2

a

b

Figure 13. An example of the perceived visual relation between two points e and g as the head is moved laterally between Positions 1 and 2 while fixating a third point f at a distance between Points e and g. The movement of the images of Points e and g on the retina is identical in Figures 13a and 13b. In Figure 13a, the perceived distance of Point e is greater and of Point g is less than its physical distance. In Figure 13b, the errors in the perceived distances of Points e and g are reversed. As is indicated, the perceptions of the directions of the motions of Points e and g for the same retinal motions are quite different (opposite directions of 8') in Figures 13a and 13b.

physical distances happen to be perceived as being at the same distance from the observer. The Occurrence of illusory motion in depth also is common. For example, when riding in a moving vehicle, parts of the landscape ahead of the vehicle often appear to move in a direction opposite to the direction of vehicle motion. According to the theory of phenomenal geometry, this probably is due to a combination of errors in the observer's perception of self motion and errors in the perceived distances of the parts of the landscape.

Analysis of Perceived S p e

151

Both the perceived motion of a physically stationary attended object as the fixation is displaced to a different object at a different distance and the perceived motions of physically stationary objects located on the sides of the road along which the observer is traveling are failures to perceive the world correctly during observer motion. However, in neither situation does the observer usually believe that the stationary objects are actually moving. Only when information or knowledge contrary to the perception of the objects as moving is absent (as can be accomplished in an experiment) is the perceived motion concomitant with the head motion mistaken for real motion. As in the case of ignoring diplopic images in binocular vision, it seems that observers learn to disregard many of the perceived lateral or sagittal motions concomitant with self-motion that happen as a result of errors in the three basic variables of phenomenal geometry, particularly errors in perceived egocentric distance. Nevertheless, as indicated in this essay, instances of apparent concomitant lateral or sagittal motion occur in a variety of situations and like diplopic images are phenomena relevant to the understanding of the processes basic to three-dimensional visual perception.

IMPLICATIONS OF PHENOMENAL GEOMETRY FOR PERCEPTUAL THEORY An important aspect of any perceptual theory is to specify the basic variables in terms of which other derived variables are expressed. For example, mass, length, and time are basic to physical descriptions of a variety of concepts such as acceleration or inertia. In a similar manner an implication of phenomenal geometry for perceptual theory is that the three basic variables of perceptual distance, perceived direction, and the perception of self motion or self position are necessary for the prediction of derived perceptions such as size and motion. Thus, for example, whenever perceived distance differs from physical distance or simulated cue distance, it is expected that the perceived distance not the physical or cue distance will be the determiner of the derived perceptions. This implications is expressed in the use of equations containing only perceptual variables. It also is consistent with the concept of cue equivalence which has similarities to the concept of metameric matches in color vision. Given particular values of the three basic perceptions, how these values were determined (i.e., by which cues or other factors) does not need to be considered in predicting the derived perceptions from the particular Values of the basic perceptions. The three basic perceptions that together localize stimulus points or parts in perceived space, regardless of how they

152

w. c.Gqgd

are produced or of what they are composed, are the final determiners of the derived perceptions. In opposition to this implication from the theory of phenomenal geometry is the view which denies that some perceptions can be used to predict others. For example, Baird and Wagner (1991) consider that they provide an alternative to the ”... often futile exercise of trying to predict one perceptual phenomenon on the basis of another, as opposed to making predictions that are based on physical quantities and the experimental context in which they are realized” (p. 862). The evidence for the theory of phenomenal geometry discussed in this essay is a refutation of that position. Also, Wallach and Berson (1989) state ”It is now accepted that size perception depends on distance registered, with a variety of distance cues contributing, and not perceived distance” (p. 288). Contrary to the implication of the above statement by Wallach and Berson (1989) there is research that directly supports the conclusion that if visually perceived distance and cue distance differ, the derived perceptions (including the perception of size) are determined by the perceived not by the cue distance. In an experiment simulating the moon at the horizon (Gogel & Mertz, 19891, the “moon” was simulated by a disc of light visually presented in a visual alley physically and perceptually extended in distance. The ”horizon” was simulated by an elongated visual surface presented vertically on the alley floor at several distances along the alley whereas the ”moon” was always at a constant physical distance (of 126 cm). In the condition of interest here, the entire display was viewed monocularly. In this condition the equidistance tendency ( E D T ) resulted in the ”moon” appearing at an increased distance and as having an increased perceived size as the ”horizon” was placed at increasing distances from the observer. Despite the constant cue of accommodation to the distance of the ”moon,” the ”moon” increased in perceived size as it increased in perceived distance. With a similar procedure, it has been found (Swanston & Gogel, 1986) that both the perceived depth and size of a monocularly viewed optical expansion (at a constant accommodative distance) increased as its perceived distance was increased as a result of the EDT. In another experiment (Gogel, 1964) a three-dimensional, binocularly viewed stimulus at a constant physical distance from the observer was perceived (by reflection from a mirror) to appear in a monocularly viewed visual alley. The back wall of the alley was moved to different distances, and, as a result of the EDT, the entire binocular stimulus appeared to increase in perceived distance and in perceived size as the distance of the wall increased. Perceived distance, not the distance from the constant oculomotor cues, was the determining factor in the change in the perception of the frontoparallel size and depth of the three-dimensional stimu-

Analysis of Perceived Space

153

lus. A similar result concerning the perception of depth from motion parallax was obtained from a study by Rivest, 01-10,and Saida (1989). It was concluded that “The results show that the visual system calibrates motion parallax with apparent distance, but not directly with the oculomotor adjustment of convergence” (p. 401). It may be that some of the resistance to the notion of perceptual interrelations comes from a concern that the interrelation denotes a causal relation between perceptions. The present view differs from this interpretation. It is assumed that specific neural conditions always are responsible for specific perceptions and causal relations when they occur must be looked for at these neural levels.

Phenomenal geometry and physical reality Predictions of the derived perceptions from the three basic perceptual variables of phenomenal geometry are independent of whether the Values of these basic variables are veridical or are in disagreement with the physical or simulated (cue) world. Phenomenal geometry involves only subjective phenomena and not the relation between perception and reality. Nevertheless, by means of the application of phenomenal geometry to the production of indirect measures of perceived distance, the theory contributes to the identification of systematic errors in perceived distance present in experimental and naturally-occurring situations and its consequences for the perceptions associated particularly with a lateral or sagittal motion of the observer. Such errors need to be explained by any comprehensive theory of perception. In particular, these are a challenge to Gibson’s theory of direct perception which essentially is a theory of correct perception. Indirect methods of measuring perceived distance consistent with phenomenal geometry provide a solution to a methodological problem; they also provide information that has theoretical consequences.

The distinction between and interrelation of perceptual and cognitive processes The problem of whether perception can be distinguished from cognition and if so whether conditions occur under which cognitive processes intrude on perceptual processes are matters of considerable importance for any theory or perception. Phenomenal geometry has contributed to this area through the use of indirect measures especially the lateral head motion procedure which presumably measures perceived distance essentially free from cognitive intrusions. It has been found that casual information indicated by examples of known perceived size, although clearly modifying verbal reports of distance did not affect perceived distance as measured

154

w.C. Gag$

by the lateral head motion procedure (Gogel, 1981). At the other extreme in the case of optical expansion, a failure of the SDIH to explain an optical expansion was attributed to off-sized (cognitive) effects in modifying perceived distance as confirmed by the lateral head motion procedure (Swanston & Gogel, 1986). On the other hand, in opposition to separate cognitive and perceptual effects in spatial responses, it can be argued that in many instances perception seems to be very similar to inferential reasoning. For example, in the perception of sagittal motion, d’s of Equation 7 could be interpreted in this manner. If the perceived motion of the head, d’h, is not equal to the change in the perceived egocentric distance, D’f D‘,,, of the stimulus, the result of this inequality must necessarily be that the stimulus has moved sagittaly a distance L I ’ ~ A .simpler interpretation, consistent with the present theory of phenomenal geometry and consistent with the way in which the visual system often reconciles opposing sources of information, is that the perception of d’g is the direct resultant of the combined but often opposite vectors of d’t and D j-D’,,. An interpretation that perception often includes inferential-like processes is supported by Rock (1983). He has provided an inferential interpretation for a range of perceptual phenomena including that of apparent motion concomitant with a lateral motion of the head. He also suggests that interrelations such as those found in the SDIH can be explained by assuming that the visual system ”knows” optical laws. Again, however, simpler interpretations consistent with the theory of phenomenal geometry are possible. According to phenomenal geometry each point of the stimulus is localized in perceived space by the three perceptual variables of distance, direction, and observer position as illustrated, for example, in Figure 1. Thus, in Figure lb, it follows that the addition of the location of the successive points of the stimulus, perceptually localized in this manner, determines the perceived size of the stimulus. No knowledge by the perceptual system of optics is needed. The perceived motions illustrated in Figures l a and l c also can be explained in this way except that the successive localizations of the stimulus point need to be accumulated in memory. Nor must inferential processes be ascribed to the situation of Figure l a or to the equation (Equation 1) associated with Figure l a because lateral head motion is involved. It is likely that the conclusion as to the absence of inferential processes obtained from using static and dynamic viewing in the study by Gogel and Tietz (1992a) as discussed earlier in this chapter will also apply to Figure la. As discussed in relation to Figure 11 it is assumed that the three basic perceptual variables of phenomenal geometry are consistent in that they all contribute to the localization of a stimulus point at the same perceived position in space. This consistency is a property of the visual sys-

Analysis of Perceived Spce

155

tem which results in the perception representing a physically possible stimulus even though the stimulus object or configuration may not be veridically perceived in all its aspects. Thus at least for lateral motions or rotations of the stimulus and for a laterally moving or stationary head, the explanation of a wide range of phenomena follows simply as an extension and validation of the consistency assumption. It has been suggested (Gogel & Da Silva, 1987a) that cognitive processes can either mimic or seem to refute perceptual laws (e.g., the SDZH). If so, a failure of a theory to distinguish between the contribution of cognitive and perceptual processes to the observer’s response will limit the ability of the theory to appropriately specify the body of phenomena to which it can apply. Acknowledgment. The preparation of this chapter was supported by the United States Public Health Service Grant NH39457 to Walter C. Gogel.

DISCUSSION Luigi Burigana (Department of General Psychology, University of Padua, Padua, Italy): Gogel’s essay deals with a clearly defined theme, dense with specific experimental references; it defines and illustrates the main terms and principles of a completely phenomenal geometry of perceived space, with reference to some special contexts and methods of observation of particular experimental interest. However, this essay provides several suggestions and concepts which are useful when discussing the general issues currently facing perceptual science in its various orientations. In this commentary, I would like to discuss and develop two of these concepts. The first is the assumption of ”internal consistency” of phenomenal geometry, understood as the conformity of certain characteristics of perceived space to a certain system of geometric rules; the second regards the possible “inaccuracy” of the perceptual system, as manifested in the appearance of visual illusions or errors, around which a considerable part of perceptual research revolves. The two concepts, although separate, are linked in some way, and reflection on them may serve to highlight some significant points of the debate on the sense, modes, and difficulties of scientific investigation on perception. I begin with recalling and specifylng some general concepts which are essential for later discussion on the above two topics. As already mentioned, phenomenal geometry is presented as a system of valid regularities within phenomenal space, which in turn consists of the set of spatial characteristics and relations inherent in the so-called phenomenal world.

156

w.c.Gqgd

According to the bipolar epistemological scheme which is prevailing in perceptual science, and is discussed in theorizations on ”critical realism” (Bischof, 1966; Metzger, 1967), the concept of phenomenal world is understood as combined with and counterposed to the concept of physical world; the numerous spatial characteristics and relations inherent in the physical world make up physical space, and the various regularities that are valid for these characteristics and relations make up physical geometry or geometry of physical space. More properly, these two main concepts should respectively be described as the phenomenal image and the physical image of reality, since they consist of two different manifestations, representations, or reconstructions of environmental reality (in its limited parts as they are considered case by case) which remains unique. Specifically, the phenomenal world is the image which environmental reality offers us of itself, if we examine it according to that special, basic form of exploration or empirical interrogation called vision or perceptual observation. Moreover, the physical world is the image which we can obtain of environmental reality by using the precise, reliable instruments and procedures of analysis and measurement supplied by the natural sciences, being guided by theories hypothesized within these sciences. These are, approximately, the meanings given to the two main concepts in the following discussion. However, these concepts, which are epistemologically fundamental, are very complex and to a certain extent ambiguous. As regards the first concept (the phenomenal world), we must bear in mind that its content depends directly on the meaning attributed to the term “perceptual observation” which, however, appears somewhat ambiguous and flexible. We will simply recall Gibson’s (1979) warning about the existence of various forms of vision (snapshot vision, aperture or peephole vision, ambient vision, ambulatory vision). Some authors also tend to include in the category of phenomenal aspects certain elements which are not properly included among the immediate contents of concrete perceptual scenes but which are somehow linked to them. For example, Gogel himself qualifies as ”perceived” the terms m’ = K’-W’ (the difference between perceived lateral motion of the head and perceived lateral motion of the object), d ’t (the motion in tandem of the object with the perceived sagittal motion of the head) and in general the hypothetical component vectors of perceived motions: these elements are not (presumably) authentic components of the supposed perceptual scenes, but are directly linked to such contents by means of simple derivate measurement formulas or plausible schemes of structural analysis. As regards the second concept (the physical world), the margins of flexibility and relative optionality turn out to be even wider, as we can choose between various ways of measuring the objective characteristics of

Analysis of P e r d Space

157

given realities and (at least in principle) between various physical theorizations regarding such characteristics. To be noted here is the fact that the ”ecological physics” which we find sketched in Gibson (1961,19791, is suggested as a theorization on the material characteristics of environmental reality as an alternative to ordinary physics; a theorization which Gibson presumed to be more suitable to accompany the development of a valid science of vision (Fodor & Pylyshyn, 1981; Wilcox & Edwards, 1982). It should also be noted that, in experimental research on perception, the aspects which are counterposed and compared with perceptual results (or subjects’ responses on them) are generally the conditions and factors which are deliberately and artificially established and modified by the experimenter: owing to the way in which they are generated and described, these conditions and factors cannot be generally qualified as “physical” aspects in the strict sense of the term. It was not by chance that Gogel, referring to some of his experiments on spatial perception with manipulation of visual cues to distance, found it necessary to make a distinction between “physical distance” and ”simulated cue distance” and, more generally, between ”physical world” and ”simulated cue world.” Accordingly, I believe it is better, whenever possible in this context, to avoid using the term “physical,” which may appear ambiguous and problematic in perceptual science. We will continue to reason according to a bipolar epistemological schema, which we will presume is made up of a level of perceptual data and a level of co-perceptual data: the latter includes those elements which, in ordinary terms, are called physical, material, or stimulative characteristics of any context of observation. Let some observational case c be specified, i.e., a particular segment of reality or real context in which the execution of a perceptual observation is programmed. If we also define a suitable co-perceptual modality for the analysis and description of real situations, then the presumed case c will reflect, jointly, in a percepfual frame Q‘(c)and a co-perceptual frame Q ( d .The two frames are conceived as separate but concomitant structures of empirical data: Q’(c)is the set of characteristics which the segment of reality c reveals to the subject during perceptual observation, and Q(c) is the set of information which the experimenter obtains on c by means of the fixed modality of co-perceptual analysis. It usually happens that the designated segment of reality c is not only spatially sized but also extended in time, i.e., it lasts for a certain time. We may therefore speak not only of “phenomenal spatiality” and “physical spatiality” in frames Q’(c) and Q(c)-which are fragments of the phenomenal and physical worlds-but also of ”phenomenal temporality” and ”physical temporality” inherent in the two structures of data. Applying the ordinary propositional approach (Rausch, 1985; Bechtel & Abrahamsen, 1990), we can

w. c.Gogel

158

assume that the contents which may be identified in each of the two empirical frames may generally be classified either as units or properties. A unit u may consist of an object or an event, which is coherent, clearly segregated, and univocally identified in one of the two frames; a property may consist of an attribute p characterizing a given unit u , or of a relation p linking certain units ul ,...,u , [the attributive or relational located property or proposition is shown as p ( u ) or p(u1,...,u r ) and unit u or group of units (u1,...,u,) makes up its bearer, while the attributive or relational predicate p is called a non-located property if it is abstracted from a specific bearer]. The frames of data Q’(c)and Q ( c ) are gnoseologically distinct (since they are obtained according to two different methods of empirical interrogation), but they are materially convergent (since they deal with and partially reflect the same segment of reality). Because of this material root in common, a more or less strong structural similarity may exist between the two systems. The structural similarity between Q’(c)and Q(c) may be such as to reveal that a certain content x ’ of the first frame is the direct correspondent of a certain content x of the second frame: contents x ’ and x (two units, or two located properties) are the expressions on the perceptual and co-perceptual levels of the same character or element of the given reality of observation; in these circumstances, inter-level correspondence is said to exist between contents x ’ and x or, more briefly, that x ’ and x are i.l.-correspondent. It should be noted that this concept is consistently used by Gogel in his analysis on presumed experimental situations. He distinguishes and links a physical point e and a perceived point e‘ (two units; Figure 5), physical width K and perceived width K’ of the motion of the head (two attributive properties; Figure la), physical distance D and perceived distance D’ of the object from the observer (two graduated relational properties; Figure 11, and so on. Now, let us suppose that a set C = {cl,...,ck) of distinct observational cases is specified and that each of these cases is subjected to both perceptual and co-perceptual observation, according to the agreed modality. We therefore obtain a perceptual frame Q‘(c8) and a co-perceptual frame Q(c8) in relation to the case c8, for g = 1,...,k, and overall the following two parallel series of structures of empirical data come into being: perceptual frames

observationalcases

Q’(c1) Q’(c2) Q’(c3)

Cl

c2

c3

... Q’(Ck)

...

ck

Analysis cf Perceid Space

159

Consider any two perceptual frames Q‘(cg) and Q ‘(ch), for 1 I g f h Ik, and let two special contents x i and x‘h be isolated in these frames. When comparing the two structures, we may find good reason for maintaining that these contents correspond to each other. This happens in particular when there is a certain formal affinity between frames Q‘(c8)and Q‘(ch) and when the structural position of x ’ in ~ the former is identical to that of x‘h in the latter. In these conditions, we can say that an inter-case corre~ x’h or, more briefly, spondence exists between perceptual contents x ’ and that x ‘ and ~ x ’ h are i.c.-correspondent. If these contents are special units u ‘8 and u ‘h, then i.c.-correspondence means that the two units are the reappearance or continuation of each other within the separate perceptual scenes to which they belong (imagining that situation c8 develops or changes in situation ch, or vice versa). Moreover, if these contents consist ~ )p’g(u’gl,...,u ‘gr) and p ’ h b ’ h ) = of two located properties p ’ , ( ~ ’ = p ’h(u ’hl r . . . , ~ ’ h ) , then i.c.-correspondence means that the non-located properties p’g and p ’ h are qualitatively similar (i.e./ they both qualify the same perceptual characteristic or dimension) and that the units in bearer u ’g = (u ‘gIr...,u ’g,> are i.c.-correspondent to the units in bearer u ’h = (u ‘hl,...,u ’h,). Let us now suppose that a sequence [ p ‘ ~ (’I), u ...,p’ k(u ’k)] has been formed, in which p’g(u’g),for g = 1, ...,k, is a property in perceptual frame Q’(cg), and ~ ’ ~ ( and u ’ ~p ‘ )8 + l ( ~ ’ 8 + l )for , g = 1, ...,k-1, are i.c.-correspondent. We then say that the given sequence identifies a variable V ’ which is well-defined on set C of possible observational cases. More specifically, V’ is a perceptual variable on C, since its occurrences are located properties within the perceptual scenes obtained on the cases in C. Moreover, for g = 1, ...,k, we write V‘(cg)= P ’ ~ called , the state or value assumed by variable V’ on case cg [or in frame Q’(cg)]; therefore, the states or values of a variable are conceived here as non-located properties, which sometimes are coded and ordered in numerical terms (i.e., they are measured). In the same way, but referring to located properties in co-perceptual frames Q(cl), ...,Q (ck), we can specify the concept of a co-perceptual variable V defined on the set of cases C. For g = 1, ...,k, the occurrence p’&’& of a perceptual variable V’ in frame Q’(c,) may turn out to be i.1.correspondent to the occurrence pg(ug)of a co-perceptual variable V in frame Q(c,). In this case, variables V‘ and V are called i.1.-correspondent. These are the general technical concepts used in the following analysis. I will now go on to deal with the two particular subjects mentioned at the beginning, and will first discuss the concept of the ”internal consistency” of phenomenal geometry. I wish to contribute to a coherent, logical reconstruction of this concept, which seems to be essential for Gogel’s theoretical approach but which is not exhaustively defined and developed in his essay. [Incidentally, he uses the term “consistency” in a sense dif-

160

w. c.G.zp$

ferent from the prevailing one on which I wish to comment here. This alternative sense is clear when Gogel says that ”the three basic variables of phenomenal geometry... are consistent in that together they specify a single position of a stimulus point in perceived three-dimensional space” (p. 114). I believe it would be more appropriate to speak here of the ”sufficiency” of the three basic variables for the specification of other spatial characteristics of the phenomenal world.] Gogel refers the concept of consistency, in its strictest meaning, to phenomenal geometry (p. 142),but this strict meaning may be determined progressively by means of three separate stages. In the first, the term in question is referred to a combination of possible values for a given system of perceptual variables. Let V’l,...rV’m be perceptual variables which are suitably determined, both as regards individual characteristics and mutual relations, and, for i = l,...,m, let p’i be some admissible state or value for variable V’i. The string (p’l,...,p’,,J which is formed of these values is believed to be consistent in relation to system (V’l,...,V’m) of the given variables if there exists some observational case c on which each variable V’i, for i = l,...,m, is well-defined and veridical, and such that V’i(C) = p‘i. In other words, the m-tuple p’ = (p‘l,...,~‘,) of possible values referring to m-tuple V’ = (V’l,...,V ’ J of perceptual variables is judged to be consistent if there exists at least one real situation c, so that, for every i = I,...,m, variable V’i takes on a definite value in perceptual frame Q ’ W , this value fits the value assumed in co-perceptual frame Q(c)by a variable V i which is i.1.-correspondent with V’i, and p’ is the joint value of variable V’ in frame Q’(c). I believe that this initial acceptation of the concept is suggested by some statements in which Gogel links the condition of “internal consistency” to the possibility of “specifying stimuli that are physically possible” and of duplicating an “illusory stimulus configuration” by means of a stimulus configuration ”that is veridically perceived” (p. 142), and describes this condition as ”a property of the visual system which results in the perception representing a physically possible stimulus” (pp. 154-155).In practice, a combination of possible states or values which may be referred without substantial difference both to a system of perceptual variables and to the system of co-perceptual variables which are i.1.-correspondent to the former, is judged to be consistent when those states or values are phenomenally and physically compatible (i.e., they may co-exist in some real case, both perceptually and co-perceptually). In this sense, some of the ”paradoxical perceptions” considered in the study of vision (Gregory, 1970, ch. 3; Day & Parks, 1989) are examples of inconsistent combinations of perceptual characteristics. In the second stage, the concept of consistency is referred to any perceptual regularity (of spatial characteristics). A perceptual regularity may

Analysis of Perm‘ved Space

161

be expressed by f(V’l,...rV’m),in which (V’l,...,V’m) is a system of percep tual variables, f is a condition on rn terms, and the formula, as such, states that, for every real situation in which the given variables are jointly well-defined, the rn-tuple of the values assumed by them in that situation satisfies the specified condition, i.e., formula f(V’l,...,V’,J is to be understood as an abbreviation of the following universally quantified , proposition: for every observational case c, so that values V ’ ~ ( C...,) V’&) exist in the perceptual frame Q’(c),f [V’l(c),...,V’,Jc)I is true. A perceptual regularity may be described as an “empirical law” or a “theorem” according to whether it is considered from an experimental-inductive or logical-deductive viewpoint; significant examples of perceptual regularities (of spatial characteristics) are the size-distance invariance hypothesis (SDIH), motion-distance invariance hypothesis ( M D I H ) , perceptual equations on sagittal motions, etc., mentioned in Gogel’s essay (Equations 3,4, 7, 9, etc.). They are all expressed in the form of numerical equations (given as “perceptual equations”) but regularities with different and more complex logical forms may of course be conceived. One plausible way of extending the concept of consistency to perceptual regularities is as follows: perceptual regularity f(V’1,...,V’m) is consistent when, for every rntuple ( p ’ l ,...,p’ m), so that p’i is an admissible value for variable V’i for i = 1,...,m, if this rn-tuple satisfies condition f, then it will be consistent in the sense specified above. In other words, the assumed regularity is consistent when, for arbitrary p ’1,...,p’,,, which are admissible values for variables V’l,...rV’m, if f(p’1, . . . , p ~ ’ ~ ) then an observational case c exists in which the given variables are well-defined and veridical, and such that V’i(c)= p’i for i = I, ...,rn. In practice, a condition on perceptual variables constitutes a consistent perceptual regularity if and only if that condition, if referred to the i.1.-correspondent co-perceptual variables, defines a valid physical regularity (i.e., it is a theorem in the geometry of physical space). Gogel warns that ”it is sometimes found that a physical representation of a perceptual interrelation is not always possible” (p. 143). If ”perceptual interrelation” here is understood as a synonym for “perceptual regularity,” then this statement affirms the possible existence of perceptual regularities which are not consistent in the above sense: thus, it indirectly supports the proposed second explanation of the concept. For example, if the perceptual variables S’, D’,and 8’ (perceived linear size, egocentric distance, and visual angle) were systematically linked according to the formula S ’ / D ‘ = 2 t a n ( 8 ’ / 2 ) (the perceptual SDIH in its basic form; Equation 31, we would have a consistent perceptual regularity, since the analogous formula S/D = 2 t a n ( 8 / 2 ) is generally valid for the i.1.-correspondent physical variables S, D,and 8. However, if the experimental results were to impose that the perceptual SDIH be expressed in the

162

w. c.Gag$

slightly more complex form S’/D’ = 2P tan(8’/2), in which P is a constant of proportionality different from 1, we would then have a non-consistent perceptual regularity, since the same formula is not generally valid if applied to physical variables. We now come to the third and last stage, in which the concept of consistency is referred to phenomenal geometry. In presenting his theorization on the salient characteristics in phenomenal space, Gogel mainly stresses the proposal of a certain logical order among these characteristics according to which a minimal set of basic or logically primitive variables (the perceived direction and egocentric distance of stimulus objects, and the perceived position or motion of the observer himself) is distinguished from a larger set of derived or logically subordinate characteristics (perceived size, shape, orientation, position, motion, etc., of the stimulus objects). This approach is appropriate in the presumed context: the logical arrangement of a theory is in fact generally set up by identifylng a minimal set of primitive terms and fundamental theorems (axioms) and showing how the other significant terms and theorems of the theory may be derived from the basic set by means of logical chains of various length and complexity. However, I believe that, for an immediate and clearly expressed explanation of the concept, phenomenal geometry should first be described as a coherent and complete set of regularities (or theorems) on spatial variables in the phenomenal world; as already noted, Gogel’s “perceptual equations” are notable examples of these regularities. The search for an efficient derivational order between the terms and theorems of a theory is an additional problem, which does not necessarily have a single solution (alternative axiomatizations may exist for one theory). Thus, let us conceive phenomenal geometry as a system of perceptual regularities; then it is natural to state that this geometry is consistent when each of the perceptual regularities composing it is consistent in the above described sense. In other words, to state that phenomenal geometry is (internally) consistent means stating that the regularities composing it are also regularities in physical geometry: the presumed laws in phenomenal space are also laws in physical or coperceptual space. It should be noted that the assumption of internal consistency affirms formal equivalence between regularities which are valid in both spaces; it does not affirm the systematic coincidence between values of i.1.-correspondent perceptual and co-perceptual spatial variables. By assuming that two regularities of the same logical form are valid on the two levels, we cannot by any means exclude the fact that, in certain observational cases, the values taken on by the variables in the perceptual regularity are discordant with the concomitant values taken on by

Analysis of Perceived Syace

163

the variables in the co-perceptual regularity: in these cases, we note a perceptual error or visual illusion. Although it is not fully explained in Gogel’s essay, the assumption of consistency plays an important role in his theorization. This may be seen by examining the general method he uses in obtaining the main equations of phenomenal geometry. First, he refers to some special situations of perceptual observation (cases in which the observer and/or the stimulus object moves laterally, or sagitally, and so on) and, for any of these observational situations, he represents the main terms of the resulting perceptual frame by means of a schema which consists of a planar drawing. Then, any drawing of this kind is analyzed according to the usual principles of elementary geometry and trigonometry, some systematic relations between its elements or aspects are highlighted, and formal expressions for such relations are defined. The drawings for the presumed observational situations may be considered as ”models,” and the sets of formulae which are derived by analyzing them geometrically are equivalent to ”microtheories” which Gogel aims at unifying by highlighting the features they have in common. In such a procedure, one important step is clearly the choice to represent the phenomenal aspects of the given observational situation by means of an ordinary planar drawing and to study it according to the principles of elementary (Euclidean) geometry. This choice involves the assumption that the general characteristics of phenomenal space are the same Euclidean ones which qualify physical space (indeed, Gogel represents phenomenal and physical terms in identical drawings, i.e., on a common figural basis): but this is precisely the assumption of internal consistency of phenomenal geometry in the sense explained above. Let us now consider the second of the two themes mentioned at the beginning: we will comment on the cases of perceptual inaccuracy or illusoriness, on their function in Gogel’s theorization and, more in general, on their importance in studies on perception. We are interested, overall, in all cases of perceptual distortion, erroneousness, originality, or singularity, i.e., observational cases in which the perceptual frame shows surprising discrepancies or novelties with respect to the co-perceptual frame. Clearly, the concept of perceptual erroneousness or originality is intrinsically comparative (psycho-physical) and arbitrary to a certain extent, since it presumes a comparison between perceptual and co-perceptual frames and since (at least in principle) there is a certain margin of freedom in the choice of type of co-perceptual frame. We will lay the bases for the following discussion by recalling two notable aspects of this concept. First, the illusions or singularities studied in perceptual science are very varied as regards the type and intensity of the inherent discrepan-

164

w.c.Gag$

cies between perceptual and co-perceptual frames. In particular, there are some cases (which I call structural singularities) in which the discrepancy between the two frames is radical and deals with the systems of units in the two separate structures (there are units in the perceptual frame which do not possess natural correspondents between the units in the co-perceptual frame and vice versa); and there are also other cases (which I call qualitative singularities) in which the perceptual and coperceptual frames are structurally similar and discrepancies deal with specific properties which are mutually i.1.-correspondent and included in the one or the other of the two structures. Figural demonstrations on phenomenal transparency (Metelli, 1974) or anomalous surfaces (Kanizsa, 1976) are examples of the first type and ordinary optico-geometrical illusions of the second type. Second, we must note that the inter-level discrepancy making up a perceptual singularity is mainly composite: it consists of a set of elementary contrasts, partially interrelated or complementary. In particular, in a case c of qualitative singularity we generally have a simultaneous discrepancy between certain located properties p ’ l ( u ’ I ) ,. . . , P ’ ~ ( U’J in the perceptual frame Q ’ ( c ) and specific located properties p l ( u l ) ,...,p m ( u m )in the co-perceptual frame Q ( c ) , which are i.1.-correspondent to the former. Reference to perceptual illusions, in the extended sense, is important in Gogel’s investigative method. For example, the section on the application of phenomenal geometry to stimuli extended in depth (p. 122) discusses exclusively cases of apparent rotation of an object or system of objects concomitant with lateral motion of the observer’s head, but references to illusory effects occur throughout the chapter. The perceptual singularities which Gogel considered in his theoretical essay and in previous experimental works are mainly qualitative and Composite. In the assumed situations, between perceptual and co-perceptual frames there is generally substantial structural similarity (biunivocal correspondence between units) and sometimes a partial qualitative equivalence (e.g., the presumed equality between perceived width K’ and physical width K in the motion of the head, between perceived size 8’ and physical size 8 of the visual angle, etc.). The discrepancy simultaneously involves two or more located properties which occur in both frames and which are i.1.correspondent (e.g., perceived size S’ and physical size S of the stimulus object, its perceived distance D ‘ and physical distance D, perceived width W’ and physical width W of its motion, etc.). Also, the initial mention of the ambiguity of the word ”physical” (as used in perceptual science) and the variety of possible modes of co-perceptual analysis is useful in discussing how Gogel investigates the perception of space and motion. In many of his experimental works he selectively manipulates

Analysis @Perceived S p e

165

various “cues to distance” (convergence and accommodation, binocular disparity, interposition, absolute and relative size, etc.) which, although they are all counterposed and compared with the perceptual result (i.e., attributed to the co-perceptual polarity), are clearly very different empirically. In such cases, in which a definite perceptual feature (phenomenal distance) is coupled with distinct features of the stimulus object (which do not necessarily fit each other) the same concept of “illusion” or ”perceptual error” is problematic and difficult to apply. Gogel repeats (pp. 125,128, 153) that the propositions and equations of phenomenal geometry apply equally well and with equal predictive capacity to both illusory and veridical perception; at the same time, he states that cases of illusory perception are particularly useful and indicative in investigations on the perceptual system and its processes (pp. 148, 151). We may ask: in the perceptual science, what are the true reasons for this special interest in illusions or visual singularities? What are the merits or prerogatives of these observational cases? These questions are of general importance, because a substantial part of research on perception has clearly been exerted and continues to be exerted on phenomena and effects which in one way or another may be qualified as cases of perceptual erroneousness or originality: there must be valid reasons for this systematic trend in perceptual science investigation. The questions also deal with one of the ”touchiest” and most salient points of the current debate on the sense and logic of research on vision: the point at which the “direct theory” initiated by Gibson (who assumes the prevalent truthfulness of ordinary perceptual experience) come into most immediate conflict with other theoretical orientations (Fodor & Pylyshyn, 1981; Rock, 1983, ch. 2). I do not believe that the above questions can be convincingly answered by stating that cases of perceptual erroneousness or illusion are psychologically important because they are common or important in ordinary visual experience: it is not very plausible to believe that perceptual activity is mainly misleading, and in any case the concept of “perceptual error’’ is closely linked to the method of co-perceptual analysis which is chosen and in relation to which one judges the presence or absence of such an error. Therefore, I do not believe that arguments of the type considered by Gogel under the title “How common are errors in perceived distance?” are sufficient or in any case determinant in explaining the importance of cases of perceptual error in his experimental researches and, more generally, in the perceptual science. The reasons for the importance of these cases should rather be sought on an epistemological and methodological level, in the special roles that (apart from their frequency or rarity) they may play in the scientific study of perception: they may be used to highlight

166

w.c.Ggd

and analyze certain properties, regularities, or tendencies of the perceptual function more effectively. We may state here that, working on appropriate perceptual illusions or singularities, the existence of specific autonomous principles of perceptual organization, the possible partial independence of perceptual results on the stimulus, the possibility of translocal or induction effects in phenomenal scenes, etc., can all be demonstrated. More precisely, in the following final paragraph, I would like to clarify logically one possible methodological use of qualitative and composite singularities of the type considered by Gogel: the use of such a singularity to demonstrate a relation of dependence between perceptual variables. Consider two variables V’I and V’2 and suppose we wish to verify whether a certain dependence exists between them. This verification may be the first step toward ascertainment of the shape of the dependence itself, which will be equivalent to a perceptual regularity if it is expressed in an appropriate formula. Thus, the task generally constitutes a significant perceptual problem, not a mere exercise on strange or anomalous vision. In a very general sense and rather approximately, we may say that some dependency between two characteristics exists if variations concerning one correspond to variations concerning the other. Thus, the hypothesis that the two terms to be compared are effective variables (and not constant values) constitutes a necessary condition for sensible questioning on their possible dependence (Grelling, 1939). The most natural way of verification consists of considering certain observational cases CI,...,Ck,so that variables V’1 and V’2 are jointly well-defined in the corresponding perWe could definitely identify dependence ceptual frames Q ’(cl),...,Q’(ck). between V ‘ I and V‘2 when, for arbitrary 1 I g , h I k, the result were V’1(cg)# V ’ I ( C ~if)and , only if V’&) # V’2(ch) (the two inequalities express concomitant inter-case variations of the two compared variables). Alternatively and more economically, we may proceed to consider a single observational case c, so that frames Q’(c)and Q(c) are structurally similar, perceptual variables V’I and V’2 are well-defined in Q’(c), co-perceptual variables V1 and V2 6.1.-correspondent to V ’ I and V’2) are well-defined in Q ( d , and jointly V ’ ~ ( C # )V,(c) and V ’ ~ ( C # )V ~ ( CThese ). inequalities express two elementary contrasts in the assumed data structures and therefore qualify c as a case of composite qualitative singularity; but they may also express the association between an (inter-level) variation concerning V’1 and one concerning V‘2, and thus prove the existence of a dependence between the given perceptual variables. In this way, a case of composite perceptual error is at one and the same time a demonstration of the dependence between perceptual variables: the association between the variables is proven in terms of concomitance or chaining between per-

Analysis of Perceived Space

167

ceptual errors which deal with those variables-see remarks regarding “errors which produce other errors” (pp. 122,139, etc.). In my opinion, beyond verbal explanations, this is the logical scheme which leads Gogel to link certain illusory effects in the perception of space and motion to the discussion on the equations or regularities of phenomenal geometry and to use the former as an immediate demonstration of the validity of the latter.

Gogel: Burigana discusses two aspects of the theory of phenomenal geometry. One is the role of the assumption of internal consistency in the theory. The other is the place in the theory for perceptual error or illusions. Znternal consistency. The theory of phenomenal geometry uses the concept of internal consistency in which the three basic perceptual factors of perceived direction, distance, and observer position or motion are consistent in that all three are needed to perceptually localize each point of the stimulus in three-dimensional space. This concept has several consequences for the theory. First, it follows from this concept that the perceptions of size, motion, orientation, and shape that are derived from the basic factors can always be modeled by physical events since physical events always can be related to a specific stationary or changing origin by physical directions and physical distances. Thus, it was noted in the chapter that the perceived illusory rotation, p’, of stimulus qf in Figure 4a can be modeled by a physical object rotating through a physical angle p, where p = p’. Or, in Figure 8, Situation B, the apparent (perceived) geographic sagittal motion of the physically stationary stimulus point can be modeled by a sagittally moving point, physically moving through a distance d , where d , = d ’g, etc. Perceptual situations that cannot be physically moteled are shown in Figures l l b and l l c in which the perception of the direction to the points of the stimulus are not consistent with the derived perception of the size of the stimulus. Although the domains of the physical and perceptual worlds are distinct, their independence often is restricted by the constraint imposed by the assumption of internal consistency. This, of course, does not require the derived perceptions to be veridical. If any one or more of the three basic perceptions are not veridical the derived perception, even though modeled by physical events, also will not be veridical. The effects of any factor or factors, whether internal or external to the observer, that produce non-veridicality in one or more of the three basic perceptions are expected to result in predictable illusions without necessarily producing an inconsistency in the derived perceptions.

168

w.c.G@

A second consequence of the assumption of internal consistency concerns the specifications of the perceptual interrelations as is indicated in the figures in this chapter. Burigana has noted that these contain representations of physical as well perceived characteristics. This mixture, however, mainly is used to avoid the increased number of figures that would be needed by separating the physical and perceived representations in different drawings. For the specification of the perceptual equations only the relations in the figures concerned with perceptions need to be considered. If the assumption of internal consistency does not apply (as in Figures l l b and llc) the perceptual equations cannot be derived from the diagrams. A third consequence of internal consistency is that because the derived perceptions can be modeled by physical events (whether these derived perceptions are veridical or illusory) the methods of measuring the derived perceptions (e.g., w’ for the lateral motion and d’g for the sagittal head motion) is justified. Consider the physical adjustment of the lateral separation of two posts by touch to duplicate the extent of perceived motion, w’, obtained under reduced conditions with a physically stationary object at an illusory distance. It is assumed that this physical separation of the posts measured in physical units is a representation essentially identical to the extent of motion, W’, perceived in the stimulus under the experimental conditions. Indeed, if the experimenter had presented under full-cue visual conditions the post separation adjusted by the observer to measure W’ under the illusory condition, the observer would be expected to perceive this physical separation as equal to that perceived under the illusory conditions. Or consider the adjustment of the pivot distance to measure the apparent distance of the stimulus by nulling the original apparent motion, W’. Again, the physical distance, D,, needed to produce the null setting is a physical representation (model) of the perceived distance of the stimulus from the observer. Because the distance perception can be modeled by a physical situation it can be represented by that physical situation. If the model is presented under conditions in which it is correctly perceived (e.g., full-cue conditions) it is expected that the distance perceived will be essentially identical to the distance perceived in the experimental conditions. In agreement with Burigana’s analysis, the assumption of consistency of the three basic perceptions in perceptually localizing a stimulus point in three-dimensional space is an important aspect of the theory of phenomenal geometry. The role of illusions. Burigana notes that visual illusions often are cited in this chapter in tests of the theory of phenomenal geometry but asks for the reasons for this use of illusions. For those researchers who as-

Analysis of Perceived S p c e

169

sert, as in this chapter, that the same processes are involved in illusions as in veridical perceptions, it is as meaningful to use illusory conditions in the research as it is to use situations involving only veridical perceptions. In the theory of phenomenal geometry there is no differentiation between illusory and veridical phenomena. There are only different derived perceptions resulting from the different values of the three basic perceptual variables. According to the theory of phenomenal geometry, at least in the absence of cognitive intrusions upon perceptions, the derived perceptions will agree with physical events as a happenstance of whether the three basic variables are in agreement with their physical values without this agreement between the basic perceptual and physical values being a requirement. Two types of illusions can be differentiated. One is an illusion produced by simulating proximal cues which result in perceptions that differ from the physical conditions being viewed. An example of this is a stereogram in which as a result of misleading binocular disparity a flat stimulus appears three-dimensional. An instance of this type as used in Gogel & Tietz (1992a, Experiment 1) is illustrated in Figure 4a of the present chapter. A perceived illusory orientation in depth of a physically stationary stimulus was produced by misleading binocular disparity. This resulted in a change of the perceived tilt of the stimulus as the head was moved laterally. The perceived tilt was measured under two conditions at the extremes of the lateral positions of the head by adjusting a comparison object. In the static condition, the head was physically stationary, at different times, at the extreme lateral positions. In the dynamic condition the stimulus was viewed continuously during the lateral head motion and measurement. The change, p’, in the perceived tilt was essentially the same in the two conditions. This result was used to conclude that an explanation of p’ in the dynamic condition in terms of compensation for head motion or the intrusion of inferential-like processes was unnecessary. A similar demonstration very likely supporting the same conclusion could have been achieved with no illusion present in the perceived orientation of the stimulus. In this case p’ would be zero for both the static and dynamic conditions. Consistent with the identity of the processes involved in illusions and veridical perceptions, both results are equally pertinent in the research on three-dimensional perception. The similarity of the processes involved in illusions and veridical perception from the viewpoint of the theory of phenomenal geometry is also illustrated in the perception of sagittal motion as can be seen in the discussion concerning the veridical perception of geographic stationariness illustrated in Situation B of Figure 7 and the illusory perception of geographic motion illustrated in Situation B of Figures 8 and 9.

170

w.c.Gag$

A second type of illusion is a perception that differs from physical reality because of heuristic processes internal to the observer. The equidistance and specific distance tendencies discussed in this chapter are examples of heuristic processes that can produce illusions. An instance of this type is the use of the specific distance tendency to modify the perceived depth from changing vergence in the sagittal motion study of Gogel and Tietz (1992b, Experiment 1).This use of this tendency to modify perceived distance together the perceptual inverse square law met the requirement essential to the experiment of changing the perceived depth associated with the changes in oculomotor cues without changing the oculomotor cues. The results of this experiment contributed to the application of the theory of phenomenal geometry to the perception of stimulus motion associated with a sagittally-moving in addition to laterally-moving head. From the viewpoint expressed by the theory of phenomenal geometry, important purposes are served by examining illusory as well as veridical perception. One is that illusions can provide a range of values of the variables contained in perceptual equations in order to test the validity of these equations. Another concerns the significance of the presence of illusory lateral (W’) or sagittal (d’g) motion of the stimulus as the head is moved laterally or sagittally, respectively. It is very probable that these are not a direct response to retinal changes (Figure 13), but instead signal the presence of errors in one or more of the basic variables of the phenomenal geometry. Such perceptual errors or illusions often are the result of limitations of the perceptual apparatus, as stimulus conditions become reduced at far distances or, as objects are directionally displaced from cue gradients, as is discussed in this chapter. The behavioral consequences of these illusions in three dimensions can be reduced, for example, in the responses to objects at far distances by the use of the information that the objects appear off-sized or by ignoring the illusory perceived motions, W‘ or d’g, that can occur in near environments, as a consequence particularly of fixating at other distances. Also errors in the basic variables probably can be perceptually reduced by perceptual learning. Thus, experience is likely to ameliorate the behavioral consequences of perceptual limitations.

Hiroshi Ono (Psychology Department, York University, North York, Ontario, Canada) and Michael T. Swanston (Dundee Institute of Technology, Dundee, UK):In Gogel’s theory, the visual system represents threedimensional space according to the requirements of Euclidean geometry. The theory treats the perception of direction, distance and self-motion as fundamental. From these elements, perceptions such as size, shape, and motion of an object can be derived by means of equations. Gogel argues that

Analysis OfPerceived S p e

171

these equations correspond to fundamental principles of operation in the visual system, and that they provide means of understanding the interrelations between perceived object properties. The approach is termed ”phenomenal visual geometry,” and the terms in the equation consist of perceptual variables, not experimental variables. The theory does not deal with how the elements are derived, and in principle any psychophysical relationship could exist between the perception and the distal stimulus. In this chapter, Gogel does not discuss how visual direction or perceived self-motion are derived, but he argues that perceived distance is based on multiple sources of information (cues), which may not themselves be perceived. For example, the specific distance tendency influences the apparent distance of objects towards a value of 2-3 meters, but is detectable to an experimenter only without other stronger cues. Cues to distance are equivalent in that they combine to give a single perception, whose bases are not discernible to the observer. Some of the ideas in this chapter have a long history in visual science. The idea that cues are used for space perception and that different cues can provide the same information can be traced back as far as Berkeley (1709), and that visual direction and perceived distance are distinct perceptual variables was clearly advocated by Wells (1792). The statement of the size-distance relationship (or Emmert’s law) that plays a core role in the chapter can be traced back to Brewster (1844).What Gogel adds to this historical context are (a) a treatment of visual direction and perception of linear extent under one theoretical framework, (b) a consideration of an observer’s movement as experimental and perceptual variables, (c) an attempt to overcome the weakness of size-distance invariance hypothesis, and (d)an argument and methods of distinguishing between cognition and perception. Gogel’s attempt to integrate the two types of perceptions (direction and extent) under a single theoretical framework is historically overdue, because there is extensive work on both and obviously both deal with space perception. The separate and almost autonomous paths of study of visual direction and that of size and distance perception are mirrored by some books treating one of them but not the other. For instances, Human Visual Orientation by Howard (1982) treats visual direction but not sizedistance relation, whereas Visual Space Perception by Ittelson (1960) treats size and distance perception, but not visual direction. Before Gogel’s work, “perceived visual angle” (McCready, 1965) and “difference in visual direction” (Ono, 1970) were suggested as useful concepts, but it was Gogel who combined the two perceptions in a single theoretical framework and provided experimental results.

172

w. c.Gag$

Gogel’s ideas concerning the consequence of the observer’s movement contrast his thinking with Gibson’s and Wallach’s. Gogel’s thinking is similar to that of Gibson in avoiding ”inferential” process in perception, and he argues against Wallach’s hypothesis concerning “compensation.” However, his thinking is similar to that of Wallach and differs from that of Gibson in assuming that the same processes operate under veridical and non-veridical perception. Certainly, the degree to which misperception of distance is expected in Gogel’s discussion is surprisingly high; it is not what would be forecast by Gibson’s writing. Much more extensive analyses of these issues and comparisons with other theories are warranted. Phenomenal geometry by itself has the same difficulty as the size-distance invariance hypothesis in explaining size-distance paradoxes and report of distance of an “off-sized” object. A possible solution for paradoxes with micropsia or the moon illusion is to invoke misperceived visual angle (0’ in Gogel’s equations) as suggested by McCready (1965; 1985; 1986). For example, the moon on the horizon is reported as having a larger size and a closer distance than the moon on the zenith. These reports are contrary to the predictions of the size-distance invariance hypothesis, but if the visual angle of the moon is misperceived as larger, then the reports are compatible with phenomenal geometry. Gogel’s solution for the reported distance of “off-sized” familiar object is to distinguish perceptual from cognitive processes and to argue that what is reported is the latter rather than the former. For example, familiar objects, such as people, viewed from a height, are reported as small and far away, contrary to the predictions of the known size-distance invariance hypothesis. Gogel argues that perceived distance is indeed less than the physical distance (if measured properly), but that an observer‘s report is modified by a cognitive process that scales perceived distance by the ratio of familiar (cognitive) size to perceived size. This argument by Gogel requires experimental methods to distinguish perception from cognition and he offers several methods. One such method is the indirect measurement of perceived distance inferred from the perceived motion of an object during lateral head movements. When there are discrepancies between an observer’s report and phenomenal geometry, this method would provide the “true” value of perceived extent that is compatible with phenomenal geometry. The difficulty with this approach is that the theory loses parsimony and rigor, and it is no longer an effective means of predicting the relationship among the reported perceptual elements. Perceived distance obtained with this method is an inferred state of the visual system (or what an experimenter needs to compute). If it cannot be directly reported and if it is not represented in

Analysis of Perceived Space

173

awareness, the theory is no longer one of phenomenal geometry, since one variable in the equations is not phenomenally represented. This should not be taken as a criticism of Gogel’s attempt to distinguish perception and cognition by means of experiments. The lack of good criteria for making this distinction has plagued perceptual science, and any experimental solutions are to be welcomed. Gogel’s methods are of interest because they challenge phenomenological experience as one of the criteria for classifymg a subject’s response as perceptual (Hochberg, 1956; Prentice, 1956; Zuckerman & Rock, 1957). Phenomenological experience would normally be equated with awareness, but it is not made explicit as to whether perceived distance determined by Gogel’s method is subjectively experienced. Are perceived distance and cognitive distance two different phenomenological experiences? Unless they are, Gogel’s perceived distance becomes Wallach’s ”registered” distance. What is needed is a conceptual definition of perceived distance to support the operational definition provided by his methods. The preface of this book stated that perceptual theories have a relatively short life and do not have wide acceptance. It is perhaps too early to assess Gogel’s theory against these criteria. Clearly, the theory has a place in the history of studies in space perception as a solid step forward. The long-term acceptance of phenomenal geometry may well depend on how far its predictions hold when experiments are conducted with misperceived change in visual direction or misperceived extent of head movement, and on a clear conceptual definition of perceived distance. Gogel: Several questions are raised in the comments by Ono and Swanston. One is whether the perceived distance, D’, as measured by the lateral and head motion procedure is the same as that subjectively experienced by the observer, where this subjective experience is equated with awareness. They suggest that since the D ’ of a physically stationary stimulus is computed by the experimenter from its perceived (illusory) motion, W’, the D’ so measured may not be represented in awareness. Several considerations bear upon this question. (1) In the discussion of Figure 1 of this chapter it is noted that the lateral head motion procedure reduces to Emmert’s law when the head is perceptually stationary (K’= 0). Thus, according to the theory, the D‘ computed from the lateral head motion procedure is the same D’ as that occurring when, with the same cues of perceived distance, a stationary observer views a stationary stimulus. (2) Perceived distance is not necessarily equal to physical or simulated distance particularly when only one or a few distance cues are available. However, it is expected that, under a variety of conditions, if the physical or simulated distance is changed, D ’ will change in the same direc-

174

w.c.Gag$

tion. Thus, if the lateral head motion procedure indeed measures D’ as it is usually (subjectively) experienced, this measured D ’ should be highly correlated with physical or simulated distance particularly when a variety of distance cues are available. That this will occur has been shown in a number of studies. For example, in Experiment 4 of Gogel and Tietz (1992b) a point of light was viewed in a portion of the visual alley covered with nubbly pile carpet with both the alley and point viewed binocularly. The convergence distance, D,, to the point of light was varied producing changes in the perceived distance of the point consistent with changes in binocular disparity between the pile and stimulus point. It was found that D‘ as measured by the lateral head motion procedure clearly increased with increases in D,. The Pearson product moment correlation coefficient between the measured D‘ and D, was 0.96 (see Figure 8 of Gogel & Tietz, 1992b). The values of D ‘ tended to be larger than those of D,; a result perhaps influenced by the weaker distance cues between the observer and the beginning of the carpeted area. This and other studies (Gogel, 1977, 1980, 1982) provide clear evidence that the changes in D ’ normally experienced from stimulus changes with effective distance cues also are obtained when the lateral head motion procedure is used to measure D‘. (3) The theory of phenomenal geometry does not address the issue of whether D’ must be represented in awareness, although for humans perception and awareness are usually related. In the case of a variety of animals lower in the phylogenetic scale this relation is likely to be less even though their perceptual abilities are acute. In my view a definition of perception is not enhanced by requiring that it be related to the rather ambiguous concept of awareness. Another question raised by Ono and Swanston is whether perceived and cognitive distance are two different phenomenal experiences. They suggest that a conceptual definition in addition to an operational definition of perceived distance provided by indirect measures (e.g., the lateral head motion procedure) is needed. But it is not clear, at this stage of the theory, that a conceptual definition of perceived distance is required. Perhaps indirect measures of perceived distance such as the lateral head motion procedure are sufficient. For example, a two-point stereogram viewed with a stationary head clearly produces a perceived depth. Upon moving the head laterally relative motion between the two points is perceived. The perceived motion, W’, of each of the physically stationary points is a consequence of the illusory depth and thus values of W’ can be used to provide a measure of the depth perceived. It is important in using the lateral head motion procedure in measuring D ’ to determine whether the W’ concomitant with the lateral head motion remains unaffected when the distance is cognitively rather than perceptually determined.

Analysis of Perceived Space

175

Evidence pertinent to this question was discussed in this chapter using offsized effects as an exemplar of the possible effects of cognitive factors on measures of perceived distance obtained from the lateral head motion procedure. It was found that casual suggestion to produce off-sized judgments (suggestions that the stimulus in the size of a particular familiar object) had a substantial effect on verbal reports of distance but no effect on D' as measured by the lateral head motion procedure (Gogel, 1981). When the stimulus itself was visually familiar a large effect on verbal reports of distance was found, but a much smaller (but significant) effect on D' from the lateral head motion procedure was obtained (Gogel, 1976). A clear effect of changes in both perceived distance and perceived size was obtained from optical expansion with D' measured by a tactile adjustment of comparison rods and also by the lateral head motion procedure. These results from optical expansion, however, are inconsistent with the size-distance invariance hypothesis and are interpreted as due to offsized perceptions resulting from continuous changes in stimulus size. In summary, these experiments are taken as supporting the conclusion that the lateral head motion procedure measures perceived not cognitive distance, and that cognitive distance under certain circumstances (e.g., optical expansion) can produce or modify perceived distance. This latter result suggests that a formal definition of the difference between perceived and cognitive distance at the present state of knowledge would be difficult to achieve since, under some conditions, perceived depth or distance can be a consequence of cognitive factors. There is also some evidence, at least under conditions in which cognitive distance does not intrude on (does not modify) perceived distance that the observer can be aware of the difference between these two subjective experiences. This evidence is found in studies in which the verbal reports of size and distance of familiar objects are compared under apparent and generally objective instructions. Significant changes as a consequence of such instructions on size and distance judgments of familiar objects have been found by Higashiyama (19841, by Predebon (19921, and for size but not significantly for distance, by Gogel and Da Silva (1987b). The ability of observers to give different size and sometimes different distance judgments in response to these different instructions suggests that the difference between perceived and cognitive effects often can be recognized by observers. In the theory expressed in this chapter, the three basic variables of the perceived direction of the stimulus, the perceived position of the self, and the perceived egocentric distance of the stimulus are given equal importance in determining the spatial perception of a stimulus point and thus in determining the derived perceptions of the motion, shape, size,

w. c.cos$

176

and orientation of stimuli. The role of perceived egocentric distance is most discussed in this chapter because of the amount of evidence available regarding this variable and because it can be readily manipulated so as to produce perceptual errors. Thus, it is likely that the questions raised by 01-10and Swanston and the present responses to the questions can also be directed to the remaining two basic variables. For example, a perceived lateral motion, W’, of a stimulus, whether veridical or illusory, which occurs concomitantly with a lateral motion of the head, will be reduced as a consequence of right-left head motions repeated over an extended period of time (see Hay, 1968; Post & Lott, 1992; Tietz & Gogel, 1978; Wallach & Kravitz, 1965a, 1965b). This adaptation of W’ is unlikely to be the result of a change in the perceived egocentric distance, D’,of the stimulus (Tietz & Gogel, 1978; Post & Lott, 1992) or change in the perception of the lateral motion, K’, of the physically moved head. Probably, it is a consequence of changes in the perceived direction of the stimulus from the moving observer. More generally, according to the theory of phenomenal ge~ expected , ometry any change in a derived perception, such as W’ or L I ’is to be the result of a change in one or more of the three basic variables. The two concepts (1) that modifications of the derived perceptions must occur by modifying one or more of the three basic variables of the theory of phenomenal geometry and (2) that it is the value of each of the three basic variables that is important in determining the derived perceptions regardless of how these are produced (the hypothesis of cue equivalence) contribute to the simplicity (parsimony) and range of predictions possible from the theory.

REFERENCES AMES, A., Jr. (1952). The rotating trapezoid (Cont): Explanation of visual phenomena. In F. P. Kilpatrick (Ed.), Human behavior from the transactional point of view (pp. 75-86). Washington, DC: Office of Naval Research, Department of the Navy. BAIRD, J. C., & WAGNER, M. (1991). Transformation theory of size judgment. Journal of Experimental Psychology: Human Perception and Performance, 17, 852-864. BECHTEL, W., & ABRAHAMSEN A. A. (1990). Beyond the exclusively propositional era. Syn these, 82, 223-253. [LBI BERKELEY, G. (1709). An essay towards a new theory of vision. Dublin: Pepyat. [HO&MTSl BISCHOF N. (1966). Erkenntnistheoretische Grundlagenprobleme der Wahrnehmungspsychologie. In W. Metzger (Ed.), Handbuch der psy-

Analysis of Perm'ved Spce

177

chologie: Allgemeine Psychologie (vol. 1, pp. 21-78). Gottingen: Hogrefe. [LBI BREWSTER, D. (1844). On the law of visible position in single and binocular vision and on the representation of solid figures by the union of dissimilar plane pictures on the retina. Transactions of the Royal Society of Edinburgh, 15, 349-368. [HO&MTSl CARLSON, V. R. (1960). Overestimation in size constancy judgments. American Iournal of Psychology, 73, 199-213. CARLSON, V. R. (1977). Instructions and perceptual constancy judgments. In W. Epstein (Ed.), Stability and constancy in visual perception: Mechanisms and processes (pp. 217-254). New York: Wiley. DAY, R. H., & PARKS, T. E. (1989). To exorcize a ghost from the perceptual machine. In M. Hershenson (Ed.), The moon illusion (pp. 343-350). Hillsdale, NJ: Erlbaum. [LB] FODOR, J. A. (1983). The modularity of mind: An essay on faculty psychology. Cambridge, MA: MIT Press. FODOR, J. A., & PYLYSHYN, Z. W. (1981). How direct is visual perception? Some reflections on Gibson's ecological approach. Cognition, 9, 139-196. [LBI FOLEY, J. M. (1965). Visual space: A scale of perceived visual direction. Proceedings of the 73rd Annual Convention of the American Psychological Association, 1, 49-50. FOLEY, J. M. (1968). Depth, size and distance in stereoscopic vision. Perception & Psychophysics, 3, 265-274. FOLEY, J. M. (1972). The size-distance relation and intrinsic geometry of visual space: Implications for processing. Vision Research, 12, 323-332. FOLEY, J. M. (1991). Binocular space perception. In D. M. Regan (Ed.), Vision and visual dysfunction: Binocular vision and psychophysics (vol. 9, pp. 75-91). New York : MacMillan. FUKUSIMA, S. S., LOOMIS, J. M., & DA SILVA, J. A. (1991). Accurate distance perception assessed by two triangulation methods. Paper presented at the 32nd Annual Meeting of the Psychonomic Society, San Francisco, November 22-24. GIBSON, J. J. (1961). Ecological optics. Vision Research, 1, 253-261. [LBI GIBSON, J. J. (1979). The ecological approach to visual perception. Boston: Houghton-Mifflin. [LBI GILINSKY, A. S. (1951). Perceived size and distance in visual space. Psychological Review, 58, 460-480. GOGEL, W. C. (1964). The perception of depth from binocular disparity. Iournal of Experimental Psychology, 67, 379-386. GOGEL, W. C. (1965). Equidistance tendency and its consequences. Psychological Bulletin, 64, 153-163.

178

w. c.Gag$

GOGEL, W. C. (1969a). The effect of object familiarity on the perception of size and distance. Quarterly Iournal of Experimental Psychology, 21, 239-247. GOGEL, W. C. (196917). The sensing of retinal size. Vision Research, 9, 1079-1094. GOGEL, W. C. (1976). An indirect method of measuring perceived distance from familiar size. Perception & Psychophysics, 20, 419-429. GOGEL, W. C. (1977). An indirect measure of perceived distance from oculomotor cues. Perception & Psychophysics, 21, 3-11. GOGEL, W. C. (1979). The common occurrence of errors of perceived distance. Perception & Psychophysics, 25, 2-11. GOGEL, W. C. (1980). The sensing of retinal motion. Perception & Psychophysics, 28, 155-163. GOGEL, W. C. (1981). The role of suggested size in distance responses. Perception & Psychophysics, 30, 149-155. GOGEL, W.C. (1982). Analysis of the perception of motion concomitant with a lateral motion of the head. Perception & Psychophysics, 32, 241-250. GOGEL, W. C. (1984). The role of perceptual interrelations in figural synthesis. In P. Dodwell & T. Caelli (Eds.), Figural synthesis (pp. 31-82). Hillsdale, NJ: Erlbaum. GOGEL, W. C. (1990). A theory of phenomenal geometry and its applications. Perception & Psychophysics, 48, 105-123. GOGEL, W. C., & DA SILVA, J. A. (1987a). A two-process theory of the response to size and distance. Perception 6 Psychophysics, 41, 220-238. GOGEL, W. C., & DA SILVA, J. A. (1987b). Familiar size and the theory of off-sized perceptions. Perception & Psychophysics, 41, 318-328. GOGEL, W. C., LOOMIS, J. M., NEWMAN, N. J., & SHARKEY, T. J. (1985). Agreement between indirect measures of perceived distance. Perception & Psychophysics, 37, 17-27. GOGEL, W. C., & MERTZ, D. L. (1989). The contribution of heuristic processes to the moon illusion. In M. Hershenson (Ed.), The moon illusion (pp.235-258). Hillsdale, NJ: Erlbaum. GOGEL, W. C., & NEWTON, R. E. (1969). Perception of off-sized objects. Perception & Psychophysics, 5, 7-9. GOGEL, W. C. & TIETZ, J. D. (1973). Absolute motion parallax and the specific distance tendency. Perception & Psychophysics, 13, 284-292. GOGEL, W. C., & TIETZ, J. D. (1977). Eye fixation and attention as modifiers of perceived distance. Perceptual 6 Motor Skills, 45, 343-362. GOGEL, W. C., & TIETZ, J- D. (1979). A comparison of oculomotor and rnotion parallax cues of egocentric distance. Vision Research, 19, 11611170.

Analysis of Perceizxd Splce

179

GOGEL, W. C., & TIETZ, J. D. (1992a). Absence of compensation and reasoning-like processes in the perception of orientation in depth. Perception b Psychophysics, 51, 309-318. GOGEL, W. C., & TIETZ, J. D. (1992b). Determinants of the perception of sagittal motion. Perception & Psychophysics, 52, 75-96. GREGORY, R. L. (1970). The intelligent eye. London: Weidenfeld & Nicolson. [LB] GRELLING, K. (1939). A logical theory of dependence. Proceedings of the 5th International Congress for the Unity of Science, Cambridge, MA. [Reprinted in B. Smith (Ed.), 1988, Foundations of Gestalt theory (pp. 21 7-226). Miinchen-Wien: Philosophia Verlag.] [LBI HAY, J. C. (1968). Visual adaptation to an altered correlation between eye movement and head movement. Science, 160,429-430. HIGASHIYAMA, A. (1984). The effects of familiar size on judgments of size and distance: An interaction of viewing attitude with spatial cues. Perception b Psychophysics, 35, 305-312. HOCHBERG, J. E. (1956). Perception: Toward the recovery of a definition. Psychological Review, 63, 400-405. [HO&MTSl HOWARD, I. P. (1982). Human visual orientation. New York: Wiley. [HO&MTSl ITTELSON, W. H. (1960). Visual space perception. New York: Springer. [HO&MTS] KANIZSA, G. (1976). Subjective contours. Scientific American, 234(4), 4852. [LBI KANIZSA, G. (1979). Organization in vision: Essays on Gestalt perception. New York: Praeger. KILPATRICK, F. P., & ITTELSON, W. H. (1953). The size-distance invariance hypothesis. Psychological Review, 60, 223-231. LOOMIS, J. M., & DA SILVA, J. A. (1989). Accurate blind pointing to previewed targets while walking. Paper presented at the 30th Annual Meeting of the Psychonomic Society, Atlanta, GA, November 17-19. LOOMIS, J. M., DA SILVA, J. A., FUJITA, N., & FUKUSIMA, S. S. (1992). Visual space perception and visually directed action. Journal of Experimental Psychology: Human Perception and Performance, 18, 906-921. MACCRACKEN, P. J., GOGEL, W. C., & BLUM, G. S. (1980). Effects of posthypnotic suggestion on perceived egocentric distance. Perception, 9, 561-568. MCCREADY, D. W., Jr. (1965). Size-distance perception and accommodation-convergence micropsia: A critique. Vision Research, 5, 189-206. MCCREADY, D. (1985). On size, distance, and visual angle perception. Perception b Psychophysics, 37, 323-334.

180

w.c.Gq$

MCCREADY, D. (1986). Moon illusions redescribed. Perception b Psychophysics, 39, 64-72. METELLI, F. (1974). The perception of transparency. Scientific American, 230(4), 90-98. [LB] METZGER, W. (1967). Der Geltungsbereich gestalttheoretischer Ansatze, Bericht iiber den 25. Kongress der Deutchen Gesellschaft fur Psychologie in Miinster 1966 (pp. 13-24), Gottingen: Hogrefe. [Reprinted in W. Metzger, 1986, Gestal t-Psychologie. Ausgewahlte Werke aus den Iahren 1950 bis 1982 herausgegeben und eingeleitet von Michael Stadler und Heinrich Crabus (pp. 134-144). Frankfurt am Main: Kramer.] [LBI ONO, H. (1970). Some thoughts on different perceptual tasks related to size and distance. In J. C. Baird (Ed.), Human Space Perception: Proceedings of the Dartmouth Conference (pp. 143-151). Austin, TX: Psychonomic Journals. [HO&MTSl ONO, H. & COMERFORD, J. (1977). Stereoscopic depth constancy. In W. Epstein (Ed.), Stability and constancy in visual perception: Mechanisms and processes (pp. 91 -128). New York: Wiley Interscience. ONO, M. E. , RIVEST, J. & ONO, H. (1986). Depth perception as a function of motion parallax and absolute-distance information. Iournal of Experimental Psychology: Human Perception b Performance, 12, 331337. PETERSON, M. A., & SHYI, G. C.-W. (1988). The detection of real and apparent concomitant rotation in a three-dimensional cube: Implications for perceptual interactions. Perception 6 Psychophysics, 44, 3142. POST, R. B., & LOTT, L. A. (1992). The relationship between vestibuloocular reflex plasticity and changes in apparent concomitant motion. Vision Research, 32, 89-96. PREDEBON, J. (1992). The role of instructions and familiar size in absolute judgments of size and distance. Perception b Psychophysics, 51, 344-354. PRENTICE, W. C. H. (1956). “Functionalism” in perception. Psychological Review, 63, 29-38. RAUSCH, E. (1985). h e r Eigenschaften und Pradikate. Gestalt Theory, 7,139-154. [LB] RIVEST, J., ONO, H., & SAIDA, S. (1989). The roles of convergence and apparent distance in depth constancy with motion parallax. Perception b Psychophysics, 46, 401-408. ROCK, I. (1983). The logic of perception. Cambridge, MA: MIT Press. ROCK, I., HILL, A. L., & FINEMAN, M. (1968). Speed constancy as a function of size constancy. Perception b Psychophysics, 4, 37-40.

Analysis of Perm'& Space

181

SCHLOSBERG, H. (1950). A note on depth perception, size constancy, and related topics. Psychological Review, 57, 5. SWANSTON, M. T., & GOGEL, W. C. (1986). Perceived size and motion in depth from optical expansion. Perception 6 Psychophysics, 39, 309326. TIETZ, J. D., & GOGEL, W. C. (1978). Adaptation to apparent concomitant motion in the absence of physical or retinal motion. Bulletin of the Psychonomic Society, 12, 1-4. WALLACH, H. (1985). Perceiving a stable environment. Scientific American, 252 (51, 118-124. WALLACH, H. (1987). Perceiving a stable environment when one moves. Annual Review of Psychology, 38, 1-27. WALLACH, H., & BERSON, E. (1989). Measurements of the illusion. In M. Hershenson (Ed.), The moon illusion (pp. 287-297). Hillsdale, NJ: Erlbaum. WALLACH, H., & FLAHERTY, E. W. (1975). A compensation for field expansion caused by moving forward. Perception 6 Psychophysics, 17, 445-449. WALLACH, H., & KRAVITZ, J. H. (1965a). Rapid adaptation in the constancy of visual direction with active and passive rotation. Psychonomic Science, 3, 165-166. WALLACH, H., & KRAVITZ, J. H. (1965b). The measurement of the constancy of visual direction and of its adaptation. Psychonornic Science, 2, 217-218. WALLACH, H., STANTON, L. & BECKER, D. (1974). The compensation for movement-produced changes of object orientation. Perception 6 Psychophysics, 15, 339-343. WALLACH, H., & ZUCKERMAN, C. (1963). The constancy of stereoscopic depth. American Journal of Psychology, 76, 404-412. WELLS, W. C. (1792). A n essay upon single vision with two eyes; together with experiments and observations on several other subjects in optics. London: Cadell. [HO&MTS] WILCOX, S., & EDWARDS, D. A. (1982). Some Gibsonian perspectives on the ways that psychologists use physics. Acfa Psychofugica, 52, 147167. [LB] WIST, E. R., & SUMMONS, E. (1976). Spatial and fixation conditions affecting the temporal course of change in perceived relative distance. Psychological Research, 39, 99-112. WIST, E. R., DIENER, H. C., & DICHGANS, J. (1976). Motion constancy dependent upon perceived distance and the spatial frequency of the stimulus pattern. Perception & Psychophysics, 19, 485-491.

182

w.c.c&d

ZUCKERMAN, C. B., & ROCK, I. (1957). A reappraisal of the role of past experience and innate organizing processes in visual perception. Psychological Bulletin, 54, 269-296. [HO&MTSl

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

183

ON SOME PARADOXES OF CURRENT PERCEPTUAL THEORIES Paolo Bozzi Department of Psychology University of Trieste, Italy

ABSTRACT Perceptual theories, research, and psychological and philosophical discussions on perception are based on at least six implicit assumptions: observables correspond to brain states, the brain is a physical system, other people’s perceptions are unobservable, scientific perceptual data must be public, brain states and observables are “enclosed” in a black box, and simulation of black-box processes are explanations or descriptions. These assumptions involve at least five perceptual paradoxes each of which is discussed in this essay.

Reference to epistemology is frequent among researchers in the fieId of perception. When we discuss research in progress, new models, or theoretical innovations, we always assume a shared philosophy. However, most of our assumptions are seldom made explicit so that they may be challenged. My thesis is that in our conceptions sometimes one feels a sort of false note. Although understanding the cause of this impression is no easy matter, its implications are fairly clear: one has probably the feeling that serious discussion of these assumptions might reveal ideas in clashing contrast or plain contradiction. It is my deep conviction that in the “epistemological subconscious” of most perceptual scientists dwell a number of paradoxes. In this essay, I intend to bring some of them into light and to elucidate their logical structure.

184

P.Bozzi

As an introduction, I will first briefly overview six assumptions that are often implicit in psychological or philosophical discussions. 1. Consider all objects and events that we experience when we look at a landscape, listen to music, walk in the street, or when we look in our papers for some lost memo jotted down some time ago. These objects and events may be called observables. For the perceptual scientist it is obvious to assume that any observable 0 corresponds to a specific brain state S. Of S we can have little knowledge, good knowledge, or unreliable knowledge, but we can nonetheless distinguish it theoretically from other states S’, S“,... that are related to other observables 0’,0”,... perceived at the same time by an observer. 2. All human beings have a working brain. Therefore, in the course of their lives they are constantly aware of a number of observables associated to some specific brain states. We can certainly say this of their daily lives, and in a way we can also say it in relation to those observables of which they dream when they are asleep. Here, it is necessary to point out an important aspect of the assumption. A brain, considered as a physical system, or as an information-processing device, must be studied in the framework of physical space-time, just as one would study other devices such as a watch or a calculator. Instead, observables must be studied in the framework of psychological space-time, dimensions that are prone to well-known contractions, expansions, and distortions which are not easily translated into corresponding physical parameters. Thus, for each observer there is one perceptual world, as there is one brain for each observer. 3. The following assumption is common in the philosophy of knowledge. A s there is no physically direct path connecting one brain to an... other, there is no direct access-for any of us-to the observables 0’,0”, associated to the brain states S ’, S ”,... in someone else’s brain. Thus, we cannot see or touch or in any way experience the perceptions of other people. 4. The fourth assumption derives indirectly from the three assumptions above. It says that observables are always private. By definition they are introspective data. Now, if we take a methodological stance, we have to recognize that introspective methods are subject to fatal objections. Perceptual science must be founded on reliable findings, and these cannot come from introspection. Data derived from introspection are only accessible to single subjects, whereas a science of perception needs data that can be shared by the scientific community. Data that can be shared are called protocols, and in this context protocols are appropriately recorded observable behaviors, measurements, multiple choices, possible descriptions, and so on.

Percepfual Paradoxes

185

5. The following assumption capitalizes on a number of concepts that have been developed in the field of information science in recent decades. The common sense of perceptual research assumes that brain states and the observables associated with them are closed into a metaphorical black box. We describe what comes out of it in terms of interpretable protocols. What happens in the black box is the object of logically organized speculations, based on our knowledge of its input and output, and on appropriately conceived rules. It is important to stress that protocols, when interpretable without ambiguity, have to be considered as unquestionable evidence. In the common sense approach of perceptual researchers, protocols of any kind are prototypical factual data. 6. The last assumption reads as follows. By simulating the processes that take place in the black box in some coherent way, with appropriate logical rules, and by means of appropriate devices, we can obtain an explanation or a description of causal preconditions of phenomena. We can understand what is described in the protocols. Possibly, we can even understand the process that maps the class of input elements to output elements. In short, we can reach a scientific understanding of perception.

PERCEPTUAL PARADOXES

”Sudden healing” The first paradox is something one may encounter a number of times in perceptual laboratories. I propose to call it the paradox of the ”sudden healing.” Consider a prototypical laboratory situation. An observer is asked to cooperate with the experimenter, but somehow refuses to provide the expected response. For example, the observer might not see the effect, or the response might be inconsistent with a theory. Of course, there are many possible reasons for this outcome. The experiment might be irrelevant, or not properly done. The experiment might lack some small detail which seemed irrelevant but turned out to be crucial. In the worst case, it could even be that one knows there is not much to be found within one’s experimental machinery, but in some way hopes that with the help of some more or less indirect suggestion the observer will say or do just what the theory wants. In some rare cases, the facts being studied may not even be seen, such as when chromatic stimuli are presented to a color blind observer. The paradox also arises in another case. After thirty years of experience in all sorts of experiments on perception, I can witness that observers

P.Boui quite often just want to show experimenters that their beliefs are all fibs and yarns. For example, observers may be convinced that perception is a faithful representation of stimuli. Thus they insist on denying any observation that does not correspond to what they know about visual stimuli. Such observers lie about a detail that they consider negligible, and they do so to maintain a theoretic faith in the five senses as witness of the physical world. They may lie in the name of an ideology that considers psychological experiments as manifestations of pseudoscientific gibberish. They know that experimenters will have to report their lies. Usually, subjects are university students who know that protocols are unquestionable and that respect for protocols is the hallmark of scientific research. Suppose we want to show an observer a good example of apparent motion. In dim illumination, two small lights not too far from each other are turned on and off in turn, according to the well known rules. In these conditions, anybody sees one single luminous spot moving back and forth. The observer, after looking carefully, may says: “I see two lights turning on and off in alternation, in two fixed positions.” The report cannot be questioned. Which experimenter would dare not to take it into account? Obviously, adding the latter result to the list of protocols will make this a probabilistic phenomenon. The experimenter will have to say: “about this many times out of the total, one sees... .” He will have to conclude that optimal apparent motion is seen very often, not always. Thus, one deontological rule turns into one that hinders the search for truth. Perhaps at this point we should doubt the rules of laboratory procedures. Before recording our result on a data sheet, we should check what happens to our observer when not in the laboratory. Does the observer go to the movie? Watch television? See the multifarious motions of manycolored lights suspended over the booths of a fair? Generally speaking, we should ask whether the observer realizes that daily life is replete with apparent motions between all sorts of lights, during the day and at night. If we establish that the observer sees the scenes of a movie just as we do, then we can safely conclude that in the laboratory we had recorded a lie. Unless we believe that some people fall ill as soon as they enter a laboratory, that they become prey of a peculiarly fleeting disease that affects their visual systems and from which they are suddenly healed as soon as they exit the door. Similarly, consider an experiment on size constancy: a visible object gets progressively distant from an observer and thus projects a retinal image that becomes progressively smaller. This object should look like an object that moves away from the observer, not like an object that shrinks. Suppose the observers are shown a variety of such objects, for example sur-

Perceptual Paradoxes

187

faces with variously complicated linear structures, shrinking or expanding. If observers claim that they just see the objects shrinking, and if they insist that they do so while remaining at the same distance from them, then on the basis of this report their driving licenses should be revoked. One could say that the stimuli presented in the laboratory were oversimplified and out of context. In the laboratory, the great regularities of daily life are based on the efficacy of those very mechanisms that are reproduced in the laboratory. We should also note that almost everyone is willing to drive risky night trips on streets and highways. In these conditions, the outside world is summarized by luminous spots and illuminated stripes on the terrain which look just like the simplified stimuli presented in the laboratory. Yet, people drive at night. The twenty or thirty visual effects that exhaust the visual world of a night driver surely are effective, otherwise their failure would be fatal. Given that scientific work aims at universal conclusions, theories of perception should be based much more on what people do normally than on data of narrow scope (even if motivated by rules of scientific methods), because such data are just a small subset of all the reactions one could observe in similar conditions. There is only one reasonable conclusion to be drawn: protocols are questionable. If we believe that the rules of scientific method must still be trusted, for the sake of good relations between colleagues or for love of the reputation of science as a "rigorous" endeavor, then we must be aware of the consequences that follow. It becomes necessary to admit that there are sudden failures in the functioning of observers, and these failures are followed by equally sudden healings. The last, logical consequence of this line of reasoning seems to be the following: the perceptual laboratory is the least suitable place for studying perceptual phenomena. At this point, either we get rid of the unquestionability of protocols, which are falsely "objective" products of laboratory research, or we must believe that the laboratory does not have a healthy influence on observers.

Descriptions I will discuss now another paradox concerning protocols, one that arises when protocols take the form of "descriptions" of perceptual patterns. Of course, I am aware of the current trend in perceptual research of using nondescriptive responses in place of verbal descriptions. By designing methods for collecting responses that can be described by quantitative parameters, such as motor performance or the outcome of comparisons or selections,

188

P.Bozzi

perceptual researchers hope to eliminate the difficulties of dealing with the linguistic ability of various observers. Although non-descriptive responses are useful, it remains nonetheless true that the truly important discoveries-the phenomena that open up new horizons for researchneed first of all a verbal description. Finer quantitative methods can play their role only after we have a description. I need to recall here a fact of epistemology. Although it is common place in epistemological theorizing, this fact is too often forgotten. In different fields of scientific research, observation is based on facts that are not the direct object of scientific interest. Usually, researchers are not interested in the modes of appearance of manometers, thermometers, or Geiger meters. Rather, they are interested in something which is believed to be measured by these instruments, either at the time of the observation or, in case of recordings, at some time before it. Using the old terminology of Viennese Neopositivism-old but still appropriate and effective-we should always distinguish empirical statements from protocols. In perception, however, empirical statements and protocols coincide. The object of scientific interest corresponds exactly to what the observer sees during an observation. Both for the experimental psychologist and for the observer, the observable is not a cue to something else, and above all it is not a representation of something else. The observed event is in a very precise sense a self-representation, a displaying of itself. Of course, in practice any experimenter will ask a certain number of other observers, or subjects, to witness the facts under observation in order to collect reliable data and to compute appropriate statistics. The involvement of a number of subjects seems to imply the general claim that the observables of our direct experience are questionable. Otherwise, there would be no justification for calling so many people to witness a perceptual event momentarily under investigation. What is the job of observers in this context? Their job is to provide a protocol either by means of a description, a classification, a choice, or a motor response. That is, any form of behavior that can be considered as an observable event. Now suppose the above thesis that all observables are questionable is sound. Then all protocols obtained from observer descriptions, being observables as well, are also questionable. If we assume that questionability can be dispelled by multiplying the observations, as we did initially, then we must call other subjects and ask them to observe the protocols previously obtained. And so on. Such an infinite regress is eliminated, in practice, by epistemologically leaping from one to another side of the theory. In practice, protocols are

Perceptual Paradoxes

189

assumed to be "obviously" unquestionable. But we know well that practical convenience has nothing to do with methodological rigor. Quite to the contrary, the former is the negation of the latter. If we go along with accepted practice, then the appearance of all objects within reach of our sight can be doubted, except for those objects that we intend to define as protocols. Naturally, the opportunities for doubt are very scarce when protocols take the form of numbers or of other conventional signs; scarce to the point of being a theoretical pretext (but nonetheless philosophically valid). Quite often the inspection of a perceptual event requires a gesture or a verbal description. What about the protocols that take this form? Suppose that a subject is performing a careful inspection of two samples of photometrically equal red colors. One sample is a rectangle a few centimeters wide and with sharply cut edges. The other has approximately the same size and shape, but its edges are serrated like in a stamp. As found by Kanizsa (1960), the colors of the two surfaces do not look the same. The color of the serrated surface, compared to the other, looks faded, veiled, and blurred. Suppose the subject compares the two red samples and says: "this red sample has a more veiled, blurred, and softer color than the other sample." If other subjects say more or less the same, it seems safe to suppose that among our observers there are individuals who master the English language in all its subtleties. Since descriptive terms such as veiled or blurred suffer from a certain degree of semantic indeterminacy, we might wonder what the observer actually means. There is a way to disambiguate the description. One can ask our observer to indicate which surface looks veiled. At this point, after appropriate comparisons, one "sees" what those adjectives mean in that circumstance. Perceptual researchers almost invariably adopt this tautological procedure in their pilot observations, when the discovery is still "fresh." It is through these procedures that one finds new and interesting elements that are successively subjected to coded experimental procedures. At this point, two alternative conclusions may be drawn: either we admit that protocols based on observables are themselves observables of a new species and therefore that they require other protocols, and so on to infinity (that is, unless we apply an arbitrary, dogmatic cut by saying: "up to here observations are questionable, but from there on they are not") or we interpret observer protocols by ostension, that is, by referring back to the observed objects that originated them; therefore reducing the meaning of protocols to a fact. Thus, we have either a regression to infinity or a vicious circle.

P. Bozzi

Inaccessibility Together with a great number of philosophers, most students of perception agree on a thesis that was presented clearly by the epistemologist Evandro Agazzi (1976). The thesis reads: “a nessuno consta il constare altrui,” which is closely translated as: “no one ascertains that someone else is ascertaining.” It is taken for granted that any human or animal observer has a private perceptual world which is, as Leibniz would have it, impenetrable and accessible only to its owner. If the above mentioned thesis is true, and if it can be ascertained that somebody ascertains or does not ascertain something (as common sense seems to require), we should then write: “nobody can ascertain that ’no one ascertains that someone else is ascertaining’.” Let us consider the situation more closely. First of all, let us try to ”enter” the environment of a solipsist. Suppose that in this environment, where the solipsist ascertains himself, two ghosts A and B wander. By definition, in the heads of A and B there is no private world in which percepts are ascertained or observed that the solipsist does not know. Nevertheless, they look just like two sound and refined individuals talking to each other in the presence of the solipsist. They may talk, for example, about the way they perceive a red sample on a blue background, or a tonic chord following a seventh dominant chord. In such a case the solipsist knows perfectly that, whatever they discuss, A will never ascertain how B perceives two colors or a group of notes. In the same way, B will never ascertain what A perceives. A s a matter of fact, by definition, no private perceptual world is available to either A or B. But let us get rid of this ”nightmare” and move into another “theater,” the real common world of our daily experience. We just accept the existence of private perceptual worlds as an open question (they may exist or not, or exist in a thousand different ways like the possible worlds of epistemology). After all, we always do this in our ecological niche because it is very convenient to avoid intractable dogmatisms. In this theater, the subject is not a solipsist. The subject, called P, does not have any particular belief. At a certain point, P immediately applies this principle. Immediately, P finds out that on the basis of this principle it is impossible to say that A cannot ascertain what B ascertains, or say that B cannot have access to the perceptions of A. It would not be possible to demonstrate the contrary, even if A and B tried all their best to explain even with logical demonstrations that they actually do not have mutual access to their respective private perceptual worlds. P cannot ascertain if they tell the truth.

Percephral Paradoxps

191

The least that can be said at this point is that a perceptual researcher should never allude to the inaccessibility of someone else’s perceptions for strictly logical reasons.

Black box Increasingly during the past thirty years, the most widely employed metaphor for the inaccessibility of perceptions in other minds has come to be the black box. As cognitive psychology imported the jargon of information theory into experimental psychology, the metaphor of the black box was probably adopted in part because it seemed to dissipate or dispel the most subtle and inconvenient philosophical problems concerning other minds. At a level of maximum simplification, this metaphor applies to the head of any person we have met in our daily life; sealed like a black box. It is not possible to see what its inside is like or which circuits it contains. It is not possible to say whether the clever devices hidden in it are electronic, mechanical, analogic, or digital. All we can do is to measure its input and output. Heads do not merely hide thoughts, fantasies, memories, and unconscious computations from our sight. They also hide those perceptions of the external world that all owners of a head have, and that make us share the word around us, at least as long as we are in the same environment. As a scientific observer, what I can do is to keep under observation external things as they obviously strike the sense organs of each owner of a head. At the same time I can observe the corresponding behaviors, either motor or verbal. But what happens in the heads is pure conjecturing, as far as an actual black box is concerned. The behavioral scientist can only record and classify actions, gestures, and words, sometimes as input and sometimes as output, for each black box or head momentarily observed. Show me a head and I will show you a black box. We are all boxes... wait a moment, not all of us. For example, surely I am not a black box. True, I can observe directly all the facts and events of the surrounding world that I would consider either as input or output for a black box, including mine. However, in the world of my observation there is much more. There is, interestingly, all the material that another observer would swear if securely locked inside ”my” black box. In other words, I can see perfectly what another observer would consider as my motor or verbal output; and I can see those events of the external world that the same observer would classify as input for my action. But these facts are only part of a much wider collection of observables which include a large number of things that are neither input or output, things that my colleague would consider as private processes of my mind to be approximated only by

P. Bazi

192

means of conjecture. Nonetheless, these things are definitely present in the large class of my observables. Thus, if we accept the definition given above, surely I am not a black box. Suppose then that I ask some people-some black boxes-about being black boxes. They would certainly give an “irrevocable” answer. Irrevocable and peremptory, precisely in the sense that I have defined above in the introduction. They would say that they are not black boxes, and they would give the same reasons I myself give when I assert that I am not a black box. After all, none of us believes that our shared observable world, the furnishing of the scene where both of us are acting, could depend on an analysis of our input. And even less do we believe that it depends on some conjectural interpretation of our behavior, defined in terms of output (as the view of our colleague would require). It is particularly odd that our cognitivist colleague can nonetheless point to those things that at this moment he or she considers as input for my black box, and distinguishes them clearly from those locked inside the box. The latter are, of course, private psychic processes to be discovered by means of clever conjectural procedures but, at least in some cases, our collegue could very well point to those as well. Consider the following case. Our colleague shows me the Michotte “launching effect.” In this effect, a mobile object hits another object which was stationary before being hit. Having received the hit, this object starts moving, just like a billiard ball when hit by another. The colleague will teach me that the two objects are the visual input for my black box, and so is their motion (speed, direction, type of trajectory). According to this colleague, however, the perception of the coll ision and the apparent causal dependence of the motion of the second object on the motion of the first are due to some input processing inside my black box. And this in spite of the fact that the colleague could wit these things, the collision, and the causality, by pointing his or her finger. The very same finger the colleague uses to determine the length of the rayon d’action of the passive motion of the second object and to measure it. In this case, there is an odd reciprocal penetration of black boxes. After all, if we ask other people about their being black boxes, they will truthfully state that others might be, but they certainly are not. We could conclude with the following limerick, which contains the moral of the story: If that long-held old story of the black box really were true (not only as a paradox) then you could tell no story right or wrong (not even as a paradox) on that long-held old story of the black box.

Perceptual Paradoxes

193

Simulation Finally, there is the paradox of the perfect Golem. In the cognitive approach to perceptual science, one finds the widespread belief that computer simulations provide a method for studying and explaining what is perceived. Simulations are thus said to explain precisely those facts that have been discovered, isolated, investigated, related to theories, and coordinated in general laws by the work of thousands of men and women in the last one hundred and fifty years, men and women with diverse backgrounds ranging from philosophy to physics, including biology and many other domains of organized knowledge. Computer simulations are models for the processes that cause perceptual appearances. When they are successful, simulations reproduce the processes that underlie perception, that is, the chain of occurrences (physical, physiological, neurological) that lead to seeing, hearing, tasting, and touching things in the world, as they are defined intuitively by most people. However, a simple fact about simulation must be kept in mind. Simulations are not literal reproductions. When constructing a simulation, one does not attempt to replicate the very occurrences described by some theory of perception or those that were conceived by God. If one goes out and buys copper cables and tin foil, assembles small magnets, and manufactures a small device to carry sounds over the cables, certainly one does not have a simulation of a telephone. What one has is an actual telephone, albeit technologically primitive. In contrast, if one builds an apparatus for carrying coherent light very far, and does it so that the light can vary in intensity as a function of certain mechanical oscillations induced by a voice, and if that light after several reflections ends up impinging on a magnetic head that will leave a trace on a tape, and if that trace after adequate analysis can be converted into a graph that can then be fed into a computer to reconstruct the oscillations and finally convert them into the original pressure waves-there one has a simulation of a telephone. Note that all the various steps of the simulating process can be substituted by other equivalent steps. The causal chain can be stretched or shrunk. Teams of engineers can compete in inventing yet other steps, and certainly each will come up with a different simulation of a telephone at the end of the work. But all simulations will guarantee that if one says a word here, another will hear it elsewhere. Now suppose that I have built a perfect Golem. The Golem is not to be a perfect copy of myself. If this were the case, then the Golem would be a reproduction, not a simulation. Thus, Golem hardware is completely different from my physiology of actual man, but the result is a perfect simulation. The Golem will argue with me, he will tell me about Golem

P. Boui

194

predilections in music or in poetry, about curiosities for the facts of perception. Eventually, the Golem will manifest an interest in a general theory of perception. Thus, the Golem and I will start collaborating at the development of such a theory. I will show all known optical illusions. The Golem will see them and we will enjoy discussing them, for the Golem is perfect-as a simulation, not as a measuring device (in its imperfection as a measuring device lies its perfection as a simulation). We will observe the phenomena of perceptual constancy, discuss the fundamental properties of color, puzzle over apparent motion. Being very intelligent and creative, soon enough the Golem will discover new visual and auditory effects, new problems for our theory. Every day the Golem will call me and take me to the laboratory, and show me new things, facts that I did not know yet and that were not in the literature. I will delight in taking part in the experiments designed by the Golem. We will share observations, conceive new conditions, perform other experiments. But the Golem knows perfectly well about simulations. I know that my perceptual system is different from the perceptual system I put into the Golem. And of course the Golem knows that too. In conclusion, we both know that the processes underlying Golem perception are complicated simulations of other processes, those that underlie my own perception. True, the Golem started arguing that it is my perceptual processes that are simulations of Golem perception. To this I cannot reply. At this point things have become very difficult. Being perfect, by definition the Golem perceives the world just like me, sharing my perceptual experience with characteristic nonchalance. And yet it is clear to both of us, again by definition, that Golem perceptual machinery does not resemble mine. Taken together, these two points create some difficulty to any attempt to explain human or animal perception by means of computer simulations.

DISCUSSION Riccardo Luccio (Department of Psychology, University of Trieste, Trieste, Italy): Although Bozzi’s interesting essay would probably deserve ampler discussion, I limit myself to the following three short remarks. 1. Bozzi states that subjects’ protocols are unquestionable and seems to think that this is a commonplace assumption in perceptual science. However, protocols are unquestionable in the same way as the position of the

Perceptual Paradom

195

dial on a scale of an instrument is in other empirical sciences. In fact, it is the instruthe experimenter’s task to judge whether or not the subject-r ment-is reliable. Since this is trivial, 1 suspect that Bozzi has something else in mind, but I am not able to know what this could be. 2. Bozzi states that the object of scientific interest for the perceptual scientist is exactly what appears to the subject when he or she observes. I am a little bit surprised to discover that Bozzi’s definition is exactly that of Wilhem Wundt. I would like Bozzi to explain the consequences of this “discovery” explicitly. 3. Concerning the Golem, the hypothesized fact that its perceiving machinery is quite different from Bozzi’s and that at the same time both perceive the world in exactly the same way, represents the triumph of simulation. Since also this is trivial, I think that Bozzi must mean something else. What? Bozzi:I will reply to Luccio following the order of his comments. 1.The first objection raised by Luccio makes me wonder if the published data from his researches in the field of perception and cognitive science are manipulated. Apparently, he believes that data are normally questionable. Jokes apart, Luccio raises a serious problem by comparing the observer to a measuring instrument and stating that they must be calibrated before they are used. (I agree on this point.) However, according to the current scientific common sense, what we usually really want to know from the subject is the very calibration mistake of his perceptual system, the private way of perceiving the pattern to be tested. 2. The fact that the phenomenologist’s definition of the objective of perceptual science is still held unchanged and defended after one hundred years should not be a matter of surprise. One can even go farther back in time. In the second century A. D., the physician Sexstus Empiricus (1955) wrote that “the percept not only appears as it is but it is what appears.” No revolution of the foundations of mathematics and logic has put a proposition like 2+2 = 4 out of fashion, neither in common sense nor in scientific practice. 3. Indeed, the Golem would be an extraordinary result in the History of Artificial Intelligence. But given this result, it would become apparent that the investigation of perceptual laws is totally independent from the study of their underlying computational, physiological, or linguistic processes. This is what I tried to demonstrate.

P. Bozzi

1%

REFERENCES AGAZZI, E. (1976). Psicologia ed epistemologia [Psychology and epistemology]. Milan: Vita e Pensiero. EMPIRICUS, S. (1955). Outlines of Pyrrhonism. Cambridge, MA: Harvard University Press. (Translated from the original Greek text by R. G. Bury) KANIZSA, G. (1960). Randform und Erscheinungsweise von Oberflachen. Psychologische Beitruge, 5, 93-101. (Translated by M. Riegle in G. Kanizsa, 1979, Organization in vision: Essays on Gestalt perception. New York Praeger, pp. 135-142.)

Foundations of Perceptual Theory S.C. Mash (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

197

O N EXPERIMENTAL PHENOMENOLOGY Giovanni B. Vicario Department of General Psychology University of Padua, Padua, Italy

ABSTRACT Through an analysis of the literature in the field and a discussion of facts, a tentative definition of experimental phenomenology is proposed. Experimental phenomenology is regarded as true experimentation. Its experimental variables are mental contents of direct experience rather than physical stimuli or physiological processes. Two limits of the phenomenological approach are pointed out, namely, the occurrence of mental facts that do not belong to the phenomenal scene (habits, forgetting) and the actual impossibility of distinguishing which aspects of a mental fact, such as percept, play the role of causes and which those of effects. Despite these limits, experimental phenomenology is regarded as the proper method for psychological research.

In these years there is renewed interest in phenomenological psychol-

ogy and in experimental phenomenology (Bozzi 1989; Thin& 1977; ThinPs, Costall, & Butterworth, 1991). In a sense, the phenomenological point of view has never been effaced from psychology, especially in those areassuch as personality, motivation, or psychodynamics-where no other research method is capable of depicting a sensible and consistent m a p of psychological facts. What is new, however, is that in the circle of hard experimental supporters a creeping reassessment of phenomenological aspects and of their scientific use has begun.

G. B. Vicario

198

PHENOMENOLOGY The term ”phenomenology” was coined by Johann Heinrich Lambert in 1764, and the corresponding concept has been developed by Kant, Hegel, Husserl, and Merleau-Ponty-just to mention the main philosophers who contributed to our present way of intending this term. In the words of Husserl, the slogan of phenomenology is: ”Zuruck zu den Sachen selbst!” (”Back to the things themselves!”). Translated into the psychological ”dialect,” this means that if we want to understand mental facts we must cease ”wasting time” in “daydreaming” about neurophysiological or informational models, and rather face the contents of immediate experience. Husserl was not only a philosopher, he also practiced scientific psychology (with Brentano), at least until he convinced himself that it could not help him investigate the concept of number. In psychology, the meaning of ”phenomenology” has been discussed by Gestalt psychologists, for example in the third chapter of Wolfgang Kohler’s (1947) Gestalt Psychology. In his 1935 Principles of Gestalt Psychology, Kurt Koffka says: ”For us phenomenology means as naive and full a description of direct experience as possible” (p. 73). In his 1963 Psychologie, Wolfgang Metzger is even more eloquent when trying to define the phenomenological attitude: To simply accept the facing thing as it is, even if it appears unusual, unexpected, illogical or senseless, and even if it goes against undoubted axioms or familiar ways of thinking. To let the thing speak for its own, without indulging in what we know, or we previously learned, or in what is obvious, in the knowledge of subject, in logical demands, in linguistic prejudices, or in the insufficiency of our vocabulary. To stand before the thing with reverence and love, if anything reserving our doubt and mistrust for the premises and concepts we so far used to understand the world of data (p. 12).

WHY PHENOMENOLOGY? The admonition to use the phenomenological attitude in considering mental facts must not be undervalued. The developing of neurophysiological, informational, or mathematical models, although commendable for their contribution to the progress of science and necessary for their help in the treatment of cognitive diseases, progressively distances us from the facts of immediate experience, which are the proper subject matter of the psychologist. The result is that our arguments are centered on methods

ExyerinenfalPhenomenology

199

and models, while the factual basis tends to be forgotten, so that at the end we have some difficulty in saying what we are speaking of. As an example, let us briefly consider psychophysical research in the field of optical-geometrical illusions. I think that very few research subjects in psychology enjoyed so sophisticated methodological techniques for data collection and so clever explanatory models’ as those used in research on illusions. In spite of this huge amount of work, which began at least 130 years ago, we have not even come close to the explanation or the understanding of any illusion. I had the direct experience of this fact in a recent research on an unknown illusion by Delboeuf (1865; Vicario, Vidotto, & Zambianchi, 1992) when, after having psychophysically explored the conditions of the illusory effect, and having tried to link the illusion to some better known effect and related explanatory model, I found nothing best than to propose again Delboeuf‘s description and to resort to the figure-ground phenomenon for the explanation-this phenomenon being an “explanatory tool” not less puzzling than the illusion itself. As another example, consider the fine structure of psychological time. A long list of phenomena, encompassing the so-called temporal acuity, the brightness of very brief flashes, reaction times, perceptual thresholds of succession and of the order in a succession, tapping rhythms, and so on, led theoreticians to speak in favor of a quantization of psychological time, leaving undetermined just the duration of the quanta (Stroud, 1955, Kristofferson, 1980). Several models of internal clocks or cyclic timing processes have been proposed (see Patterson’s, 1990, for a brief review). However, apart from the fact that models so far proposed fit only a small part of the overall findings, the evidence is that there is a clear contradiction between the asserted discrete nature of psychological time and the smoothness of the experience of becoming-that is, of the transition from the future to the present and from the present to the past. In my opinion, the contradiction arises from the confusion between physical fime of physiological processes and psychological time. The hypothesized underlying processes may undoubtedly be cyclic, but their period cannot be regarded as a “perceptual moment:” they have no phenomenal counterpart. The only way to avoid the contradiction is to turn back to immediate experience and to put it under the light of phenomenological analysis. We will then discover that, concerning the fine structure of psychological time, we are still at the point of the unsurpassed statement of James (1890, p. 609) about the ”specious present” as a saddleback from where we look Field models. Diffraction, retinal induction, lateral inhibition, filter, cortical satiation, and ocular-movement physiological models. Assimilation, confusion, inappropriate constancy scaling, multifactorial, and developmental cognitive models.

200

G. B. Vicario

in two directions into time, which is a masterpiece of phenomenological analysis. The same can be said for the ”traveling moment hypothesis” due to Allport (1968), who refers to the actual experience of looking to the landscape from the window of a moving train. In a sense, phenomenological analysis is more sensible and “explanatory” than a sophisticated psychophysical measurement. Another source of subjective discomfort is the mechanism itself of psychophysical research. Each time we ”measure sensations” by means of the classical indirect methods we face the fact that we come to know a lot of things about peripheral transducers and nothing about sensations. For example, to ascertain that there are auditory events only when the frequency of the pressure wave is between 20 Hz and 20 kHz tells us very much about the ear but nothing about sounds. If by any chance we had found that sensitivity of the ear is between 30 Hz and 30 kHz, this finding would not have any consequence on our auditory experience: the reasons of tonal qualities are not in the values actually found, while the actual values find their functional explanation in the biological ecosystem. In other words, every psychophysical function-whatever its beauty and precision-is degraded to a mere recipe of stimuli necessary for eliciting a certain sensation and, far from explaining anything, tells us nothing about the experienced qualities of this sensation. I see the reason of this in the fact that stimulus dimensions (for acoustics: frequency, amplitude, wave form, and envelope) do not have a biunique correspondence with the dimensions of sensation (for audition: pitch, loudness, timbre, attack, but even volume, brightness, density, consonance, and so on). Very close to the aforesaid complaint is the recognition that each time we perform experiments where the free observation of some perceptual phenomenon is limited by physical constraints that exclude parasite effects, we come to know many things about these effects and almost nothing about the phenomenon under study. Consider for example those researches in vision where the head or the chin of the subject are immobilized by an appropriate device. Any difference between the results we obtain by means of this procedure, and the results we obtain by means of free observation, far from enlightening the content of visual experience, illustrate the weight of anomalous conditions in the building up of the phenomenon, namely, the undoubted importance of proprioceptive reafferences. One can find another example in dichotic listening: apart from the fact that this procedure may give raise to phenomena that have no counterpart in everyday experience, the point is that their recognition turns into a better knowledge of the peripheral treatment of acoustic stimulus in the nervous system, not into a deeper understanding of auditory events. In addition, let us consider the fact that knowledge of loci and ways of neurological

Experilnentul Phenotnenology

201

treatment of acoustic stimuli do not improve our intelligence of tonal qualities: had we found that the VIII nerve is addressed to a cortical area different from the one we know, our tonal experience would not have a different quality. Obviously, the intention of depriving these investigations of any scientific meaning is very far from me. Instead, what I desolately feel is that any intervention on the physical and physiological sides of perceptual phenomena is useless since it does not contribute to a better knowledge of the phenomena themselves. To sum up, phenomenology is necessary: as we use physical tools to test physical phenomena so we must use phenomenological tools in order to investigate experienced phenomena. I reassert that psychophysics and psychophysiology are commendable and in some cases even necessary, but I maintain that they are not true psychologies. If the job of the psychologist is to explain mental facts, we should not “immolate” them to physiological or mathematical models, or force them into experimental paradigms that are foreign to their nature. The reason is quite simple: we shall never grasp the very nature of mental facts in examining their physical and physiological counterparts. If we do so, we fall in the error called ”violation of the rules of categorical analysis” by Lorenz (1973), that is, the explanation of facts at a certain level of complexity (e.g., mental facts) with facts at a lower level of complexity (e.g., physical and physiological facts).

SOME HISTORICAL FACTS Many contemporary students believe that the phenomenological method is a rather questionable innovation brought into psychology by the so-called ”Berlin school” (Wertheimer, Kohler, and Koffia) and carried out by those who refer to the Gestalttheorie. Things are otherwise. As anyone knows, psychology as a science was born in Germany, and its establishment is commonly attributed to Wilhelm Wundt, who made two choices: one in favor of explaining mental facts in terms of the physiology of the central nervous system, and the other in favor of the experimental method (Boring, 1950, ch. 17; see also Thin& et al., 1991). Many of our colleagues are yet inclined to forget that at almost the same time a parallel movement was initiated in Germany by Franz Brentano. He made two other choices: one in favor of the autonomy of mental facts (that is, of their irreducibility to physical stimuli or to related physiological processes), the other in favor of the ”empirical” method of demonstration (we will consider it later).

202

G. B. VicariO

Everyone knows how things developed. Wund t's choices progressively won. For example, Titchener and Hall exported them in the USA, where they persisted even in the form of behaviorism and cognitivism; Kiesov and Gemelli imposed them in Italy (Turin and Milan, respectively). On the contrary, Brentano's ideas were accepted by a minority. They were developed only by Husserl (in philosophy) and by Stumpf and Meinong (in psychology). Among the pupils of Stumpf were Kohler and Koffka (and thereafter the Berlin school and the Gestalttheorie); among the pupils of Meinong was Benussi (and thereafter Musatti, Metelli, and Kanizsa). This shows that the phenomenological point of view is not a foreign body in the trunk of scientific psychology, thrust in it at a certain stage of its development by the fancy of some successful researchers; rather it is a way of thinking and a methodological choice that were active from the beginning of the psychological enterprise. This clarification may perhaps help to realize that the current way for explaining mental states and behavior only in terms of processes in the nervous system is not an unquestionable truth, but just one of the two historically grounded ways for the solution of the problem of psychism (alias, the mind /body problem). In other words, underneath every follower of Wundt you will probably find a philosophical monist, and underneath every follower of Brentano you will probably find a philosophical dualist. Whether you chose the Wundt's or the Brentano's side is not a matter of science, but of a philosophical conviction. A similar argument could be upheld for the experimental method in psychological research: its adoption is a matter of choice, not a must.

EXPERIMENTATION AND DEMONSTRATION I will now point out a singular aspect of phenomenological inquiry that hardly can be traced back to the experimental paradigm. In so doing I will raise the suspicion that the phenomenological method cannot be labeled as "experimental" and "scientific." This singular aspect of phenomenology is briefly summarized in what Gaetano Kanizsa used to say in his lectures, namely, that he performed his own experiments on the pages of his books. I refer to those pictures that "prove" or "disprove" under the eyes of the reader certain hypotheses on perceptual mechanisms. In my opinion, a big problem is concealed under the paradoxical tenet of Kanizsa. The canonical experimental procedure-with the independent and dependent variables, the control group, the statistical analysis

Experimental Phenomenology of results, and so on-is ing (1950) wrote:

203

foreign to phenomenological inquiry. In fact, Bor-

Thus Brentano, in argumenting about the optical illusions, was quite ready to draw new forms of old illusions and so pictorially to submit his case on the printed page to the experience of the reader: this is the empirical method in concrete form, the experimenturn crucis. But Brentano never undertook to measure the amount of illusions under different conditions by the psychophysical methods; this course would have been the experimental method and would have yielded more precise information about the points in question. The experimenturn crucis belongs in an argument and is thus apt to be part of the empirical method. Systematic experimentation yields precise description and is the sine qua non of the experimental method (p. 360).

A few lines before, Boring annotated: ”Brentano had respect for the results of experiment, but he believed that all this stressing of experimentation led to an overemphasis upon method and blindness for the main issue.” The conclusion of Boring is therefore that Brentano’s psychology was empirical but not experimental. We had to follow this conclusion in saying that the phenomenological method is undoubtedIy empirical, but that it cannot be credited with the attribute of “experimental.” At this point, it is perhaps useful to report an enlightening comparison carried out by Pomerantz and Kubovy (1986)among the four main theories of perception: structuralism, Helmholtzean (including cognitivist and neuropsychological theories), Gestalt, and Gibsonean. They say correctly that while the method of structuralists is introspection and that of Helmholtzeans experiment, the method of Gestalt psychologists (that is, of phenomenologists) is demonstration. Pomerantz and Kubovy (1986) say that In [the phenomenological] method the observer... [is] asked to view a stimulus and to describe its apparent organization. These stimulus patterns ... [are] designed so that, in principle, a number of different and distinct organizations were possible... To the extent that different observers agree on the organization they report perceiving, we have evidence for rules of perceptual organization, rules that are claimed to produce the simplest possible organization of the stimulus (p. 36-39).

In other words, one first notes the multiplicity of the logically possible perceptual results (this is the so-called plurivocity of the stimulus; Metzger, 1963), and then ”demonstrates” that just one of them comes into reality, thus validating the argument about the processes of perception, of which the empirical observation is an integrating part.

G. B. Vicario

204

EXPERIMENTAL PHENOMENOLOGY In spite of the many and manifest discrepancies between what we call “experimental” and what we call ”phenomenological,” in the realm of psychology there is place even for such a thing as ”experimental phenomenology.” What does it mean? The above mentioned Carl Stumpf is credited to have started the discipline (Boring, 1950, p. 369), because of the way he treated auditory sensations in his celebrated Tonpsychologie (1890). According to Things (1977, pp. 69 and 135), his experimental work deserves being called “phenomenological” in that for Stumpf the description of tonal qualities was more important than the refinement of laboratory techniques. In line with Stumpf is David Katz who ameliorated our knowledge about color and active touch by means of true experiments suggested by penetrating analyses of the mode of appearance of perceptual objects (Katz, 1911, 1925). Yet, experimental phenomenology gained a recognized international status only after the work of Albert Michotte (19461, who was able to treat experimentally some perceptions of high complexity, such as the impressions of ”launch” and ”transport” in the interaction of movements of small objects. Indeed, a masterpiece of phenomenological cleverness are his investigations in phenomenal permanence. As to Gestalt psychology, we can say that each representative of this school showed a similar ability in joining observational refinement with experimental rigor. Leaving out the founders-Wertheimer, Koffka, and Kohler-we face famous works like the Visuelle wuhrgenommene Figuren by Edgar Rubin (1911), or that monument to the science of vision represented by Wolfgang Metzger’s (1975) book Gesetze des Sehens, where the phenomenological attitude bears its best fruit: the discovery of new perceived things. Yet we lack a comfortable definition of experimental phenomenology, notwithstanding a superabundant literature full of subtle discussions. Perhaps phenomenologists think that their work-like every other object-is speaking by itself. Neither Michotte (maybe with Metzger the most philosophically oriented of the phenomenologists) defines his method by means of structural terms. If I correctly interpret the point of his pupil Things (1977, p. 139), Michotte found no conflict in applying experimental methods to phenomenal experience simply because he thought that, in inspecting the stimulus situation, the observer casts a look into reality-a sort of Gibsonean attitude ante litteram. What most resembles a definition is, in my opinion, the following series of statements by Kanizsa (1984): The aim of experimental phenomenology in vision is not different from that of other research fields of psychology: the discovery and the analy-

Experimental Phenomenology

205

sis of necessary functional connections among visual phenomena, detecting the conditions that favor or prevent their appearance and their degree of evidence; in other words, establishing the laws that govern the phenomenal field. All this without going out of the phenomenal domain, that is, without any reference to the underlying neurophysiological processes (unknown, for the most part) or to psychic non-visual concurrent activities (logic, memory, emotional, and so on, which are no less enigmatic than vision)... The experimental phenomenology of vision does not deal with the brain but with seeing which is the result of the activity of our brain. It is not a makeshift choice, justified by the too slow progress of neurosciences and related uncertainty of prospects: it is a methodological option imposed by definite epistemological reasons. Mainly, by the firm belief that phenomenal reality cannot be confronted-and less than ever explained-by a neuroreductionist approach, since we deal with a level of reality having its own peculiarity, a reality that demands and legitimates a kind of analysis adequate to its peculiarities (pp. 38-39).

I agree with this definition. So I conclude that “to practice experimental phenomenology” stands for “to rnanipulafe phenomena.” In other words, the experimental phenomenologist, when trying to understand his objects of inquiry, does not merely act by means of systematic, blind manipulation of the stimuli but is satisfied with what he observes at the level of phenomena. The independent and dependent variables to take into account are those of the phenomena and not those of the stimuli that produce the phenomena. When one wants to fix the conditions that lead to a mental fact-e.g., a perception-ne has to forbear from the bare analysis of the stimulus situation and from a blind variation of the stimulus parameters. Instead, one has to proceed to a careful inspection of the phenomenon, to discover its peculiar dimensions by means of the phenomenological analysis, and to manipulate only those stimuli that produce variations in the chosen dimensions of the phenomenon. On these dimensions one has to act, and the fact that one can manipulate phenomena only through the manipulation of physical stimuli is in principle irrelevant for the understanding of these same phenomena. No example of this procedure is better than the famous Wertheimer’s (1923) investigations of the mutual segregation of objects in the visual field-those that led to the “principles of unification.” In considering the conditions for the formation of perceptual units out of the sensory mosaic, he moved black dots across a white surface, not the ink heaplets on that cellulose support which is the sheet of paper. Wertheimer’s proximity has nothing to do with the millimeters of physical space that separates the ink heaplets on the sheet of paper (or with the excited receptive fields on the retina), but is a relational property that we see between a

206

G. B. Vicario

couple of them. When Wertheimer moved dots on a paper to see what happened, he moved phenomenal dots in phenomenal space, not ink heaplets across a cellulose support. We can perhaps find a more convincing argument in the auditory field. There we speak of tones, noises, and phones as they were “stimuli,” and we are unaware that they are true phenomena which come out from the processing of a physical signal, continuous and unidimensional in amplitude, which already underwent a transformation into perceptual events. For example, in the acoustic stimulus that gives raise to the perception of a major chord, tones do not exist at all: there is just a pressure wave characterized by a rather complex course in time. The tone that gives the chord its peculiar appearance or feeling (that is, the tone that detaches itself by a major third from the lowest tone, the “fundamental”) does not exist in the pressure wave. It is the outcome of a process that has been done that time, and that has already discriminated in total wave-in presenting them on the phenomenal scene-a fundamental tone, a tone at the major third and another tone at the fifth. When we say that, in substituting the major third interval with a minor third interval, we modify the appearance of the chord (that from major becomes minor), we do not refer to something that is present in the stimulus (the pressure wave), but to something that is already present at the phenomenal level (the middle tone of the chord). Therefore, when we shift the middle tone downward by a semitone, we do not act on stimuli but on phenomena: we do not go in for psychoacoustics, but for experimental phenomenology of audition. In specifying the values of the signal for each instant of the pressure variation, we do not care for the waveform: our play is object oriented, in the sense that we operate on an object (the middle tone) that is already the outcome of processes exerted by the perceptual system on that acoustic wave. As Kanizsa (1984) says, these processes are the job of the neurophysiologist, not of the psychologist. To sum up, the expression ”experimental phenomenology’’ is justified because it refers to a manipulation of variables like in any other domain of natural sciences. The distinguishing difference is in the nature of variables: in experimental phenomenology these variables are mental, not physical.

ONE LIMIT OF EXPERIMENTAL PHENOMENOLOGY As is well known, the main justification for the use of experimental phenomenology in psychological inquiry is that experienced facts have to be explained only in terms of other experienced facts. This axiom has its

Experimental Phenomenology

207

basis on the famous paper by Kohler (1913) against the unbemerkte Empfindungen (unnoticed sensations), in which he demolished-or tried to demolish-the Helmholtzean hypothesis of the machinery in the brain. The existence of unconscious ratiomorphic processes, on which cognitivists-the late epigones of Helmholtz-base their "fortunes," has been repeatedly challenged by means of various arguments. The first is that if the conscious reasoning or computing had to be the model of ratiomorphic processes, we would be hopelessly lost. In fact, consider the many faults (inaccuracies, oversights, paralogisms, and so on) of actual thinking (Bozzi, 1989).The second argument has already been mentioned in this essay: if we explain mental facts by means of supposed underlying processes (in terms of neurophysiological events or computational or mathematical models), we shift toward a lower level of explanation, violating the law that imposes every fact to be analyzed at its proper level of systemic complexity (Lorenz, 1973). The third is that this way of arguing justifies whatever fancy-if only ingenious and expressed in formal terms-provided that the supposed lower-level mechanisms are saved from any control, and that to each mental fact may correspond a countless number of equally plausible underlying mechanisms (see Piccinini, 1993, and Uttal's, 1990, discussion of the second Moore theorem). In a way, this argument reminds us of the strong behavioristic attack to the fancies of introspectionism, and I think that cognitivists have been no less imaginative than introspectionists in transforming their subjective experience in hypothesized underlying mechanisms (for example, see Neisser, 1964, on visual search). The fourth argument is that every sort of brain machinery requiring measurable quantities of physical time is in contradiction with the everyday experience: when we open our eyes, for example, we see an extremely complex visual scene that is suddenly given with no delay at all. If these four arguments are well grounded and crucial, one has to conclude that psychology cannot escape from phenomenologically describable facts, that its sole proper method should be experimental phenomenology, and that every assumption on the machinery of the brain, although fruitful for the study of the central nervous system and necessary in the treatment of cognitive diseases, would be devoid of any true psychological meaning. Unfortunately, this conclusion turns out to be partially misleading: reality is more complex than our expectations. Once again, we must credit Kohler for having made the point with an extreme lucidity and disarming frankness. In his paper on the mind/body problem, Kohler (1960) maintains that the psychologist cannot limit himself to the study of the "phenomenal scene:" he is concerned also with facts that are undoubtedly "mental" but

208

G.B. Vicario

at the same time are not functional parts of the phenomenal world. Kohler refers to memory, and points out that while memory retrieval has phenomenal evidence, the retention or memory loss have no phenomenal counterpart. The same can be said about habits, and about motives and emotions: we are aware of their phenomenal and behavioral effects but we cannot inspect their causes or their mechanisms. In a sense, Kohler restated in a better way something that was well known: in 1901 Marbe was amazed by the fact that while a subject is perfectly able to judge which of two compared objects is heavier, and to report a lot of sensations and associations accompanying the comparison task, the very act of judgment is saved from any form of introspection (this is the so-called imageless thought, a field of researches of the Wiirzburg school). Now, since we cannot deny that memory, habits, motives, and so on, pertain to psychology, and since all these facts are inaccessible to the phenomenological method, we have to conclude that this method cannot cover all psychological objects of study. Because of this, it cannot be the only method of psychological inquiry. This unavoidable conclusion is especially unpleasant for those who firmly trusts that only the phenomenological method can deal with the psychism-i.e., the immediate experience-and that the psychological research based on neuropsychological processes turns into a more and more precise knowledge of the machinery in the brain, leaving at all unsolved the problem of the direct experience itself. Only a naive identification of mental facts with the corresponding brain processes can carelessly take these facts at one level for a way of describing those at the other level. This jump would never be made by a philosophically shrewd researcher. Yet we must surrender to reality, that is, to the antinomy in the conclusion that neither phenomenological nor neurophysiological descriptions can cover the totality of psychological facts, and that there is no way to put them at the same level. The Eccles (1990) attempt to bridge the gap between the opposite banks of mental life is ingenious, but fated to displease both phenomenologists and neurophysiologists. In any case, the phenomenological method has at least the aforesaid limit. In my opinion, if we want at all costs find a coherent frame of reference for immediate experience and neurophysiological research, we can resort to Jackendoff's (1987) theorization. He makes a distinction between the phenomenological mind and the computational mind: the first should be characterized by consciousness, the second by those processes that, although unobservable, could have effects on phenomenally observable mental contents. According to Jackendoff, the phenomenological mind should be a projection of a subset of the computational mind, something like a light spot on a scene for the rest plunged in the darkness. I am

Exyerimental Phenomenology

209

aware that Jackendoff's effort leaves unsolved the problem of why a subset of the computational mind should come into the light of the phenomenological mind. Yet I find that this theorization can at least legitimize the duplicity of psychological research: phenomenological analysis for conscious contents, neurological experimentation for silent processes.

ANOTHER LIMIT OF EXPERIMENTAL PHENOMENOLOGY As I said before, in working with the method of experimental phenomenology, we use the axiom that phenomenal facts have to be explained only with other phenomenal facts. This means that there are facts that assume the role of causes and others that of effects. In fact, this is the practical significance of the term "explanation" in every natural science, from mechanics to biology. Unfortunately, this is not the case in psychology. We are taught by experience that, whenever in a global phenomenon we try to identify those aspects that could take up the role of causes and those other aspects that could take up the role of effects, we enter a vicious circle: we can no longer distinguish what comes first. For example, let us consider the case of perceptual transparency (Kanizsa, 1955; Metelli, 1974). In order to see a surface as transparent, several conditions must be met. Some are physical-relative reflectances of the areas in the display-and some figural--continuity of contours, topological relations among surfaces, and so on. Well, when figural conditions are manipulated to distinguish basic from accessory conditions, we conclude that a surface is seen as transparent only when object stratification takes place. But this stratification is at work only when an object is seen as transparent. In the same way, transparency is the feature of a surface that, even if made up of different regions, is perceived as unitary. But the possibility to see multiple adjacent regions as an unitary surface is grounded on the possibility to see this surface as transparent, entirely or in part. I have the impression that this state of affairs is the same for every perceptual phenomenon, although only phenomenological psychologists have stressed it. The amodal completion of an object (Burke, 1952; Kanizsa, 1980; Michotte & Burke, 1951) is realized just when a part of the visual field is perceived as a screen (occlusion), but that part of the visual field is seen as a screen just when there is an object to complete. An object can be seen as big only if it is perceived as far, but it can be seen as far only when it is perceived as big; a movement can be perceived as "passive" just only if in the field there is another movement that takes upon the "active" feature. In stroboscopic motion, the displacement of the first

210

G. B. VicariO

light occurs as soon as the second light occurs in the field, so we are led to the conclusion that the member of the kinetic structure that comes after is in some sense the “cause” of the displacement of the first. What is puzzling in this case is that we see the first light in motion before we see the point of arrival-so that we have a phenomenal before/after that is not congruent with the physical before/after. (For other examples of this sort see Vicario, 1989). In conclusion, at least as regards perceptual phenomena, we have some difficulty in identifying causes and effects, especially because we cannot establish the temporal sequence that characterizes the status of the elements in a configuration. It goes without saying that the differentiation before/after is the cue for the distinction cause/effect. In static displays, all elements are present simultaneously, so that they can mutually exchange the roles of cause and effect; in kinetic displays the physical temporal order is reversed in the phenomenal datum. Now, I do not know whether we can call ”experimental” a method that involves so great a confusion about the things to which we should univocally apply the concepts of cause and effect. In manipulating a variable, we do not know what we are really doing. In this sense, I see a limit in labeling phenomenology as “experimental.” In fact, I fear that the effort of some of us to make phenomenology experimental, is influenced by some paradigms-like mechanics or chemistry-that are by no means representative of all natural sciences. Bozzi (1989, p. 39) stressed that even natural sciences deal with field phenomena (e.g., magnetic phenomena), whose final configuration is determined by the simultaneous presence of multiple events to which it is impossible to ascribe the role of a cause or effect-because of their simultaneity. In my opinion, we can apply the paradigm of mechanics in very few natural sciences, since biological and chaotic phenomena suffer the same vicious circle that we have in perceptual phenomena. Academic psychology seems bounded to a representation of the physical and biological worlds that is no longer in use in these sciences: the simple reading of the popular book by Nicolis and Prigogine (1987) can give us the warning. To be sure, Kohler (1947) had an unending roll of physical, chemical, and biological phenomena, in order to justify his own refutation of any ”mechanical” theory of perception. In his proposal of a ”dynamic” theory, his examples were drawn from electrostatics and fluid dynamics. Even in chemistry, the so-called Belousov-Zhabotinski reaction shows astonishing selforganizing properties, just like those properties that some psychologists deny to perceptual phenomena.

Experilnsital Phenomenology

21 1

CONCLUDING REMARKS To sum up, I think that psychological research cannot avoid using the phenomenological method, since descriptions or explanations of direct experience in terms of physical stimuli or of physiological processes turn out to be, in the long run, better restatements of the physical or physiological conditions of direct experience, never a sensible explanation of this experience itself. If psychologists’ job is to investigate mental facts, let them manipulate what appears on the phenomenal scene, and not what is under or behind it. I agree that there are phenomena-like habits or forgetting-that challenge phenomenological procedures, but the adoption of the phenomenological method at least avoids the grave mistake of confounding direct experience with physical stimuli or with physiological processes (stimulus and experience errors). I think that experimental phenomenology is a sensible research approach, even if the proper tool of the phenomenological method seems to be demonstration instead of experimentation. After all, there are sciences that are not experimental: for example, astronomy or geology. What makes the difference between the classic experimental and phenomenological models, is that in the former we manipulate physical variables and in the latter phenomenal variables. Sure, mental phenomena exhibit the uncomfortable peculiarity of being constituted of parts to which we cannot apply with certainty the labels of causes and of effects. However, today physicists and chemists are grappling with phenomena of the same sort without being embarrassed: they make a virtue of necessity. Perhaps, the reader will find a certain theoretical laxism in my arguments, in the sense that I make the point but I do not exclude alternative solutions to the posed problems. In this way, I am a true follower of the phenomenological attitude: we face a complex and puzzling reality, and we cannot force it in our logic categories. If mental facts exhibit properties irreducible to those we are acquainted with, we must use proper methods of investigation instead of exclusively using those from the other sciences.

DISCUSSI 0N Giorgio Vallortigara (Institute of Philosophy, Pedagogics, and Teaching of Modern Languages, University of Udine, Udine, Italy) and Mario Zanf o r l i n (Department of General Psychology, University of Padua, Padua, Italy): We believe that science (all science) arises not from a priori definitions of its objects, but rather from problems. Let us therefore

212

G. B. ViCariO

consider an example of the sort of problems facing experimental phenomenology. Place a pile of coins on a table so that the perceived height of the pile corresponds to the size (diameter) of a single coin. Then, put another coin upright and compare it with the height of the pile. The pile will appear lower than the coin. We are thus faced with a problem: the height of the pile is first the same and then not the same as the diameter of the coin. Are we to say that the correct measurement of the diameter of the coin is given by the height of the pile or by the height of the vertical coin? Which of the two appearances is ”illusory?” Faced with these phenomena, the experimental phenomenologist, like any other scientist, will try to check whether a general law of nature has been found. Indeed, this can easily be demonstrated in that there seems to be a relation of functional dependence between two phenomenal variables which is always valid for human perceivers, that is, perceived length depends on perceived orientation. In principle we could be satisfied with this state of affairs. We have found a law of nature, we have described it. However, scientists are usually not entirely satisfied with this. They want to know “why” things are as they are. At this point we disagree with Vicario’s proposals because, in our opinion, there is no way in which this “why” question can be answered without resorting to logical constructs that are not (and cannot be) part of our phenomenal experience. It is obvious to us that the answer to the “why“ question resides in the perceptual system, in its make up, in the way it works, and in the purpose for which it has developed in the course of biological evolution. Of course, the notion of “perceptual system,” and for that matter even the notion of ”biological evolution,” are “mental constructs” or ”logical inventions,’’ not experienced phenomena in themselves. Do we need constructs which are outside our phenomenal experience in order to explain phenomenal experiences? We believe that the answer is definitively positive. The alternative view, championed by Vicario, who claims that experienced facts must be explained only in terms of other experienced facts appears untenable to us. For, if all these facts were phenomenally experienced, that is, if we were consciously aware of them, we would not seek an explanation. We would be already conscious of the explanation because, by definition, this explanation is part of our phenomenal experience. There would simple be no need for academic psychology, because people would experience the “why” of their phenomenal experiences; they would be aware of the answers. One could maintain that the explanation of experienced facts lies in the relationship between experienced facts. However, is this ”relation-

Expitnen tal Phenoinenology

213

ship” directly experienced? In other words, do we directly perceive that perceived length depends on perceived orientation, or do we need to use ”standardized” measures to deduce it? It is clear that we simply experience the results of this functional relationship, and that we experience these results as a puzzle, as a problem. Furthermore, the relationships between phenomenal variables are exactly what we want to explain, and it is therefore logically absurd to maintain that they could be explanations. Discovering a functional relationship between phenomena is the first step in doing science. The next step is to ask why such a relationship exists. Vicario seems to be disappointed because in our mental life there are facts (actually, the majority of facts) that are not part of our phenomenal world. Things are indeed even worse than Vicario would admit: we are never consciously aware of why our phenomenal experience is as it is. It does not really matter if we speak of memory instead of perception. When we perceive a red triangle, there is no phenomenal experience of why we see a red triangle instead of a green circle, except the naive attitude ... ”because there is a red triangle there.” If we take Vicario’s proposal seriously, contemplation seems to be the only activity left for ”pure” phenomenologists. We disagree. We believe that in perceptual science, as well as in any other realm of psychology, we need hypotheses and models. This is not a peculiarity of psychology. The same is true for all natural sciences. The concept of ”force” in physics is just as unexperienced as that of ”anisotropy of the visual field in psychology. What we experience are the results, the phenomenally testable effects of these hypothetical entities. Experimental phenomenology. We claim that the ”phenomenological attitude” is not an alternative to developing explanations based on models of underlying processes or “silent processes,” but it is simply the initial and mandatory starting point for any scientific enterprise. A naive and exhaustive as possible description of the phenomena is in fact a first step common to all sciences. In this chapter, Vicario sets the method of experimentation against that of demonstration. We think that this dichotomy is only apparent. Experimental phenomenologists also perform experiments. They simply do so after an initial description of the phenomena. Usually, phenomenologists start with a description of a certain phenomenal experience, and then modify it systematically (through manipulations of the stimulus conditions) until a certain phenomenon is apparent with the greatest vividness. Then, further manipulation of the stimulus conditions are used to test hypotheses about the why things appear as they do. It is really true that phenomenologists do not employ the traditional parametric methods of experimentation? Obviously not. For, if we want to

214

G. B. Vicario

use a visual display as a sort of “rhetorical trick to sustain our point, we have first of all to check for the better conditions producing the phenomenon. Thus, experiments by Gestalt psychologists seem to be mere demonstrations without canonical parametric studies only because these parametric studies have been performed before the presentation of the final “case in point.” Admittedly, there are two important differences with respect to other psychological traditions, such as behaviorism or cognitivism. First, the latter traditions have tended to neglect the initial phase of the description of the phenomena-this has in fact been Konrad Lorenz’s major complaint about the work of behaviorists in animal behavior (Lorenz, 1965). Second, typical cognitive experiments yield their results indirectly. That is, instead of describing and measuring the direct experiences under investigation, they take some indirect measures (e.g., reaction times) as ”indices” that the direct experience has occurred. We think that the phenomenological attitude is preferable, particularly in the preliminary phases of a psychological research because, as Vicario recognizes, it is better for discovery of new perceived things. This is probably because phenomenological observations are not (or only to a limited extent) constrained into a theory that has been built up before looking at the phenomena and which may have to disregard some aspects of the phenomenon because they are “irrelevant” with respect to that particular theory. Direct experience, logical constructs, and levels of explanation. Vicario asserts that if we explain mental facts in terms of supposed underlying processes we shift toward a lower level of explanation, violating the law that every fact should be analyzed at its proper level of complexity (Lorenz, 1973).There seems to be some confusion here. Sensory experiences are the origin of all factual knowledge. They are the starting point of any scientific enterprise. We have two languages, that of sensory experiences and that of scientific constructs. Scientific constructs are not part of our phenomenal experience. However, they can be verified or falsified by translating them as logical tenets of the type ”if ... then” in the language of phenomenal experiences. If, as Vicario claims, direct experience must be explained in the language of sensory experience without any sort of logical constructs, then it follows that all sciences are performing a sort of ”categorical mistake” (admittedly, with the only exception of the empirical phenomenology proposed by Vicario). Yet, even in the field of the phenomenology of vision there are logical constructs which are not “phenomenally given,” since we experience them in terms of their effects. For instance, we do not experience “the rules of perceptual organization.” Instead, we infer their

Experimental Phenoinenology

215

existence on the basis of their phenomenal effects. How can the rule of proximity be demonstrated? Well, we have to translate the construct in a proposition of the ordinary language, for example "if I move these points so and so, then I shall see such and such." We do exactly what physicists do. In physics, the concept of "force" is a construct the existence of which can be verified in terms of propositions in the language of sensory data. If we do this and this... then we see this and this. Levels of explanation thus refer to the logical constructs of the various sciences, and not to the phenomenal experiences to which all sciences should refer as the source of factual knowledge. Of course, logical constructs of the various sciences have a certain independence, in the sense that each science tends to verify its constructs using quite different aspects of sensory experience. Neurophysiologists verify their constructs translating them into the language of those sensory experiences that could be obtained when one looks at the nervous system activity (if I put my microelectrode in that way, then I shall see nerve cells responding in such and such a way). Psychologists verify their constructs translating them into the language of those sensory experiences that could be obtained when one looks at human behavior, including verbal behavior (if I put this display in front of the subject in such and such a way, then I shall hear my subject saying so and so).Eventually, the two sorts of translation could converge. Constructs originally validated in their own proper field may turn out to be useful for predictions in the other field. The reason (or hope) why this may occur is that we are describing the same thing from different viewpoints. We disagree with the idea that when studying "silent processes" we psychologists are doing "neurological research" (and we suspect that neurologists would also disagree). We are doing psychology simply because we are studying psychological problems, that is problems that have arisen from careful phenomenological analysis of an organism's behavior, not that of its nerve cells. Vicario: I never claimed that logical constructs are an integrating part of phenomenal experience. I just stated that the terms by means of which we describe mental facts, and which we use to build logical constructs, have to be derived from phenomenal experience. I agree with Vallortigara and Zanforlin in considering logical constructs necessary for the explanation of phenomenal experience, as a mere contemplation of reality is not an "explanation." Perhaps, I failed to make clear that if there is the need for logical constructs in explaining phenomenal experience then the terms connected to form logical constructs also have to be phenomenal. This condition is acknowledged in other sciences, and I cannot see why it

216

G. B. ViCario

should be refused in psychology. For example, let us consider the explanation of planetary motion in physical terms. We form our logical constructs by connecting physical terms, such as places, times, masses, accelerations, and so on. To be sure, we do not use terms foreign to physics, as in the past, when planetary motion was attributed to the thrusts exerted by gods or angels to celestial spheres. By analogy, I maintain that in explaining mental facts the terms used in the formation of logical constructs must be phenomenal. Perceptual transparency is explained by connecting terms like ”continuity,” “unitariness,” ”stratification,” and so on, which refer to perceived features. There is no use in arranging the reflectances of surfaces into formulas, since these formulas specify only the conditions for reproducing the perceptual effect. I never stated that ”in our mental life there are facts... that are not part of our phenomenal world’’ (p. 213). This is a contradiction in terms. I just affirmed that we face facts-like the process of forgetting-to which we cannot deny a psychological status, even if they are inaccessible to the phenomenological method. Consequently, I pointed out the special limitation of the method, which seems to mirror the symmetrical inability of the experimental method to escape from mere psychophysics or from neuronal circuitry to get at the very substance of everyday experience. Certainly, I am disappointed by the fact that the method I prefer is affected by a severe limitation of its application. However, I am at least aware of this, so I can consider the matter as a problem to be investigated. I agree with Vallortigara and Zanforlin in considering the Boring (1950) distinction between experimentation and demonstration to be rather specious. This is the reason why I pointed out that some celebrated sciences, like astronomy and geology, are not experimental at all. What Vallortigara and Zanforlin maintain, namely that there is no distinction between experimentation and demonstration since the phenomenologist performs his parametric studies before the presentation of the ”case in point,” is exactly what I also stated, namely that psychophysics provides only the recipes for obtaining phenomena, without really dealing with the subject under discussion. I cannot reply to the last remarks of Vallortigara and Zanforlin because they attribute to me opinions that I do not have-as I tried to clarify at the beginning of this reply. The plain truth is that they are Wundt’s followers, and therefore they seize any opportunity to claim that in comparing mental facts with physiological processes “we are describing the same thing from different viewpoints” (p. 215). On the contrary, I am a follower of Brentano and thus persist in asserting the uselessness of describing and explaining mental facts with something other than phenomenal experience itself.

Experimental P h m m l o g y

217

REFERENCES ALLPORT, D. A. (1968). Phenomenal similarity and perceptual moment hypothesis. British Journal of Psychology, 59, 395-406. BORING, E. G. (1950). A History of experimental Psychology. New York: Appleton-Century-Crofts. BOZZI, P. (1989). Fenomenologia sperimen tale [Experimental phenomenology]. Milan: I1 Mulino. BURKE, L. (1952). On the tunnel effect. The Quarterly Journal of Experimental Psychology, 4, 121-138. DELBOEUF, M. J. (1865). Note sur certaines illusions d'optique. Bulletin de I'Acade'mie royale des sciences des lettres et des beaux-arts de Belgique, 34(II, 191, 195-216. ECCLES, J. C. (1990). The mind-brain problem revisited: The microsite hypothesis. In J. C. Eccles & 0. Creutzfeldt (Eds.), The principles of design and operation of the bruin (pp. 549-568)' Pontificiae Academiae Scientiarum Scripta Varia, n. 78. Rome: Pontificia Academia Scientiarum. JACKENDOFF, R. (1987). Consciousness and the computational mind. Cambridge, MA: MIT Press. JAMES, W. (1890). The principles of psychology (vol. 1). New York: Holt. KANIZSA, G. (1955). Condizioni ed effetti della trasparenza fenomenica [Conditions and effects of phenomenal transparency]. Rivista di Psicologia, 49, 3-19. KANIZSA, G. (1980). Grammatica del vedere [The grammar of seeing]. Bologna: I1 Mulino. KANIZSA, G. (1984). Vedere e pensare [Seeing and thinking]. Ricerche di Psicologia, 8, 7-42. KATZ, D. (1911). Die Erscheinungsweisen der Farben und ihre Beeinflussung durch die individuelle Erfahrung. Zeitschrift fur Psychologie, special number 7. (English translation: The world of colour. London: Kegan Paul, 1930.) KATZ, D. (1925). Der Aufbau des Tastwelt. Leipzig: Barth. KOHLER, W. (1913). Uber unbemerkte Empfindungen und Urteilstauschungen. Zeischrift fiir Psychologie, 66, 51-80. KOHLER, W. (1947). Gestalt Psychology. New York: Liveright. KOHLER, W. (1960). The mind-body problem. In S. Hook (Ed.), Dimensions of mind (pp. 3-23). New York: New York University Press. KOFFKA, K. (1935). Principles of Gestalt Psychology. London: Harcourt, Brace. KRISTOFFERSON, A. B, (1980). A quanta1 step function in duration discrimination. Perception & Psychophysics, 27, 300-306.

218

G. B. Vicario

LORENZ, K. (1965). Evolution and modification of behavior. Chicago: University of Chicago Press. [GV&MZl LORENZ, K. (1973). Die Riickseite des Spiegels. Miinchen: Piper. METELLI, F. (1974) The perception of transparency. Scientific American, 230(4), 90-98. METZGER, W. (1963). Psychologie. Darmstadt: Steinkopff. METZGER, W. (1975). Gesetze des Sehens. Frankfurt a. M.: Kramer. MICHOTTE, A, (1946). La perception de la causalite'. Louvain: Institut Superieur de Philosophie. (English translation: The perception of causality. London: Methuen, 1963.) MICHOTTE, A., & BURKE, L. (1951). Une nouvelle enigme de la perception: le "donne amodal" dans l'experience sensorielle. In Proceedings of the 23th International Corzgress of Psychology (pp. 179-180), Stockholm. [Also in A. Michotte (Ed.), 1962, Causalite', permanence et rialite' phe'nome'nales (pp. 372-373). Paris: Bbatrice-Nauwelaerts.1 NEISSER, U. (1964). Visual search. Scientific American, 201(6), 94-102. NICOLIS, G., & PRIGOGINE, I. (1987). Exploring complexity. An Introduction. Miinchen: Piper. PATTERSON, R. (1990). Perceptual moment models revisited. In R. A. Block (Ed.), Cognitive models of psychological time (pp. 85-100). Hillsdale, NJ: Erlbaum. PICCININI, L. (1993). Sistemi, scatole nere e intelligenza artificiale [Systems, black boxes, and artificial intelligence]. Rivista di Psicologia, in press. POMERANTZ, J. R., & KUBOVY, M. (1986). Theoretical approaches to perceptual organization. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.), Handbook of perception and human performance (vol. 2, ch. 36, pp. 1-46). New York: Wiley. RUBIN, E. (1911). Synsoplevede Figurer, Copenhagen. (German translation: Visuell wahrgenommene Figuren. Copenhagen: Gyldendals, 1921.) STROUD, J. M. (1955). The fine structure of psychological time. In H. Quastler (Ed.), Information theory in psychology: problems and methods (pp. 174-205). Glencoe, IL: Free Press. STUMPF, C. (1890). Tonpsychologie. Leipzig: Hirzel. THINES, G. (1977). Phenomenology and the science of behaviour. London: Allen & Unwin. THINES, G., COSTALL, A., & BUTTERWORTH, G. (1991). Michotte's experimental phenomenology of perception. Hillsdale, NJ: Erlbaum. UTTAL, W. R. (1990). On some two-way barriers between models and mechanisms. Perception b Psychophysics, 48, 188-203.

Experinen fa1 Phmumenology

219

VICARIO, G. B., VIDOTTO, G., & ZAMBIANCHI, E. (1992). Variations on a theme of Delboeuf. Unpublished manuscript. VICARIO, G. B. (1989). Forma ed eventi [Form and events]. In 0. Longo (Ed.), Forma, rappresentazione e struttura [Form, representation, and structure] (pp. 115-129). Napoli: Laboratorio Servizio Tecnologia. WERTHEIMER, M. (1923). Untersuchungen zur Lehre von der Gestalt. Psychologische Forschung, 4, 301-350.

This Page Intentionally Left Blank

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

221

THE "INSIDE-OUTSIDE PROBLEM" AND WOLFGANG KOHLER Nicholas Pastore Department of Psychology Queens College of the City University of New York, Flushing, New York

ABSTRACT Kohler's formulation and resolution of the "inside-outside problem" is described. This problem concerns the attempts of theorists such as Helmholtz and Schopenhauer to explain the appearance of objects outside our bodies. They supposed a hypothetical entity, sensation, which, being a presumed attribute of neural processes, was localized in the head. Kohler resolves the "inside-outside problem," which he regards as a pseudoproblem, by distinguishing between "organism" and "body." A paradox in Helmholtz's and Schopenhauer's treatment of the problem is elucidated.

External reference is a general feature of visual percepts. When I look about me in my study, the objects I see have a "thereness" in space. I see them as detached from my body and usually at some distance from it. When I look at my hand and then at some other object, say, a pencil on my desk, the pencil is evidently at some distance from my hand. Of course, I see other objects as surfaces in the space between my hand and the pencil. Upon closing one eye, I can see part of my nose and also that all other objects are at some distance away from it. When I touch an object with my finger, I still see this object as detached from my finger Ce., not part of my body), though, to be sure, I do not see, and cannot see, any distance separating them. This account of my experience follows Kohler's comprehensive phenomenological description of his own direct experience (e.g., Kohler, 1947).

N.Pastore

222

The ”inside-outside problem” preoccupied Kohler for over thirty years following his first formulation of the problem and its solution in 1929 (Kohler, 1971a). He discussed the problem in works intended for psychologists (Kohler, 1947, pp. 206-214) or for philosophers (Kohler, 1971b). Clearly, he must have regarded the problem as a significant one.

I In 1929 Kohler states the inside-outside problem as follows: Why are objects of the phenomenal world perceived as before us, outside of ourselves, even though today everybody knows that they depend upon processes inside of us, in the central nervous system? (Kohler, 1971a, p. 125).

He elucidates the “why“ question with reference to what ordinarily is termed the ”causal theory of perception,” although Kohler does not use the expression: Anatomy, physiology, and pathology teach us that about one point there can no longer be any possible doubt. The physical processes between object and sense organ are followed by further events which are propagated through nerves and nerve cells as far as certain regions of the brain. Somewhere in these regions processes take place which are tied to the occurrence of perception in general and, therefore, also to the existence of phenomenal objects (Kohler, 1971a, p. 127).

In respect to vision, a sequence of physical processes originates in the radiation from a physical object and terminates in certain brain processes, these processes being ”tied” to a phenomenal object. The particular brain processes, of course, are somewhere ”inside” the head. On the other hand, Kohler points out, there is no doubt “we have the phenomenal objects before us and outside of ourselves.”

Kohler‘s answer to the ”why” question involves the distinction between body and organism. Body is a phenomenal entity which is defined from the phenomenological standpoint; it includes hand, face, etc. From this ”I” standpoint, the ”object” seen before us is a phenomenal object, and the distance between this object and body is likewise phenomenal. On the other hand, organism relates to the domain of physical objects. Inside the organism are brain, brain processes, central nervous system, etc.

InsideoutsideProblem

223

”Hand” as a physical entity is an outer part of the organism. At some distance from this hand, or perhaps in close proximity to it, is the world of physical objects, such as a pencil. Distance in this context, of course, pertains to the physical domain. Kohler cites an experiment to show the necessity of distinguishing ”between the physical organism and ... the body percept” (1971b, p. 94). A person is seated inside a cylinder which has alternating vertical white and black stripes. When the cylinder is set in clockwise rotation the person, who is stationary, feels his body rotating counterclockwise. Kohler (1971b) points out that the ”body-percept” moves although the ”physical organism” remains stationary. (A similar phenomenon is common among subway travelers when, say, an express train overtakes a local.) Kohler did not rely exclusively on observations, experimental or otherwise, to show the necessity for the distinction between organism and body. But he stressed logical analysis of the inside-outside problem, which he presented in a historical context.

m According to Kohler, ”philosophers from Schopenhauer to Whitehead seem to have been convinced that the genuine, the original, location of percepts must indeed be somewhere in our interior” (1938, p. 127). It would appear that these philosophers believed that because a percept was “tied” to or correlated with certain brain processes, the original location of the percept, too, must be inside the head. On this view, the percept originally is inside the organism’s physical head and, subsequently, translocated outside it. These interpretations seemed very strange to Kohler. He noted that Schopenhauer had to make the ”wildest assumptions” in dealing with the “why“ question (1971a, p. 125). Kohler did not spell out the views of Schopenhauer or anyone else on this question. Schopenhauer insisted that any sensation is inside the organism. Thus, in dealing with the sense of sight, he wrote, “the only immediate datum is the sensation experienced by the retina ... This sensation is entirely subjective, it only exists within the organism and under the skin” (1903, p. 66). To account for the objectification of the visual sensation, he held that the “Understanding,” by virtue of an apriori law of causality, effects ”a powerful transformation... by which subjective sensation becomes objective perception” (1903, p. 60). In further elaboration of his views, Schopenhauer (1903, pp. 68-75) maintained that the sensation is upside down “within our eye,” that there are two sensations (one in each eye), and that the sensation is

224

N. Pasfore

“merely planimetrical.” In each case, the ”Understanding converts sensation into perception” so that we see upright, singly, and stereometrically (ibid. ). These are some of the views that Kohler must have had in mind when he referred to Schopenhauer’s “wildest assumptions.” Clearly, Schopenhauer endows the ”Understanding” with miraculous powers. But even on his own terms, a paradox arises, which he did not touch upon. Just as with sensation, the understanding also should be regarded as being inside the organism. Since the understanding creates the perception, the logical conclusion should be that the perception also would be inside the organism. Therefore, the apriori law of causality could not have explained the external reference of percepts. Kohler indicated that scientists as well as philosophers also supposed the original location of a percept in the organism. He quotes Helmholtz: The objects present in space appear to us clothed in the qualities of our sensations. They appear to us red or green, cold or warm, they have smell or taste, etc., while these sensory qualities belong, after all, only to our nervous system and do not at all extend into outer space (Kohler, 1971a, p. 125 n.).

This striking statement implies that qualities such as redness or greeness are inside the organism, just as the nervous system to which they belong. In a similar vein is James’s quotation of Helmholtz to which Kohler (1938, p. 127 n.) calls attention: Sensations are what we call the impressions on our senses, in so far as they come to our consciousness as states of our own body, especially of our nervous apparatus; we call them perceptions when we form out of them the representation of outer objects (James, 11, p. 33 n.).

Finally, Helmholtz, in a discussion of vision, stated that ”throughout our lives we have felt excitations in the optic nerves” (Helmholtz, 1971, p. 131) (emphasis added). Thus Helmholtz now must resolve the same problem that confronted Schopenhauer, namely, to explain the transition from internal sensations to objectified percepts. One solution that Helmholtz adopted was similar to Schopenhauer’s in that Helmholtz postulated an apriori law of causality (Pastore, 1978, pp. 362-364, p. 373 n. 27). However, Helmholtz’s solution would be subject to the same paradox as Schopenhauer‘s. Helmholtz offered another solution which stressed associations based on the sense of touch. But this appeal to touch does not eliminate the paradox. Tactile sensations, like visual sensations, would belong to the

Insideoutside Problem

225

nervous system. Thus, the associations between visual and tactile sensations would not account for the appearance of a phenomenal object before us.

An accurate account of the causal theory of perception requires two separate descriptions, phenomenological and scientific. The externality of percepts described in the first paragraph of this chapter is based on the phenomenological standpoint. Kohler‘s statement “objects of the phenomenal world [are] perceived before us” represents a description from this standpoint. The scientific standpoint refers to the description of the sequence of physical events such as light (photons) issuing from a luminous source, retinal excitations, nervous impulses, and processes in the brain. The scientist, who remains exclusively in the physical domain in studying the physical basis of perception, cannot make any statement about the phenomenological standpoint. To complete his study, he requires information obtained from a perceiver to establish relations between percepts and anatomical structure of the brain and processes occurring in the brain. Obviously, Schopenhauer’s and Helmholtz’s belief that sensation was in the organism could not have been based on the phenomenological standpoint. This belief can be explained in terms of their misconception of the causal theory of perception. Having noted that the endpoint of the physical causal chain is a process in the brain, they identified the location of the psychological effect of this process, a sensation, with the location of the physical process itself. Consequently, they had the problem of explaining the external reference of a percept or, in their language, the projection or transfer of sensation into space. Thus to account for the supposed projection they invoked an apriori causal law or associations between visual and tactile sensations as explanatory principles.

V For Kohler, the ”why” question represents a pseudoproblem. The pseudo-character of the problem essentially arises from a theorist’s confusion of phenomenal and physical domains or between psychological facts (percepts) on the one hand and correlated neural processes on the other. This confusion led to the belief that sensation was localized in the brain. As a consequence of this confusion, theorists such as Helmholtz and Schopenhauer presented elaborate pseudo-explana tions of the externality of percepts.

N.Pastme

226

DISCUSSION Sergio C . Masin ( D e p a r t m e n t of General Psychology, University of Padua, Padua, Italy): Pastore’s insightful historical analysis of Kohler’s solution of the ”inside-outside problem” is provocative and interesting. However, I would like to raise two points, one about Kohler‘s interpretation of the ”inside-outside problem” and one about Pastore’s analysis of Kohler’s work. From my point of view, it seems that Kohler’s description of the “inside-outside problem’’ is misleading. He states: Why are objects of the phenomenal world perceived as before us, outside of ourselves, even though today everybody knows that they depend upon processes inside of us, in the central nervous s y s t e m ?

(emphasis added) Clearly, in this description “US“ has two distinct meanings. In ”before us“ this term refers to our “self,” and in “inside of us“ to the “central nervous system.” Thus, Kohler conveyed the meaning that our self is our central nervous system or a part of it. Additionally, he implicitly stated that “everybody knows” that this is true, which is most probably false. Given that Pastore centers his essay on Kohler, it would be most interesting if Pastore explains why he feels that Kohler was not misleading in his ambiguous use of the word “us.” Nevertheless, Pastore has made an important contribution to the discussion in this volume by the stress he places on the importance for perceptual scientists of distinguishing between the phenomenal and physical domains. Failure to make this distinction forces perceptual scientists to develop pseudo-explanations. Pastore astutely indicates that this misinterpretation could be the essential reason why current perceptual theories are so short-lived. Pastore could confirm my interpretation of his intended message by giving us some example of this failure to correctly answer or understand the ”inside-outside problem.” Pastore: Masin points out a subtle possible ambiguity in the use of ”us” in my first quotation of Kohler, which never occurred to me. Perhaps my knowledge served as a context in my reading of the passage, thus leading to my interpretation. However, my second quotation from the same work by Kohler dissipates the ambiguity.’ The possibility of ambiguity is absent in Kohler’s original article, which was published in German, since the German corresponding to the phrase ”inside of us” does not occur (Kohler, 1929, p. 395). Instead, the phrase “in unserem Innern” appears, which may be trans-

1nsideUutsideProblem

227

Masin reasonably requests a contemporary example of the ”failure to correctly answer or understand the ’inside-outside problem’.’’ To satisfy this request, I select the neuroscientist Horace Barlow. Barlow wishes to show that Helmholtz’s doctrine of “unconscious inference’’ offers a correct description of the formation of ”percepts,” a doctrine which he believes is “rarely discussed or quoted” (Barlow, 1990, p. 1569). Although Barlow does not quote or cite Helmholtz, the source of his discussion of unconscious inference is Section 26 of the Southall edition of Helmholtz’s Optics (Helmholtz, 1924, 111, pp. 1-37). Helmholtz’s use of a phosphene (a light-appearance arising from pressure exerted on an eyeball) is essential to understand Barlow’s account of unconscious inference. According to Helmholtz, when the right ”eyeball is mechanically stimulated at the outer corner of the eye... we imagine that we see an appearance of light in front of us somewhere in the direction of the bridge of the nose” (ibid., p. 2). Having explained the imagined appearance in the nasal field as an ”unconscious conclusion,” Helmholtz writes: It may be ever so clear how we get an idea of a luminous phenomenon: in the field of vision when pressure is exerted on the eye; and yet we cannot get rid of the conviction that this appearance of light is actually there at the given place in the visual field; and we cannot seem to comprehend that there is a luminous phenomenon at the place where the retina is stimulated (ibid., p. 5) (emphasis added).

In the last passage, Helmholtz postulates two kinds of luminous phenomena. One kind is the ”idea of a luminous phenomenon,” the other, the “luminous phenomenon at the place where the retina is stimulated.” In Helmholtz’s theory, the first kind (“idea”) represents a perception, and it is this that we are conscious of; the second kind (the retinal location of the luminous phenomenon) is a sensation, an entity of which we are not conscious. It would seem that Helmholtz invoked an unconscious inference to account for the “idea”-the externality of the appearance of light and its directionality-instead of the retinally localized luminous phenomenon. Although Barlow’s brief account of Helmholtz’s notion of “unconscious inference” is puzzling, it is evident that he shares Helmholtz’s assumption concerning retinal localization even though his language is not the

lated as “in our interior.” The critical portion of the first quotation would now read ”... objects of the phenomenal world ... depend upon processes in our interior, in the central nervous system ...” (The only translation of Kohler’s article appeared in English in 1971, some years after Kohler’s death.)

228

N.Pastore

same as Helmholtz’s. In alluding to the pressure phosphene, Barlow writes:

... one refers the excitation to the nasal field even when it is actually caused by mechanical pressure on the temporal retina. However to ”see” retinal stimulation in the position in the visual field that normally causes such excitation seems such a straightforward phenomenon that one is initially unwilling to attach much importance to it, let alone to call it an inference (Barlow, 1990, p. 1569). In this passage, Barlow supposes that excitation or equivalently stimulation is a localized retinal event. Furthermore, since excitation is presumed to be the starting point of a viewer’s unconscious inference, it can be regarded as a surrogate for Helmholtz’s ”luminous phenomenon at the place where the retina is stimulated.” A similar line of thought is evident when Barlow sets forth a ”syllogism” which is intended to describe the steps of unconscious thinking that result in the production of a percept. Under the caption ”Perception,” the syllogism reads: Major premiss Stimulation of the temporal retina always results from luminous objects in the nasal field Minor premiss The temporal retina is being stimulated Conclusion Therefore there is a luminous object in the nasal field (From Barlow, 1990, Table 1, p. 1569).

Barlow does not explain the meanings of the two premises and the conclusion of this syllogism, apparently leaving it to the reader to infer them. In any case, since the topic of the syllogism is a percept or ”Perception,” the role attributed to retinal stimulation in inferential thinking is more conspicuous than in my first quotation of Barlow. The minor premise relates to the mechanical pressure on the temporal side of an eyeball which produces stimulation at the temporal retina. The “luminous object” in the conclusion represents a conclusion the viewer infers on the basis of the mechanically-produced temporal retinal stimulation. The “luminous object” here corresponds to Helmholtz’s ”idea of a luminous phenomenon.” One problem with Barlow’s ”syllogism” is that it is not a syllogism. ”Luminous objects” in the major premise are physical objects emitting photons. On the other hand, #‘luminousobject” in the conclusion is a phenomenal datum (phosphene). Since the “luminous object” of the conclusion is not

Insideoutside Problem

229

included in the class of “luminous objects” of the major premise, Barlow’s purported “syllogism” in fact is a pseudo-syllogism.

REFERENCES BARLOW, H. (1990). Conditions for versatile learning, Helmholtz’s unconscious inference, and the task of perception. Vision Research, 30, 1561-1571. HELMHOLTZ, H. v. (1924). Treatise on physiological optics. 3 vols. J. P. C. Southall (Ed.). Rochester, NY: Optical Society of America. (Dover reprint, 1962.) HELMHOLTZ, H. v. (1971). The relation of the natural sciences to science in general. In R. KahI (Ed.), Selected wrifings of Herman von Helmholfz (pp. 122-143). Middletown, CT: Wesleyan University Press. (Editor’s substantial revision of H. W. Eve’s translation which appeared in 1873.) JAMES, W. (1890). The principles of psychology. 2 vols. New York: Holt. KOHLER, W. (1929). Ein altes Scheinproblem. Die Naturwissenschaften, 17,395-401. KOHLER, W. (1938). The place of values in a world of facts. New York: Liveright. KOHLER, W. (1947). Gestalt psychology. New York: Liveright. KOHLER, W. (1971a). An old pseudoproblem. In M. Henle (Ed.), The selected papers of Wolfgang Kohler (pp. 125-141). New York: Liveright. (Originally published in 1929, translated by Erich Goldmeier.) KOHLER, W. (1971b). A task for philosophers. In M. Henle (Ed.), The selected papers of Wolfgang Kohler (pp. 83-107). New York: Liveright. (Originally published in 1966.) PASTORE, N. (1978). Helmholtz on the projection or transfer of sensation. In P. K. Machamer & R. G. Turnbull (Eds.), Studies in perception (pp. 355-376). Columbus, OH: Ohio Sate University. SCHOPENHAUER, A. (1903). O n the fourfold root of the principle of sufficient reason and on the will in nature. London: Bell. Revised edition. (Translated by K. Hillebrand.)

This Page Intentionally Left Blank

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

231

PERCEPTUAL ARTIFACTS AND PHENOMENA: GIBSON’S ROLE IN THE 20TH CENTURY James E . Cutting Department of Psychology Cornell University, Ithaca, New York

ABSTRACT One of the most influential frameworks for the study of perception has been James J. Gibson’s ecological approach. This approach is not a theory, but a metatheory, of how we perceive and understand the world around us through our senses. As a metatheory it dissolves old problems and creates new ones, fostering new ways to think about perception and creating new antinomies to ponder. This essay outlines the successes of the approach, some of its new problems, and traces some of its more and less fruitful leads.

The ancient problem of space perception became my burden. It was worrisome, for, as I gradually came to realize, nothing of any practical value was known by psychologists about the perception of motion, or of locomotion in space, or of space itself (Gibson, 1967, p. 135). With this autobiographical statement James J. Gibson described the conundrum that faced him more than 25 years earlier, i n 1941, while serving in the Aviation Psychology Program of the United States Army Air Corps. Early optimism changed to disappointment as Gibson reflected on the practical applicability of nearly 100 years of research in perception. Why? Observers in typical perceptual experiments before (and indeed long after) Gibson’s lament could not do what people do everyday. They could not explore what they saw, and they could not act directly on the basis of

I. E. Cutting

232

what they saw. Such experimental viewing conditions often offer no environmental background to frame the stimuli, and no visible rationale for their motion; stimuli were disembodied without earthly context. Thus, Gibson quickly learned that the results of such scientific studies were not typically useful for understanding how pilots fly aircraft. Indeed, Gibson came to doubt if they were useful for any practical perceptual task and for the next 35 years proposed that a completely new psychology of perception was necessary.

”THE ANCIENT PROBLEM” Any “ancient problem” deserves respect. Such problems are well-worn, complex, broad, deep, and resist theoretical solution. Any contemporary theory of perception which proposes a solution to one of these will almost certainly fall well short of its goal. Rather than proposing solutions, then, Gibson proposed new ways of thinking about such problems. He created a metatheory. Not surprisingly, theoretical problems about perception remained but they were new problems, or at least new versions of old ones, and therein lay the fruitfulness of Gibson’s approach. The particular ancient problem impressed on Gibson by the war effort was the problem of “space perception” most generally, and ”depth perception” in particular. Its ancient configuration suggested to Gibson that psychological experiments were not alone in failing to address practical questions about perception, space, and depth. The received tradition in philosophy elaborated from the Greeks discussed the concept of space and how it was perceived: Since the retina of any eye is locally two-dimensional and since the world around us three-dimensional, space and depth must be reconstructed from fragments of information (typically called ”cues”) projected on the retina. The means of reconstruction might be learned, or they might be inborn. After grappling with it for many years, Gibson eventually found this traditional account confused and without practical merit: Psychologists were trying to apply the theory of depth perception to the problems of aviation, especially the problem of how a flier lands an airplane. Pilots were given tests for depth perception... The trouble was that none of these tests based on the cues for depth predicted the success or failure of a student pilot, and none of the proposals for improving depth perception by training made it any easier to learn to fly. I was deeply puzzled by this fact (Gibson, 1979, pp. 147,148).

233

NOT SPACE, DEPTH, AND CUES

BUT LAYOUT, SURFACES, AND THE OPTICAL ARRAY Gibson recognized he could not solve the problem of depth perception, so he chose not to try. Instead, he tried to dissolve it, showing its premises ill-conceived: The notion of space of three dimensions with three axes for Cartesian coordinates was a great convenience for mathematics... but [is] an abstraction that [has] very little to do with actual perception (Gibson, 1979, p. 148).

With a penchant for linguistic analysis of terms based on their meaning in everyday usage, Gibson noted that to speak of ”space perception” and ”depth perception” was loose talk. We do not see either space or depth. Space is an empty vessel and is invisible; thus, space itself could never be perceivable. And depth, but one mathematical dimension of space, is equally invisible and thus equally imperceivable. Rather than perceiving space or depth, according to Gibson, we perceive surfaces revealed to us by reflected light. The layout of the textures on those surfaces, their shading, and any coherent motion that may occur then specify the structure of the ground, the objects on it, and our position with respect to them. This layout is displayed in the optical array, the spherical projection of light to a point (at which an eye might be located). Thus, except for the occasional transparent object, light coming from any local region of the optical array comes from a single object at a single depth value. That patch of light represents ambient reflection from the object‘s surface, which is locally two-dimensional just as the retina is two-dimensional. The local orientation of a surface is typically different than the local orientation of the retina, and the difference in orientation gives rise to texture gradients, changes in the size, shape, and orientation of markings on the surface. This bold and new account of Gibson’s, however, has not dissolved all aspects of the ”ancient problem.” Because most objects are opaque and because light travels in straight lines, nearer objects often interpose themselves between the observer and the reflected light from farther objects. The layout of surfaces in the optical array then shows abrupt discontinuities where the edge of a nearer object ends and the revealed surface of the farther object begins. Thus, there are abrupt discontinuities of depth in the optical array. In the traditional account of perception the existence of interposition is called the cue of occlusion; in Gibson’s account it is called an ”occluding edge.” This is a case where terms have changed but the problem remains the same.

1.E. Cuffing

234

How do we perceive the amount of depth between an occluding edge and an occluded edge? Motion, particularly motion generated by the movement of the observer, may provide some information. Binocular parallax may provide yet more. But more simply perhaps this problem, too, is ill-posed. Perhaps when perceiving the layout of objects in depth we don't perceive metric relations. Perhaps we only perceive depth orderwhich object is nearer than another (Gibson, 1954a; see also Todd & Reichel, 1989). Perhaps perceiving depth is not about perceiving amounts of depth. Space and depth versus surface layout and occluding edges are examples the new ways of thinking Gibson gave us. Theoretical discussions of space, he would claim, led to little of practical value; theoretical discussions of layout, on the other hand, were proposed in the hope they would have considerable merit. And they have. In what other perceptual domains did Gibson have influence? And where have they led us?

BEYOND THE LEGACIES OF GIBSON Whereas Gibson's later work has profoundly shaped psychology, his earlier work did not. For example, in the field of perception it reacted to (Gibson, 1929), then provisionally accepted (Gibson & Crooks, 1938), but finally roundly rejected (Gibson, 1951, 1971b) central aspects of Gestalt psychology. Gibson also tinkered with phenomena in other research areas, such as adaptation effects (Gibson, 1933, 1937; Bergman & Gibson, 19591, learning theory (Gibson & Hudson, 19351, memory research (Gibson & Raffel, 19381, and even social psychology (Gibson, 1950a; see also Gibson, 1967; Reed, 1988). None of these works, however, had the impact of his later perceptual research, and none of his empirical work in perception had the impact of his metatheory. Called by some "our one original, irreplaceable creative genius" (Restle, 1980, p. 291) Gibson wrote in his later years with "strange authority, merely stating his position rather than marshaling experimental evidence" (Restle, 1980, p. 291). Gibson's "ecological approach is best captured by a relatively small cluster of ideas. Here I will focus on five: (1) the everyday surround, (2) functionalism, (3) exploration and the interrelation of perception and action, (4) information and its adequacy for perception, and (5) the difference between the perception of pictures and of objects in the everyday surround. Each of these ideas has been fruitful; each has led to new theoretical inconsistencies with which he and his followers grappled.

GWsLegacies

235

THE ECOLOGICAL WORLD OF PERCEPTION: WHAT IS THE NATURE OF ITS ECOLOGY? Control and Phenomena The essence of experimentation in any science is the control of independent variables in order to observe their effect on dependent variables. The essence of experimentation in perceptual psychology is the control of stimuli to observe their effects on what is perceived (see Cutting, 19914. But such control can create a metatheoretical tension, particularly in perceptual science. As Neisser (1976) effectively suggested, there was something odd about the stimuli typically found in the experiments of perceptual and cognitive psychology during the 30-year period after World War 11, and even the period before. Control became linked with brevity. Visual stimuli in particular were so brief they came ”very close to not existing at all” (Neisser, 1976, p. 35) much less being representative of the ,,serious business of perceiving the world” (Gibson, 1971, p. 31). Surely, pleaded Neisser, we cannot generalize to everyday perceptual phenomena from phenomena unrepresentative of what occurs outside the laboratory. Such a plea, however, was not new. Indeed Raymond Dodge, inventor of the modern tachistoscope, made a similar statement: I find that the tendency to reduce the physical exposure time to a minimum wherever the aim is to present an adequate exposure of the simplest kind is a methodological mistake, based on a psychophysical misconception. It introduces unusual conditions altogether foreign to the natural fixation pause and leads, or may well lead, to a distorted analysis of the processes of apprehension; making the conclusions, in so far as they are referred to normal perception, not merely valueless but false (Dodge, 1907, p. 32).

Dodge and Neisser thus warned us of a pernicious fact: Experimental control will always create perceptual phenomena. We must then always ask ourselves: Are these phenomena important? Can we be assured they are more than epiphenomena in our laboratories? If we cannot, what is their worth? Such questions are worth asking, but there is also a common retort: If we relinquish control how are we to study perception and still conduct fruitful experimental research?

Ecology and Control Gibson offered a way to avoid the horns of this dilemma. He suggested we start not with the concept of control, but with the phenomena of everyday perception in the natural environment. This theme was present in

236

1.E. Cutting

his work as early as in Gibson and Crooks (19381, but is perhaps broadest and clearest in Gibson (1966) where his presentation of the capabilities of all our senses focused on the needs and tasks common to us and our forebearers. It was from this appeal that Gibson fashioned his ecological approach to perception. With the help of powerful computers to generate complex, controlled stimuli (Cutting, 1991a), this approach has proven rich and empirically rigorous. The empirical foci of research embracing the ecological approach have focused many phenomena relatively new to the empirical study of perception: on information available when we move through the environment (e.g., Gibson, 1950b, 1958; then Lee, 1980; Warren, Morris, & Kalish, 1988; Cutting, 1986; Cutting, Springer, Braren, & Johnson, 19921, on the perception of events (e.g., Gibson, 1966; Gibson & Kaushall, 1973; then Cutting, 1981; Pittenger & Shaw, 1975; Warren & Shaw, 1985); on the perception of surfaces (e.g., Gibson, 1950c; then Cutting & Millard, 1984; Todd & Reichel, 1989) and the utility of their layout around us (Warren, 1984; Mark, 1987); and on manual exploration (e.g., Gibson, 1962; then Burton & Turvey, 1990; Barac-Cikoja & Turvey, 1991; Chan & Turvey, 1991). All these tasks areas seem fundamental and important, they seem “ecological,” and in no case has experimental control been sacrificed.

Which ecology? The underlying appeal of Gibson is to the ecology of the perceiver. But it is a particular ecology, deeply and fundamentally biological. Gibson was most concerned about natural environments, not carpentered worlds. Perceptual errors are seen to be relatively uncommon in the natural world because of the close-knit relation between perceptual systems and the environment they evolved within. To be sure, errors are thrust upon us occasionally, but they arise typically by dint of our technology (Gibson, 1979). Our inventions, such as large panes of glass, are omnipresent and can lead to serious injury if they are not treated properly. They are new, and did not constrain our evolution. Place glass over a small chasm and, as they should, even the youngest viewers become wary (E. J. Gibson & Walk, 1960). The biological underpinnings of ecology in Gibson’s ecological approach contrasts with an earlier idea. The ecology of Brunswik (1943, 19561, for example, is the surround of the perceiver. It is abiological, and based on personal experience molded by society. Perhaps at the end of the 1950s, with the rise of information processing and its disinterest in context, the two ecologies seemed closely allied. Today they seem less so. The best-known term capturing the appeal to everyday phenomena is ”ecological validity.” But interestingly, this phrase came from Brunswik

237 (1956), to whom it was given by Lewin (see Brunswik, 1943, pp. 259 n., 267 n.). Thus, the term was not originally Gibson's although it is now wholly attributed to, and appropriated by, those who follow the ecological approach. At issue in the 1990s, however, is that Gibson (1957, 1961) rejected Brunswik's ecology, but many of those who espouse the ecological approach have not. The issue at stake may be seen clearest in a comparison between Gibson (1979) and Neisser (1976). Despite similarities between these works and mutual acknowledgments by the authors, a stark contrast can be drawn. For Neisser, nothing would be more "ecological valid" than having a child sit in front of a television set; for Gibson, on the other hand, nothing would be less so. The television is an ever-present aspect of our 20th century environment, found in most homes in Western societies; but the television is also a technological device used to present cinematic sequences or series of pictures, about which I will say more later. For Gibson (1979) pictures, moving or otherwise, are not perceived "directly;" and we did not evolve to look at television. To be sure, evolution might be said to run in the reverse direction. There is a nontrivial sense in which televisions evolved to fit our visual systems. However, such a statement is inadequate as a solution to the problem. The geometric optics of televisions typically present to viewers not sitting directly in front of them a world which should be seen as containing no rigid objects (Cutting 1987,1988, 1991b). Yet, of course, rigidity is seen more or less as it is in the outside environment.

Two houses Ecos means "house," but when discussing ecology is it the house in which we evolved or the house which we have built? Therein lies a tension between in all appeals to the "natural" world. The general character if not underlying nature of the textures, the surfaces, the spaces, and the lighting in the two "houses" is quite different. In our manufactured surround the textures are much more regular, the surfaces much more planar or more regularly curved, the spaces much more "geometric," and the lighting more local, focal, and multidirectional than in our nonurban, outdoor surround. The problem of two (or even more) ecologies was recognized by Gibson, and recognized by those who follow the ecological approach (e.g., Michaels & Carello, 1981). Unfortunately, it is too often and too quickly dismissed: It is a mistake to separate the natural from the artificial as if there were two environments; artifacts have to be manufactured from natural substances. It is also a mistake to separate the cultural environment from

238

J. E. Cuffing the natural environment, as if there were a world of mental products distinct from the world of material objects. There is only one world, however diverse, and all animals live in it although we human animals have altered it to suit ourselves (Gibson, 1979, p. 130).

Such an answer does not suffice. The tension between the appeal to the two different ”houses” lies at the foundation of perception. If biology is to rule in perception-and clearly there is a very important sense in which it must-then evolution plays the major role of selecting the properties of our perceptual systems, presumably over millennia and even larger epochs. If culture is to rule, then humankind invents and manufactures what is seen over the course of a relatively few number of years, and evolution can play no role. To be more concrete, let me pervert Koffka’s famous question in two ways (Koffka, 1935; see also Gibson, 1971b; Cutting, 1991~).First, ”why do we see certain biological, geological, chemical, and meteorological things as we do?“ The answer can only be that our visual systems evolved in environments containing such objects and events, and the forces of evolution played upon these systems generally selecting out the properties needed for survival. Second, “why do we see architectural, technological, and graphical things as we do?” The answer here is much less clear. We did not evolve to see these objects. Although there must be some relation between the structure of this second class of entities and the structure of the first, that relation is unknown and certainly worthy of further study. But because this class of artifacts is “manufactured from natural substances” (Gibson, 1979, p. 130) does not guarantee we will perceive tokens of artifactual class in the way we perceive tokens of the natural class. Nevertheless, the appeal to nature, whether something that fashioned us or something that we fashion, has had deep an lasting impact on the field of perception. Moreover, the idea that the structure and function of visual systems are tightly fit to tasks they must do everyday has already been appropriated into other fields, particularly computer vision (Marr, 1981) in the form of “computational theories.” These are theories, not of computation per se, but about what needs to be computed. Everyday tasks seem to govern the selection of such theories. Indeed, some computational theories about extracting one’s movement vector during locomotion (Hildreth, 1992; Perrone, 1992) look like corresponding ecological theories (Warren et al., 1988). Thus, the ecological approach has been sufficiently fruitful that those espousing virtually no other tenets of Gibson often wind up following in his tracks.

GibsonSLeganes

239

FUNCTIONALISM, BIOLOGY, AND TECHNOLOGY AFFORDANCES AND THEIR CREATION Nowhere is the conflict between biological and cultural ecologies so clear as in the study of affordances. Affordances are a useful contrivance of Gibson’s, coined and modified by him from Lewin’s notion of Aufforderungscharakter (Gibson, 1979, p. 138). Most simply, affordances are offerings of potential actions-picking up, grasping, shaking, eatingwhich perceivers can carry out with objects (seealso Turvey, 1992). They are also the functionalist core of the ecological approach. Affordances are readily perceived (Gibson, 1979).For example, one can readily see that a small stone is throwable and, upon hefting it, one can tell how far it might be thrown (Bingham, Schmidt, & Rosenblum, 1989); one can see that a surface whose height is between one’s knees and one’s hips is sit-on-able (Mark, 1987); and one can see that a vertically uniform aperture a bit wider than one’s shoulders is pass-through-able (Warren & Whang, 1987). But plainly one can also see that a piece of paper affords a nearly uncountable number of actions (Cutting, 1982), as I will discuss later; and that the handles on most doors afford opening, but in many modem buildings they occasionally afford only confusion and bewilderment (Norman, 1988,1992).’ Modern technological objects are either multiply affording or they afford things that didn’t exist before; indeed, one can say the driving force of invention is to increase the number of affordances around us. There is a deep and important sense in which the concept of affordance is more applicable to artifacts than to natural kinds. Moreover, I predict that future systematic study of affordances is likely to create further rift between the two ecologies-the biological and the cultural-within the ecological approach. But such a tension only highlights the fruitfulness of the overall approach; it leads researchers and theorists to new venues with new ideas and to encounter new problems.

Norman’s (1988, p. 219) account of the biological/cultural conflict in affordances is particularly telling: The notion of affordance and the insights it provides originated with J. J. Gibson... I believe that affordances result from the mental interpretation of things, based on OUT past knowledge and experience applied to our perception of things about us. My view is somewhat in conflict with the views of many Cibsonian psychologists, but this internal debate within modem psychology is of little relevance here.

Thus, for Gibson affordances have a biological origin, for Norman they have a cultural one.

1.E. Cutting

240

PERCEPTION AND ACTION ISN’T THERE SOMETHING MORE TO PERCEPTION THAN WHAT OCCURS IN EXPLORATION? Another pre-eminent theme in Gibson’s work concerns the relation between perception and action. In essence, according to Gibson, we perceive things which offer action, that action allows us to perceive anew, we act again, and so forth. This idea was apparent in Gibson (1950b), but systematically broached only later (Gibson, 1958) when it then became a central theme in all his later works (Gibson, 1966,1979). The past decade of research has shown stunning examples of the relation between perception and action. For example, based on visual information adjustments in grasping and hitting continue to be made in the last 100 msec before contact with a ball (Bootsma & van Wieringen, 1990; Savelsberg, Whiting, & Bootsma, 1992; see also Watts & Bahill, 1990). There have also been examples of perceptual abilities exquisitely yoked to requirements dictated by moving through the environment (Cutting et al., 1992), and perceptual judgments seemingly dictated by rules and physics of motor production (Viviani & Stucchi, 1992). The coupling of certain aspects of visual perception and action is compelling. This marriage is consummated in exploration, which the ecological approach takes as its paradigm case. We perceive things of interest; we then move our heads and eyes, which changes the information available to us; we then often approach objects, bringing us new information; we then frequently grasp objects and turn them, which brings yet more information; and so forth. This is a perception-action cycle of great persuasiveness (Neisser, 1976). Each act is performed uniquely according to the situation, and the flow and sequence of perception is guided uniquely by these acts.

Divorcing perception and action Nonetheless, to focus exclusively on where there is a tight relation between perception and action is to lose sight of many perceptual and cognitive abilities researchers ought to study. Outside the case of exploration perception-action couplings may be few, and there is quite a lot in the ”serious business” of perception (Gibson, 1971, p. 31) which is not exploration. Listening and reading, for example, are two perceptual skills with little if any need for overt action. This is true despite the fact that arguably the closest linkage between perception and motor control might be said to occur in them. Speech perception, in particular, is domain with many variants of motor theories of perception (e.g., Liberman & Mattingly,

Gibson's Legacies

241

1985). Nonetheless, one can learn and understand speech, and even read, without the ability to talk (Lenneberg, 1962). Moreover, the ability to read print need not entail any action. Although the alternations of saccades and fixations during reading look like a perception/action coupling, it is clear that, if the necessity of saccades is removed by rapidly presenting strings of words in succession at the same place on a computer display, then reading becomes even faster. These saccadic acts may make normal reading possible, but they are basically only a mechanical convenience; reading is better, faster, and more engrossing when saccades are not needed? Moreover, the lack of perception-action coupling is not confined to language sources. For example, olfactory stimulation depends on breathing and sniffing (Halpern, 1983), but the act of sniffing is relatively stereotypic and does not differentiate what will be smelled. Similarly, although the taste of liquids is modulated by sips to keep adaptation from occurring, sips are essentially alike yet the tastes of the liquids different. In both modalities action makes perceptions occur, but the actions are not linked to specific perceptions they are only linked to perceiving of any kind. Such a linkage is not particularly compelling. Perhaps the most important nonvisual arena for discussion of perception and action occurs with "active t o u c h (Gibson, 1962, later called haptic exploration (Gibson, 1966). Gibson (1962) reported that active exploration of various cookie-cu tter shapes yielded identification results superior to passive exploration (having someone else move your hand over the objects). Indeed, this study has been cited as among the twenty most important experiments in the history of science (Harrb, 1981). However, the superiority of active over passive touch has not universally been found (see Appelle, 1991); indeed, it may not exist when proper controls are included. What should be clear, then, is that perception and action sometimes come together in exquisite ways. However, outside the domain of overt exploration the two do not seem to be as closely linked as Gibson would have us believe. Moreover, to study perception in the absence of action is by no means an empty pursuit. And to study perception exclusively in the context of action runs the risk of missing important aspects of sensory qualities (e.g., color, tone, taste, odor, temperature, pain), whose discussion has dominated the history of perception.

The technique is often called RSVP (rapid serial visual presentation).When one presents a succession of a small series of words in a story at fixation such that saccades are not needed, and give the reader control over the rate of presentation, that reader can (without practice) read faster than he or she does normally (Michael Kubovy, personal communication;see also Potter, Kroll, & Hams, 1979).

242

1.E. Cutting

ADEQUACY AND NUMBER OF INFORMATION SOURCES: SPECIFICATION AND INVARIANTS Gibson’s notion of information was new; it was not Shannon and Weaver’s (1949) measured in bits, and it had no relation to the number of alternative possibilities implied by the existence of an object (Garner, 1962; see also Cutting, 1986b, 1991~).Gibson’s information is information about objects and events (Gibson, 1966), and in vision it is typically measured in the geometry of projections in the optical array. Throughout his later career Gibson worked with the idea that information specified what was to be perceived. Information, according to Gibson, doesn’t typically lie; all a perceiver need do for accurate perception is attend to a pertinent object or event, and pick up the appropriate information available in the optical array. This logical gambit was an important counter to Plato, Aristotle, and most subsequent thinkers. Contrary to centuries of thought, Gibson felt the perceptual senses could be trusted and relied upon. The traditional argument in philosophy-the argument from illusion (if the senses can be deceived, how do we know they do not always deceive us?)-was considered desperately wrong by Gibson. In its place he presented a new biological pragmatism-what I call the arguinent from evolution (if the senses were deceived too frequently, we would have surely become extinct long ago). The trustworthiness of perception for Gibson is built upon information available to the perceiver. Since the typical variables of sensation and psychophysics yielded results that were not sufficiently trustworthy, higher-order variables were then thought to be the carriers of information. These higher-order variables were first gradients (Gibson, 1950), then invariants (e.g., Gibson, 1961), and later even complexes of invariants (Gibson, 1979). Gradients are unidimensional measures (or maps; Cutting, 1984; Stevens, 1984)taken on projections of objects or textures lying on a surface which reflect the change in their orientation with respect to a particular viewpoint; invariants are measures taken on optical projections of objects which do not change with viewpoint; invariant complexes may often turn out to be affordances.

Specifiers: Many or One? When information is a specifier of an object or event, that information is said to predict (more or less) completely what ought to be perceived by an alert and attention-paying perceiver. But as Gibson passed from being a global psychophysicist interested in geometric projections of the world’s surfaces (Gibson, 1950c, 1954a, 1959) to an ecological psychologist interested in the properties in ecological optics (Gibson, 1961, 1966, 19701,

Gibson’sLegacies

243

there was a systematic change in his outlook on the nature of information. Specification remained, but an earlier pluralism gave way to monism. Gibson as a global psychophysicist felt the information in the world was rich and it multiply specified what to be perceived. For example: The [psychophysicall hypothesis does not assert that there is only one variable of the energy flux with which a given phenomenal variable is in correspondence. Two or more variables of stimulation can yield the same quality of experience (Gibson, 1959, p. 466)

and Under optimal conditions of illumination there is generally more than enough information for perception-it is redundant (Gibson, 1960a, p. 30).

Gibson as an ecological psychologist appeared to give up on this idea and promote a theory of perception in which there was only one source of information, typically a ”higher-order” source, which specified each object, event, or property thereof. For example: The specific hypothesis is that the invariant component in a transformation carries information about an object and that the variant component carries other information entirely, for example, about the relation of the perceiver to the object (Gibson, 1965, p. 68).

Note the articles and implied singularity throughout. Indeed, those following the ecological approach have generally embraced these singularities, or one-to-one mappings; one source of information is said to specify each object or event that is to be perceived (e.g., Burton & Turvey, 1990; Stoffregen, 1990). The major problem with the notion of one-to-one mappings between information and object/event properties is that information appears to be richer than the later Gibson would have us believe. Indeed, there are even cases where more than one invariant can be shown to exist-for a moving plane, the cross ratio of four coplanar parallel lines and the yoked velocities in optical flow-and yet an observer can be shown to use the former when a stimulus rotates and the latter when it translates (Cutting, 1986b). Moreover, even where invariants may not exist, other simultaneously existing sources may convey differing information. In the case of texture gradients, for example, the relative size gradient and the density gradient of texture elements seem to be good sources of information about surface

244

J. E. Cutting

planarity but not of curvature, yet a compression (or foreshortening) gradient in the same stimulus is a good source of information about surface curvature but not of planarity (Cutting & Millard, 1984). Thus, information-whether invariant or otherwise-is overly rich and available for observers to use at various times and occasions for various tasks. In summary, the safest conclusion concerning specification is that information may, or it may not, specify what is to be perceived (Cutting, 1991a, 199113. The specifying power of information depends entirely on the circumstances under which perception takes place. If the presentation of objects is degraded by the psychologist or by nature (as in extreme daytime haziness or in any nighttime viewing), measurable information may indeed not specify what is to be seen and cognition may have a heavy hand in perception; if object presentation is not degraded, then cognition may have little role, but the observer must then combine or select various sources of information prudent to the situation (Cutting, 1986b). But what is the role of invariants?

Can invariants account for perception? The notion that perception is guided by invariants is not new. The idea that a mathematical group of displacements reveals the invariant structure of what has been displaced can be found in Helmholtz (1878, p. 3841, Poincar6 (1905), Cassirer (1944), and more recently in Palmer (1991) and Leyton (1992). But these earlier and later works focus on the displacements (or transformations) rather than on the invariants themselves. Gibson’s contribution was his focus on invariants as they are revealed by transformations. There have been several critiques of the concept of invariant as borrowed from mathematics and used by Gibson (e.g., Ullman, 1980; Cutting, 1986b). When bruted about too loosely, invariants lose power and meaning-such as when Gibson (1979, p. 271) wrote of the ”invariant cat,” which is apparently the higher-order information which specifies a cat. Given the potential of such broad emptiness it seems safest, then, to try to stay as close to the mathematical origins of the term as is possible, and when possible look to projective geometry for help (Cutting, 1986b). Within this stringency, however, invariants then appear to become too few to guide perception. My own view of the global effectiveness of invariants in their ability to account for perception has changed markedly. After spending the better part of 15 years in their active search, my view is that invariants for perception exist, but they are atypical perceptual information. I have found effective invariants for the perception of human gait (Cutting, Proffitt, & Kozlowski, 1977; Cutting, 1978a); for the perception

GibsonSLqpcies

245

of relative smoothness of rolling wheels (Proffitt, Cutting, & Stier, 1979; Cutting & Proffitt, 1982); for the perception of appropriate aging in a human face (Cutting, 1978b; see also Pittenger & Shaw, 1975); for the perception of one’s direction of heading during locomotion (Cutting et al., 1992); for the perception of rigid planarity (Cutting, 1986b); and I have also discussed several other invariants found by others (Cutting, 1986aL3 But the search for useful invariants has been hard work and, after quite a long period of time, the ground that has been worked appears not overly fertile. It seems likely that the number of useful invariants isolated since Gibson first espoused them (Gibson, 1950, p. 15311) probably number less than two or three dozen. Thus, although invariants worth the mathematical name do exist for perceptual systems to use, the slow pace at which they have been uncovered suggests that invariants might be relatively rare. Moreover, they are surely too few for perception to operate by invariants alone. In summary, then, there is great utility in Gibson’s concepts of information and specification for perceptual psychology. Nonetheless, the notions of one-to-one mappings and of invariants may not be a part of the same long-lived theoretical armamentarium. The search for invariants has been sufficiently fruitful to warrant continued interest in them: but the results of this search also warrant skepticism about their overall utility.

PAPER, PICTURES, AND REALITY Humankind’s most deeply troubling invention is the flat sheet of paper (or, more adequately, its predecessors). From the perspective of the ecological approach, the affordances of paper are legion. As I once suggested: A piece of paper affords equally writing gibberish and sonnets; it affords writing a shopping list or a note to a colleague; it affords making a map; it affords writing nothing upon; it affords wadding up and throwing away; it affords making paper airplanes; it affords shredding, cutting into pieces...; it quite simply affords all the possible things I can do with it. My behavior is virtually unconstrained by its affordances. To be sure, it does not afford flying to Baghdad upon, but the exclusion of a More recently, Niall and Macnamara (1989, 1990; Niall, 1992) have documented the Y p t u a l nonuse of various invariants from projective geometry. The idea of invariants has become so popular in late 20th century visual science that it now seems possible to have a large book on invariants for machine vision barely mentioning Gibson’s work or name (Mundy & Zisserman, 1992).

J.E. Cutting

246

large domain of behaviors does not diminish the fact that an infinity remain (Cutting, 1982, p. 216).

For the theoretical study of perception, the most problematic aspect of paper is that marks can be made on it; these “fundamental graphic acts” (Gibson, 1979) create pictures. The problem is that although pictures lie flat on the sheet of paper and thus are two-dimensional, through the increasing craft of the artist they can be made to look like a three-dimensional world. Most of the history of perceptual psychology has been devoted, advertently or not, to the study of static pictures presented in tachistoscopes, on sheets of paper, or on computer screens. For those who follow the ecological approach such pictures remain interesting (e.g., Rosenblum, SaldaAa, & Carello, 1993) but their perception is thought overwhelmingly nonrepresentative of our perceptions everyday. Pictures are interesting precisely because they are perceived differently than the everyday objects around us which we evolved to see (Gibson, 1979). Gibson was continually interested in pictures throughout his career. Moreover, he had at least three different theories of picture perception (Gibson, 1954b vs Gibson, 1960b vs Gibson 1971a, 1978). The first embraced the idea of “fidelity” and, in more modern terms, would effectively try to measure the differences pixel-region-by-corresponding-optical-array-region between an image and the reality to which it corresponded. This idea has merit, but fails in the face of caricature and nonrepresentational art. The second theory kept the idea of fidelity, but concentrated on edges and contrast rather than on intensities. The original problems remained. The third embraced “formless” invariants of structure in attempt to account for pictures with and without fidelity.

Restrictions on pictorial invariants Unfortunately, with respect to this last theory of Gibson’s, it is difficult to find invariants in a medium where there can be no transformations. Gibson (1978, p. 228) acknowledged this problem but pressed on. Moreover, he claimed invariants in pictures were “weaker” but were everywhere, specifying everything seen, with no contribution of the perceiver to be made in act of perception except information pickup: I have argued that a Rorschach blot is a picture of sorts containing not only bleeding hearts and dancing bears but dozens of other events. It is different from a regular picture in that the invariants are all mixed up together and are mutually discrepant, instead of being mutually consistent or redundant (Gibson, 1978, p. 232).

Gibsons~!qacki

247

All this seems unlikely; it is Gibson speaking with his ”strange authority” (Restle, 1980, p. 291). However, there is at least one construal of notion of invariants which is appropriate to pictures. Consider the case of a picture of a textured surface. Texture is composed of texture elements and, by definition, each texture element is more or less the same in shape, size, coloration, and so forth. If we consider the aggregation of texture elements on a surface to be identical to one another, but transformed by displacement and rotation through space while adhering to the surface, then each texture token represents a different view of the same texture type. These displacements and rotations form a group, and the invariant structure of the single texture is revealed; moving logically in the reverse direction, the transformations of the single texture then reveal the shape of the surface. The problem for the notion of pictorial invariants, however, is that other than texture and similar repeating elements in pictures, the term would seem to be an oxymoron.

Direct and indirect perception I claim that Gibson’s theories of picture perception were a driving force behind his broader theories. For example, Gibson discussed his concept of direct perception in the context of picture perception (Gibson, 1954b),long before he discussed it in the context of everyday perception (Gibson, 1972, 1973). Much has been written about direct perception (Cutting, 1986b; Michaels & Carello, 1981; Ullman, 19791, perhaps too much (Hochberg, 19901, so only a capsule summary will be given here. Gibson’s earliest theory of picture perception (Gibson, 1954b, p. 3) began with a discussion of ”experiencing at first hand” (observing the world) and ”experiencing at second hand” (looking at pictures). The first was called direct; the second indirect. The more faithful the picture could be made to reality, the closer the two became. Thus, the more the picture looked like a real segment of the environment the more direct was its perception. Such a statement implies a continuum between the two types of perception. Gibson (1960b) later gave up on “first- and second-handedness” and on the idea of a continuum between pictures and reality, but he always maintained that pictures were perceived indirectly, reality directly: ”Direct perception is what one gets from seeing Niagara Falls, say, as distinguished from seeing a picture of it” (Gibson, 1979, p. 147). Indirect perception was mediated by devices (like cameras and telescopes); direct perception was not (even by glasses). Such a distinction creates confusion and Gibson’s followers have debated whether picture perception should be considered direct or indirect (Michaels & Carello, 1981).

1.E. Cuffing

248

But as the term direct perception became applied to the perception of the natural environment it came to imply other meanings and created further confusion. Part of the problem with the use of the term direct perception is that Gibson borrowed it from the philosophy of perception without acknowledging its rich 250-year history. Instead, he cited only one source (Austin, 1962). Cutting (1986b) detailed eight different, older meanings of the term, each with a long history. On top of this melange, Gibson created a new meaning: Direct perception occurred when perceptual information was adequate and specified what could be perceived, which I have discussed earlier. For my part, Gibson’s last theory of picture perception is, to use one of his own favorite expressions, a muddle. He resisted the discussion and use of pictorial cues in perception, which are useful, many, and could even be said to have the power to “specify” what can be perceived; he was later wedded to one-to-one mappings between information and objects seen, embracing singular invariants and further negating the manifold of cues; and he pressed for the theoretical use of invariants in a medium that allowed no change. From his early theories of picture perception he then foisted upon us a term of deep confusion and polysemy, direct perception. Picture perception is thus a central part of the ecological approach, but also probably its most flawed and has proven least fruitful. Since some central concepts of the ecological approach seem to work least well in the domain of pictures and since some of its more general concepts originated in the pictorial domain, one could legitimately wonder about the integrity of the whole enterprise.

CONCLUSION That now obvious rite of passage from global psychophysicist to ecological psychologist produced Gibson’s metatheory, a system for appreciating and for thinking about the problems of perception. As a metatheory it has been extremely fruitful where it has been applied, but this fruitfulness cannot hide the incongruities and inconsistencies that remain. We have an appreciation for the role of evolution in shaping our perceptual capacities; we now have a small set of invariants and another cluster of affordances both of which seem sensible and rigorously studied; we can appreciate that perception and action often go together, often elegantly in the context of games or of exploration; and we do distinguish between reality and pictures of reality. However, we do not know how to understand and intermix the biological and cultural ecologies which underlie perception; we do not yet know where the study of affordances will lead

GWslqam

249

us; we still have not recognized the costs of studying perception solely in the context of action and exploration; and we need to assess the full utility of perceptual information and the role that invariants, gradients, and other sources of information play. Acknowledgment. Supported by National Science Foundation Grant DBS 92-12786 to James E. Cutting. This essay is based, in part, on a talk given at a symposium organized by Julian Hochberg entitled “Perceptual theories at the end of the 20th century” given at the 25th International Congress of Psychology in Brussels, July 1992. I thank Nan E. Karwan for her interest, encouragement, instigations and for many discussions of the ideas presented here; and thank Paul Braren, Matthew Cornillon, David Field, James Fu, Beena Khurana, Daniel Levin, Daniel Simons, Peter Vishton for their comments on a draft of this paper.

DISCUSSION Sergio C. Masin (Department of General Psychology, University of Padua, Padua, Italy): According to Cutting’s fine analysis, J. J. Gibson’s ecological approach shows “incongruities and inconsistencies,” and one could even ”legitimately wonder about the integrity of the whole [Gibson] enterprise” (p. 248h5 Cutting’s analysis provides the opportunity to examine the possible reasons for the decline of a modem perceptual ”metatheory.” Although there may be particular reasons why theories or metatheories are destined to fail, it is possible that Gibson’s approach shares some common fundamental problem with other past theories or metatheories. I think it would be most interesting and important if some of these problems were elucidated here. To contribute to this discussion I offer my own opinion on this matter. I think that the basic reason for the decline of Gibson’s metatheory is his implicit adoption of the naive-realist view of reality. This view is best illustrated in Gibson’s notion of the “optical array,” this being the ”spherical projection of light to a point.” Using Cutting’s words, according to Gibson “light coming from any local region of the optical array comes from a single object at a single depth value” (p. 233) and ”... most objects Undoubtedly, Gibson greatly contributed to the advancement of perceptual science. For example, he developed the important notion of “invariant,” which is central in his approach. However, Gibson’s approach seems weak also on this point. Cutting concludes that ”The search for invariants has been sufficiently fruitful to warrant continued interest in them, but the results of this search also warrant skepticism about their overall utility” (p. 245). This conclusion is particularly important because it comes from an expert perceptual scientist who devoted “the better part of 15 years” to this search.

250

I. E. Cutting

are opaque and because light travels in straight lines, nearer objects often interpose themselves between the observer and the reflected light from farther objects. The layout of surfaces in the optical array then shows abrupt discontinuities where the edge of a nearer object ends and the revealed surface of the farther object begins” (p. 233) (emphasis added). There are three possibilities: in these statements ”light” means (1 something that we see (2) something fictitious (3) the well-known physical concept. Possibility 1 is false because we do not see light traveling ”in straight lines.” Gibson was too fine an observer to believe that this possibility was true. Possibility 2 means that ”light” is something imagined and without any physical effect. Gibson cannot have meant this because he believed that objects may stop light reflected by other objects. Then, it remains that Gibson used ”light” in the usual physical sense. But this usage in the above statements implies the belief that seen objects reflect or emit photons. This belief reveals that Gibson implicitly adopted the naive-realist view of reality. There are at least six logical arguments showing that seen objects do not reflect or emit photons (see p. 53, this volume). Therefore, the naive-realist view is wrong. In my opinion, the naive-realist view of reality should be banned from perceptual science both because it is wrong and because it has the detrimental effect of diverting the attention of perceptual researchers from the basic objective of their science. In fact, by considering seen objects as entities that reflect light, these objects tend to be (wrongly) considered as entities pertaining to the physical domain and therefore with no need of an explanation on the part of the perceptual scientist. To reiterate, although often governed by physical laws, seen objects do not pertain to the physical domain because in no case do they comprise elementary particles or reflect or emit photons. Thus, contrary to what is implied by the naiverealist view, explaining why and in which conditions seen objects occur is a fundamental objective of perceptual science. I think that a theory or metatheory that distracts from this objective is doomed to failure. Cutting: Let me make two points in response. First, and more quickly, my analysis questions the coherence of Gibson’s metatheory but it does not question its fruitfulness for psychology. Indeed, I believe coherence is often overemphasized as a design feature of theories: many physicists doubt the coherence of quantum electrodynamics and many biologists doubt the coherence of nonsaltationist theories of evolution. Nonetheless, the former remains a fruitful basis of prediction for certain microphysical phenomena and the latter a fruitful framework for understanding most of the diversity in life. In a roughly similar vein Gibson’s ecological approach has been fruitful, not only because of an emphasis on invariants

GibsonsLegacres

251

(which Masin acknowledges), but more broadly because of its general emphasis on the study of everyday phenomena and their importance to perception, on the global sources of information which specify objects and events which populate everyday perception, and on its rejection of traditional approaches to perception based on sensation. Moreover, it is not at all clear, as in implied by Masin, that Gibson’s metatheory is in decline. Indeed, Hochberg (1990) even describes it as a majority view. Second, and in much more detail, let me address the important issue of Gibson and naive realism. Russell (1940, p. 14) defined naive realism as “the doctrine that things are what they seem;” Kohler (1938, p. 405) defined it as ”the identification of percepts with physical things.” Both of these definitions seem consistent with Masin’s usage. As I understand his argument, Masin’s rejection of naive realism is similar to Russell’s (1940, p. 15): ”Naive realism leads to physics, and physics, if true, shows that naive realism is false. Therefore naive realism, if true, is false; therefore it is false.” Naive realism is usually contrasted with critical realism (or indirect realism), in which care is taken to dissociate the phenomenal world from the physical world. It is often said that in the commerce of negotiating everyday life even the most skeptical scientist is a naive realist-it is most practical to be so-but that in his or her research he or she must be a critical (indirect) realist. I assume Masin (the scientist) is a critical realist and would argue that the ”basic objective” of perceptual science is that of traditional psychophysics: We must observe the mappings between the phenomenal and physical worlds. Before Gibson, this was the prototypic epistemological position for a perceptual psychologist. Gibson tried to forge something new, and with mixed success. Gibson’s relationship with naive realism was complex, and is perhaps best captured by Henle (1974), some of whose arguments I will follow. As an introduction, however, let me say that Masin is partly right: Gibson embraced certain aspects of naive realism (Gibson, 1967b), but he also rejected other aspects of it (Gibson, 1971b). Gibson also rejected critical realism, and the error of ”concluding that we can know nothing but our perceptions... Once having made this argument, a theorist is trapped in a circle of subjectivism and is diverted into futile speculations about private worlds” (Gibson, 1959, pp. 462-46311). Instead, Gibson embraced levels of ’privacy’ in perception. All observers can obtain exactly the same information about a tree if they all walk around it and get the same perspectives. Each observer gets a somewhat different set of perspectives of his own hands than any other observer gets, although there is much in common. But the perspective of one’s own nose is

252

I. E. Cuffing obviously unique and no one else can ever see it from that particular point of view ... The tree, the hand, the nose, are increasingly private (Gibson, 1967b, p. 171).

Thus, Gibson maintained that most of perceived world around us is objective and that conspecific perceivers can generally share percepts about that world. But Gibson was not as ”naive” a realist as one might think. For example, One might conceive that the stimulus for motion is simply motion. But this would be a serious misconception... The displacement of a body in space is mapped not as a displacement of a figure in an empty visual field, but as a figural transformation (Gibson, 1966, p. 203). Thus, phenomenal objects and events can be said to be less closely identified with physical objects and events than they are with the information about those objects and events, and information about their transformations. Such information supports perception, and occasionally it can lie about the true states of physical affairs (Gibson, 1979). But information does not typically lie; instead, it much more typically specifies what should be perceived. Information is generally trustworthy, and thus perception is generally trustworthy. In keeping with his analyses from the everyday meanings of words, Gibson both embraced, and tried to escape from, naive realism. His approach was to use the following linguistic duality: We perceive objects and events in the physical world around us, but our perceptual systems pick u p information about the world in the form of invariants, gradients, and other higher-order variables. In this manner, and going beyond Henle (19741, one might say that Gibson was a naive realist when talking about the facts of perception, but a critical realist when talking about the basis of perception. Such a stance attempts to preserve the adequacy of everyday language when discussing perception, but also attempts to preserve the scientific enterprise in determining its basis. Gibson (1972, 1979) called this position direct realism, in contrast to both naive realism and critical realism. It tries to avoid the patent errors of naive realism, so clearly noted by Masin, and also the encapsulating subjectivism of critical realism. It remains a duality, but it is not a Cartesian duality; it is a duality of discourse. Percepts, objects, and events on the one hand, and information and its pick up on the other, are all objective, but objective at different levels. In placing Gibson within the fold of naive realism, Masin provided a short analysis of the psychology of light. As possible meanings inherent in Gibson, Masin correctly rejects the ideas that we ”see” light (we don’t,

GibsdsLqyck

253

we see objects and events) or that light is ”something imagined and without any physical effect’’ (p. 250). By method of residues, Masin than correctly assumes that Gibson used the concept of light in the standard physical sense. But Masin then argues that this stance ”implies the belief that seen objects reflect or emit photons” (p. 250). Such a statement is a Rylean category error: it mixes levels of analysis which Gibson worked hard to separate. Photons are no more (or less) real than objects and events: they simply exist at a different level of reality. Moreover, psychologists need not try to understand physical objects in terms of photons any more than metereologists need try to understand thunderstorms in terms of electrons, or economists need to understand monetary exchange in terms of the chemical composition of coins and paper, despite the fact that all are equally ”real.” Seen objects are things we perceive, and exist at one level of discourse with an adequate language to describe them; photons are part of the metaphysical substructure of reality which physics tells us is sufficiently convenient for understanding matter, and exist at a completely different level. Thus, Gibson would claim that the perceptual psychologist’s task is not that of traditional psychophysics. It is not to discern the correspondences between physical dimensions and psychological dimensions (which are traditionally almost always dimensions of sensation). This approach is wrong according to Gibson because perception is not based on sensation. Instead, the perceptual psychologist’s task is to understand and to measure the nature of the information in the world which supports perception. This approach to perception entails two stages in perceptual research, although they are not always equally acknowledged by the followers of Gibson. One must first isolate candidate sources of information which lawfully correspond to a given object or event (always acknowledged in the ecological approach); one must then adequately demonstrate that this candidate information is used in perception (sometimes omitted from researchers based on the ecological approach). The latter is necessary because, as I noted in this chapter, it is not clear that more than one source of information may exist for a given object and event and that information use may be context sensitive. Moreover and more simply, perceptual information is not information unless it is used by perceivers in at least one demonstrable context.

Masin: I feel I have to repond to Cutting on two points. The first is that I did not mix levels of analysis--”a Rylean category error.” Cutting attributes an error to me that I impute to Gibson. It is Gibson who mixed

J.E. Cuffing

254

levels of analysis, not me. The second minor point concerns Cutting’s arbitrary assumption that I am a critical realist. The perceptual approach that I present in this volume rejects all the above mentioned kinds of realism. Cutting: Ah! One must be careful with any modifications of realism. Espousing realism in the study of perception allows the scientist and philosopher commerce with discussions of, and connections to, biology. It also allows the formulation of an understanding of perceptual solutions to tasks performed in a biologically relevant context. The more the form of one’s realism is modified, the more one’s discussion of perception becomes removed from both biology and from everyday life.

REFERENCES APPELLE, S. (1991). Haptic perception of form: Activity and stimulus attributes. In M. A. Heller & W. Schiff (Eds.), The psychology of touch (pp. 168-188). Hillsdale, NJ: Erlbaum. AUSTIN, J. L. (1962). Sense and sensibilia. Oxford: Oxford University Press. BARAC-CIKOJA, D. & TURVEY, M. T. (1991). Perceiving aperture size by striking. Journal of Experimental Psychology: Human Perception and Performance, 17, 330-346. BERGMAN, R. & GIBSON, J. J. (1959). The negative after-effect of the perception of a surface slanted in the third dimension. American Journal of Psychology, 72, 364-374. BINGHAM, G. P., SCHMIDT, R. C., & ROSENBLUM, L. D. (1989). Hefting for a maximum distance throw: A smart perceptual mechanism. Journal of Experimental Psychology: Human Perception and Performance, 15, 507-528. BOOTSMA, R. J. & VAN WIEIUNGEN, P. C. W. (1990). Timing an attacking forehand drive in table tennis. Journal of Experimental Psychology: Human Perception and Performance, 16, 21-29. BRUNSWIK, E. (1943). Organismic achievement and environmental probability. Psychological Review, 50, 255-272. BRUNSWIK, E. (1956). Perception and the representative design of psychological experiments. Berkeley, CA: University of California Press. BURTON, G. & TURVEY, M. T. (1990). Perceiving the lengths of rods that are held but not wielded. Ecological Psychology, 2, 295-324. CASSIRER, E. (1944). The concept of group and the theory of perception. Philosophy and Phenomenological Research, 5, 1-35.

CHAN, T.-C. & TURVEY, M. T. (1991). Perceiving the vertical distances of surfaces by means of a hand-held probe. Iournal of Experimental Psychology: Human Perception and Performance, 17, 347-358. CUTTING, J. E. (1978a). Generation of synthetic male and female walkers through manipulation of a biomechanical invariant. Perception, 7, 393-405. CUTTING, J. E. (1978b). Perceiving the geometry of age in a human face. Perception & Psychophysics, 24, 566-568 CUTTING, J. E. (1981). Six tenets for event perception. Cognition, 10, 7178. CUTTING, J. E. (1982). Two ecological perspectives: Gibson vs. Shaw and Turvey. American Iournal of Psychology, 95, 199-222. CUTTING, J. E. (1984). Reflections on surfaces: A cross-disciplinary reply to Stevens. Journal of Experimental Psychology: General, 113, 221-224. CUTTING, J. E. (1986a). Perceiving and recovering structure from events. In N. I. Badler & J. K. Tsotsos (Eds.), Motion: Representation and perception (pp. 141-147). New York North Holland. CUTTING, J. E. (1986b). Perception with an eye for motion. Cambridge, MA: MIT PresdBradford Books. CUTTING, J. E. (1987). Rigidity in cinema seen from the front row, side aisle. Journal of Experimental Psychology: Human Perception and Performance, 13, 323-334. CUTTING, J. E. (1988). Affine distortions of pictorial space: Some predictions for Goldstein (1987) that La Gournerie (1859) might have made.

Iournal of Experimental Psychology: Human Perception and Performance, 14, 305-311. CUTTING, J. E. (1991a). Four ways to reject directed perception. Ecological Psychology, 3, 25-34. CUTTING, J.E. (1991b).On the efficacy of cinema, or what the visual system did not evolve to do. In S. Ellis, M. Kaiser, & A. Grunwald (Eds.), Pictorial communication in virtual and real environrnen ts (pp. 486495). London: Taylor & Francis. CUTTING, J. E. (1991~).Why our stimuli look as they do. In G. R. Lockhead & J. R. Pomerantz (Eds.), Perception of structure: Essays in honor of Wendell R. Garner (pp. 41-52). Washington, DC: American Psychological Association. CUTTING, J. E. & MILLARD, R. T. (1984). Three gradients and the perception of flat and curved surfaces. Journal of Experimental Psychology: General, 113, 198-216. CUTTING, J. E. & PROFFITT, D. R. (1982). Minimum principle and the perception of absolute, common, and relative motions. Cognitive Psychology, 14, 211-246.

256

J.E. Cutting

CUTTING, J. E., PROFFTIT, D. R., & KOZLOWSKI, L. T. (1978). A biomechanical invariant for gait perception. Journal of Experimental Psychology: Human Perception and Performance, 4, 357-372. CUTTING, J. E., SPRINGER, K., BRAREN, P. A., & JOHNSON, S. H. (1992). Wayfinding on foot from information in retinal, not optical, flow. Journal of Experimental Psychology: General, 121, 41-72. DODGE, R. (1907). An experimental study of visual fixation. Psychological Review Monograph Supplements, 8(4), 1-95. GARNER, W. R. (1962). Uncertainty and structure as psychological concepts. New York: Wiley. GIBSON, E. J. & WALK, R. (1960). The visual cliff. Scientific American, 202(4), 64-71. GIBSON, J. J. (1929). The reproduction of visually perceived forms. Journu1 of Experimental Psychology, 12, 1-39. GIBSON, J. J. (1933). Adaptation, after-effect and contrast in the perception of curved lines. Journal of Experimental Psychology, 16, 1-31. GIBSON, J. J. (1937). Adaptation with negative after-effect. Psychological Review, 20, 553-569. GIBSON, J. J. (1950a). The implications of learning theory for social psychology. In J. G. Miller (Ed.), Experiments in social process: A symposium on social psychology. New York: McGraw-Hill. GIBSON, J. J. (1950b). The perception of the visual world. Boston: Houghton-Mifflin. GIBSON, J. J. (1950~).The perception of visual surfaces. American Journal O f Psychology, 63, 367-384. GIBSON, J. J. (1951). What is a form? Psychological Review, 58, 403-412. GIBSON, J. J. (1954a). Ordinal structure and the possibility of a global psychophysics. Proceedings of the 14th International Congress of Psychology (pp. 178-179). Amsterdam: North Holland. GIBSON, J. J. (1954b). A theory of picture perception. Audio-Visual Communication Review, 1, 3-23. GIBSON, J. J. (1957). Survival in a world of probable objects. Contemporary Psychology, 2, 33-35. GIBSON, J. J. (1958). Visually controlled locomotion and visual orientation in animals. British Journal of Psychology, 19, 182-194. GIBSON, J. J. (1959). Perception as a function of stimulation. In S. Koch (Ed.), Psychology: A study of a science (vol. I, pp. 456-501). New York McGraw-Hill. GIBSON, J. J. (1960a). The information contained in light. Acta Psychologica, 27, 23-30. GIBSON, J. J. (1960b). Pictures, perspective, and perception. Daedalus, 89, 216-227.

GWsLegacies

257

GIBSON, J. J. (1961). Ecological optics. Vision Research, 1, 253-263. GIBSON, J. J. (1962). Observations on active touch. Psychological Reviezu, 69,477-491. GIBSON, J. J. (1965). Constancy and invariance in perception. In G. Kepes (Ed.), The nature and art motion (pp. 60-70). New York: Brazilier. GIBSON, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton-Mifflin. GIBSON, J. J. (1967a). James J. Gibson. In E. G. Boring & G. Lindzey (Eds.). A history of psychology in autobiography (vol. 5, pp. 127-143). New York: Appleton-Century-Crofts. GIBSON, J. J. (1967b). New reasons for realism. Synthese, 17, 162-172. GIBSON, J. J. (1970). On theories of visual space perception: A reply to Johansson. Scandinavian Journal of Psychology, 11, 75-79. GIBSON, J. J. (1971a). The information available in pictures. Leonardo, 4, 27-35. GIBSON, J. J. (1971b). The legacies of Koffka’s Principles. [ournal for the History of the Behavioral Sciences, 7, 3-9. GIBSON, J. J. (1972). A theory of direct visual perception. In J. Royce & W. Rozeboom (Eds.), Psychology and knowing (pp. 215-240). New York: Gordon & Breach. GIBSON, J. J. (1973). Direct visual perception: A reply to Gyr. Psychological Bulletin, 79, 396-397. GIBSON, J. J. (1978). The ecological approach to the visual perception of pictures. Leonardo, 11, 227-235. GIBSON, J. J. (1979). The ecological approach to visual perception. Boston: Houghton-Mifflin. GIBSON, J. J. & CROOKS, L. E. (1938). A theoretical field analysis of automobile-driving. American Journal of Psychology, 51, 453-471. GIBSON, J. J. & HUDSON, L. (1935). Bilateral transfer of the conditioned knee-jerk. Journal of Experimental Psychology, 18, 774-783. GIBSON, J. J. & KAUSHALL, P. (1973). Reversible and nonreversible events (film). State College, PA: Psychological Cinema Register. GIBSON, J. J. & RAFFEL, G. (1936). A technique for investigating retroactive and other inhibitory effects in immediate memory. Journal of General Psychology, 15, 107-116. HALPERN, B. P. (1983). Tasting and smelling as active, exploratory sensory processes. American Journal of Otolaryngology, 4, 246-249. HARRE, R. (1981). Great scientific experiments. Oxford: Phaidon Press/Oxford University Press. HELMHOLTZ, H. v. (1978). The facts of perception. In R. Kahl (Ed. and trans.), Selected writings of Hermann von Helmholtz (pp. 366-407). Middletown, CT: Wesleyan University Press.

258

J. E. Cutting

HENLE, M. (1974). On naive realism. In R. B. MacLeod & H. L. Pick, Jr. (Eds.), Perception: Essay in honor of James 1. Gibson (pp. 40-56). Ithaca, NY: Cornell University Press. HILDRETH, E. C. (1992). Recovering heading for visually-guided navigation. Vision Research, 32, 1177-1192. HOCHBERG, J. (1990). After the revolution. Contemporary Psychology, 35,750-752. KOFFKA, K. (1935). Principles of Gestalt psychology. New York: Harcourt. KOHLER, W. (1938). The place of values in a world of facts. New York: Liverigh t. LEE, D. N. (1980). The optic flow field: The foundation of vision. Philosophical Transactions of the Royal Society of London, B290, 169-179. LENNEBERG, E. (1962). Understanding language without ability to speak: A case study. Journal of Abnormal and Social Psychology, 65, 4 19-425. LEYTON, M. (1992). Symmetry causality mind. Cambridge, MA: MIT Press/Bradford Books. LIBERMAN, A. M. & MATTINGLY, I. G. (1985). The motor theory of speech perception revisited. Cognition, 21, 1-36. MARK, L. S. (1987). Eyeheight-scaled information about affordances: A study of sitting and stair climbing. Journal of Experimental Psychology: Human Perception and Performance, 13, 361-370. MARR, D. (1981). Vision. San Francisco: Freeman. MICHAELS, C. F. & CARELLO, C. (1981). Direct perception. Englewood Cliffs, NJ: Prentice-Hall. MUNDY, J. L. & ZISSERMAN, A., (Eds.) (1992). Geometric invariance in compziter vision. Cambridge, MA: MIT Press. NEISSER, U. (1976). Cognition and reality. San Francisco: Freeman. NIALL, K. K. (1992). Projective invariance and the kinetic depth effect. Acta Psychologica, 81, 127-168. NIALL, K. K., & MACNAMARA, J. (1989). Projective invariance and visual shape constancy. Acta Psychologica, 72, 65-79. NIALL, K. K., & MACNAMARA, J. (1990). Projective invariance and picture perception. Perception, 19, 637-660. NORMAN, D. A. (1988). The psychology of everyday things. New York: Basic. NORMAN, D. A. (1992). Turn signals are the facial expressions of automobiles. Reading, MA: Addison Wesley. PALMER, S. (1991). Goodness, Gestalt, groups, and Garner: Local symmetry subgroups as a theory of figural goodness. In G. R. Lockhead & J. R. Pomerantz (Eds.), Perception of structure: Essays in honor of Wendell R.

cibswzsLq.mk5

259

Garner (pp. 23-40). Washington, DC: American Psychological Association. PERRONE, J. A. (1992). Model for the computation of self-motion in biological systems. Journal of the Optical Society of America, A, 9, 177194 PITTENGER, J. B. & SHAW, R. E. (1975). Aging faces as viscal-elastic events: Implications for a theory of non-rigid shape perception. Journal of Experirnen tal Psychology: Human Perception and Performance, 1, 374-382. POINCARE, H. (1905). Science and hypothesis. Paris: Flammarion. (Reprinted by Dover, 1952.) POTTER, M. C., KROLL, J., & HARRIS, C. (1979). Comprehension and memory in rapid sequential reading. In R. Nickerson (Ed.), Attention and Performance VlII (pp. 395-418). Hillsdale, NJ: Erlbaum. PROFFITT, D. R., CUTTING, J. E., & STIER, D. M. (1979). Perception of wheel-generated motions. Journal of Experimental Psychology: Human Perception and Performance, 5, 289-302. REED, E. S. (1988). lames J. Gibson and the psychology of perception. New Haven, CT: Yale University Press. RESTLE, F. (1980). The seer of Ithaca. Contemporary Psychology, 25, 291293. ROSENBLUM, L. D., SALDANA, H. M., & CARELLO, C. (1993). Dynamical constraints on pictorial action lines. Iournal of Experimental Psychology: Human Perception and Performance, 19, in press. RUSSELL, B. (1940). A n inquiry into meaning and truth. New York: Norton. SAVELSBERG, G. J. P., WHITING, H. T. A., & BOOTSMA, R. (1992). Grasping tau. Iournal of Experimental Psychology: Huinan Perception and Performance, 17, 315-322. SHANNON, C. E., & WEAVER, W. (1949). The mathematical theory of communication. Urbana: University of Illinois Press. STEVENS, K. N. (1984). On gradients and texture "gradients." Ioiirnal of Experimental Psychology: General, 113, 217-220. STOFFREGEN, T. (1990). Multiple sources of information: For what? Newsletter of the International Society for Ecological Psychology, 4(1), 4-6. TODD, J. T. & REICHEL, F. D. (1989). Ordinal properties in the visual perception and cognition of smoothly curved surfaces. Psychological Review, 96, 643-657. TURVEY, M. T. (1992). Affordance and prospective control: An outline of the ontology. Ecological Psychology, 4, 173-187.

260

j. E. Cutfing

ULLMAN, S. (1980). Against direction perception. The Behavioral and Brain Sciences, 3, 373-415. VIVIANI, P. & STUCCHI, N. (1992). Biological movements look uniform: Evidence of motor perceptual interactions. journal of Experimental Psychology: Human Perception and Performance, 18, 603-623. WARREN, W. H. (1984). Perceiving affordances: Visual guidance of stair climbing. journal of Experimental Psychology: Human Perception and Performance, 10, 683-703. WARREN, W. H., MORRIS, M. W., & KALISH, M. (1988). Perception of translational heading from optical flow. Journal of Experimental Psychology: Human Perception and Performance, 14, 644-660. WARREN, W. H. & SHAW, R. E., (Eds.) (1985). Persistence and change. Proceedings of the first international conference on event perception. Hillsdale, NJ: Erlbaum. WARREN, W. H., & WHANG, S. (1987). Visual guidance of walking through apertures. Journal of Experimental Psychology: Human Perception and Performance, 13, 371-383. WATTS, R. G. & BAHILL, A. T. (1990). Keep your eye on the ball: The science and folklore of baseball. San Francisco: Freeman.

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

261

THE ROLE OF COMPUTATIONAL COMPLEXITY IN PERCEPTUAL THEORY John K. Tsotsos Department of Computer Science University of Toronto, Toronto, Canada

ABSTRACT The validity of perceptual theories cannot be considered only in terms of how well the explanations fit experimental observations. Rather, it is argued that sufficient consideration must also be given to the physical realizability of the explanation. Experimental scientists attempt to explain their data and not just describe it, in essence, providing an algorithm whose behavior leads to the observed data. Thus, computational plausibility is not only an appropriate but a necessary consideration. One dimension of plausibility is satisfaction of the constraints imposed by the computational complexity of the problem, the resources available for the solution of the problem, and the specific algorithm proposed. It is shown that such constraints play critical roles in the explanations of perception, intelligent behavior, and evolution.

The foundation of many modern perceptual theories arises from the computational hypothesis: biological perception can be modeled computationally as an information processing task. However, many argue that computational theories cannot explain biological behavior and that a computational theory would at best be an analogy. Is there any other type of explanation? In physics, cosmology, or chemistry, explanations and theories are put forward and the only requirement for their validity is that they account for the experimental observations. Would a cosmologist be required to create a universe in order for his theories to be taken seri-

262

1.K Tdm

ously? Or a biologist life? A theory that accounts for more observations than another is a better theory. Theories whose predictions are falsified are modified or rejected. Further, computation plays a large role in modern theory formation in the above disciplines. Computer simulation in particular has been a very powerful tool in the physical sciences. Yet no cosmologist would claim that he is creating a universe when building a computer simulation, and no one would criticize that cosmologist for not doing so. Yet the resulting theories would be considered valid if actual observations were explained. So, modeling as used in this essay has no implications of creating artificial life: rather computation is used as the formalism for an explanatory theory of perception with predictive power. A key difference here is that disciplines such as physics or cosmology do not appear to inherently involve information processing, whereas perception and intelligence in general do appear to involve information processing. It seems inconceivable that we will ever be able to construct a universe of the magnitude and complexity of the one we live in. But, it does seem possible to soon construct machines with the same number of processors and connectionsas the human brain.' Given the computational hypothesis, I claim that there is one basic issue that constrains all theories, regardless of implementation, namely computational complexity (amount of time and processing hardware required to reach a solution). Unfortunately, it appears that all problems are too hard in their general form (require unrealizable amounts of time or hardware or both). Thus, a new style of complexity analysis is required that attempts to solve these too hard problems in the context of the available resource limits and performance requirements. The full generality of the problem will necessarily be sacrificed in order to achieve this. Thus, problem complexity resource limits performance specifications form an important first set of constraints that must be satisfied. If one is concerned with brain models, then values relating to human brains and performance must be considered. If one is building a machine system, the type of analysis is the same, even though the results of the analysis will differ. Other design constraints include: cost to develop cost to replicate The most recent computer from Thinking Machines Corporation, for example, the CM-5, has a peak processing rate of about 10" operations per second, while the human visual cortex may have about l O I 5 operationsper second. This is not too far from the numbers of neurons and connections in the brain; in addition, each of the CM-5 processors seem to have much more power than a neuron.

Computatwnal Gnnplm'ty

263

physical shape and size, or packaging weight power consumption temperature control communication requirements and restrictions. How d o all of these constraints interact? It does not seem sensible to approach design as an optimization task of any sort: optimizing along one design variable necessarily will affect the others. We need to seek satisfying solutions, that involve design trade-offs along all variables in order to yield a solution. The trade-offs may differ depending on the implementation medium: in particular, trade-offs for a silicon implementation may not be the same as those for a neural implementation. This contribution focuses on the first of the above constraints: problem complexity. The combinatorial problems are very apparent, and in fact in most (if not all) natural problems, optimal solutions are computationally intractable in any implementation, machine or neural. A few examples are in order. i) Vision (the first two examples will be elaborated below): Visual Search with unknown targets using a passive sensor system is NP-complete (Tsotsos, 1989,1990a); Visual Search with unknown targets using an active sensor system is NP-complete (Tsotsos, 1992b); Polyhedral Line-labeling is NP-complete (Kirousis & Papadimitriou, 1988). ii) Reasoning: Finding the best explanation for a class of independent problems using probability theory (and several other forms of abduction) is NP-hard (Bylander, Allemang, Tanner, & Josephson, 1989); Abductive reasoning for all but the simplest theories is NP-complete (Selman & Levesque, 1989a); Many forms of default reasoning are NP-hard (Kautz & Selman, 1990; Selman & Kautz, 1990); Many of the strategies for defeasible inheritance in taxonomic hierarchies are intractable (Selman & Levesque, 1989b). iii) Neural Networks: For directed Hopfield Nets, determining whether a stable configuration can be found is NP-complete (Godbeer, 1987); PERFAOF,, is NP-Complete (the loading task for neural networks) (Judd, 1990).

1.K Tsotsas

264

This listing only scratches the surface of the literature on the topic: there are many more examples and they form quite broad and natural problem classes. It appears that any interesting intelligent problem has the characteristic that it is susceptible to combinatorial explosion. It is important to stress however that the examples given above do not by themselves prove that these problems or that cognition are computationally intractable. They simply constitute evidence that the computational issues are real and may place severe constraints on algorithms proposed for the problems of cognition.

A BRIEF INTRODUCTION TO COMPUTATIONAL COMPLEXITY Computational complexity is studied to determine the intrinsic difficulty of mathematically posed problems that arise in many disciplines. See Garey & Johnson (1979) and Stockmeyer & Chandra (1979). Many of these problems involve combinatorial search, i.e., search through a finite but extremely large, structured set of possible solutions. Examples include the placement and interconnection of components on an integrated circuit chip, the scheduling of major league sports events, or bus routing. Any problem that involves combinatorial search may require huge search spaces to be examined: this is the well-known combinatorial explosion phenomenon. Complexity theory tries to discover the limitations and possibilities inherent in a problem rather than what usually occurs in practice. After all, the worst case does occur in practice as well. This approach to the problem of search diverges from that of the psychologist, physicist, or engineer. In the same way that the laws of thermodynamics provide theoretical limits on the utility and function of nuclear power plants, complexity theory provides theoretical limits on information processing systems. If biological vision can indeed be computationally modeled, then complexity theory is a natural tool for investigating the information processing characteristics of both computational and biological vision systems. If the results of these analyses provide deeper insights into the problem and yield verifiable predictions, this would constitute evidence in favor of the computational hypothesis. Using complexity theory, one can ask for a given computational problem C, how well, or at what cost can it be solved? More specifically, the followingquestions can be posed: (1) Are there efficient algorithms for C? (2) Can lower bounds be found for the inherent complexity of C? (3) Are there exact solutions for C?

265 (4) What algorithms yield approximate solutions for C?

(5)What is the worst-case complexity of C? (6) What is the average complexity of C? Before studying complexity one must define an appropriate complexity measure. Several measures are possible, but the common ones are related to the space requirements (numbers of memory or processor elements) and time requirements (how long it takes to execute) for solving a problem. Complexity measures in general deal with the cost of achieving solutions. Complexity theory begins with a 1937 paper in which the British mathematician Alan Turing introduced his well-known Turing Machine, providing a formalization of the notion of an algorithmically computable function. He postulated that any algorithm could be executed by a machine with an infinitely long paper tape, divided into squares, a printer that writes and erases marks on the tape, and a scanner that senses whether or not a given square is marked. This imaginary device can be programmed to find the solution to a problem by executing a finite number of scanning and printing operations. What is remarkable about the Turing Machine is that in spite of its simplicity, it is not exceeded in problem solving ability by any other known computing device. If the Turing Machine is given enough time, it can in principle solve any problem that the most sophisticated computer can solve, regardless of serial/parallel distinctions or any other type of ingenious design. As a result, the fact that a problem can be solved by a Turing Machine has been accepted as a necessary and sufficient condition for the solvability of the problem. A similar thesis was also put forward by another mathematician, Alonzo Church (19361, and thus it is usually referred to as the Church/Turing Thesis: any problem for which we can find an algorithm that can be programmed in any programming language running on any computer, even if unbounded time and space are required, can be solved by a Turing Machine. Perception can in principle be solved;2 it can thus be implemented on a Turing machine and its computational nature confirmed. Turing proved that the problem of logical satisfiability-for a given arbitrary formula in predicate calculus, is there an assignment of truth values of its variables such that the formula is true?-cannot be decided by any algorithm in a finite number of steps. This provided the basis for A simple-minded, in principle solution to perception is: store all possible images of all objects and events one may ever encounter; then for each stimulus search that store until a match is found; link that match to an appropriate action by searching through all possible stimulus-action associations. This solution is guaranteed to be correct; however, it is impossible to ever construct a simulation of it or to realize it with neural hardware simply because far too many space and time resources are required. Recall however, that Turing Machines have infinite tape. If one considers doing this for say a day, by using two video cameras, one recording what the eye sees, and the other recording the agent's actions, the task no longer seems so formidable.

other similar proofs of intractability. Once one could prove problems were inherently intractable, it was natural to ask about the difficulty of an arbitrary problem and to rank problems in terms of difficulty. In what sense are complexity results inherent to a particular problem? Certain intrinsic properties of the universe will always limit the size and speed of computers. Consider the following argument from Stockmeyer and Chandra (1988): The most powerful computer that could conceivably be built could not be larger than the known universe (less than 100 billion light-years in diameter), could not consist of hardware smaller than the proton cm in diameter), and could not transmit information faster than the speed of light (3 x l@m/s). Given these limitations, such a computer could consist of at most pieces of hardware. It can be proved that, regardless of the ingenuity of its design and the sophistication of its program, this ideal computer would take at least 20 billion years to solve certain mathematical problems that are known to be solvable in principle. Since the universe is probably less than 20 billion years old, it seems safe to say that such problems defy computer analysis. In a subsequent section a new example with biological importance will be introduced which further demonstrates this point.

Some Basic Definitions The following are some basic definitions common in complexity theory (Garey & Johnson, 1979). A problem is a general question to be answered, usually possessing several parameters whose values are left unspecified. A problem is described by giving a general description of all of its parameters and a statement of what properties the answer, or solution, is required to satisfy. An instance of the problem is obtained by specifying particular values for all of the problem parameters. An algorithm is a general stepby-step procedure for achieving solutions to problems. To solve a problem means that an algorithm can be applied to any problem instance and is guaranteed to always produce a solution for that instance. An important issue here is whether or not a proposed algorithm is decidable (or solvable). Basically, the requirement for this is that there exists a Turing Machine which can compute yes or no for each element of the set A for the following question: if the set A is countably infinite? and there is another set B which is a subset of A, is a given element of A contained in B? A proof of decidability is sufficient to guarantee that the a problem can be modeled computa tionally. The time requirements of an algorithm are conveniently expressed in terms of a single variable, n, reflecting the amount of input data needed to A set is countable if there is a one-to-one and onto mapping from the natural numbers (integers beginning with 0)and the set. The set may be finite or infinite.

describe a problem instance. A time complexity function for an algorithm expresses its time requirements by giving, for each possible input length, an upper bound on the time needed to achieve a solution. If the number of operations required to solve a problem is an exponential function of n, then the problem has exponential time complexity. If the number of required operations can be represented by a polynomial function in n, then the problem has polynomial time complexity. Similarly, space complexity is defined as a function for an algorithm that expresses its space or memory requirements. Algorithmic complexity is the cost of a particular algorithm. This should be contrasted with problem complexity which is the minimal cost over all possible algorithms. The dominant kind of analysis is worstcase: at least one instance out of all possible instances has this complexity. A worst-case analysis provides an upper-bound on the amount of computation that must be performed as a function of problem size. If one knows the maximum problem size, then the analysis places an upper bound on computation for the whole problem as well. Thus, one may then claim, given an appropriate implementation of the problem solution, that processors must run at a speed dependent on this maximum in order to ensure real-time performance for all inputs in the world. Worst-cases do not only occur for the largest possible problem size: rather, the worst-case time complexity function for a problem gives the worst-case number of computations for any problem size; this worst case may be required simply because of unfortunate ordering of computations (for example, a linear search through a list of items would take a worst-case number of comparisons if the item sought is the last one). Thus, worst-case situations in the real world may happen frequently for any given problem size. Many argue that worst-case analysis is inappropriate for perception because of one of the following reasons: 1) relying on worst-case analysis and drawing the link to biological vision implies that biological vision handles the worst-case scenarios: 2) biological vision systems are designed around average or perhaps best-case assumptions: 3) expected case analysis more correctly reflects the world that biological vision systems see. Each of these criticisms will be addressed in turn. 1) This kind of inference is quite incorrect. As was shown in (Tsotsos, 1990a), it is impossible for the biological (or any other) visual system to handle worst-case scenarios. The whole argument exists only to prove that all worst-case scenarios cannot be handled by human vision in a bottom-up fashion and that the quest for general solutions is futile. 2) It is far from obvious what kind of assumptions (if any) went into the design of biological vision systems. Vision systems emerged as a result of a

268

J. K Tsotsm

complex interaction of many factors including a changing environment, random genetic mutations, and competitive behavior. It is probably the case that the best we will ever be able to do under such circumstances is to place an upper bound on the complexity of the problem, and this is all worst-case analysis will provide. 3) Analyses performed by other authors (Grimson, 1988, for example) based on expected or average cases, depend critically on having a wellcircumscribed domain and an algorithm. Thus the complexity measures derived reflect algorithmic complexity and not problem complexity as is the goal of the present paper. Only under those conditions can average or expected case analyses be performed. In general, it is not possible to define what the average or expected input is for a vision system in the world. Furthermore, the result of the analysis will be valid only for the average input, and does not place a bound on the complexity of the vision process as a whole. This also would not provide any guidance in the determination of required processing power for real-time performance. See also Uhr (1990). Critical ideas in complexity theory are that of complexity class and, related to it, reducibility. If a problem S is known to be efficiently transformed (or reduced) to a problem Q then the complexity of S cannot be much more than the complexity of Q. Efficiently reduced means that the algorithm that performs the transformation has polynomial complexity. The class P consists of all those problems that can be solved in polynomial time. If we accept the premise that a computational problem is not tractable unless there is a polynomial-time algorithm to solve it, then all tractable problems belong in P. In addition to the class P of tractable problems, there is also a major class of presumably intractable problems. If a problem is in the class N, then there exists a polynomial p ( n ) such that the problem can be solved by an algorithm having time complexity 0(2P(n));the time complexity function is asymptotically (as n becomes large) dominated by the polynomial p ( n ) . A problem is NP-complete if it is in the class NP, and it polynomially reduces to an already proven NP-complete problem. These problems form an equivalence class. Clearly, there must have been a first NP-Complete problem. The first such problem was that of satisfiability (Cook’s 1971 Theorem). There are hundreds of NP-Complete problems. If any NPComplete problem can be solved in polynomial time, then they all can. Most doubt the possibility that non-exponential algorithms for these problems will ever be found, so proving a problem to be NP-complete is now regarded as strong evidence that the problem is intrinsically intractable. If an efficient algorithm can be found for any one (and hence all) NP-complete problems, however, it would be a major intellectual breakthrough.

269

Implications of NP-Completeness What can be done when confronted with an NP-complete problem? A variety of approaches have been taken: (1) Develop an algorithm that is fast enough for small problems, but that would take too long with larger problems. This approach is often used when the anticipated problems are small. (2) Develop a fast algorithm that solves a special case of the problem, but does not solve the general problem. This approach is often used when the special case is of practical importance. (3) Develop an algorithm that quickly solves a large proportion of the cases that come up in practice, but in the worst case may run for a long time. This approach is often used when the problems occurring in practice tend to have special features that can be exploited to speed up the computation. (4) For an optimization problem, develop an algorithm which always runs quickly but produces an answer that is not necessarily optimal. Sometimes a worst-case bound can be obtained on how much the answer produced may differ from the optimum, so that a reasonably close answer is assured. This is an area of active research, with sub-optimal algorithms for a variety of important problems being developed and analyzed. (5) Use natural parameters to guide the search for approximate algorithms. There are a number of ways a problem can be exponential. Consider the natural parameters of a problem rather than a constructed problem length and attempt to reduce the exponential effect of the largest valued parameters. NP-Completeness effectively eliminates the possibility of developing a completely satisfactory algorithm. Once a problem is seen to be NPComplete, it is appropriate to direct efforts toward a more achievable goal. In most cases, a direct understanding of the size of the problems of interest and the size of the processing machinery is of tremendous help in determining which are the appropriate approximations. One could hypothesize that the evolutionary process discovered these methods through millennia of experimentation.

ON ALGORITHMS "GOOD " vs BIOLOGICALLY PLAUSIBLE The notions of a good algorithm and an intractable problem was developed in the mid-to-late 1960's. A good algorithm is one whose time requirements can be expressed as a polynomial function of input length. An intractable problem is one whose time requirements are exponential functions of problem length, or in other words, a problem which cannot be

270

1.Ic TS0k05

solved by any polynomial time algorithm for all instances. Note that the boundary between good and bad problems is not precise. A time complexity of nlooo is surely not very practical while one of 20.0°1 is perfectly realizable. Yet empirical evidence seems to point to the fact that natural problems simply do not have such running times, and that the distinction is a useful one. Biological plausibility of a given theory or algorithm is not the same notion as that of good algorithm, yet few bother to make the distinction. Usually, physical limitations, however real, do not enter into the discussion just like they do not enter the discussion in any theoretical complexity argument (for example, see Gopalkrishnan, Pamakrishnan, & Kanal, 1991). It is also true in complexity theory that algorithms with polynomial complexity are believed to be good while those with exponential complexity are bad; yet, there are an infinite number of values of exponents and variables that would lead to the exact reverse when an algorithm is physically realized. Consider simply the following pair of functions: O(AnX)and 0 ( 2 X n / A ) It . is easy to see that there is an infinite space in which the polynomial function has actual value larger than the exponential depending on the values of the constants A and x . And of course, there is an infinite number of such function pairs that we may compare. Early complexity theorists of course understood this problem. Yet, they claimed that polynomial functions with bad behavior do not occur in practice and likewise exponential functions with good behavior also do not occur in practice. Thus, the search for polynomial and sub-polynomial complexity functions is the driving goal of theory. But an important issue seems forgotten: if the practice of complexity analysis is to lead to tangible benefits then the theorems must lead to algorithms that must be physically realizable and the physical realization must in some way be better than others with respect to time or space efficiency. No matter what the time and space complexity functions, there is an infinite space of possible variable values or problem sizes which will not be practically realizable. The fact that all computers have finite memories is sufficient to guarantee this. One cannot in practice take infinite time to read or load an infinite Turing Machine tape. Engineering design specifications always impose constraints: the amount of memory may be limited by power consumption or cost; the number of processors is likewise constrained: real-time response places a hard constraint on time complexity and thus on problem size. These constraints cannot be ignored in any complexity discussion which may eventually be used to solve real problems. And the whole point of complexity theory is to formally provide insights on the relative difficulty of real problems. Yet, virtually all theoretical discussions do exactly this. The concern of this essay is on

Computational Cmn,dm'ty

271

what are the constraints whose satisfaction is required in order for a theory to be biologically plausible. It is claimed that it is not sufficient for a perceptual theory to only explain a set of experimental observations: experiments typically can use no more than a minuscule subset of all possible stimuli. Broader considerations beyond experiment are needed. Biological plausibility of a perceptual theory will thus be characterized in three stages. First, a theory must of course be sufficient to explain the observations. Second, it is important to define the size of problem which the algorithm must be able to handle, and this follows: The algorithm that embodies the theory accepts up to the same number of input samples of the world per unit time as human sensory organs. It is a non-trivial task to determine exactly the quantitative nature of the input to the human sensory system. With respect to the visual system, there are two eyes; each has about 110-125 million rods and 6.3-6.8 million cones; each eye can discriminate over a luminance span of 10 billion to one; the spatial resolution of the system peaks at about 40 cycles/degree while the temporal resolution peaks at about 40 Hz but the two are not independent; finally, there are many inputs from other sensory and motor areas. See Dowling (1987) for further discussion. The implementation that realizes the algorithm exists in the real world and requires amounts of physical resources which exist. The output behavior of the implementation as a result of those stimuli is comparable both in quality, quantity and timing to human behavior. The behavioral literature on exactly what the quality, quantity, and timing of human behavior is to a variety of stimuli is immense, but far from complete. What is required however, are responses from the algorithm that agree qualitatively and quantitatively with human responses and that are generated with the same time delays as human responses. The third stage of the definition requires that the functions for time and space complexity of any algorithm which we claim performs some information processing task in the brain only permit values of their variables which lead to brain-sized space requirements and behaviorally-confirmed time requirements. Issues of polynomial vs exponential do not enter the discussion of biological plausibility at all. In other words: solutions should require significantly fewer than about 109 processors operating in parallel, each able to perform one multiply-add operation over its input per millisecond; processor average fan-in and fan-out should be about 1000 overall; and

272

1.K.T&

solutions should not involve more than a few hundred sequential processing steps. Any perceptual theory must satisfy the above characterization: and similarly, any theory of any other aspect of intelligent behavior would have a corresponding characterization of biological plausibility.

ON COMPUTATIONAL MODELING AND PERCEPTION Complexity theory is as appropriate for analysis of visual search specifically and of perception in general as any other analysis tool currently used by biological experimentalists. Experimental scientists attempt to explain their data and not just describe it: it is no surprise that their explanations are typically well-thought-out and logically motivated, involving procedural steps or events. In this way, a proposed course of events is hypothesized to be responsible for the data observed. There is no appeal to non-determinism nor to oracles that guess the right answer nor to undefined, unjustified, or undreamed-of mechanisms that solve difficult components. In essence, experimental scientists attempt to provide an algorithm whose behavior leads to the observed data. Attempts at providing algorithmic explanations appeared even before the invention of the computer. For example, perception as hypotheses and unconscious inference theory (Helmholtz, 1963) is remarkably similar to the current reasoning paradigm in artificial intelligence, where reasoning is formalized as a logical process using formal mathematics. The basic formal requirement for the computability of perception is that perception be formally decidable (see Davis, 1958, 1965, for in-depth discussions of decidability). If a problem can be formulated as a decision problem, that is, we wish to know of each element in a countably infinite set A, whether or not that element belongs to a certain set B which is a proper subset of A, then the problem is decidable if there exists a Turing Machine which computes yes or no for each element of A. This requires that perception, in general, be formulated as a decision problem. This formulation does not currently exist. Visual search, an important sub-problem however, can be formulated as a decision problem (Tsotsos, 1989) and is decidable (it is an instance of the Comparing Turing Machine defined in Yashuhara, 1971). More research is needed to try to formalize other subproblems of perception in the same way. If some aspect of perception is determined to be undecidable, this does not mean that all of perception is also undecidable nor that other aspects of perception cannot be modeled computationally. For example, one of the most famous undecidable problems is whether or not an arbitrary Diophantine equation has integral so-

Computational colnplexdy

273

lutions (Hilbert’s 10th problem). This has theoretical interest, but more importantly, this does not mean that mathematics cannot be modeled computationally! Similarly, another famous undecidable problem is the halting problem for Turing Machines: it is undecidable whether a given Turing Machine will halt for a given initial specification of its tape. This too has important theoretical implications, but since Turing Machines form the foundation of computation, it certainly does not mean that computation cannot exist! Appeals to non-algorithmic explanations cannot seriously be entertained because, by definition of algorithm, they would not give a step-bystep procedure for achieving a solution to a problem. Thus, the problem would remain unsolved except by appeals to inexplicable processes, and this does not lead us any closer to understanding perception. Since biological scientists provide algorithmic explanations, computational plausibility is not only an appropriate but a necessary consideration. One dimension of plausibility is satisfaction of the constraints imposed by the computational complexity of the problem, the resources available for the solution of the problem and the specific algorithm proposed. Any computational paradigm is a candidate for use in constructing a biologically plausible model. Neural network approaches are not the only ones that are biologically plausible as is often believed. Neural networks are Turing-equivalent and they are subject to the same constraints of computational complexity and computational theory as any other implementation (see Judd, 1990, for further discussion and proofs of this statement). It is important to note that relaxation processes are specific solutions to search problems in large parameter spaces and nothing more. Neural networks use variations of such search procedures which in general may be termed optimization techniques. If optimization is the process by which real neurons perform some of their computation, it is subject to precisely the same considerations of computational complexity as any other search scheme.

Visual Search Visual search is a common if not ubiquitous sub-task of vision, in both man and machine. A basic visual search task is defined as follows: given a target and a test image, is there an instance of the target in the test image (Rabbitt, 1978)? Typically, experiments measure the time taken to reach a correct response. Region growing, shape matching, structure from motion, the general alignment problem, connectionist recognition procedures, etc., are specialized versions of visual search in that the algorithms must determine which subset of pixels is the correct match to a given prototype or description. The basic visual search task is precisely what any model-

274

1.K Tsofsas

based computer vision system has as its goal: given a target or set of targets (models), is there an instance of a target in the test display? Even basic vision operations such as edge-finding are also in this category: given a model of an edge, is there an instance of this edge in the test image? It is difficult to imagine any vision system which does not involve similar operations. It is clear that these types of operations appear from the earliest levels of vision systems to the highest. In Tsotsos (1989), a computational definition of the visual search task was presented, and the unbounded case was distinguished from the bounded case. Unbounded visual search refers to a search task where the target is not given explicitly in advance, and even if it can be given it is not used by the sensory apparatus to optimize search in any way. Bounded visual search on the other hand, is a search task where the target is known explicitly in advance and it is used to optimize the search process. An equivalence was drawn between unbounded search and bottom-up processes, and bounded search and task-directed visual processes. It was shown in Tsotsos (1989,1992b) that unbounded visual search, regardless of whether the images are time-varying or the camera system is dynamically controlled (active), is NP-complete. This is due solely to the fact that the subset of pixels in an image which corresponds to a target cannot be predicted in advance and all subsets must be considered in the worst case. The bounded problem, on the other hand, requires linear time for the search process. This qualitatively confirms all of the visual search data that has been experimentally discovered (say, by Treisman, 1988). These results are true for an active camera system as well (Tsotsos, 1992b). The four theorems proved in those papers show that in general, a bottomup approach to perception (as suggested by Marr, 1982) is not only computationally intractable, but biologically implausible. Yet, task-directed approaches do have direct biological counterparts.

ON COMPUTATIONAL COMPLEXITY AND EVOLUTION In the section introducing complexity theory, an example due to Stockmeyer and Chandra (1979) was given in order to demonstrate the concept of an intractable problem. A new example that has direct biological relevance is now presented to further support this notion. Consider for a moment the following simple-minded and straightforward evolutionary strategy. First, suppose that an organism named Protorasis was the very first organism with a visual system (Figure 1). Its visual system consists of a single eye, whose retina contains a single photoreceptor, which responds uniquely to only 10 shades of gray. Of those shades of gray, only 7 have

computational complexty

275

meaning to the organism, and are linked to some sort of action. Thus, the only visual processing requirements for Protorasis' brain are that those 7 models are somehow represented and that matching can be done (presumably by a simple network of neurons).

stimuli to which Protorasis' photoreceptor responds

itorasis

models of meaningful stimuli linked to actions

00 .....

..... ...... ...... .... ...

...... ...... ........... .....

i.:.:..

0 .

Figure 1. A fanciful depiction of the very first organism with a visual system, Protorasis. The visual system consists of a single eye, whose retina contains a single photoreceptor which responds uniquely to only 10 shades of gray shown at the top. Of those shades, only 7 have meaning to the organism, and are linked to some sort of action.

This network could be as simple as that depicted in Figure 2, where 7 output neurons are completely connected to the 10 photoreceptor outputs with excitatory and inhibitory connections. Also, suppose that random mutations can cause one or more of the following to change: the number of eyes; the number of photoreceptors in an eye; the range of stimuli to which each photoreceptor can uniquely respond; the number of neurons (and their

connectivity) available for storing and matching models. Also assume that the perceptual and behavioral strategy for each subsequent organism was exactly the same as for Protorasis.

excitatory connection inhibitory connection

-----

Figure 2. The network required to solve the task of linking a small number of perceptual stimuli to units whose response initiates action for Protorasis. The network has 10 input units, 7 output units, and 70 connections.

What constraints are there on subsequent visual systems so that they may still function as well as that of Protorasis? Let: E represent the number of eyes (without any assumptions about whether they are convergent on the same portion of the scene or not); Pi be the number of photoreceptors in eye i; N be the number of models which may be stored and matched (coarsely speaking, this gives a measure of the amount of brain devoted to visual processing); S be the number of unique stimuli to which each photoreceptor uniquely responds.

compltationalComplexity

277

It is easy to characterize the resulting number of possible images and required number of units for matching in a quantitative manner. The number of possible images is given by

i=l

If each of these images has some significance to an organism, then

i=l

otherwise N has some value less than this. In either case the number of connections in the model of Figure 2 is given by S*N. Now suppose that Protorasis-2 was the result of some mutation that increased the size of the brain for model storage and matching from 7 to 700, and also increased the number of photoreceptors from 1to 4. The number of possible images would be 104. Even though there was a comparatively much larger increase in brain size, there is no longer sufficient computation power to recognize more than 7% of the possibilities using the simpleminded strategy of Protorasis. Similarly, if Protorasis-3 resulted from an ability to detect many more shades of gray in the environment, say 100, and included an increase in brain size from 700 to 10,000. the problem is even more acute. Small changes in P or S lead to exponentially large increases in N. In this case, there are lo8 potential images for the 10,000 storage units! Perceptual power for an organism may be estimated using the quotient N

This reflects the percentage of world events to which the organism can perceive and react. The larger this value is, the more powerful the perceptual capabilities of the organism are with respect to its sensory apparatus. This of course assumes a constant time recognition strategy as is assumed with the network of Figure 2. These are just the static images. If 2 is the time interval in seconds during which significant time-varying events may occur, and the visual system may sample every a seconds then the total number of possible image sequences would be given by

1.K. T d m

278

(n i=l

spir*

It does not require much further analysis or discussion in order to see that this simple and straightforward strategy cannot possibly be the one evolution actually used. Our brains would be wildly larger than they are (recall the characterization of biologically plausible). It is clear that not all possible images will have significance to any given organism. However, it may be postulated that greater perceptual power, via the ability to recognize a larger and richer set of images, would lead to better likelihood of survival for an organism. For example, a greater variety of food sources could be recognizable as would a greater variety of predators. So, an evolutionary goal could be to achieve large values of E, S, and P for a given value of N. Formally, as mentioned earlier, the problem of visual search-finding a target in an image-requires exponential time in its worst case using a single processor (or exponential processors for a constant time solution), and the strategy described for Protorasis is similarly exponential in nature (in number of processors and connections). Could it be that through random mutations, evolution discovered the same principles of approximation and optimization that have been determined to be appropriate for dealing with NP-complete problems? The theory of computational complexity permits these conclusions: and further, to lay a theoretical foundation proving why evolution did not take the direct and simple path of Protorasis. Moreover, as described earlier, the theory gives guidelines on how to deal with such exponentially difficult problems, and the surprise is (or perhaps it is not that surprising after all!) that many of the suggestions have biological counterparts: Develop a fast algorithm that solves a special case of the problem, but does not solve the general problem: the observation that not all combinations of locations in an image need be considered in a matching process because objects and events are spatio-temporally localized permits spatiotemporally localized receptive fields to be used as an approximating measure. This special case is solved much faster (the exponential is reduced to a low order polynomial function), but the general problem is not solved since general location combinations are not considered (Tsotsos, 1988). Develop an algorithm that quickly solves a large proportion of the cases that come up in practice, but in the worst case may run for a long time: the observed serial bottleneck believed to be the reason for visual attention may be a manifestation of this. Simpler tasks can be solved quickly in parallel, while more complex tasks require serial, selective attention (Tsotsos, 1991).

Use natural parameters to guide the search for approximate algorithms: hierarchical organization and hierarchical abstraction are wellaccepted methods for reducing search and these methods reduce the search dramatically in perception (Tsotsos, 1988). A model that incorporates the above approximations and abstractions leads to the possibility of Protorasis’ recognition system performing its tasks with different time requirements. That is, different objects or stimuli may be recognized with different time costs. Thus, a different comparative measure of power is possible: the number of different perceptual events recognizable divided by the time required for their recognition:

j=1

where model j g N requires time Ti. The larger this quotient, the more powerful the perceptual system, and this is independent of the details of the sensors themselves (number of eyes, photoreceptors, etc.). The organism which can recognize and act on a larger set of perceptual events, on average faster than another organism, has a competitive advantage over that other organism. This function naturally accounts for the fact that many events may be recognizable very quickly while others may take more time; and that a larger proportion of the former is better than a larger proportion of the latter. Unfortunately, it is not obvious how these measures can be put into practice. It is probably not possible to ever know the value of N for any organism: however, for a given large set of objects or event stimuli, the corresponding times for recognition could be measured and thus different organisms compared. It would be illuminating to carry out such a comparative experiment.

ON COMPUTATIONALMODELING AND BEHAVIORISM The philosophy for realizing intelligent behaviors in machines as articulated by Brooks, his colleagues and others, has received a great deal of attention (Brooks, 1991a, 1991b). Brooks believes that machines constructed out of simple modules with simple communication will exhibit intelligent behavior as an emergent property; the behavior is not directed by a single homunculus nor is it explicitly specified in the machine in any way. These principles are the cornerstones of the subsumption architecture Brooks proposed in 1986 for intelligent control. A simple description of the

subsumption idea includes: control layers define a total order on a robot’s behaviors: the dominance of layers follow a hypothesized evolutionary sequence: each layer may spy on layers at lower levels and inject signals into them. It is claimed that the structure is scalable to human-like behavior and Brooks argues strongly against: the sense-model-plan-act framework for robot control: the representation of intermediate or hierarchical computations: the explicit representation of goals: and, 9 CAD-like models of the world. He goes on to claim that perception is connected to action, and further that his approach can be extended to cover the whole story, both with regards to building intelligent systems and to understanding human intelligence. As proof of his position he offers compelling evidence: many mobile robots that seem to have robust and interesting performance. Brooks seems to be re-kindling the torch of old behaviorism, a philosophy appearing about 1913 in the psychology community (Watson, 1919). Behaviorism stood for one basic belief humans are biological machines and as such do not consciously act, do not have their actions determined by thoughts, feelings, intentions, or mental processes. Human behavior is a product of conditioning: humans react to stimuli. Behaviorism is not popular currently in psychology nor in cognitive neuroscience. Similarly, arguments against Brooks’ position are not new. For example, Kirsh (1991) focuses on one of Brooks’ claims, that intelligent behavior is concept-free. Kirsh claims that concepts are necessary for some types of behavior and also can make computational processes simpler. He argues for the need of representation in a theory of perception simply because vision is complex and must be sometimes solved in general ways. But Brooks is not alone in his belief that some sort of behaviorist theory is the most appropriate. Ramachandran’s (1990) utilitarian theory is remarkably similar. Ramachandran rejects previous well-known theories of perception (Helmholtz’s perception as unconscious inference, Gibson’s direct perception, Marr’s natural computation) and proposes rather that perception does not involve intelligent reasoning, nor resonance with the world, nor the creation of internal representations. Rather, perception is a bug of tricks. Through millions of years of evolution, the visual system has evolved numerous short-cuts, rules-of-thumb, and heuristics each one adopted only because it works and not because of any other appeal. Ramachandran is particularly critical of computational theories. Although he does make some valid points, he has developed a perspective on perception that can be labeled as a behaviorist approach just like Brooks, and thus is subject to the same criticism, as will be outlined next.

Behaviorists seem haunted by one of their claims, namely that their paradigm and the solutions formulated within it will scale up to problems which are human-like in their size. This is particularly true of Brooks, who claims a solution to intelligence in general. The arguments Brooks presents on scaling are inadequate (Brooks, 1991a, 1991b). Although Brooks mentions the issue, these arguments never appear in any concrete and direct fashion. Ramachandran seems unaware of this issue. It can be proved that strict behaviorism (that is, not deviating in any way from the published principles and dogma, specifically, that no explicit targets are permitted) is not supported by current biological evidence and may require time to execute that is given by an exponential function in the image size in the worst-case (Tsotsos, 1992a). It does not matter what kind of computational medium is used for the implementation (recall the Church/Turing Thesis); the exponential worst-case behavior depends solely on the inability of a behaviorist system to know where the stimuli that trigger tricks or behaviors are found. Parallelism does not help; if the search is conducted in parallel, an unrealizable number of processors (given by an exponential function of image size) will be needed, again something which is not biologically plausible. It does not matter if the visual system is passive or active, the same conclusions are reached. It is this search action which is inherent in the behaviorist or utilitarian view but which is never explicitly addressed that results in the rejection of these theories. Small signals (such as simple voltages, or sonar blips) would not lead to the same problem; thus the success of the current implementations. The alternative is to employ a satisfying set of approximations and optimizations (Tsotsos, 1988,1990, 1992a, 1992b) that tie the behaviors or tricks together.

CONCLUSION In this essay I argued for the need to consider issues of realizability within biologically plausible limits for any theory that is proposed as an explanation for perception, or intelligence in general. The theoretical foundations for realizability can be laid within the framework of computational complexity theory. Further, that theory provides guidelines for how to deal with problems that appear to be unrealizable. In previous papers, it was shown that a small number of unifying approximations and optimizations are sufficient for reducing the potential combinatorial explosion and satisfying the definition of biological plausibility outlined earlier (Tsotsos, 1988,1990,1992a. 1992b).

1.K Tdm

282

Now, this kind of argument is not new: Uhr (1980) and Feldman and Ballard (1982) among others, have attempted to make similar arguments. Each drew their own conclusions: Uhr that pyramid structures were needed: Feldman and Ballard argued for massive parallelism. However, none of the previous authors tied such back-of-the-envelope calculations directly to a formal theory and none put all the elements together to show that they satisfy biological plausibility. The results force a change to Marr’s (1982) view of computational vision, namely, that in principle solutions are not necessarily realizable and thus are not necessarily acceptable. A necessary condition on their validity is that they must also satisfy the complexity constraints of the problem and the resources allocated to its solution. Similarly, the results force a change to the behaviorist approach to intelligence. One final point: we cannot assume that evolution finds optimal solutions in the same sense that complexity theory seeks. Evolution finds satisfying solutions and it is those solutions which perceptual theorists are attempting to find. It would be an uninteresting conclusion if complexity theory applied only to artificial computation problems and not natural ones. Thus, this essay argued for a new style of complexity analysis, that attempts to balance problem complexity, available resources for its solution and required performance time in the context of the computational modeling of biological perception. Acknowledgment. Parts of this paper were written while the author was visiting the Multimedia Systems Institute of Crete at the Technical University of Crete, with the kind support of Prof. Stavros Christodoulakis. The author is the CP-Unite1 Fellow of the Canadian Institute for Advanced Research. This research was funded by the Information Technology Research Center, one of the Province of Ontario Centers of Excellence, the Institute for Robotics and Intelligent Systems, a Network of Centers of Excellence of the Government of Canada, and the Natural Sciences and Engineering Research Council of Canada.

DISCUSSION V. S. Ramachandran (Neurosciences Program, University of California at Sun Diego, La JoZZa, CA): In this essay Tsotsos raises several interesting issues concerning the computational approach to vision. It seems to me that he and I see eye to eye on many issues but not on all. In this ”reply” I will not comment on the more formal aspects of his theory but will confine myself, instead, to some of the meta-theoretical questions that he ad-

dresses. It is not clear to me what he means by the term ”behaviorist.” I should point out as the answer that my criticisms were directed mainly against the Marr school of Computational Vision rather than computational vision in general (Ramachandran, 1985b, 1990; Churchland, Ramachandran, & Sejnowski, 1993). In this essay I shall try to summarize some of these ideas. David Marr’s ideas created nothing short of a revolution in our understanding of human vision comparable to the Chomskyian revolution in linguistics. The major strength of his approach to vision is that it allows a much more precise and rigorous formulation of perceptual problems than what one could achieve by doing psychophysics or physiology. Unfortunately, there are also several major pitfalls associated with his approach and I shall take this opportunity to spell them out briefly. Levels of Analysis. Any complex information processing systems-including the human visual system-can be understood at several distinct “levels”+.g., the level of the ”computational problem,” the level of algorithm (a sequence of steps) and finally, least important (in Marr’s scheme), the actual neural hardware that is used to implement the algorithm. To ensure progress in understanding vision it is important not to get “confused” between these levels, especially since the logical structure of arguments at each level is quite independent of the other levels. This argument may be valid for some simple machines, but when we are talking about complex biological systems, I would like to submit that the only sure way to progress, in fact, is to deliberately get confused between these levels-deliberately make what orthodox philosophers might call ”category mistakes.” There is now a wealth of experimental evidence which suggests that our perceptual experience of the world is powerfully constrained by the actual neural machinery, i.e., the ”hardware” that mediates perception (e.g., see Ramachandran, 1985b, 1992; Ramachandran & Gregory, 1978, 1991; Ramachandran, Rogers-Ramachandran, Stewart, & Pons, 1992; Ramachandran, Stewart, & Rogers-Ramachandran, 1992). And, in general, I think no important discovery in science has ever been made by respecting the distinctions between levels. For example, consider Mendelian inheritance. You can’t think of two more different levels than the behavior of pea plants and the structures of molecules, and yet it is by bridging these two that the science of Biology was born. Identifying the computational problem. According to Marr, the single most important step in understanding human vision is to provide a precise mathematical formulation of the “computational problem” confronting the organism. In doing this it is best to start from first principles (e.g., by considering ”natural constraints”) and to avoid being confused by results obtained by psychophysical and physiological methods.

284

1.K TS&m

Unfortunately it is not always obvious what the so-called computational problem is in any given situation. (Try answering the simple question: what is the goal of color vision?) Indeed the real visual system often seems to subdivide any given problem into many ”sub-problems” many of which would be difficult to discern unless you do experiments and acquire a certain familiarity with the phenomenology of human vision. It should come as no surprise, therefore, that most of the computational problems that AI researchers are currently preoccupied with were in fact identified by psychophysicists (e.g., the stereo-correspondenceproblem by Julesz and Wheatstone; the structure from motion by Wallach, the aperture problem by Wallach, and the motion correspondence problem by Ternus). They certainly weren‘t deduced from “first principles.” Modularity. According to Marr’s doctrine of modularity, ”early vision” processes, such as stereo, motion correspondence, shape-from-shading, structure from motion, etc., are mediated by several autonomous modules. These modules remain largely insulated from each other and convey the results of their computations to higher visual centers for subsequent processing. Vision, in this scheme, is a strictly bottom-up affair. It may indeed be useful to treat vision as modular at least as first approximation but there is now a great deal of evidence that the modules must interact with each other significantly even at the very earliest stages of visual processing. We have shown, for example, that both motion correspondence (Ramachandran, 1985a; Ramachandran & Anstis, 1986) and stereopsis (Ramachandran, 1986; Nakayama, Shimojo, & Ramachandran, 1990)can be strongly influenced by image segmentation based on implied occlusion. More remarkably, we find that a jumping sound source superimposed on a dynamic noise display will cause the noise to ”jump” along with the sound-an example of cross-modal motion capture (Ramachandran, Intrilagator, & Cavanagh, unpublished manuscript). A simple version of cross modal motion capture can be produced by using a single dot blinking on and off adjacent to a white square. Subjects viewing this display usually do not see any motion-they just see a spot blinking on and off. We then added an auditory stimulus presented by earphones. Simultaneous with the blinking on of the light, a tone is sounded in the left ear; simultaneous with the blinking off, a tone is sounded in the right ear. Subjects see the single dot move to the right behind the occluder. In effect, the sound ”pulls” the dot in the direction the sound moves (Ramachandran, Intrilagator, & Cavanagh, unpublished manuscript). This is convincing evidence for some form of ”heterarchy,” and against a pure, straight through, noninteractive hierarchy. (A weak subjective motion effect can be achieved when the blinking of the light is accompanied by somatosensory left-right vibration stimulation to the hands.)

It comes as no surprise that visual and auditory information is integrated at some stage in neural processing. After all, we see dogs barking and drummers drumming. What is surprising about these results is that the auditory stimulus has an effect on a visual process (motion correspondence) that Pure Vision orthodoxy considers "early." Segmentation. This is a special case of the modularity argument. According to this view, certain elementary visual functions such as stereopsis, motion, color, etc. are mediated relatively early in visual processing by specialized modules, whereas segmentation of the visual scene into separate objects is assumed to be a more complex process that can actually use the output of these early vision modules. Since the modules perform their functions prior to image segmentation, the argument goes, one can successfully model them and study them experimentally without worrying about segmentation (Marr, 1981). Contrary to this view, out evidence suggests that image segmentation can profoundly influence a number of early visual processes such as stereopsis (Ramachandran, 1986; Nakayama, Shimojo, & Ramachandran, 1990), structure from motion (Ramachandran, Cobb, & Rogers-Ramachandran, 1988), motion correspondence (Ramachandran, 1985a; Ramachandran, Rao, & Vidyasagar, 19731, and shape-fromshading (Ramachandran, 1988). The implication is that the early vision modules are not autonomous-they interact significantly with each other and with segmentation. Any program of research on perception must take these facts into account. Consider stereopsis, the matching of slightly dissimilar images from the two eyes to recover stereoscopic depth. Julesz stereograms (Julesz, 1971) are often cited by Marr and his colleagues to illustrate the view that stereopsis is a prime example of modularity-of an early visual process that is relatively autonomous and insulated from other visual processes such as segmentation. The stereogram depicted in Ramachandran (1986, Figure 7) flatly contradicts this view. We created this stereogram using two illusory squares by introducing small horizontal disparities between the vertical edges of the cut sectors. The disks themselves were at zero disparity in relation to the surrounding frame. If the top pair (conveying crossed disparities) is stereoscopically fused, one sees a striped square standing well in front of a background consisting of black circles on a striped mat. If the bottom pair (uncrossed disparities) is fused, one sees four holes in the striped opaque foreground mat, and through the holes, well behind the striped mat, one sees the four corners of a partially occluded striped square on a black background. These are especially surprising results, because the stripes of the perceived foreground and the perceived background are, by definition, at zero disparity. The only disparity that exists on which the brain can base stereo depth per-

286

J. K. Tsotsrxs

ception comes from the edges of the pacmen. Notice that in this display, the illusory contours must emerge after stereoscopic fusion and yet these contours can in turn influence the matching of finer elements in the display. Assuming that perceiving subjective contours is a ”later” effect requiring global integration, and that finding stereo correspondences for depth is an “earlier” effect, then this result appears to be an example of “later” influencing-in fact enabling-”earlier.” The emergence of qualitatively different percepts (illusory square in front of disks, versus illusory square behind portholes) cannot be accounted for by any existing stereo algorithms. Most of these algorithms would simply predict a reversal of in sign of perceived “depth” if the disparities are reversed (Ramachandran 1986; Nakayama, Shimojo, & Ramachandran, 1990). Absence of “top-down“ influences. According to Marr, the computations of early vision modules are unaffected by high level object knowledge and semantics. The segmentation of Gregory’s “Dalmatian dog” according to this view, occurs not because we know it is a dog and use this knowledge to segment the image but because of certain hidden cues intrinsic to the image, e.g., collinear edges that generate illusory contours around the edge of the dog. But if this is strictly true, why does a hollow mask (viewed from the inside) look convex rather than hollow? Are Helmholtz (1963) and Gregory (1970) incorrect in assuming that the reason faces look convex is because we know them to be faces? This is an important issue, for if they are right then it would be a striking example of the role of “top-down” influences in vision and would imply that even semantic knowledge can influence the processing of early vision modules such as those concerned with shape from shading and stereopsis. But does this depth reversal effect really have anything to do with faces? Is it possible, for example, that the reversal of the hollow mask results simply from a generic assumption that objects are usually convex? Or does high-level semantic knowledge also play a role? To find out, Richard Gregory, Kerrie Maddock, and I presented subjects with two adjacent masks, one of which is right side up, the other is upside down. Upside down faces are often poorly recognized, and in any case, upright faces are what we normally encounter. In the experiment, subjects walked slowly backwards away from the pair of stimuli, starting at 0.5 m, moving to 5.0 m. At a distance of about 0.5 m, subjects see both masks as depth inverted (concave). At about 1 m, subjects usually see the upright mask as convex; the upside down mask, however, they continue to see as concave until they are at a distance of 1.5-2.0 m. Because the stimuli are identical except for orientation, this experiment illustrates that ”later” process (face categorization) has an effect on an ”earlier” process (shading and stereopsis).

Hierarchical Processing. Marr’s scheme implies that vision is largely a “bottom-up” process with a one-way flow of information from the sense organs to the motor output. Although generating an appropriate motor output is the ultimate goal of vision there has, until now, been no evidence that the motor programs themselves (that are used to generate the output) can influence the early stages of perception. This idea has been dubbed ”dead vision” by Ballard (1989) to contrast it with what Brooks (1986) has called “active vision.” It is remarkable that this myopic view of vision has held sway for so by especially given the flatly contradictory evidence from physiologythe existence of massive backprojections from so-called ”higher” to lower visual areas. It is a well known, but often glossed over fact, for example, that there are three times as many fibers coming back from V1 to the LGN than vice versa-even though the textbooks usually mislead as by showing only forward projecting arrows. It is usually assumed tacitly that these back projections may simply be involved in some aspect of overall gain control but that they may not be crucially involved in the actual computations that lead to perception. The fact that what we see depends not only on the input but also on what you intend to do with the information (i.e., the type of behavior you wish to generate) receives support from a new series of experiments that we have been doing on patients with squint (Ramachandran, Cobb, & Valente, 1992). Exotropia is a form of squint in which both eyes are used when fixating on small objects close by (e.g., a foot from the nose) but when looking at distant objects, the ”squinting” eye deviates outward by as much as 40” to 60”. Curiously, the patient does not experience double vision-the deviating eye‘s image is usually assumed to be “suppressed.” It is not clear, however, at what stage in visual processing the suppression occurs. Surprisingly, it is claimed by orthoptists that in a small subset of these patients, “fusion” occurs not only during inspection of near objects, but also when the squinting eye deviates (see Duke-Elder, 1949, for a review). This phenomenon, called ”anomalous retinal correspondence” or ARC, has not always been taken seriously, perhaps because it was assumed that ARC implies a rather improbable lability of binocular receptive fields. Clinicians and physiologists raised in the Hubel-Wiesel tradition usually take it as Gospel that (1) binocular connections are established in area 17 in early infancy and that (2) binocular ”fusion” is based exclusively on anatomical correspondence of inputs in area 17. For instance, if a squint is surgically induced in a kitten or an infant monkey, area 17 displays a complete loss of binocular cells (and two populations of monocular cells) but the maps of the two eyes never change. No apparent compensation such as

288

J. K.Tsokm

”anomalous correspondence” has been observed in area 17 and this has given rise to the conviction that it is highly improbable that an A R C phenomenon truly exists. To explore the possibility that there might be more to the ARC reports, Ramachandran, Cobb, and Valente (1992) recently studied two patients who had intermittent exotropia. Ramachandran’s two patients appeared to “fuse” images both during near vision and during far vision-when the left eye deviated outward-a condition called “intermittent exotropia with anomalous correspondence.” To determine whether these patients do indeed have two (or more) separate binocular ”maps” of the world, Ramachandran, Cobb, and Valente (1992) devised an experimental procedure that tested the binocular alignment of after-images; the after-image for the right eye being generated independently of the after-image for the left eye. Here is the procedure: (1) The subject (with squint) was asked to shut one eye and to fixate on the bottom of a vertical slit-shaped window mounted on a flashgun. A flash was delivered to generate a vivid monocular afterimage of the slit. He was then asked to shut this eye and view the top of the slit with the other eye (and a second flash was delivered). (2) The subject opened both eyes and viewed a dark screen, which provided a uniform background for the two afterimages. The results were as follows: (A) The subject (with squint) reported that he saw afterimages of the two slits that were perfectly lined up with each other, so long as he was converging within about arm’s length. (B) On the other hand, if he relaxed vergence and looked at a distant wall (such that the left eye deviated), the upper slit (from the anomalous eye) vividly appeared to move continuously outwards so that the two slits eventually became misaligned by several degrees. They then repeated this experiment on two normal control subjects and found that no misalignment of the slits occurred for any ordinary vergence of conjugate eye movements. Nor could misalignments of the slits be produced by passively displacing one eyeball to mimic exotropia in the normal individuals. Ramachandran, Rogers-Ramachandran, Stewart, and Pons (1992) have dubbed this phenomenon “dynamic anomalous correspondence.” The phenomenon itself is not new but these authors have been able to establish its existence clearly and have pointed out a number of implications that appear not to have been recognized by the Neuroscience and AI community. 1. Binocular correspondence can change continuously in “real time” in a single individual depending on the degree of exotropia. Hence, binocular correspondence (and ”fusion”) cannot be based exclusively on the anatomical convergence of inputs in area 17. The relative displacement observed between the two afterimages also implies that the “local sign” of retinal

points (and therefore binocular correspondence) must be continuously updated as the eye deviates outwards. 2. Since the two slits would always be “lined up” as far as area 17 is concerned, the observed misalignment implies that feedback (or feedforward) signals from the deviating eye must somehow be extracted separately for each eye and must then influence the egocentric location of points selectively for that eye alone. This is a somewhat surprising result, for it implies that “remapping” of egocentric space must be done very early-before the “eye of origin” label is lost-i.e., before the cells become completely binocular. Since most cells beyond area 18 (e.g., MT or V4) are symmetrically binocular we may conclude that the correction must involve interaction between reafference signals and the output of cells as early as 17 or 18. It is quite remarkable that a complete remapping of perceptual space in x-y coordinants can occur selectively for one eye‘s image simply in the interest of preserving binocular correspondence. It would be interesting to see if this remapping process can be achieved by algorithms of the type proposed by Zipser and Anderson (1988) for parietal neurons or by “shiftercircuits” of the kind proposed by Van Essen and Anderson (1990). Identifying ”natural constraints.” An important idea put forth by Marr is the notion of ”natural constraints.’’ Marr points out (as did J. J. Gibson, R. L. Gregory, and Helmholtz) that the evolving visual system did not have to cope with problems of arbitrary complexity (i.e., not like solving a problem in number theory, for example). The system can capitalize, instead, on certain statistical regularities in the natural world-regularities based on the physics of matter, and these properties can be used to impose constraints on solutions to perceptual problems. But how do you go about identifying these constraints? It would be wonderful if they could be deduced from first principles, of course, but you really can’t do this because you never know which particular constraints a given creature is exploiting unless you watch what it is doing. For example, at some abstract level both bats and humans have the same problem-avoiding obstacles and grasping edible objects (either with the mouth or with the hands)-but bats use echolocation and humans use a variety of depth cues-primarily visual-such as stereo, motion parallax, convergence, etc. And there is no way you could have guessed that bats used echolocation unless you did bat psychophysics-e.g., jamming their sonar to see what happens to their behavior. In this context, Tsotsos also makes a valid point. His work suggests that in addition to natural constraints (imposed by the environment), there is also another important source of constraints, namely, that arising from computability and resources available for computation. This is just as real

and in some ways more fundamental from a theoretical perspective since such constraints would apply regardless of sensory modality or domain of application. Finally, it is surely obvious that natural constraints, by themselves, do not impose a unique solution to perceptual problems; there are usually far too many theoretically plausible solutions and the only way to find out which particular one is used is by doing psychophysics and physiology. Conclusion. It would seem, therefore, that many of M a d s ideas are fundamentally flawed (e.g., the notion that segmentation does not constrain early vision), whereas others may be only partially true (e.g., the idea that early vision is relatively immune from top-down influences). I hasten to add, however, that this long list of criticisms should not in any way be seen as detracting from the originality and importance of Marr’s contribution. Marr was a brilliant scholar and had he been alive today he would almost certainly have cheerfully acknowledged these shortcomings. I do hope, however, this commentary will stimulate at least some of his colleagues to incorporate our findings into a new and more viable theory of human vision. Acknowledgment. I thank the ONR and AFOSR for funding this commentary and Francis Crick, Patricia Churchland, Terry Sejnowski, Dan Plummer, Steve Cobb, and Richard Gregory for stimulating discussions. Tsotsos: Since computational behaviorists cite Ramachandran’s “collection of tricks” metaphor as biological evidence for their models, I included his work in my broad view of ”behaviorism” in order to strengthen my arguments by extending their domain of applicability to include a biological model. Unfortunately, it is clear that the term behaviorism has no single interpretation. Ramachandran’s utilitarian view was never intended as a formal model nor should it be classified as behaviorist. What does matter however, is how Ramachandran’s collection of tricks is to actually work so that human perception is the result. This is a goal of the computational behaviorists. Are all tricks always active, always looking at the whole visual field to see if they should react? It can be easily shown that this is an intractable solution. Does each simply look at specific parts of the visual field in order to reduce the amount of computation? This would not lead to the flexibility of function that human visual systems possess. The only tractable yet flexible solution is that each is activated only by an appropriate stimulus; thus an integration strategy is needed. The computational behaviorists provide one, but do so in an ultimately intractable and biologically implausible manner. Ramachandran’s contribution is to illuminate some of the interactions which must be

comprtational complexity

291

explained. Together, we both stress the fact that theorists and modelers alike must respect computational and biological realities. The physical constraints I list at the beginning of my paper are all orthogonal dimensions in design to those discussed by Marr (1982).According to Marr, the computational level of a theory addresses the questions: What is the goal of the computation? Why is it appropriate? and, What is the logic of the strategy by which it can be carried out? Marr called solutions at this level ”in principle” solutions. At the representational and algorithmic level one asks: How can this computational theory be implemented? What is the representation for the input and output? What is the algorithm for the transformation? And, finally, at the implementational level one asks: How can the representation and algorithm be realized physically? Complexity considerations (problem complexity, resources, performance specifications) span these three levels and are not just implementational details as Marr implies. If the task to be performed or the algorithm to be implemented is tractable, then perhaps efficiency is only an implementational detail. However, if the task is an intractable one, as vision in its most general form seems to be, complexity satisfaction is not simply a detail to contend with during implementation, just as discretization and sampling effects or numerical stability are not simply implementational details. Complexity satisfaction is a major constraint on the possible solutions of the problem. It can distinguish between solutions that are realizable and those that are not. Ascertaining how much computation can be performed will strongly constrain which computations are chosen to actually solve the problem. It is this class of “natural constraints” which I propose play important, but until now, ignored roles in perceptual theories. It is not the case as Ramachandran states that we should purposely confuse the levels. Rather, the levels are intimately related, and they are related by other orthogonal design dimensions. Finally, I would like to strengthen Ramachandran’s argument against the independent modules view proposed by Marr. When Marr proposed the independent modules view, he was working on a hypothesis that, in the mid-to-late-I970’s, reflected current best knowledge of neurobiology. John Allman and Jon Kaas had recently discovered area MT in the owl monkey which seemed to be concerned exclusively with motion computations (Allman & Kaas, 1971). Semir Zeki had reported observations on area V4 (Zeki, 1977), and it appeared as if the role of V4 was to process color independently of motion. Since these two areas had such unique and seemingly independent properties, a good hypothesis to test would be whether or not the independence applied throughout the visual cortex. This would also be good for computational modelers; we could work on solving simpler and smaller sub-problems, and then only worry about their

I. K Tkc&m

292

integration into a whole rather than have to deal with the many interactions among functionalities. This was a very sensible thing to propose at the time, and David Marr left his mark on the field for realizing this. Evidence accumulated since then, however, paints a very different picture of the visual cortex and a serious look at the current neurobiology leads to strong contradiction. The paper by Felleman and Van Essen (1991), for example, if anything else, is a crystal clear demonstration that no area of the visual cortex is without massive input from many other areas, most of the pathways are both bottom-up as well as top-down, and further that we are quite in the dark about the details of what each of the visual areas is computing. Even the independent P and M pathways distinction has fallen by the wayside (Maunsell, 1992; Martin, 1992). The view recently proposed by Oliver Braddick on the computations underlying the perception of motion is even more problematic (Braddick, 1992). He cites evidence that leads him to believe that the computations are composed of many interacting computational loops and re-entrant processing streams. No independent modules here! The hypothesis has been refuted with respect to biological visual systems and those who continue to follow that perspective are out of date.

REFERENCES ALLMAN, J. M., & KAAS, J. H. (1971). A Representation of the visual field in the caudal third of the middle temporal temporal gyrus of the owl monkey. Brain Research, 31, 85-105. BALLARD, D. (1989). Reference frames for animate vision. In Proceedings of the Eleventh lnternational joint Conference on Artificial Intelligence (pp. 1635-1641).Palo Alto, CA: Morgan Kaufmann. [VSR] BRADDICK, 0. (1992). Visual Perception: Motion may be seen but not used. Current Biology, 2, 597-599. BROOKS, R. (1986). A Layered Intelligent Control System for a Mobile Robot. IEEE Journal of Robotics and Automation, 2, 14-23. BROOKS, R., (1991a). Intelligence without representation. Artificial Intelligence, 47, 139-159. BROOKS, R. (1991b). Intelligence without reason. In Proceedings of the Twelve International joint Conference on Artificial Intelligence (pp. 569-595).Palo Alto, CA: Morgan Kaufmann. BYLANDER, T., ALLEMANG, D., TANNER, M., JOSEPHSON, J. (1989). Some results Concerning the Computational Complexity of Abduction. In Proceedings of the First lnternational Conference on Principles of

Knowledge Representation and Reasoning (pp. 44-54). Palo Alto, CA: Morgan Kaufmann. CHURCH, A. (1936). An unsolvable problem of elementary number theory. American Journal of Mathematics, 58, 345-363. CHURCHLAND, P., RAMACHANDRAN, V. S., & SEJNOWSKI, T. (1993). A critique of pure vision. Cambridge, MA: MIT Press. [VSRI COOK, S. (1971). The complexity of theorem-proving procedures. In Third Annual Symposium on Theory of Computing (pp. 151-158). New York Association for Computing Machinery. DAVIS, M. (1958). Computability and Unsolvability. New York: McGraw-Hill. DAVIS, M., (1965). The Undecidable. New York: Hewlett Raven Press. DOWLING, J. (1987). The Retina: A n Approachable Part of the Brain. Cambridge, MA: Harvard University Press. DUKE-ELDER, S. W., (1949). Textbook of ophtalrnology (vol. 4). St. Louis, MS: Mosby. [VSRI FELDMAN, J., & BALLARD, D. (1982). Connectionist models and their properties. Cognitive Science, 6, 205-254. FELLEMAN, D., & VAN ESSEN, D. (1991). Distributed hierarchical processing in primate cerebral cortex. Cerebral Cortex, 1:1, 1 4 7 . GAREY, M., & JOHNSON, D. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco: Freeman. GODBEER, G. (1987). The Computational Complexity of the Stable Configuration Problem for Connectionist Models (Technical Report No. 20888). Toronto: University of Toronto, Department of Computer Science. GOPALKRISHNAN, P., PAMAKRISHNAN, I., & KANAL, L. (1991). Approximate algorithms for the knapsack problem on parallel computers. Information and Computation, 91, 155-171. GREGORY, R. L. (1970). The Intelligent Eye. New York: McGraw-Hill. [VSRI GRIMSON, E. (1988). The Combinatorics of Object Recognition in Cluttered Environments using Constrained Search. In Proceedings of the Second International Conference on Computer Vision (pp. 218-227). Silver Spring, MD: IEEE Coputer Society Press. HELMHOLTZ, H. v. (1963). Handbook of Physiological Optics. New York: Dover. (Translated by J. P. C. Southall. Originally published in 1867). JUDD, J. S., (1990). Neural network design and the complexity of learning. Cambridge, MA: MIT Press. JULESZ, B. (1971). Foundations of Cyclopean Perception. Chicago: University of Chicago Press. [VSRI

294

J. K TkhX

KAUTZ, H., & SELMAN, B. (1990). Hard Problems for Simple Default Logics. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (pp. 189-197). Palo Alto, CA: Morgan Kaufmann. KIROUSIS, L., & PAPADIMITRIOU, C. (1988). The complexity of recognizing polyhedral scenes. Journal of Computer and System Sciences, 37, 14-38. KIRSH, D. (1991). Today the earwig, tomorrow man? Artificial Intelligence, 47, 161-184. M A R R , D. (1982). Vision: A computational investigation into the human representation and processing of visual information. San Francisco: Freeman. MARTIN, K. (1992). Visual Cortex: Parallel pathways converge. Current Biology, 2, 555-557. MAUNSELL, J. (1992). Functional visual streams. Current Opinion in Neurobiology, 2, 506-510. NAKAYAMA, K., SHIMOJO, S., & RAMACHANDRAN, V. S. (1990). Transparency: Relation and depth, subjective contours, luminance and neon spreading. Perception, 19,497-513. [VSRI RABBITT, P. (1978). Sorting, categorization, and visual search. In E. Carterette & M. Freidman (Eds.), Handbook of Perception: Perceptual Processing (vol. 9, pp. 85-136). New York: Academic Press. RAMACHANDRAN, V. S. (1985a). Apparent motion of subjective surfaces. Perception, 14, 127-134. [VSRI RAMACHANDRAN, V. S. (1985b). Guest editorial: The neurobiology of perception. Perception, 14, 97-105. [VSRI RAMACHANDRAN, V. S. (1986). Illusory contours capture stereopsis and apparent motion. Perception 6 Psychophysics, 39, 361-373. [VSRI RAMACHANDRAN, V. S. (1988). Perception of depth from shading. Scientific American, 269(8), 76-83. [VSR] RAMACHANDRAN, V. S. (1989). Visual perception in people and machines. Presidential lecture given at the annual meeting of the Society for Neuroscience, Phoenix, AZ. [VSR] RAMACHANDRAN, V. S. (1990). Interactions between motion, depth, color, and form: The Utilitarian theory of perception. In C. Blakemore (Ed.), Vision: Coding and efficiency (pp. 346-360). New York: Cambridge University Press. RAMACHANDRAN, V. S. (1992). Blind spots. Scientific American, 266(5), 86-91. [VSR] RAMACHANDRAN, V. S., & ANSTIS, S. M. (1986). Perception of apparent motion. Scientific American, 254(6), 102-109. [VSRI

RAMACHANDRAN, V. S., COBB, S., & ROGERS-RAMACHANDRAN, D. (1988). Recovering 3-D structure from motion: Some new constraints. Perception & Psychophysics, 44, 390-393. [VSRI RAMACHANDRAN, V., COBB, S., & VALENTE, C. (1992). Dynamic anomalous retinal correspondence: A problem for theories of binocular vision. Unpublished manuscript. [VSR] RAMACHANDRAN, V. S., & GREGORY, R. L. (1978). Does colour provide an input to human motion perception? Nature, 275,55-56. [VSRI RAMACHANDRAN, V. S., & GREGORY, R. L. (1991). Perceptual filling in of artificially induced scoromas in human vision. Nature, 350, 699702. [VSRI RAMACHANDRAN, V., INTRILAGATOR, J., & CAVANAGH, P. (unpublished manuscript). Moving sound sources generate motion capture. [VSRI RAMACHANDRAN, V. S., RAO, V. M., & VIDYASAGAR, T. (1973). Apparent motion with subjective contours. Vision Research, 13, 1399-1401. [VSRI RAMACHANDRAN, V. S., ROGERS-RAMACHANDRAN, D., STEWART, M., & PONS, T. (1992). Perceptual correlates of massive cortical reorganization. Science, 258, 1159-1160. [VSR] RAMACHANDRAN, V. S., STEWART, M., & ROGERS-RAMACHANDRAN, D. (1992). Perceptual correlates of massive cortical reorganization. Neuroreport, 3, 583-586. [VSRI SELMAN, B., & KAUTZ, H. (1990). Model-Preference Default Theories. Artificial intelligence, 45, 287-322. SELMAN, B., & LEVESQUE, H. (1989a). Abductive and Default Reasoning: A Computational Core. In Proceedings of the Eighth National Conference on Artificial Intelligence (pp. 343-348). Palo Alto, CA: Morgan Kaufmann. SELMAN, B., & LEVESQUE, H. (1989b). The Tractability of Path-Based Inheritance. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (pp. 1140-1145). Palo Alto, CA: Morgan Kaufmann. STOCKMEYER, L., & CHANDRA, A. (1988). Intrinsically difficult problems. Scientific American Trends in Computing (vol. 1, pp. 88-97). New York: Scientific American. TREISMAN, A. (1988). Features and objects: The fourteenth Bartlett memorial lecture. Quarterly Journal of Experimental Psychology, 40(A2), 201-237. TSOTSOS, J. K. (1988). A 'complexity level' analysis of immediate vision. International Journal of Computer Vision, 1, 303-320.

296

1.K. T&

TSOTSOS, J. K. (1989). The Complexity of Perceptual Search Tasks. In Proceedings of the Eleventh International Ioint Conference on Artificial Intelligence (pp. 1571-1577). Palo Alto, CA: Morgan Kaufmann. TSOTSOS, J. K. (1990a). A Complexity Level Analysis of Vision. Behavioral and Brain Sciences, 13, 423-455. TSOTSOS, J. K. (1990b). A Little Complexity Analysis Goes a Long Way. Behavioral and Brain Sciences, 13, 459-469. TSOTSOS, J. K. (1991a). Is Complexity Analysis Appropriate for Analyzing Biological Systems? Behavioral and Brain Sciences, 14, 770-773. TSOTSOS, J. K. (1991b). Localizing Stimuli in a Sensory Field Using an Inhibitory A t tentional Beam (Technical Report RBCV-TR-91-37). Toronto: University of Toronto, Department of Computer Science. TSOTSOS, J. K. (1992a). Behaviorist intelligence and the scaling problem (Technical Report RBCV-TR-92-42). Toronto: University of Toronto, Department of Computer Science. TSOTSOS, J. K. (1992b). On the relative complexity of active vs passive visual search. International Journal of Computer Vision, 7, 127-141. TURING, A. (1937). On computable numbers with an application to the Entscheidungs problem. Proceedings of the London Mathematical Society, 2, 230-265. UHR, L. (1980). Psychological motivation and underlying concepts. In S. Tanimoto & A. Klinger (Eds.), Structured computer vision (pp. 1-30). New York Academic Press. VAN ESSEN, D., & ANDERSON, C. H. (1990). Reference frames and dynamic remapping processes in vision. In E. L. Schwartz (Ed.), Computational Neuroscience (pp. 278-294). Cambridge, MA: MIT Press. [VSRI WATSON, J. B. (1919). Psychology from the Standpoint of a Behaviorist. Philadelphia: Lippincott. YASHUHARA, A., (1971). Recursive Function Theory and Logic. New York: Academic Press. ZEKI, S. (1977). Colour coding in the superior temporal sulcus of the rhesus monkey visual cortex. Philosophical Transactions of the Royal Society of London, B197, 195-223. ZIPSER, D., & ANDERSON, R. (1988). A back propagation network that simulates response properties of a subset of a posterior parietal neurons. Nature, 331,676-684. [VSRI

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

297

ON THE NEED FOR A GENERAL QUANTITATIVE THEORY OF PATTERN SIMILARITY James T. Townsend and Robin D. Thomas Department of Psychology Indiana University, Bloomington, Indiana

ABSTRACT The concept of similarity evokes different meanings for different people. However similarity is conceived, it certainly plays an important role in the modeling of pattern perception. The contrasting approaches toward psychological similarity taken by the measurement theorists, the psychometricians of multidimensional scaling, and the process model oriented cognitive psychologists should be reconciled if a full account of the role of similarity in perception is to be adequately developed. This essay attempts to initiate a preliminary synthesis of these approaches while introducing some important philosophical questions concerning the application of multidimensional scaling ( M D S ) models of similarity. These questions arise from a deeper analytical investigation of the foundations of modeling perception. Along the way, the reader is introduced to mathematical concepts from topology and geometry that underlie the use of M D S . It is hoped that the discussion will provide some tutorial benefits as well as open the door to a more unified treatment of similarity and its role in psychological representation.

The general goals of the present anthology involve a search for reasons that a generally accepted theory of perception has not arisen after more than a century of concerted experimental and allied theoretical attack. As asserted in the Preface, this state of affairs calls for a determined examination of the conceptual and philosophical foundations of perceptual science. A second possible subsidiary aim is the analysis of the reductionistic case for perception. Before taking up the main purpose specific to

298

1.T. TolonsenAandR. D.Thomas

this essay, a few comments are in order regarding the goals that are general to the book as a whole. Just as in any complex question in science, there are probably a number of contributing causes to the absence of a general and accepted theory of perception. Some of these are likely remediable whereas others may be inherent to the field. Inherent difficulties involve some parts of the reductionistic problem. Scientists work at a myriad of different levels of perception, from macroscopic regions such as perceptual categorization and perception of emotional expression, to biochemistry and quanta1 effects at sensory synapses. The very languages of the different levels, not to mention the standard prejudices (Dr. Neuroscientist: ”Research on macroscopic models and behavioral data is sloppy and unscientific.” Dr. Macro-perceptual-scientist: ‘Neuroscience is usually so microscopic as to bear almost no relation to real perceptual phenomena.”) militate against much in the way of interdisciplinary progress. Indeed the very plethora of levels under study suggest that a truly general, level-encompassing theory may be a chimera-impossible in principle. Quite obviously, even though chemistry can in principle be reduced to physics, only a tiny paucity of interconnecting laws have actually been formulated. This state of affairs is even more true of fields like organic chemistry, biochemistry, and microbiology. Without wishing to give short shrift to the deep puzzles associated with the reductionist question, let us just make the following statement: Our own preference is that the behavioral or black-box theories not be in obvious contradistinction to the physiological or anatomical facts or ”laws.” However, outside of that mild prescription, we believe that it is legitimate and worthy to develop process models and theories, even socalled connectionist ones, without undue homage to the physiological world. This does not imply, of course, that provocative bridges cannot be built across behavioral and physiological disciplines. Perhaps a more profound reason for the failure of a general perceptual theory to surface, even one at a single level of discourse, is a combination o f 1. Continually emerging challenging sets of data that upset contemporary theoretical “apple carts.” 2. An inability of laboratories utilizing different theoretical and methodological tools to synthesize their findings, not to mention their perspectives, in order to produce a widely cogent theory. Thus, we find even at roughly the same level of attack, that some investigators focus on quite local phenomena, others quite broad phenomena. Perceptual scientists run the gamut with regard to their sophistication in mathematics, perceptual and /or psychophysical background and knowledge, and acquaintance with physiological lore, information pro-

cessing vs Gestalt vs Ecological vs (insert your own favorite "school" of thought) factions. The last problem brings up the particular subject matter of the present essay. A central hallmark of much research into several major areas of perception has been the concept of similarity. Such areas include many aspects of form perception (recognition, memory, discrimination, gestalt vs analytic, independent feature perception, etc.), categorization, study of perceptual dimension, perceptual scaling and measurement. The theme of similarity crops up increasingly in "higher processes" such as decision making and problem solving and thinking, and is considered to form a major axis of thought by a number of philosophers. Yet it seems fair to say that even a generally accepted theory of similarity, much less a general theory of perception, is far from reality. In searching for the reasons for this lacuna, we may hope to locate some of the causes of the analogous difficulty in more general theories. However, our foremost goal will concern similarity per se. Certainly, even within this relatively limited arena, there are many directions a (somewhat philosophically bent) scientific sleuth might take. Our own investigation naturally centers around quantitative descriptions of the perceptual /similarity issue. In particular, it has struck us as extremely unfortunate that several different quantitative approaches, each of which has offered valuable information on the similarity qua perception topic, have not somehow been brought together, to the mutual benefit of each, and certainly to the perceptual community at large. We now move to discuss this specific issue and some of the many ramifications and enigmas it prompts. The enormous amount of research accomplished on the psychological scaling of similarity roughly breaks down into three overlapping regions: the foundational approach, the substantive model based approach, and the descriptive multidimensional scaling approach (MDS). This is not the place to attempt a detailed description of these approaches, or indeed even a thorough comparison, a task that might be valuable although challenging, having to our knowledge never been attempted. Also, the focus in this paper will be on relatively low-level pattern processes, rather than on higher level cognitive mechanisms (e.g., see van Leeuwen, 1992). For instance, it has long been evident that the brain is sufficiently agile to simulate digital or analog machinery, as the task demands. In any event, an added attraction (we hope) in the following account and discussion is a certain technical tutorial, but we feel valuable, background required for our deliberation. In order to get things started, and at the risk of brevity in extremis: 1. The foundational approach examines the conditions on psychological

300

1.T. Tuumsendand R. D. Thomas

scales treated as qualitative objects that are necessary and sufficient for their representation in various types of mathematically specified spaces. This approach has largely been confined to deterministic (non-probabilistic) spaces (e.g., see Krantz, Luce, Suppes, & Tversky, 1971; Luce, Krantz, Suppes, & Tversky, 1990; Suppes, Krantz, Luce, & Tversky, 1989). 2. The substantive modeling approach typically assumes some type of perceptual or psychological space, in many cases, endowed with probability distributions and then investigates predictions for various kinds of experimental paradigms. One example of this approach is the general recognition theory of Ashby, Townsend, and colleagues, which is a generalization of signal detection theory to the multidimensional case (Ashby & Townsend, 1986; Ashby & Perrin, 1988; Ashby & Gott, 1988; Ashby & Lee, 1991; Kadlec & Townsend, 1992a, 1992b). Other examples of multidimensional models of perception and similarity include the generalized context model of Nosofsky (Nosofsky, 1984, 1985, 1986) and the stochastic model of similarity and judgment of Ennis and colleagues (Ennis & Mullen, 1986a, 1986b; Ennis, Palen, & Mullen, 1988; Ennis & Mullen, 1992). 3. The descriptive MDS approach is most often applied to similarity ratings or other "proximity" data with the object of unveiling the underlying psychological space (e.g., Shepard, 1964a; Kruskal & Wish, 1978; Carroll & Arabie, 1980). The present study will touch on each of the three throughout the discussion. Although it is difficult, if not impossible, to be an expert in all these areas, we agree with Uttal (1988, 1992) and Newel1 (1991) that more theoretical and empirical syntheses are needed in cognitive sciences today.' First, a disclaimer is in order. The similarity judgment format is intended only to provide a milieu for the raising of critical issues concerning psychological spaces, not to review data or come to theoretical conclusions about how it takes place. The concept of similarity judgment enables the putting aside of ancillary issues that arise in other perceptual and psychophysical contexts, such as identification, recognition, discrimination and so on. However, because some of these paradigms are currently popular in psychology, and because many of the most interesting theoretical work has been done in these contexts, we often have recourse to their approaches in our deliberation. It should be noted, though, that the concept of similarity can be very task dependent. Stimuli that are similar according to discriminability measures (e.g., same-different RTs) may not be rated as similar by subjects in a similarity judgment task. For example, We have attempted to deliver a set of references to readers that will aid them in broaching various literatures. Needless to say, in such a broad enterprise as the present, there is serious danger of omitting any particular reader's pet reference,not to mention one of their own important articles. We apologize in advance for any such transgression.

PuffemSimhriity

301

a common finding is that a tilted T is much easier to detect among a background of upright T’s than is an L among upright T’s (see Pomerantz, 1981, for a review). When asked to judge pairwise similarity, however, subjects rate the tilted T as more similar to upright T’s than the L is to upright T‘s. If one accepts the hypothesis that ease of discrimination is inversely related to similarity these results appear to be contradictory. We believe the best approach to this problem is to develop a process model that systematically accounts for results of different paradigms. A popular way of modeling similarity in psychology is to posit that percepts or other psychological “data” are represented as points (or probability distributions, if the system is noisy, as in Ennis, et. al., 1988) in an abstract psychological space and that (didsimilarities correspond to the distances between points in the space (see, Nosofsky, 1992, for a review). One reason, among others, for the success of these geometric models of similarity is the intuitive result of having a small number of dimensions with which to characterize a set of stimuli. In fact, part of deriving a scaling representation is to discover the smallest number of dimensions that, together with the distances between the points in the space, adequately capture the observed similarity orderings. Also, in some non-distance based models of similarity, such as the version of the aforementioned general recognition theory that applies to the similarity rating task (Ashby & Perrin, 1988; Ashby & Lee, 1991), psychological dimensions are still assumed to exist and play a central role in the derivation of similarity.2 The foundational approach too, typically assumes that some sort of primitive psychological ”scales” exist to represent values on the equally primitive ”dimensions,” but the nice spatial properties are derived from weaker qualitative notions and machinery, rather than being assumed a priori, to exist unlike the other methods. For instance, in the MDS descriptive tradition as opposed to the foundational, one assumes to begin with, that, say, one of the members of the Minkowski family or ”power” metrics applies, and uses one of the MDS algorithms to attempt to uncover which one and what the actual configuration is.

*

Some may be concerned about the applicability of geometric models of similarity due to demonstrations of violations of the basic metric axioms by Tversky (1977).However, it is the opinion of the authors that dimensional representations may be appropriate and many of the observed violations are perhaps due to stimulus or response biases entering into the decision process (e.g., see Nosofsky, 1991,1992). Thus, a fullprocess model needs to be specified so that contributions from each part of it may be assessed empirically. Furthermore, it is sometimes overlooked that many of the topological and algebraic conditions that underpin Tversky’s feature model, are the same as those leading to dimensional representations. Only the relaxation of certain key links permits the abrogation of such predictions as the triangle inequality. Hence, many of the questions raised in the context of dimensional and metric representation surface again with regard to such models.

302

1.T. Townsendand R. D.Thomas

Within this context we set out the issues with which we shall deal. There will be lots of questions and few answers, but we feel that the discussion will help to open up important avenues of theoretical, methodological and empirical investigation. One of the central questions we will be concerned with is that of the origin and nature of the psychological dimensions. This topic necessitates some introduction to the concept of dimension as employed in mathematics, but also how dimensions may relate to stimuli on the one hand and mental representations, such as memories on the other. Another issue concerns the implications that the “true” dynamic perceptual and cognitive transformations of these spatial representations have for the uncovering and modeling of the dimensions and spatial structure. Thus, it might be asked ”why do MDS procedures seem to work as well as they do?” So far, there has been a paucity of research that establishes the MDS algorithms on a mathematically rigorous basis. Some cognitive psychologists, on the other hand, seem to feel that “if it works, why fix it.” We discuss this aspect further below. The foundational approach is certainly rigorous but faces similar queries. For instance, one may ask whether the kind of primitive assumptions that measurement theorists make about the psychological values actually mirror something of the essence of the way the brain acquires dimensional information about real-world information. How different are these assumptions and theorems from simply assuming the spaces a priori, and how are they helpful in our understanding? And yet further, are plausible psychological transformations on stimuli and later within the cognitive apparatus, likely to preserve or evoke the constraints required to produce the desired spaces? Thus, it may be asked whether such more primitive and weaker assumptions are more resistant to deformation than would be the tighter metric information, should one just postulate the latter. We shall discuss these and other issues, such as dimension or feature selection within a general topological framework. To begin, consider the question as to whether the tenets that permit the establishment of a pleasing geometry are likely to be met by reasonable perceptual processes. To some this issue may seem to belong to the domain of psychophysics rather than cognitive psychology. In fact, some have argued that cognitive psychologists should not be concerned with the dependence of psychological attributes on physical properties but only with the structural relationships among the perceived objects in an abstract psychological space (e.g., see Shepard, 1982, 1987; Nosofsky, 1992). Nevertheless, we propose that it is the task and variation in the (physical) stimulus that together with psychological transformations produce dimensionality, the topology, and geometry (metrics, etc.) of this

PuffemSimilarity

303

psychological space. Without denying the value of the psychological space per se, we tend toward the view of S. S. Stevens (19511, who claimed that one cannot understand perception without understanding the nature of the stimulus, presumably in relation to the perceptual response. We would extend this notion to include the experimental variation that results in the set of stimuli presented to an observer, as well as the stated task requirement for that observer. In the simplest case, the situation is the same as that stipulated by the foundational measurement theorists, namely, that each psychological dimension will be some function of the corresponding physical one (e.g., see Beals, Krantz, & Tversky, 1968; Tversky & Krantz, 1970). In more complex cases, the psychological dimensions may be many-many functions of a number of physical dimensions, but they are functions of the physical characteristics nonetheless. Most investigators tacitly appear to accept this fact, while perhaps overtly denying to have interest of it, when they explicitly manipulate specified physical dimensions (such as size or orientation of angle) often orthogonally to obtain similarity data. At present, any investigation of the foundational issues of "cognitive scaling" must rely on the measurement approach which, in turn, predicates the above scenario. Even if one accepts the attempt to disengage psychological and physical geometry, it remains to be justified theoretically why or whether, in fact, a real organic cognitive system needs to possess representations that are mathematically or analytically "nice" such as metric spaces. Ultimately, mental representations have to serve the needs of an organism responding to stimuli (i.e., physical stimuli) in the environment. Why and how a metric distance representation of similarity should arise to serve this need, and be preserved throughout the dynamic processing flow, remains to be explained. For instance, could it be that arguments in the vein of the evolutionarily optimal assumptions proposed by John Anderson (1990) might be advanced? Or, may cogent ideas based on postulates that cover very large classes of models (e.g., employing general structures such those based on geometric measures as in Shepard, 1987) or generation through concepts of ecological necessity, (e.g., Gibson, 1986; Burton & Turvey, 1990; Cutting, 1991)be put forth? Of course, although deductions following from the latter two approaches are certainly testable, it is not obvious that the more philosophical precepts under which they were initiated are falsifiable. In order to fully comprehend the issue of perceptual similarity, one must understand the origin of the psychological space with respect to the environment in addition to any subsequent generalization processes that act on it. Now, it seems reasonable to conclude from the many multidimen-

304

1.T. Townsendand R. D.Thomas

sional scaling studies, that mutually related psychological dimensions do in fact exist with, at least, ordinal properties. However, the existence and especially the uniqueness of particular metrics must impress the disinterested reader as much less well-founded. Even the claim that the city-block metric is (or should be) associated with separable stimulus dimensions has come under increasing doubt. In our opinion, an ultimate goal should be the enfolding of all three of the above approaches to psychological similarity into the substantive modeling approach. In fact, our perspective throughout this paper will be to conceive of the overall cognizer as a dynamic system, which will ultimately serve as a foundation for other theoretical ventures. First we break the overall system into a small set of subsystems, whose basic responsibilities are time-honored. These are: Early transformation and, when needed, feature analysis, and then a later comparison or matching phase, followed finally by a possibly biased response. A difference from previous approaches is that we are beginning an investigation of what happens to dimensional structure and similarity structure throughout the processing chain. The present study therefore is also encouraging the institution of a synthesis of process models with measurement models and with topological and geometric questions. A fully temporally specified information processing model of similarity ratings must ultimately specify the actual dynamic of processing. Our discussion is intended to broach wider questions of measurement, topology and dimension within the context, but without the specifics, of dynamic information processing. A word is in order concerning the ubiquitous effects of context, particularly on scaling results. Early research on psychophysical scaling centered around discovering "the" function, be it logarithmic, power, etc., relating subjective magnitude to physical magnitude or intensity. Lurking behind this body of research was the tacit assumption that early sensory and low level perceptual processes are relatively invariant across situations in their structure and mechanisms. This view has come under increasing doubt. A striking example of this failure of invariance can be found in a classic experiment by Garner (1954) in which, on each trial, he asked subjects to state whether a second tone was more or less than half as loud as a first tone presented at the beginning of the trial. However, only half of the subjects heard tones that were lying above as well as below the intensity level conventionally accepted as half as loud as the standard tones. The other subjects should have protested as they only heard tones below the accepted half-way point. In fact, they did not protest, which has been taken as evidence that context seems to have forced subjects to scale the stimuli differently than in a standard magnitude estimation paradigm (for implications of this finding see Laming, 1991, in his

PuffernSirnllmity

305

commentary of Krueger, 1989). More recently, Marks (1992) demonstrates another dramatic effect of stimulus context on subjective loudness perception. He showed that relative loudnesses of two tones of fixed but different frequencies changed reliably as a function of the intensity range comprising the stimulus set in both a scaling paradigm and a direct matching task. Other empirical phenomena in scaling and dimensional judgment literature such as the semantic congruity effect, stimulus density and frequency effects, among others, speak to the obvious need to include context in any full model of the perceptual process (Banks, 1977; Birnbaum, 1974, 1978; Cech & Shoben, 1985; Holyoak & Mah, 1981, 1982; Parducci, 1965, 1992; Petzold, 1992). In the present paper, however, we will have to overlook context effects in our treatise not because they are unimportant but simply to keep the discussion at a manageable level. A1though some topics from relatively abstract mathematics will be employed, considerable care will be taken to ensure that the reader with at least a background in calculus will be able to follow the line of discussion?

TOPOLOGY, UNIFORM SPACES, AND DIMENSION An important aspect of our discussion centers around foundational measurement work on psychological scales of distance and similarity. The background with which the foundational approach begins, includes an impressive history of mathematical work in geometry and related fields. We cannot hope even to adequately limn in this history and the reader is referred to Suppes, et. al., (1989; vol. 2) for a review and many additional references. However, it seems to us that to start to appreciate the excitement as well as the daunting challenges of the similarity scaling problem, a brief acquaintance with the some of the coarser spaces underlying geometry is invaluable. We want to note, in starting that some of the following topological notions can be supplanted in measurement structures by algebraic counterparts, although certain technical "analytic" conditions are always present. We are of the belief, now that experimental psychology journals are no longer terrified of some calculus and elementary probability theory (albeit often consigned to appendices), that the time is nigh where psychologists could, with profit, bring to bear on theoretical problems, more advanced avenues of mathematics (see Cliff, 1992, for related comments w t h respect to measurement theory). Some writers, including us on occasion, whose own research necessitates quite abstruse tools, attempt to avoid frightening off the reader by trying to reduce the discussion to common parlance. This strategy can be pedagogically valuable. However, we suspect that sometimes it may be preferable to begin to introduce readers to some of the common terms and concepts employed in such fields in order to help them begin to delve into them on their own.

306

I. T. Taumsendand R. D.Thomas

Basically, a topology on a set of points X is a collection, z, of subsets of X, called ”open sets” with the following property: This collection is closed under finite set intersection and unlimited set union. In addition, the whole set, X, and the empty set, 4, are in z (i.e., are members of the collection of open sets). Closed sets are defined as the complements of open sets in the sense that C is a closed subset of X if and only if there exists an open set 0 such that C = X-0. Special cases of open and closed sets are the open intervals and closed intervals of the real line, with its ordinary geometry. Strictly, a topological space is denoted by the tuple (X,z) but often just called X with the topology assumed. Such spaces can be so ill-organized that little of interest can be said about them. One can build topological spaces of increasing ”strength by imposing more and more constraints. After sufficient such conditions are imposed, the topological space is metrizable, that is, a metric d ( x l , x 2 ) can be defined on all points XI and x2 in X obeying the usual properties:

Such a metric must deliver the same topology with which one began. That is, all the open sets of the original topology must be derivable from sets of the form, B(x, d, T ) where B is a ”ball” or ”sphere” around the point x, based on metric d, of “radius” T. Such sets form a so-called ”basis” of the space and all open sets can be generated from these by taking unions and finite numbers of intersections. Of course, one can in many cases simply assume that a metric, for example, the Euclidean, applies to a space of points (in this case, with the usual set of orthogonal coordinates), and the topology generated immediately from that metric (see Munkres, 1976, for more details). A very interesting type of space exists intermediate between ”raw” topological spaces and metric spaces; these are known as “uniform spaces.” These are a bit more abstract and the reader meeting them for the first time may not fully comprehend them. However, their importance in the present context can probably be appreciated. There are several equivalent ways of defining them. The one we use seems fairly reasonable. A uniform space, like a topological space, is based on a class of subsets. However, in this case the class of subsets U of a set X is a set of subsets from the Cartesian product XxX, that is, U is composed of pairs of points from X. Moreover, in this instance, the class is closed under finite intersection and inclusion, instead of finite intersection and arbitrary

Pattern Similarity

307

union. The inclusion implies that if set A is in the class, and A is a subset of set B, then B is in the class also. Sets such as A, B that are in U are typically called "ensembles" (alternatively some authors call these "entourages") and generically denoted by E. Also unlike topological spaces, the empty set q?~ is not included in the class, although the "universe" set, XxX, the set of all pairs of points from X, is included in U. We do need the notion of "concatenation" of the ensemble sets, for example, AB = C, also a member of U. This concatenation builds another ensemble by forming, for all pairs ( X I , x 2 ) and ( ~ 2x,3 ) the pair ( X I , x 3 ) . All such final pairs are in C. In addition there are some additional conditions that a uniform space must meet: 1. The intersection of all ensembles in U is precisely the diagonal, D. That is, D equals the set of all pairs ( x , x ) where x is contained in X. 2. For any ensemble E, E-1 is also an ensemble, where E-I is the set of pairs (x2, X I ) where the pairs ( X I , x2) are contained in E. Thus, E-I is made up of the reverse pairs of E. 3. For any E in U there is another ensemble B such that BB = E (for an introduction to uniform spaces and their relation to topological spaces see James, 1987). Although the above description is indeed rather abstract, we can espy in them a primitive and qualitative premetric structure. To see this, suppose we take a metric space, X, with metric d, and view the resultant ensembles and their relationships. First, construct the ensembles by setting E , = { ( X I , x 2 ) E XxX I & X I , x g ) c E}, that is all pairs whose distance in X is less than E go into the particular ensemble associated with the positive real number E. Now, we can discover in (I) a primitive, nonnumerical version of the minimality of a metric, that d ( x , x ) = 0, in the fact that the diagonal [with points of the form ( x , x ) ] is a subset of every ensemble, since (x, x ) belongs to all such ensembles. Obviously, due to the symmetry of the metric d, Condition (2) is trivially satisfied. Hence, (2) is a precursor of the symmetry found in the metric formulation. For (3), consider any ensemble E, and form the new ensemble E(&p].By the triangle inequality, E ( 4 2 ) E(&p)c E,so Condition (3) is fulfilled. Hence, (3) is a qualitative version of the triangle inequality. Finally, the reader may check that the other properties, such as closure in supersets (all sets containing smaller ensembles are also ensembles), are also satisfied in the metric case. Now it can be shown that every uniform space generates a topology but more interestingly, every uniform space permits something close to a metric to be defined on it, a so-called pseudo-metric. A pseudo-metric has all the properties of a metric except that & X I , xg) can be equal to 0 without XI = xg. That is, one can find points that are not the same point, yet have zero distance between them. That could be a good thing in some psycho-

308

\. T. Townsendand R. D.Thomas

logical applications. Note too, that the powerful triangle inequality is in force. Thus, the qualitative structure inherent in a uniform space is formidable, and the original classes of ordered sets of pairs can be reproduced through the use of the numerical pseudo-metric. Even topological spaces that do not satisfy the conditions for a uniform space always permit a so-called semimetric to be imposed on them (see Kopperman, 1988). A semimetric has properties that are analogous to metrics but the ”values” do not necessarily satisfy the stringent order relations of the real numbers. Returning to uniform spaces, with some upgrading of the conditions, actual metrics can be brought forth, that reproduce the ”uniformity” that is, the uniform space, just as a metric may reproduce the original topology. Foundational measurement investigators, in collaboration with a mathematician and drawing on classical qualitative geometric research in mathematics (e.g., Blumenthal, 1950; especially Buseman, 19551, employed the strong implications associated with the ordered classes of ensembles, to derive impressive metric space results in the 1960s (e.g., Beals & Krantz, 1967; Beals, et. al., 1968). The important point here, of course, is that the qualitative notions accompanying these primitive spaces, demand less in assumptions than simply assuming specific metric spaces. Or, more accurately, they tell what conditions must be obeyed in real world systems, in order for a metric to exist. Yet, if the psychological data obey the qualitative conditions (along with some untestable ”technical” conditions”), then we may be assured that the implicated psychological metric space exists, and at least in principle, can even construct it. Perhaps the most important conditions for psychologists, in addition to the uniform space assumptions, are those “betweenness strictures” that help to produce ”geodesics” between any two points in the space. Geodesics are analogs to straight lines in Euclidean space and thus take on the character of distance in the more general spaces. Beals and Krantz (1967) show that their conditions allow the imposition of unique geodesics on their spaces, geodesics that are unique up to multiplication by a positive scale (much like the ratio scale concept). For a less technical account with psychological discussion see Beals, et. al., (1968). Further work applied knowledge gained in research on general foundational scaling issues, for instance, extensive, difference, and conjoint measurement, in order to specify conditions that were sufficient to define orthogonal coordinates and more specific and refined metrics (e.g., Tversky & Krantz, 1970). The scale question plays an important role in such developments. Thus, suppose psychological distance only exists on an ordinal scale, then any transformation can be accomplished on the measurements that preserves

the order of distance. But this leaves the uniform structure unimpaired, which is what we need. Conversely, the pseudo-metric that can be defined on any uniform space might be only ordinally unique, or might lie on a stronger scale, such as ratio. These questions deserve much more treatment, including the relationship of the ordinal metric or pseudo-metric to the scales of the individual object measurement. They shall have to be left aside for now. In addition to the works on measurement listed above, Townsend and Ashby (1984)cite dangers in ignoring questions of scale type and Townsend (199213 applies measurement scale principles to reaction time. Townsend (1990b) gives results concerning a hierarchy of distributional relationships that are impervious to monotonic perturbation and hence are robust up to ordinal scale types. We have been emphasizing premetric and metric structure in our brief description, but lurking in the background is the notion of dimension, a concept not always fully understood outside mathematics and a small group of practicing scientists. Often, we still may tend to think of dimension as simply the number of quantities or measurements that are necessary to specify something. There is some truth in this statement, but like many qualitative ruminations, danger lurks in the absence of a precise formulation. For instance, Cantor (1874, e.g., see Noether & Cavaillbs, 1937) demonstrated a one-to-one correspondence between the unit interval and the unit square, seemingly implying that two dimensions could be made "equivalent? to one. However, this function was not continuous. Furthermore, Peano (1890) showed that it is possible to contrive a function that maps the unit interval in a continuous fashion, onto the entire unit square. Thus, in this mathematical sense, two numbers in the plane are like one number on the unit interval. But this function was not one-to-one. That is, two points in the square correspond to a single point on the line. This kind of research eventually led to a rigorous definition of dimension, especially through the respective work of Brouwer, Menger, and Urysohn (e.g., see Hurewicz & Wallman, 1941). A rigorous discussion of topological dimension appears in the appendix of this essay. Informally, a space of dimension n can be covered with arbitrarily small "cubes" (generalized to the notion of n-sided cubes) in some manner so that no point of the space is contained in more than n + l of the cubes; in addition, if the cubes are small enough, then at least n+l of these cubes must have a point in common. Moreover, dimension in this sense is preserved by socalled "topological" functions. The latter are one-to-one, onto, and continuous in both directions, that is both f ( x ) and f - Ware continuous. Such a function goes by the technical name of homeomorphism. Homeomorphisms always preserve topological properties, but not necessarily geometric properties. For instance, if a space is connected (i.e., cannot be de-

310

1.T. Taunsendand R. D.Thomas

composed into two nonintersecting open or closed sets), then a homeomorphism to another space must necessarily preserve this feature. However, it would not necessarily preserve distance between two points or, in vector spaces, the angle between two vectors. A small intriguing "aside" that can be skipped on first reading: Interestingly, if we consider only the rational numbers on the unit interval, we no longer have one dimension, but zero dimension! This is one of the paradoxes (or more likely, "antinomies," an apparent paradox) of the application of mathematics to science. Even though the rational numbers suffice to describe any physical phenomenon (i.e., there are enough of them and they are close enough together), most of the mathematics modeling the real world cannot be produced by the rationals alone (at least at present). And, the concept of dimension plays a strong role in science; yet, the dimension of the rationals, as pointed out, is zero. It seems likely that limitations in the accuracy of real world measurement and possibly the presence of statistical error, imply that our natural laws, taken in reference to these "coarse" measurements, act as though they were actually on the real line; for all practical purposes. The sparseness of the rationals cannot make themselves felt in such circumstances. Various philosophical and scientific aspects regarding the application of mathematics to science are discussed in a recent paper by Narens and Luce (1992). Townsend and Kadlec (1990) discuss the use of mathematics in psychology. How should stimulus patterns be defined? In many cases, a single stimulus can be specified by its values on physical dimensions. However, in even moderately complex patterns, there exist an infinity of ways in which it could be deformed to produce other patterns. It is in the potential regularity of variation in a sample of stimulus patterns that an observer must select dimensions or features to which to attend, or in any case, to employ in various psychological tasks. A fortiori, aspects of a set of stimuli that are not undergoing change are useless in assessing similarity, discrimination and so on. Consider for illustration an observer shown a graph of a continuous function y = f i x ) , with say, x lying between 0 and 1. Now there are an uncountable set of points at which the experimenter could, in principle, perturb the function in order to produce a new one. She/he might alter the third derivative, add a sine wave etc. Only the variation can tell the observer what to use to perform the necessary task. Note also in this connection, that a set of potentially infinite dimensional objects can often be defined by a single dimension. Thus, the class of functions y = f ( x ) = exp(-at) is defined by the single parameter a, hence by a single dimension, the latter having an infinite number of potential valUeS.

Pattern Similarity

31 1

A

m

c

0

c

04

Y

m m

10 .50

Frequency 10 0 Figure 1. Subjective loudness surface as a function of tone frequency and intensity fitted using SYSTAT to the data of Robinson and Dadson (1956). The curves of constant height running from the back to the front of the surface are the equal loudness contours often projected onto the frequencyintensity plane when plotted as in Fletcher & Munson (1933) and Robinson & Dadson (1956).

Any finite set of stimuli probably can be produced from a finite number of dimensional variations. Of course, these might be impossible, from a practical standpoint to ascertain. However, in some cases, such as face perception, the capability of performance in certain tasks, such as samedifferent discrimination, is so capacious, as to suggest an almost infinite dimensional perceptual space. More on high dimensional perceptual spaces later. Another important fact is that although the number of dimensions describing a space is invariant under a homeomorphic transformation, the way in which a space depends on the dimensions could be very different indeed. One such example is that of the auditory perception of a pure sinusoidal tone. As the name suggests, pure sinusoidal tones can be characterized as a sine-wave corresponding to the displacement of air particles as a function of time having the components of maximum amplitude (or in-

312

1.T.ToronsendandR. D.Thomas

tensity): frequency, and phase angle. Ignoring phaseI5a pure tone can be completely described physically by the amplitude of the wave and the frequency or cycles per unit time. The two major subjective attributes associated with pure tones are loudness and pitch. Hence, we have a two dimensional physical space being mapped into a two dimensional psychological space. However, loudness perception has been shown to be a function of both intensity and frequency (e.g., see Fletcher & Munson, 1933; Licklider, 1951; Stevens & Davis, 1938) thus violating a strong form of separability (see below). Figure 1, based on data from Robinson and Dadson (1956), shows the subjective loudness surface, measured in phons, plotted against intensity and frequency of the tone. The solid curves that run from back to front at a constant height are called equal-loudness contours and represent tones whose combination of frequency and intensity produce the same subjective loudness. The fact that loudness depends on frequency as well as intensity can be seen in the curvature of these contours which indicate a maximal sensitivity with respect to loudness in the midrange of frequency for a given intensity level. In contrast to loudness, pitch perception, according to Licklider (1951), seems to depend primarily on the frequency of the tone (see also, Stevens, 1935; Morgan & Garner, 1947). Pitch, in non-musical contexts (see below), measured in mels, is a monotonic increasing function of tone frequency alone. Because subjective pitch, in mels, increases less and less rapidly as the stimulus frequency is increased linearly, it can be approximated, for our purposes, by a logarithmic function. We can discuss this situation in more quantitative terms. Let the physical space, a,be composed of dimensions intensity and frequency denoted as X with values x and Y with values y, and the psychological space, Y, be composed of dimensions loudness and pitch denoted as U with values u and V with values o. We can describe the psychophysical transformation as a mapping, p: + Y where p is the vector function ( x , y) -+ [f(x, y), g(y)l = (u, v). Here f is the function taking amplitude and frequency into subjective loudness (shown in figure) and g is monotonic function taking frequency into pitch. The requirements for p to be a homeomorphism is that it is one-to-one, onto, and bicontinuous. It is easy to see that p is onto since there are no points in auditory space that do not get hit by some combination of frequency and intensity. To verify one-to-one-ness (also known as injectiveness) is more difficult. Without knowing the exact analytical nature of the functions we offer the following qualitative argument. For In this paper we will use amplitude or intensity as generic terms for pressure, power, energy, etc. However, in acoustics special meanings are invoked for these terms. For example, ititensity always means energy flux density. Phase information is also contained in the sine-wave representation. However, subjects can only discern this when presented with a reference (Licklider, 1951).

Pattern S i m W t y

313

an injection, we have to show that given a particular intensity and frequency pair, ( X O , yo), we have only one possible loudness and pitch pair, (UO,ug). This is equivalent to showing that the inverse function, p-l: Y -+ a,is well defined. Suppose we have a loudness-pitch pair, (UO,00). Because g is one-to-one and onto, we can find g-' (710)= y ~ some , frequency, uniquely. We combine this frequency value with the original loudness value, UO, consult the equal loudness contours to determine the unique intensity level, X O , that gives that loudness at that frequency. We can do this because at a fixed frequency, loudness is monotonically related to intensity. Hence, g1is well defined. From this we conclude that p is one-toone. Clearly, p-l is continuous since all function involved are bicontinuous. So, finally, if the qualitative forms of the various functions involved are correct, as indicated by the data, we may conclude that the function from intensity-frequency space to loudness-pitch space is a homeomorphism. One might worry about the fact that the physical dimensions are actually unbounded whereas our ability to discriminate tones at the extreme ends of pitch and loudness disappears or is distorted greatly due to mechanical aspects of the ear. In this case, the transformation may not be a homeomorphism of all of frequency-intensity space because the set of tones that are audible may form a compact set (i.e., closed and bounded) in pitch-loudness space. Compactness is a topological property and, hence, is preserved by homeomorphisms. One way out would be to restrict the domain of the psychophysical mapping to be compact as well so that this restricted function could now be considered a homeomorphism. On the other hand, bounded sets may not necessarily be compact, particularly if they do not contain what are called limit points. The true psychological representation of tones may be immeasurable at the extreme ends of loudness and pitch due to experimental error, mechanical distortion, nonlinearities, etc. Characterizing the psychological space as bounded but open may be appropriate in this case. Hence, the transformation may still be a homeomorphism6 In an earlier technical report, Zagorski (1973) attempted to test the hypothesis that p, the mapping from frequency-intensity space to pitchloudness space, is, in fact, a homeomorphism in conjunction with the hypothesis that the metric that represented stimulus similarity for pure tones was isotonic in form. Isotone metrics are of the form I[rn(Ax),n(Ay)l, A concrete example to illustrate a homeomorphic mapping of an unbounded set into a bounded but open set can be seen in the fact that the whole real line can be mapped, homeomorphically, onto the open interval from -1 to 1, (-1, 1).The appropriate map h: '3 + (-1, 1) is given by h(x) = 2x / [l + (1+42)'/2]. The inverse function is given by h-' = y / (1-y2). One can check that this map is one-to-one, onto, and bicontinuous.

314

J.T.TaonsendandR.D.Thomas

where I, m, and n, are strictly monotonic (isotone) functions (I in both arguments m and n) and Ax is the difference between stimuli on dimension X and Ay is the difference on dimension Y. A special case of isotonic metric is the popular Minkowski metric. He proved that if the psychophysical transformation is a homeomorphism and the metric describing similarity on the perceptual space is isotonic then the set of (two-dimensional) stimuli that are judged equally dissimilar from two reference stimuli must form an arc when plotted in the physical space. In a multidimensional bisection task, subjects were given two reference tones and then were presented with a test tone in which they could manipulate either frequency or amplitude (but not both) so as to make the test tone equally dissimilar to the previously presented reference tones. Zagorski found that, when plotted in frequency-intensity (amplitude) space, the set of tones judged equally dissimilar did not form an arc but rather formed a criss-cross pattern. From this, he argued that an isotonic metric, in particular a Minkowski metric, was inappropriate to describe the representation of stimulus similarity. Subjects appeared to utilize either pitch or loudness but did not combine them on any given trial. It may be, however, that the method of responding induced the subjects to selectively attend to one of the dimensions given the fact that they could only manipulate one of the physical characteristics of the stimuli in the bisection task. Other evidence exists indicating that subjects do combine information from both dimensions when making decisions (Zagorski, 1973, 1975,1978; Garner, 1974). In any case, the evidence does not convincingly rule out that the psychophysical transformation from frequency-intensity space to pitch-loudness space is a homeomorphism but seems to be relevant to the issue of separability versus integrality of the two dimensions. Later, we will return to the issue of perceptual or decisional separability and investigate how these concepts are related to our framework. Certainly, not every transformation in which the perceptual system engages is a homeomorphism. One such example is the case of musical pitch perception in subjects who are familiar with the diatonic scale (e.g., Shepard, 1965; Deutsch, 1973). The relevant physical dimension is the tone’s frequency. Now, however, the perceiving is done in a musical context. Consider the notes of a piano keyboard: A, B, C, D, E, F , and G which repeat themselves. Perceptually, notes of the same letter (i.e., an octave apart) are more similar than notes less than an octave apart. An octave interval represents a doubling in the frequency of the tone. This empirical result, known as octave generalization has led many investigators to argue that there are two dimensions of tonal perception, tone chroma, which corresponds to pitch of a tone within an octave, and tone height, which represents overall pitch (Meyer, 1904, 1914; R6v6s, 1913;

Pattern Sim&zrity

315

Ruckmick, 1929; Bachem, 1948; Shepard, 1964b). This phenomenon of octave generalization was the basis for the representation of the notes on the scale as a one dimensional helix embedded in a three dimensional Euclidean space, as shown in Figure 2 (see Shepard, 1982, for a historical review).

Tone Chroma -> Figure 2. The helical model of musical pitch (as in Shepard, 1965). T h e two dimensions of musical pitch are termed tone height, representing the overall pitch level, and tone chroma, denoting within octave ordering of pitch. Pitches differing by an integral multiple of an octave (i.e., having the same name) line up vertically so that the Euclidean distance is minimized reflecting their high similarity.

A topological embedding is a map with certain properties. Suppose that f: X 4 Y is one-to-one where X and Y are topological spaces. Now the image set Z = f (X)is a subspace of Y. That is, Z can be considered as a space which inherits its topology from Y. More precisely, the open sets in Z are the open sets in Y intersected with Z. In this example, X is the one dimensional frequency space which is essentially the positive real line, Z

316

I. T. Taonsendand R. D.Thomas

corresponds to the one dimensional helix representing musical pitch and Y would be three dimensional Euclidean space in which the helix lies. The property that makes the map f an embedding is that, when restricted to the subspace Z, f is a homeomorphism, thus preserving dimension in the subspace. An interesting conundrum occurs if we note how the empirical observation that tones differing by exactly an octave are judged more similar than other pairs of nonidentical tones is being predicted by this representational scheme. It is the Euclidean distance in the embedding space, s3,that is calculated to arrive at similarity and not arc length along the helical curve, the embedded space. This seems to be problematic when viewed philosophically. In the figure above, let the length of the straight line segment connecting the note C to the note C‘ that is an octave away be the Euclidean distance representing dissimilarity of the two tones. Notice that no other points on this line segment besides the endpoints are realizable as possible tone perceptions. This means that, if this model is correct, the perceptual system has to traverse through something like a “no-man’s land” where no tones are representable in order to evaluate similarities. Would it be preferable to develop an alternative geometric representation, or surface, that could capture the same distance orderings as this helical model while requiring distance calculations to be made on the surface itself? It is unclear at this time whether a (continuous) mapping from the above scheme to such a representation exists. More elaborate geometric characterizations of musical pitch perception capturing other similarity relationships, such as thirds, fifths, etc., which, however, meets up with similar questions, can be found in Shepard (1982) and Krumhansl & Kessler (1982). Perhaps the best known example in perception is that of color, where hue, deriving primarily from the linearly ordered electromagnetic spectrum, curves around on itself under the transformation imposed by the visual system. First, if the psychological hue curve is conceived as topologically closed (i.e., contains all its boundary points), then the related transformation cannot be a homeomorphism because the part of the spectrum that is mapped into this curve seems to be an open interval (although possibly, we could artificially define two absolute thresholds at the top and bottom of the visible spectrum as boundaries of the visible spectral set). This is because whether a set is closed or open is a so-called topological invariant, that is, is preserved under homeomorphism. More critically with regard to the present discussion about dimension, if the eye were like the ear with regard to wavelength, it would be infinite dimensional, because within just-noticeable-differences,every wavelength can be heard at arbitrary intensities. Of course, we only see combinations of the primary hues (seeKrantz, Luce, Suppes, & Tversky, 1989,

Paffern Simtlarity

317

ch. 15, for more on this topic). So,in the case of hue there is a dimensional reduction as well as a curved transformation occurring. The present writers suspect that many more phenomena in psychology can be described in terms of topological and geometric structures, but these may turn out to be more general than the ubiquitous Euclidean and Minkowski metrics in scaling methodology.

THE ENTRANCE OF DYNAMIC SYSTEMS THEORY At this point, we need to discuss some aspects of dynamic systems theory. Our general perspective assumes that there exist three basic subsystems that are arranged sequentially, X, Y, Z, and that are responsible for an early transformation, a match or comparison operation, and a response bias and response selection operation. Although these are arranged sequentially and the immediate information flow is "upward" from X to Y etc., they can operate simultaneously, just as do most dynamic systems (e.g., Luenberger, 1979; Beltrami, 1987; for some special cases in elementary cognition, see Ashby, 1982; Bingham, 1991a, 1991b; Busemeyer & Townsend, 1989, 1992; Gregson, 1988; McClelland, 1979; Townsend & Ashby, 1983; Townsend & Busemeyer, 1989;Townsend, 1992a, 1992b; and in animal learning, see Killeen, 1992). Further, in general we believe there can exist feedback and top-down flow among these subsystems, but the present "barebones" discussion will have to ignore that aspect. Obviously, given that some neuroscientists believe there to be at least sixty known subsystems in the brain serving visual functions, the present scenario is surely a gross approximation, but we must start somewhere. We write the state transition map for the first subsystem, X, asf: TxTxXxLl +X. The state of X, which we call x, becomes the input to Y and so on. The function f tells how a state x(to) at starting time to gets transformed through time and with input u(t),to c t < tl to a new state x ( t l ) . U is the set of acceptable inputs, X denotes the set of potential states, and T the time index. Hence, we could write x ( t l ) =f[to, tl, x(to), ul in functional notation where f is our state transition function. Actually, in many cases of interest, the system is time invariant, which means that the starting point of the system is not critical, only the time interval over which the input persists. This allows us to simplify the notation to x ( t ) =fTt, d o ) , ul. The next function, g, acts on x(t), the value in X, over the same time interval, which of course, causes a transition of its own state over that interval: y(tl) = g[t, y(O), XI.Note that although y can depend on x over the entire interval of time, all its information about the original input comes from x, not from the input u, directly.

318

1.T. TownsendandR. D. Thomas

We will concentrate on the first two subsystems in this paper. The presence of decisional or other biases, arising in the third subsystem, and their potential distorting influence on multidimensional scaling procedures has been recognized for some time (Townsend, 1971; Holman, 1979; Nosofsky, 1991). For instance, bias could mask underlying symmetry in a metric or perceptual similarity match, or even distort the minimality assumption, that the similarity between anything and itself is minimal, and the same for all objects. Nevertheless, here we wish to examine what might be going on early in the processing chain, with regard to dimensional and metric (and premetric) structure; namely in subsystems X and Y. Another constraint is that in this paper, we shall neglect other extremely important perceptual and elementary cognitive tasks such as low accuracy recognition, identification and confusion experiments, and categorization. The ultimate application of the ideas expressed in this paper to accuracy-confusion frequencies, reaction time and other dependent variables, in such milieus will be undertaken in further investigations. At that point, links will be drawn with general recognition theory (e.g., Ashby & Townsend, 1986; Ashby, 1989; Kadlec & Townsend, 1992a, 1992b) and other theories of identification and categorization (e.g., Nosofsky, 1986; Kruschke, 1992; Massaro, 1987). What can happen in the first “stage” of processing? Certainly there is much loss of information due to limitations in our sensory organs, processing capacity and the like. In general, the function must be many-many in the sense that several distinct inputs can produce the same internal percept (e.g., Cutting, 1991; for an opposed view, see Burton & Turvey, 1990) and a single input may have the potential for producing a number of different perceptual results (e.g., as espoused in Bennett, Hoffman, & Prakash, 1989). However, in order to focus on what are for present purposes, the most important factors, let us assume that we have pared down the stimulus descriptions so that it is feasible for the observer’s sensory apparatus to map the input in a one-one fashion to some central location. There will be ample opportunity in the future to relax such assumptions. Let us consider, moreover, the relatively nice case in which the mapping is homeomorphic (see above), not only one-one but onto some image set of points, and bicontinuous. In some senses, all an observer needs in interacting with the real world is a homeomorphic map. Except in special cases, where she/he might also need velocity information, such a “smooth” and point-to-point correspondence should allow trouble free interactions. Indeed, it may be difficult to prove that higher order information, such as angle identicality or isometry (distance preservation), actually occurs in most cases. Of course, we are all aware of the many illusions, nonlinearities and probable necessity for a role of learning. Never-

Pattern similarity

319

theless, many theorists and experimentalists behave as if information is processed through the system in a relatively uniform fashion. In any event, we shall see that even what appear to be minimal requirements for premetric information, can easily be disrupted. Thus, homeomorphisms, as would be expected, distort distances in general. For instance, even the innocuous function y = f i x ) = ax where a # 1 clearly alters distances. The order of distances of numbers is not, however, changed. But, in general, homeomorphisms also damage the order of distances. A yet stronger type of transformation also is still too weak, one that is also one-one and onto, but is further uniformly continuous in both directions. In order to avoid long strings of conditions, let us agree to call such a function a "uniomorphism." Ordinary continuity implies that for any point x in X, say, one can find a small region around it so that any point x ' in the region is as close as one likes to f ( x ) in the range space, Y. Note that the size of the region around x can depend on where x lies. On the other hand, if a function is uniformly continuous, then, for a given disparity in the range space, Y, one can impose a region size in X so the regardless of where x lies in X, we are guaranteed that when x' lies in any such region, f (x') will be in that close proximity to f (x). Thus, uniform continuity is stronger than continuity. It turns out that uniform continuity going back and forth between two uniform spaces, preserves much of interest in the two spaces, and thus the linking of the names for the spaces and the transformations. Nevertheless, even a uniomorphism can, as claimed, change the order of distances. This can be seen in the simple example of y = f ( x ) = x2 where x is confined to lying between 0 and 1 with the latter points included in the domain. Let f -'(y) = + y1/2. These functions are uniformly continuous on the closed unit interval and are one-one and onto; thus fulfill the definition of a uniomorphism. It can be seen that in the domain, 1/4 is farther from 0 than 4/5 is from 1, the respective distances being 1/4 and 1/5. After the squaring transformation, the respective distances of the separate pairs of points are 1/16 vs 9/25, the latter clearly larger, reversing the order of the distances. Indeed, such transformations can even distort a premetric order of distances in the primitive uniform space underlying a metric structure. This follows logically from the above example, since the ordinary Euclidean metric imposes a uniform structure on the unit interval and the order of inclusion of the ensembles in the domain space is therefore violated after the transformation. Thus, what we need is a transformation that is weaker than an isometry (preserving the actual distances) and stronger in the proper sense, than a uniomorphism. We can think of an ensemble in a uniform space as encompassing all points with a disparity less than some non-numerical

320

J. T. T d a n d R.D.Thomas

level. Ensembles that contain the previous one, include even larger disparities and so on. Further, we may consider a transformation that preserves disparities as one that preserves the order of ensembles. Basically, we can state the definition as follows: A transformation between two uniform spaces that is one-one and onto, preserves disparities in both directions, is one in which the order of inclusion of the ensembles is preserved. That is, i f f is the transformation f: X + Y, and is one-one and onto then f preserves disparities if and only if whenever E l c E2 in X , then F1 c F2 in Y , where F l contains all the pairs of points mapped from E l and none others and similarly for F2. More specifically, if ( X I , x2) contained in E l implies that (XI, x 2 ) is contained in E2/ then [ f ( x l ) ,f(x2)I is in F l by definition and is required to also be in F2. We make the same demands in the inverse mapping from Y to X. An example of a distance order-distorting transformation can be found in the modeling of the identification and categorization relationship by Nosofsky (e.g., 1986, 1987). In identification tasks, the subject must produce a unique response when presented with a given stimulus. That is, identification requires a one-to-one map from stimuli to responses. In categorization tasks, the subjects assigns one response to several stimuli, a different response to other stimuli and so on. Here, we have a many-to-one mapping of stimuli to responses. Nosofsky has developed a model, which is a generalization of Medin and Schaffer’s (1978) context model, that serves as a bridge between the two tasks. With this model, he has successfully predicted categorization performance based on knowledge of identification performance. The procedure he adopts is to first fit the identification data using Shepard’s (1957; see also Luce, 1963) M D S choice model. This step yields a multidimensional psychological space that captures the underlying “similarity” relationships between stimuli as used in the choice function contained in the model. The basic tenets of multidimensional scaling hold in that the similarity parameters of the choice model are assumed to be inversely monotonically related to the distance between the respective stimuli in the psychological space. Using this derived representation, together with the hypothesis that subjects distribute their atten tion appropriately in order to maximize performance, Nosofsky is able to predict subsequent categorization performance. The attention-optimization hypothesis can be realized in, for example, a categorization situation in which only one of, say, two dimensions are relevant for the task. Subjects are assumed to distribute attention in a way which is equivalent to stretching the space along the relevant dimension(s) and shrinking it along irrelevant ones and then recalculating distances between stimuli.

Pattern Similarity

321

It is clear that pairwise distance orderings will, in general, be distorted as a result of the attention transformation. In fact, it is necessary for this to occur in the model if it is to successfully predict categorization data. Presumably, if the new distorted representation is stable, obtaining similarity judgments, post categorization, should reveal these new similarity orderings. Such experiments have been done, but with somewhat ambiguous results (Shin & Nosofsky, 1992).

CASE STUDIES EXAMPLES OF SPACES UNDER PSYCHOLOGICAL TRANSFORMATION Disquiet of some 18th century mathematicians concerning the Godgiven quality of Euclidean axioms and the absolute essence of Newton’s incorporation of such spaces in his Principia, gave way in the 19th and early 20th centuries to a wholesale revolution. It became understood that any particular set of geometric axioms was not necessarily better in general than another. From the mathematicians point of view, classes of geometries are like a room full of games with somewhat different rules to play by. From the empirical scientist’s perspective, a geometry (for that matter a topology etc.), is simply a model of a specific piece of reality that has to be empirically tested. Einstein was the first to really seize the opportunity to implement non-Euclidean geometries in science, although the mathematical foundation for his exploits had been laid by mathematicians such as Gauss, Lobachevski, Bolyai, and Riemann. Interestingly, Minkowski, an eminent mathematician of his day, was reportedly rueful that he failed to preempt Einstein in the application of Riemannian geometry to physics. In psychology, there is a substantial tradition of research attempting to specify the geometry most appropriate for human vision (e.g., see the review in Suppes, et. al., 1989, particularly discussing the work of Blank, Luneburg, and more recently, Foley and Indow). In any event, the outside world, whether it is the visual, olfactory, auditory, or tactile (not to mention the internal sensory world of kinaesthesis etc.), does not necessarily have an absolute spatial description, when taken in reference to psychological phenomena. It has often proven convenient to start with standard physical descriptions of the stimulus patterns, when they exist, but the perceptual concomitants of these should not be taken to be equivalent, or even easily related, without demonstration. Moreover, it seems quite likely that the standard dimensions of classical physics, length, mass, and time were chosen over histor-

322

1.T. Townsendand R. D.Thomas

ical time because they are perceptually salient to human observers and more or less perceptually orthogonal, in their effects. In the paradigm under discussion, the observer is presented with two objects and asked to rate their similarity or dissimilarity. Thus, they must both be transformed into an internal pattern or code and then matched.

Case I. A Finite Dimensional Euclidean Space Consider an ordinary run-of-the-mill Euclidean space, one where the external dimensions are representable as a finite, orthogonal vector space endowed with the Euclidean metric, and it is invariant over time. For notational convenience, suppose it is three-dimensional, although this is entirely arbitrary. Thus, u ( t ) = [ u l ( t ) ,u2(t), ug(t)l = (ul, U Z , u3). Assume that we consider the asymptotic stable percept lirn x ( t ) = lirn fit, u, x(to)l. Even iff maps to another three-dimensional Euclidean space, the dimensions could be complicated functions of the external dimensions, for example, x(-) = fl-, u, ~(011= [uz lug(ul), sin(uz)-sec(ul), ( U ~ ) ' / ~ I . Thus, dimensional structure may be disfigured even though the number of dimensions is preserved. When will the order of distances be distorted? In most cases, from one perspective. A sufficient condition to preserve distance orders is of course, an isometry, which is defined as distance preserving. Note that even an isometry can distort the visual picture of a form. For instance, a sheet of paper can be wrapped into a cylinder while leaving distances unchanged. However, a more interesting sufficient condition is to multiply each object (i.e., vector) in the space by a positive number. This alters Euclidean distance by the same number and leaves the order of distances unchanged. As observed earlier, the mild generalization of this concept to multiplying (i.e., stretching or shrinking) the different dimensions by different positive numbers, fails to leave the order of distances unchanged. If such linear transformations cause havoc with the distance orders, it is obvious that non-linear transformations would generally do the same. Readers may convince themselves that even letting the function of each dimension in Y be a strict monotonic function of a respective dimension in X and further requiring that all these functions be the same, will not generally preserve distance order. A generalization of the earlier one dimensional example is found by letting yl = (xllZ, y2 = (x2I2, and y3 = (x#; note that the dimensions are stretched in the same nonlinear way, but distance orders are not preserved. These kinds of transformation can be given a higher sense of possible reality by hypothesizing that, say, a generalized Poisson counting rate q ( t ) is a monotonic function of the dimension i value, for i = 1, 2,3. It is

Pattern Similarity

323

thought that firing frequency of neurons may be an important coding principle on the part of the brain. If q ( t ) approaches a stable limit as t becomes large, then we can form instantiations of the above possibilities. If, say, q ( t ) is affected by dimension 2 as well as dimension 1 then we might write q ( t ;x2). If the limits are functions only of their respective external counterparts and are linear functions of the input values then lim q ( t ) = kl x l and so on. Next comes the operation of comparison or matching, which as we noted earlier, involves the mapping of the two psychologically specified three-dimensional depictions into the real numbers, usually the positive reals. Both the depictions and the result of the mapping may be non-numerical objects. For instance, the rating could just lie on an ordinal scale leading back to the notion of the uniform space concept. In any case, we will assume a numerical representation, since at some point the observer has to respond with a number name. (But be aware that this does not imply ratio scale properties!) How is this comparison made? Will the result bear any relationship to a metric? If, say, a similarity rating is monotonically related to psychological distance, where could one find that out; for instance, how could one ascertain the satisfaction of the triangle inequality? In fact, it is hard in general to do that without knowing the specific function that relates a similarity rating to underlying distance. On the other hand, one should be able to test the proposition that nothing is more similar to an object than itself [akin to the diagonal being contained in every ensemble in uniform spaces and d(x, y ) = 0 implies x = y, in metric spaces]. And, the same goes for the proposition that all objects are equally similar to themselves [forming an equivalence class of object pairs on the diagonal in uniform spaces and d(x, x ) = 0 for all x in metric spaces]. Whether one can test for symmetry, depends on giving an interpretation to the order of the objects in d(x, y ) and d(y, x). In some contexts, this makes sense, in others it may not. What about something like a cross-correlation, I; X i yi , a well known statistical procedure? In the pattern recognition and mathematical communications theory literature, it is shown that this procedure forms a socalled matched filter in certain cases (e.g., see Townsend & Landon, 19831, and when any added noise is white (zero correlation from one instant to the next) and Gaussian, then such a filter maximizes the signal-to-noise ratio. Furthermore, under more stringent conditions on the Gaussian distributions, it can be shown to deliver a minimum distance classifier. Of course, in such cases, one is dealing with the situation where a pattern is input to a classifier rather than with the context of matching two patterns for similarity or dissimilarity. The present situation precludes those conclusions.

324

1.T. T d a n d R. D. Thomas

For a given 2 ( x z + y?), we do see an inverse monotonic relation between the cross product and the Euclidean distance. But, observe that the similarity of a pattern to itself, being constant across patterns, is not found with this measure, nor even that the similarity of a pattern to itself will be larger than non-identical patterns. It may be possible through some sort of normalization strategy in specific cases, to reinstate such properties, but it should be clear that they will not come about automatically.

Case 11. Forms as Manifolds: Infinite Dimensional Pattern Spaces Case ZZA. Resting Manifolds. At this point we must outline what a manifold is. For more rigorous definitions, we refer the reader to standard works such as Boothby (19861, Auslander & MacKenzie (19771, or Spivak (1979), and for lots of high level intuition, Koenderink (1990). Actually, some of the intuitive backdrop to manifold theory can be garnered from studying surfaces in 3-dimensional Euclidean space and an excellent beginning text there is ONeill (1965). Within or close to psychology we again recommend Koenderink (1990), and for more advanced applications from differential geometry, Hoffman (1966) and Lappin (1990). Recently, progress has been made on the contribution to three dimensional stereopsis to form perception (e.g., Norman & Todd, 1992) and also the influence of motion (e.g., Norman & Lappin, 1992) both within the context of geometries. However, the applications of such topics to psychology, have hardly begun to be tapped, and we predict that the rich knowledge base residing within topology and geometry will provide powerful tools for important segments of psychology for years to come. A inanifold is a space that can locally be mapped into an ordinary ndimensional Euclidean space. That is, for every point in the space, there is a region, known as a neighborhood, around it, with the property that this neighborhood can be transformed in a smooth fashion (i.e., continuously to and from) to a neighborhood in Euclidean space. This is done carefully for every region in the original manifold with the edges of the neighborhood appropriately pasted (mathematically) together, and with consistency of the transformation for overlapping regions. The result is that operations on the original, possibly very abstract, space can be much more readily accomplished in the well-understood Euclidean space. Perhaps the simplest, not totally trivial, manifold is a two dimensional surface in three dimensional Euclidean space. Consider a very elementary example where a surface can be represented as a function that maps part of the Euclidean plane into a curved "roof" of some sort lying above the plane. This, of course, can be supplemented by a similar function carrying points on the plane to a "floor" below the plane and then connecting up the floor with the roof to make a closed, "empty" form.

Pattern Simllmify

325

Now suppose our set of stimuli is composed of such forms with different functions carrying parts of the plane to the surfaces. And let us assume that an internal homeomorphic representation exists for these forms. We set aside momentarily the issue of dynamics. Even if the map from external to internal representation is an isometry (distances are preserved) of the forms themselves, the question still arises as to the appropriate topology and/or geometry for this particular set of stimuli. Thus, the properties of the space would differ when one pattern is a balloon among a set of other toys as opposed to different types of elliptical objects, such as other balloons, a class of objects filled with air-but not necessarily balloons and so on. Furthermore, in general we shall have to think of a "filled-in" space with more points than the present finite set of objects. In order to employ the classical and also powerful recent topological and measurement tools, the space must be sufficiently rich. This concept was touched on earlier in the chapter and can be vividly seen in the technical axioms required by the foundational measurement investigators to establish their results. When all the points of a form can be important in a task, or are simply employed by an observer for comparison or an analogous task, we have to construct an infinite dimensional space, and think about metrics and similar concepts on such spaces. In some special cases, it may be possible to compare forms by constructing metrics or weaker comparisons on the functions that define them. For instance, consider the space of all continuous functions on the closed unit interval, [O, 11, mapping it onto another unit interval. As we wrote above, f: [O, 11 + [0, 11. There are many metrics that could be used. One common metric on two such functions is d(f, g) = [ f ( x )- g(x)I2 dx, that is, the integrated, squared distance of the functions from one another. Another is d(f, g) = m a x I [ f ( x ) - g ( x ) I 2 ) , (the absolute value would also work in either case). In spaces where the functions or the difference may be bounded but that bound may not be attained by the functions, we may substitute " l u b (least upper bound) for "max." In any event, the first metric takes the distance of all points into account whereas the second depends only on the largest distance. Interestingly, the topologies generated by these metrics are not comparable. This fact implies that important topological notions that are even more general than metric ones, may be very different in the two spaces, even though the objects, that is the class of functions, are the same. Observe that this space of continuous functions on the unit interval is infinite dimensional, even uncountable (like the irrational number on the line, but even bigger). This is because there are an uncountable number of points along the interval [O,1] where the two functions can differ.

326

1.T. T d a n d R. D.Thomas

Infinite dimensional spaces immediately run into problems that do not encumber finite dimensional spaces; for instance, in many cases, no metric may exist at all on them. Moreover, some of the key concepts, such as a set of unique geodesics between points (remember, in more general spaces, these are the equivalents to straight lines in Euclidean space, and determine the general distance in small regions in the more general spaces), may no longer hold in such spaces. Thus, there is no unique “ p a t h of minimal distance carrying us from one specified function f, to another g, in our current example. This is an important consideration when we consider general shape perception questions, in high dimensional spaces. For instance, in pitch discrimination or face discrimination tasks (e.g., same-different tasks), the human sensorium is so high dimensional, it can probably be considered infinite dimensional as a good approximation to reality. Or, with regard to the question of geodesics, what is the shortest path of faces leading from one face to another? Obviously, the question will usually be nonsensical, given the complexity of real-life faces. To be sure, the above concept, while extremely useful, is probably too specific and tied to some original domain space to be of wide applicability. How about moving two forms into some sort of standard position before comparison? That might permit the use of the approach just discussed, for example. That strategy has been very common in artificial intelligence pattern recognition situations. It has been derided sometimes by theorists as to particularistic. However, Palmer (e.g., 1989, 1992; Palmer, Simone, & Kube, 1988) argues that objects possess intrinsic reference frames which allows shape comparisons to occur regardless of differences in orientation, size, position, etc. According to this reference frame hypothesis, objects can be brought into a canonical position and orientation so they can be appropriately matched. People can be pretty good at mental rotation (Shepard & Cooper, 1982) and there is some evidence that humans mentally mimic Newtonian mechanics or kinematics in their mental physics (e.g., Carlton & Shepard, 1990a, 1990b). So a rapid mental rigid transformation that brings two forms into as close an approximation as possible is not beyond the realm of possibility. It need not be a fixed position, but could depend on the two figures. For instance, a dynamic program operating on a hill-climbing, or gradient descent principle based on the disparity or distance measure, along with a class of rigid transformations (we are assuming rigid objects here), could make this procedure function effectively. Then, the final “minimum” disparity could be taken as the dissimilarity. Obviously, we must mention the importance of the Gestalt principles of invariance and symmetry (e.g., Koffka, 1935) in all areas of perception

Patfern Simdarify

327

and cognition. Recently, investigators have begun to employ these and more contemporary analogs in structural notions of perception and perceptual cognition (e.g., see Leyton, 1986a, 1986b; Imai, 1992; Buffart & Leeuwenberg, 1983; Chen & Chen, 1982,1987). These may be fruitful in the enterprise initiated here, but space and time (and limited capacity on the part of the authors!) preclude further discussion herein. Another more abstract possibility, at least for well known objects, is that there exists a memory representation that is an equivalence class of all possible “real” transformations on an object, that serves in comparison operations. This hypothesis is surely wrong in any universal sense, as indicated by difficulties in recognition of, say, faces when they are turned upside down (e.g., Bruce, 1988; Valentine, 1988). Of course, if the comparison is based on easily measured features, or on more abstract principles (e.g., “give a rating that indicates the similarity in the manual use of the two objects”), then there would be an intermediary mapping that measures the appropriate quality or quantity, but does not necessitate this ”physical” standardization strategy. In the present context, it should be even more obvious than with finite dimensional stimuli, that preservation of specific geometric or topological aspects is arbitrary or at least peculiar to particular sets of forms as stimulus patterns and the requirements on the observer’s processing systems. Thus, in some tasks the curvature (there are several types) of a form may be highly important and form a set of dimensions according to location, whereas in other tasks the number of holes or other qualitative aspects might be critical. Nevertheless, once we specify the information required for a task, then we can ask about dimensional and topological structure relevant to that task, and the preservation of such structure from external to internal representation. In this vein, as noted above, we consider same-different face discrimination to be virtually infinite dimensional since any two of the millions of faces present on earth can easily be distinguished. However, long-term memory of faces is quite another matter and the dimensionality of the underlying memorial space could be much reduced. Analogously, Todd and Reichel (1989) have questioned whether metric information is preserved in certain shape perception tasks, or only ordinal information. Such investigations are of great importance and we need many more in that spirit, optimally paired up with sophisticated theoretical tools. To be sure, just as in the finite case, even if there has been preservation of external to internal metric (or premetric) structure, the observer’s comparison model may well not preserve that information any further. Also, even if the observers are using a consistent dimensional strategy on psychological representations, there is no current multidimensional procedure

328

I. T. Townsendand R. D.Thomas

for dealing with an infinite number of dimensions. We are somewhat dismayed that the ingenious results on the psychological scaling of Riemannian manifolds (Lindman & Caelli, 1978), apparently have not been followed u p or much applied. However, these strategies too are meant for finite dimensional manifolds. As we have seen, a space of finite manifolds can be itself infinite dimensional. We close this section by making a few remarks about the early dynamics involved in the percept of a manifold type of form. Knowledge regarding nonlinear dynamics in finite dimensional spaces is still growing by leaps and bounds, and is far from complete. That involving infinite dimensional spaces is much more inchoate. Nevertheless some things are known. For instance, the notions of asymptotic stability of a point (the trajectory approaches this attractor point as a limit across time) carry over nicely as do a number of other concepts. Hence, we can think of a percept of a form existing in an infinite dimensional space as approaching a stable percept after being presented. Case IIB. Manifolds In Motion. This section will be very brief, but we do want to initiate discussion of situations where forms are in motion, for instance, rigid motion. Consider the example of a ballet dancer perceived over some time interval. From the great body of work stimulated by Johansson (1950, 19731, it seems very likely that even in situations where the facial and body structure precludes identification of the individual when motionless, that an expert choreographer can identify many performers simply from their motion. How can we capture this kind of perception in our theoretical structures? Basically, the idea is that the trajectory itself of the dancer in motion and/or special features of that trajectory becomes the form. The dancer can, f?r now, probably be adequately described as a coupled set of individual parts moving in rigid motion. Eventually, describing more plastic motions such as a change of expression, require infinite dimensional systems, as for example, partial differential equations (see Beltrami, 1987; Zachmanoglou & Thoe, 1976). Again, differential geometry and its handmaid, tensor analysis, should aid greatly in this endeavor. Lappin and colleagues (e.g., Lappin, 1990; Lappin & Wason, 1991)) W. Hoffman (1966) and D. Hoffman and Bennett (1985,1986) have made progress on related themes, and the work of Caelli, Hoffman, and Lindman (1978a, 1978b) could also be helpful in this regard. The similarity of two motion forms could be determined through the same kind of metric on functions, this time on shapes moving through space, that were illustrated above. Alternatively, as suggested by Lappin (1990), such features as the fundamental metric tensor (which characterizes the curvature of the space and permits the calculation of paths) may

Paftem Similarity

329

be abstracted by observers (e.g., Lappin & Wason, 1991; Lappin & Love, 1992). A particularly exciting line of research, closely related to the present topic, goes under the name of ”event perception.” The literature is already growing vast but some starting references are Ullman (19791, Warren (1977), Shaw (1988), Rosenbaum (1975), Lee (19801, Cutting, Proffitt, & Kozlowski (1978), Algom & Cohen-Raz (19871, and Bingham (1987a, 1987b). In the more formal treatments, mathematical dynamic expressions enter explicitly into the formulation and predictions (e.g., see Bingham, 1991a, 1991b).

Case 111. Extraction of Features Now let us begin with a space of some variety, perhaps describable as a manifold, as many visual objects will be. It seems likely when first meeting a more or less novel form, that the entire form is allowed access to the repositories of visual long term memory, including outlying recesses. However, we may view this neurally and psychologically huge expanse as endowed with a distribution of salience across it. Only the most salient or ”primed” locations will respond sufficiently to enter consciousness or to implement other associations. Of course, when a form belongs to a well established category, for instance, faces, then mechanisms often will go into play that focus on individual features. Furthermore, in learning to discriminate among a set of patterns, or identify them individually, it behooves a limited capacity system such as visual perception to reduce the processing load by allotting capacity only to a certain region or subset of the global information (e.g., Eriksen & Murphy, 1987; Bundesen, 1990; van der Heijden, 1975; Sperling & Dosher, 1986; Shiffrin, 1988; Townsend, 1981; LaBerge & Brown, 1989; Townsend, 1990a). What is going on in terms of the present topological and geometric issues in this ubiquitous phenomenon? Interestingly, the dimensionality may not change. Consider the allocation of attention to a spatial subregion of the overall figure. If the form is three dimensional, then in many cases the subregion, wherein the sought-for feature may lie, will also be three dimensional. Thus, even though the focusing on a smaller region will typically require less capacity, the literal dimensionality of the space is equal to that of the entire form. In fact, one may envision cases where the dimensionality of the subspace, perceptually speaking, could be larger than that of the original perceptual space. For instance, suppose the perceptual concomitant of a colored form were composed only of the geometry of the form, without analysis of the color, perhaps due to limited capacity. Then the allocation of attention to subparts of the form could include color and thus augment the dimensionality of the form.

330

1.T. T d a n d R. D.Thomas

In other auspicious cases, the subspace will be of lower dimensionality. Thus, consider a situation where the observer must evaluate the curvature of a (not necessarily straight) line that lies on a two dimensional surface. In that event, the dimensionality of the line feature is definitely less than the dimensionality of the original surface. The human (and nonhuman, for that matter) visual system seems to be excellent at abstracting information of this kind from real or schematic faces-the well known efficacy even of poorly drawn cartoons being a prime example. What is the topology of a subspace? Strictly speaking, in topology, a subspace of points inherits the so-called "subspace topology'' of the original space. The subspace topology is formed composing the open sets of the new topology from intersections of the old open sets of the original topology with the subset of points under consideration. This accomplished, one may ask all the questions associated with any topology. It is important to point out, however, just as the topology of the entire form may not correspond to that usually employed in our externalized model of reality, so the subset of points of the original form may not (in fact, usually will not) necessarily be a true topological subspace of the original form. Recall that the perceptual topology is derived from the perceptual task at hand, including the dimensions needed for comparison or other operation. This is perhaps most obvious in a relatively artificial situation, where the global contours are made up of smaller objects, sometimes with a completely distinct "meaning" (e.g., Navon, 1977; Kinchla, 1974; Uttal, 1988). Even when the task involves discrimination among a set of forms, the topology may differ depending on whether global information is employed from each form, or whether features are extracted and used to make the discrimination. Thus, a global comparison might utilize the overall physiognomy of a head or face whereas, a featural comparison might evaluate the size and curvature of the lips. The topology and geometry would typically differ greatly in the two cases. What about metric or qualitatively premetric information? Much the same points of discussion ensue as above. The mappings that carry pairs of features into similarity or dissimilarity ratings, and sets of such pairs, will typically be based on individualistic "distance" measurements, according to the specific features. Thus, a comparison of eyes of people will often include a measurement of hue, whereas that of ears typically would not. After learning has occurred, or under instruction, an observer may decide to allocate attention to a selected set of features. If this set is sufficiently small, compatible, and specified with respect to relative spatial position, then the processing may be in parallel, otherwise, serial pro-

PaftemSimtlariQ

331

cessing may have to be implemented. More detailed recent models of attention will be helpful in bringing together this information processing aspect of perception with the topological and geometric aspects (e.g., LaBerge & Brown, 1989; Bundesen, 1990). However, we need much more work in this area, especially as concerns the synthesis of information processing concepts with the topological. For instance, Massaro’s (in press) review of information processing research over the past decade reveals a growing, and long awaited, concern with the state space and type of coding, in human information processing systems. However, there is little evidence of the kind of synthesis to which we refer here. Exceptions are the research tracks followed by Ashby and colleagues (e.g., Ashby, 1989; Ashby & Gott, 1988; Ashby & Perrin, 1988) and Nosofsky and associates (e.g., Nosofsky, 1985, 1986, 1987; Nosofsky, Kruschke, & McKinley, 1992) where elementary dimensions of the percepts compose a critical part of the perceptual operations and decisions. Biederman and colleagues’ theory of geons is close in spirit to the present topic and the two perspectives probably have much to offer one another (e.g., Biederman 1987; Hummel & Biederman, 1992). The line of research on dimensional separability vs integrality and independence vs dependence (e.g., Garner, 1974; Shepard, 1987; Ashby & Townsend, 1986; Kadlec & Townsend, 1992a, 1992b) can also play an important role in this challenging domain.

CONNECTIONIST MODELS AND THEIR GEOMETRIC IMPLICATIONS There are more connectionist models out there today than one can reasonably shake a stick at, but most of them rely at least in part on applied mathematical strategies that have proved of use in engineering and applied physics, particularly in pattern recognition fields. (To be sure, cognitive science theorists have made important contributions to the ongoing theoretical developments as well.) For instance, an early linear transformation of the input is common (e.g., Kohonen, 1989; Kruschke, 1991). What if we assume that the physical space, U,is a finite dimensional Euclidean vector space and that the early transform of U to X is indeed linear, X = AU, where A is a matrix? First off, we have noted earlier that even this simple-minded transformation will, in general, alter the order of the pattern distances. Now suppose that the observer performs some comparison process which we can express as y = C ( q ,q )for two perceptual pattern vectors X I , x2 and where y is a number. (More generally, y could simply be a member of a simply ordered set.) Under what circumstances will y be a distance, or at least

332

1.T. Tawnsendand R. D.Thomas

monotonic with distance? A favorite "chestnut" in the literature on pattern recognition is to let C be the dot product (known in psychology, somewhat inappropriately, as the cross-correlation; cf. Papoulis, 1965) of XI and x2. In identification operations, a second stage linear mapping to assess the strength of each candidate response, turns out to be optimal if the associated dot product has certain properties (e.g., Nilsson, 1977; Fukanaga, 1990). The fact mentioned in an earlier section, that under certain circumstances, it yields the optimal matched filter, as well as the minimum distance classifier is one example. Hence, if such situations are transferred to similarity matching, then the correlation operation can be viewed as monotonic with distance. Such questions can be asked in the domain of general comparison functions, C. Such functions bear a close resemblance to discriminant functions, which are enacted on incoming patterns in identification paradigms, in order to classify them (e.g., see Kohonen, 1989; Townsend & Landon, 1983; Ashby, 1992, ch. 1). And, in fact, the questions raised in the present context, that of similarity matching deserve to be raised in other paradigms such as identification and categorization. In any event, let us consider another alternative, that where C is a so-called quadratic form. That is, C(x1, x2) = XI B x2 where B is a square matrix. Interestingly, if B is positive definite [which means that (3x1, x2) as defined above is zero when XI = xq if and only if XI = 0, the zero vector], then we can used it to define a norm. [A norm is a measure of the magnitude of the vectors, represented by the positive numbers such that it is zero if and only if the original vector is zero, if multiplication of the vector by a number is the same as multiplying the norm or the vector by the absolute value of that number, and if norm(xl+x*)c norm(xl) + norm(x2), that is, the norm is subadditive.] The norm can then be employed to define a metric simply by taking the norm of the difference between two vectors. It can be shown that this operation meets all the requirements of a metric, including the critical triangle inequality. However, it should be noted that the quadratic form imposed on two vectors to, say, measure similarity, will not be symmetric in general unless the matrix B is symmetric. Quadratic forms implemented on two comparison vectors, or on their difference vector to compose a distance, are easily realized in neural networks, and hence form a viable modeling possibility. It is intriguing to the present writers, that these fairly common types of functions are so close to being metric computations. If the sensory apparatus and brain actually perform something like these operations, we may have one good reason why multidimensional scaling programs work as well as they do, even without taking into account a process model of whence the geometry arises.

Pattern Similarity

333

Still the basic conundrum is not quite resolved since as shown above, it is almost trivially easy to disrupt even the order of distances (or premetric concomitants of distance). The worst case scenario would be that our MDS routines are acting as sophisticated Rorschachs, allowing us to "unveil" the geometry we seek rather than the psychologically "true" space. The best case would probably be that even though neural transformations may be distorting the distance orders (not to mention the actual distances), the perturbation is sufficiently minor that MDS software is able to rectify the damage. It appears that more work on linear and nonlinear operations employed in topical connectionist and other process models, with regard to their effects on physical and perceptual geometries, could be quite valuable.

DIFFERENT TYPES OF SEPARABILITIES During the earlier discussion of the example of pitch and loudness perception we alluded to the issue of separability versus integrality that is of interest in modeling perceived similarity. Such questions have a deep history in the philosophy of thought, culminating in the nineteenth century in the opposing dialectic camps of German phenomenology vs British Empiricism. The former emphasizing the global uniqueness of thought products (and incidentally their innateness) while the latter endorsed the presumed construction of thoughts and concepts from atomistic pieces (and incidentally, the criticality of learning and impact of the environment). Of course, these philosophical roots gave rise on the one hand to Gestalt Psychology and on the other to Structuralism (early) and Behaviorism (later). The modern approach embodied by such investigators as Roger Shepard and Wendell Garner, has implicitly been something of a synthesis of the Gestalt and Structuralist position, since by definition, a pair of stimulus dimensions might be either integral (i.e., Gestalt-like) or separable (i.e., like two independent atoms). Views on separability in the context of multidimensional scaling during the 1960s and 1970s often centered around the type of metric that best described similarity relationships of the stimuli under study (Shepard, 1964; Garner, 1974). Separable dimensions were defined, somewhat informally, as those that remained distinct and analyzable when processed and selective attention could be given to them. Also, when a multidimensional scaling solution was derived for proximity data, the city-block metric fitting best was an indicant that the stimuli were composed of separable dimensions.

334

I. T. Townsendand R. D.Thomas

In contrast, integral dimensions were deemed to be unitary, unanalyzable wholes which could not benefit from selective attention and the Euclidean metric was associated with this type of dimension. We have already noted the questionable nature of associating a particular metric with certain types of dimensions. Also, problems with this characterization of dimensional interactions are well laid out in Ashby and Townsend’s (1986) introduction to general recognition theory. Part of the trouble with the traditional view is that perceptual effects were not teased apart from decisional effects. Stimulus dimensions may or may not interact perceptually and perceptual dimensions may or may not be combined when arriving at response decisions. In addition, perceptual dimensional interaction may take the form of a dependency of dimensions within a stimulus or an integrality of dimensions across a stimulus set, these actually forming distinct concepts. The formulation of general recognition theory (Ashby & Townsend, 1986) helped to exhibit this distinction. If two stimulus components or channels were independent within a stimulus set and within observation trials the concept was termed “perceptual independence‘‘ and is due to probabilistic independence or the absence of a (possibly nonlinear) correlation in the statistical sense. An invariance of a components characteristics across stimuli was dubbed ”perceptual separability.” These concepts had their inception in our earlier treatment of perceptual effects of features in letters (e.g., Townsend & Ashby, 1982). A theoretical structure such as general recognition theory also helps to relate several different notions of separability and integrality in a common framework. In the absence of such a framework, different operational definitions of separability and independence can lead to seeming contradictory empirical findings when the various concepts are confused. For example, Zagorski (1978) outlines such contradictory separability results in the context of auditory pitch perception. Scaling studies (Carvellas & Schneider, 1972) and filtering tasks (Garner, 1974) indicate that the dimensions of pitch and loudness were integral and yet other psychophysical evidence indicated that they need not interact in certain tasks (e.g., Zagorski, 1978). This apparent paradox was dispelled somewhat when he observed that perceptually the dimensions showed evidence of independence yet decisionally they would often be combined prior to the subject making a response. With only the type of metric available to them, it is unclear how MDS based models can capture this distinction between the source of interaction unless there is a concomitant process model proposed (as in general recognition theory or Nosofsky’s generalized context model, Nosofsky, 1986). In any event, when examining the issue of perceptual separability, in general, one can appreciate that there may be several

Pattern Simrlarily

335

levels of dimensional separability throughout the cognitive processing chain. At the very beginning, a failure of separability of the physical dimensions may occur directly in the transformation from the physical space to the psychological space. This was the case in the pitch-loudness example in that the function p: (x, y) + [fix, y), g(y)l. This is perhaps the most interesting and yet most difficult type of dimensional interaction to identify. However, if present, it would surely be evidenced in more standard means of analysis. For example, when one changes the frequency of a tone, both loudness and pitch would change. Hence, loudness and pitch could be considered to be linked in some way. This would presumably be detected by a MDS analysis. For example, using the Euclidean metric, stimuli generated by orthogonal combinations of frequency and intensity would never line up in a rectangular configuration in the derived solution. Another way to explore separability is to examine the perceptual space post transformation. One can ask, within this space, can all points in the Cartesian product of the two (now psychological) dimensions be realized? In the case of loudness and pitch perception, this is almost true. Every loudness can, in principle, be experienced with every pitch with one exception: every loudness has to have some positive pitch, and vice versa. Some have used this kind of existence dependence as a defining property of integral dimensions. However, this may be too severe. When both dimensions have positive value, one could maintain a constant loudness and vary pitch, but both frequency and intensity will have to be changed. For example, in the midrange, if pitch is to be increased, frequency will be adjusted upwards while intensity will be need to be decreased in order to maintain a constant loudness. Nonetheless, almost all points in the loudness x pitch space are possible perceptions. This is not so in the case of color perception. The full Cartesian product of hue, saturation, and brightness is the volume of a cylinder. Much less than this full space is perceptually realizable. This can be seen in Figure 3 which contains a simplified rendering of the traditional color solid as a subspace of a cylinder (Munsell, 1915; Newhall, Nickerson, & Judd, 1943). Other often used stimulus dimensions are the size of a (semilcircle and the angle of incline of a radial line. These dimensions have often been shown to be separable by standard techniques (Shepard, 1964; Garner & Felfoldy, 1970; Hyman & Well, 1967; but see Ashby & Maddox, 1990; Nosofsky, 1985). They also are able to enjoy the full Cartesian product of size x angle possibilities. Perhaps it is this type of separability that is at work in the standard Garner filtering task. In this task, separability is implicated if varying irrelevant dimensions (irrelevant as defined by

336

1.T. TuwnsendandR. D.Thomas

task demands) does not interfere with processing the relevant dimension(s). From one point of view, psychological dimensions are now orthogonal, in the sense that the full Cartesian product is available, and, hence, we should be able to pick points (e.g., a line of varying pitch orthogonal to a line of constant loudness, say) such that no interference occurs.

Figure 3. A simplified Munsell color solid sitting inside a cylinder. The full Cartesian product of hue, saturation (i.e., chroma), and lightness corresponds to the volume of the cylinder. The color space is a proper subset of this Cartesian product and, hence, leads to a violation of a kind of separability.

In their early work on the foundations of multidimensional scaling, Krantz, Tversky, and colleagues (Beals, et. al., 1968; Tversky & Krantz, 1970; Krantz & Tversky, 1975) argued that a certain kind of separability was necessary to even define psychological dimensions. Dimensions, in order to be considered valid psychological dimensions, had to contribute additively to the overall distance between stimuli. This interdimensional additivity property is analogous to the requirement of conjoint

Pattern Similarity

337

measurement in that variables need to have additive effects on some measure in order to be considered “independent” in their contributions to that measure. Their actual mathematical results were posed in terms of transformations of physical scales. The discussion at the end of the Tversky and Krantz (1970) paper, which advised the operational defining of psychological dimensions in terms of criteria such as interdimensional additivity, taken in conjunction with their tangible mathematics has an implication. It implies that their results on scaling, actually work in a direct fashion only if the physical scales map in a ”separable” fashion, into the psychological dimensions. Otherwise, the investigator would first have to ascertain the laws of interaction (i.e., the maps carrying the physical dimensions into the psychological dimensions), and then show that these new dimensions exhibited interdimensional additivity. With regard to the metric criterion, it is interesting to note that all Minkowski metrics satisfy interdimensional additivity. That is, both the city-block and the Euclidean (among others), from the conjoint measurement point of view, are consistent with a type of separability. In any case, the metric argument itself, based on the peculiarity of the city block distance, might be strengthened by embedding it within a process model. For instance, suppose that early processing of stimulus dimensions satisfied some of the early requirements discussed above, for separability. Then suppose that evaluation of similarity took place within the observer by way of a serial operation which computed the absolute value of differences on the separate dimensions and then combined this information additively. This model gives a psychologically plausible sense to the fashion in which a metric could be associated with ”separability.” On the other hand, it is of course true, that cognitive systems could act much like that scenario, for instance operating serially on feature sets, without producing a metric result.

FURTHER THOUGHTS ON FOUNDATIONAL MEASUREMENT VIS-A-VIS PROCESS MODELS An Achilles heel of foundational measurement is widely believed to attach to its as yet undeveloped statistical underpinning (e.g., see Cliff, 1992; Falmagne, 1992; Marley, 1992). Due to this lacuna, aside from the mathematical beauty of some of the literature, it is safe to say that many of the implications have been within the arena of ”hard” sciences, especially Newtonian physics. A s far as the psychology is concerned, the primary drive has perhaps been ”philosophy of science” in nature, although there have been important inroads into decision theory (e.g.,

1.T.ToronsendandR. D. Thomas Fishburn, 1982; Krantz, et. al., 1971; Suppes, et. al., 1989). From this point of view, the results that relate to psychological geometry could turn out to be of most direct impact to the behavioral sciences. Although probabilistic aspects will likely play an important role in the latter, their scarcity in the present context does not seem to be so troublesome. Nevertheless, there are a number of open problems that remain to be successfully attacked, several mentioned in the foregoing discussion. The linkage of foundational measurement geometry with process models and multidimensional scaling analysis is one that has been harped on throughout this account. First, the skeptical process modeler or experimentalist might ask whether, given that the qualitative structures proposed by the measurement investigators are sometimes so close to being a metric space to start with, and so easily disrupted by possible psychological transformations, every-day researchers should undergo the arduous training required to actually work with (as opposed to "culturally experiencing") the theory. The authors of this chapter plump down on the affirmative side, but the question merits further debate. Unfortunately, as with a number of technical developments in the behavioral sciences, many psychologists appear to possess little to no knowledge of this branch of research, even in regions where results can affect their own conclusions. An example is the regular abuse of psychological scales in empirical and psychometrics research (e.g., see Townsend & Ashby, 1984; Luce, et. al., 1990; Roberts, 1979). There is another potential research area that we have not yet touched on. This topic concerns the development of process models that lead in a natural way to qualitative measurement structures of the sort studied by these investigators. If all the process models are always expressed in terms of nice traditional real-valued functions in well-behaved (usually Euclidean) metric spaces, how shall we ever bridge the gap? Just to state that psychological structures might be weaker qualitative entities, without knowing how they might arise, leaves a serious vacuum. Does a weakening of structure occur due to stochastic noise, or are we missing some fundamental link, perhaps a new way to represent massive neural networks or process models in general, that allows a proper synthesis and mutual benefaction? On the other hand, some researchers have stated that as long as, say MDS, works in the sense of presumably revealing the underlying psychological space, then they are unconcerned with the kinds of questions brought up in this paper. We certainly agree that methods can work in a pragmatic sense, long before their underpinnings are secure. A case in point is the Heaviside function (e.g., see Lighthill, 1958) which physicists

P a f t mSimifarfy

339

used for fifty years before it was endowed by mathematicians with a rigorous setting. However, in the present situation, we feel that there are purely empirical reasons to pursue such theoretical goals. First, the revealed psychological space must have "traveled" from whatever process last contributed to its present characteristics, without almost any perturbation, as shown in earlier arguments above. Furthermore, the nature of such transformation, from that particular representation, to the output, must surely be of interest to psychology. The same should be said of the transformations from the physical world, through the sensorium and pertinent cognitive processes. Thus, we would propose that such investigations hold considerable value from a scientific, and simply mathematical, perspective. Finally, there is a small set of literature that seems quite at home within the foundational setting, and in some ways, seems like a very natural way to approach the goal of providing an underpinning for M D S . It appears not to have received much notice to date. We will refer to it as the "distance set approach because that rubric is common in the attending papers. Basically, the investigator considers a set of positive (possibly including 0) numbers and asks whether it can realized as a set of distances in a certain space or class of spaces. Clearly, that is, to put it colloquially, "part and parcel" of the M D S program. Although some of the theorems are naturally somewhat esoteric, some of the others are rather striking in their implications. For example, Kelly (1951) demonstrates the existence of n+k (k even and positive including 0) numbers that cannot be distance sets for any subset of an n-dimensional Euclidean space! But now the conundrum of monotonicity arises yet again. That is, if we assume that internal psychological information may have been perturbed so that empirical data are monotonic transformations of the psychological distances, then it must be okay to re-transform them to regain the psychological space. But then the investigator is in danger of transforming data that itself cannot be put into any, say, Euclidean space into virtually anything, and in fact something that cuddles quite nicely into an n-dimensional Euclidean space. On the other hand, there exist even infinite sequences of non-negative numbers that can be embedded in many spaces. The upshot is that there seems to be little that is ruled out when one permits oneself to perform arbitrary monotonic transformations on data. One of the hallmark papers in this literature is Kelly & Nordhaus (1951), who also list a number of relevant papers. Some of the names are well-known in mathematical circles, such as Erdos, Sierpinski, Coxeter, and Picard.

1.T. TownsendandR. D. Thomas

340

Thus, again we have to face the importance of considering what transformations are actually occurring within psychological processes. Such knowledge, and the building of such constraints into our process models of psychological geometry, might be conjoined with the mathematical results of the distance set approach, to not only produce effective M D S transformations, but to place restrictions on what those transformations might be. The fact that the M D S functions that are actually employed (in contrast to any arbitrary monotonic transformation) turn out to be a restricted set (e.g., see Young, 1975, and Bentler & Weeks, 19781, might be highly useful when analyzed in conjunction with probable classes of psychological transformations. The paragraph above illustrates the associating specific metric assumptions to particular M D S procedures and these together to process model concepts. An alternative tactic, well demonstrated by Holman (19781, is to employ only ordinal betweeness relationships in estimating positions of objects within an n-dimensional coordinate system (but sans metric or even additional premetric assumptions). From one point of view, Holman’s (1978) paper realizes the goal of a purely ”nonmetric” scaling methodology .

CONCLUSION In the preceding sections, we have ranged over some of the important mathematical concepts underpinning physical and psychological similarity and distance. These concepts were discussed in the context of psychological process theories, particularly with regard to preservation of characteristics that would allow the embedding of similarity or dissimilarity ratings (or other like dependent variables) into metric spaces. It was emphasized that such concepts as dimension and feature, not to mention metric, are meaningful only when the psychological functions of a specific task, and therefore also the implied stimulus variation, are taken into account. Once the hypothesized psychological elements of a task are made manifest, plausible psychological models can be implemented and their topological and geometric implications, in addition to their usual predictions, studied. Within this milieu, some aspects of similarity as relating to finite and infinite dimensional spaces, to objects in motion and to feature extraction were reviewed. Yet another benefit of such an enterprise might be the resolution of the paradox of most information process models: the form of the information and what happens to it, are usually absent from the models. Taking in account the transformation of spatial in-

Pattern Similarity

341

formation (in the broad sense) of stimuli, and throughout the psychological system, could help to eliminate the paradox. In conclusion, it seems clear that the time has arrived for more intensive investigation of the triad, foundational measurement theory, psychological process theory, and numerical mu1tidimensional scaling methodology, taken in concert. Finally, a few remarks are in order regarding the overall goals of the present tome. The fact that three of the most rigorous approaches to a specific perceptual topic have shown so little evidence of convergence, is not especially encouraging with respect to the much more ambitious aim of a unified, and perhaps reductionistic, theory of perception in general. What is the outlook for such a general theory? A high degree of speculation is in order here, and our predilection for formal theory will be apparent. We foretell (soothsay might be more apt) that in the indefinite future, a loosely knit, hierarchy of theoretical structures on human cognition will come into being after many, many decades of challenging empirical and theoretical effort. This macro-structure will be defined by a complex interplay of dynamically defined subsystems. Particular systems, such as “memory” or “form perception” will be thought to engage vast, though somewhat separable neural processes. Their theoretical definition will depend on the one hand, on empirical task demands, and on the other, with hypothesized (and partially verified) dynamical interactions among subsets of functional subsystems [which in turn, may depend on wide-spread and in some cases distributed (in the connectionistic sense) neural elements]. That is, one hallmark of the grand theory of perception, will be that specific subprocesses of perception will rarely be strictly definable by single, unique and self-sufficient modules (although researchers may have recourse to that wrong assumption for certain useful approximative purposes), much less by ineluctable physiological structures. At a single level of analysis (a ”horizontal” section of the hierarchical macro-theory), theory and spin-off models will be reasonably tightly defined and connected with one-another. For instance, at a moderate process level, let’s say, the regions of interface between early visual processing of symbolic stimuli and the systems of short-term memory will be rigorously specified. However, the (vertical) ligaments connecting largescale phenomena with more fine grain, for instance, physiological, operations will exist in principle, but will be fuzzy and only invoked in detail in the presence of great need, and under considerable duress for the scientist. The concept of similarity will exist in various modes, related to the special subsystems and the cognitive task under consideration. The disparate similarity incarnations will also possess varying degrees of quan-

342

J. T. T

d and R. D. Thomas

titative and metric properties. The implications of the overall, as well as that pertaining to similarity, scenario for truly scientific applied spheres of psychology, for instance, human factors and applied decision research as well as clinical psychology, are quite fascinating, but for now, we may ponder at the local pub.

APPENDIX On the Mathematical Definition of Dimension Here we present a more rigorous discussion of dimension using the ”covering dimension” definition developed originally by Lebesgue (see Munkres, 1976). We need to introduce several preliminary notions. The following definitions are taken after Munkres (1976). Definition: Given a collection A of subsets of a space X, another collection rZ of subsets of X is a refinement of A if each element w of R is contained in (i.e., is a subset of) at least one element of A. One can think of the refining process as crushing the original sets into “smaller” ones, like stones into pebbles; hence the term refinement. The pebbles can be thought of as being contained in some larger stone. Definition: A collection A of subsets of a space X has order m +1 if there exists a point of X that lies in m +1 elements of A but no point of X lies in more than m +I elements of A. Captured in this definition is an intuitive notion of the overlap of sets. Suppose the collection in question has order m +1, then the maximum number of sets allowed to ”overlap” in one place is m +l;but, there has to be at least this many ( m +1)sets overlapping in some place. Now we are ready to state the formal definition of dimension due to Lebesgue. Definition: A space X is finite-dimensional if there is some integer m such that for every possible collection A of open subsets of X whose union contains X (also known as an open covering of X), there is another collection D of open subsets of X whose union contains X, that is a refinement of A and has (i.e., R has) order at most m +l.The topological dimension of X is defined to be the smallest value of m for which this statement holds. An example will help to illustrate this rather abstract definition. We know that the plane, 912, is a two dimensional space. Now, let us use the definition to corroborate our knowledge. In Figure 4a, we have covered the plane by open circles which overlap each other in various places. The order of this collection of circles is four since in the shaded region four sets overlap. This tells us the plane is finite dimensional because four is a finite integer. What is the least such integer, m, here? Consider shrinking (or crushing) the circles into smaller overlapping circles keeping in mind

Pattern Simtlarity

343

we need to cover all the points in the plane. In Figure 4b we see this refining process results in the order now being three. That is, the maximum number of overlapping sets anywhere is three but there has to be some place in which three sets overlap or else some points in the plane would not be covered. This can be seen in Figure 4c. Here, the open sets have been

Y

a

b

C

Figure 4. (a) A local view of one possible covering of the plane. The area of maximal overlap is the shaded region which corresponds to the overlap of four sets. (b) A refinement of the previous covering. Now, the maximal overlap (shaded regions) corresponds to only three sets. (c) A further refinement that cannot be a covering because the point, *, is not in any of the open sets. We see from this series of refinements that the dimension of the plane is two.

refined so much that only their boundaries touch. But, note that the boundary of a given disk is not in that set because the set is open. Thus, in this particular refinement, the point in the center is not in any set, so this is not a valid covering of the plane. To include that point, we need some overlap of at least three of the sets. Hence, we conclude that the plane has dimension two.

Acknowledgment. This work was supported in part by National Science Foundation Grant BNS 9112813, Human Cognition and Perception to the first author and by an NDSEG fellowship to the second author. The authors thank Geoff Bingham and Mike Stassen for help with Figure 1 and Martin Rickert for stimulating discussions concerning auditory perception.

1.T. Townsendand R. D. Thomas

344

DISCUSSION Vicki Bruce and Mike Burton (Department of Psychology, University of Stirling, Stirling, Scotland): Townsend and Thomas have presented a detailed technical review of some of the basic issues that arise when trying to formulate an appropriate account of pattern similarity. In order to understand the nature of the psychological space lying at the front end of perception, we need to understand the mathematics of the possible spaces and mappings that could relate physical dimensions such as frequency and intensity, to psychological dimensions such as "loudness." The issues raised are complex, and somewhat daunting for the jobbing experimental psychologist trying to understand object perception. More important than their complexity, however, is the fact that it seems to us to be extraordinarily difficult to apply these underlying approaches to similarity spaces to the kinds of percepts that many of us find interesting. In most of their essay, Townsend and Thomas consider the perception of stimuli which can readily be understood to be manufactured from some combination of values on a set of comprehensible physical dimensions, such as the frequency and amplitude of a pure sinusoidal tone. Given the clarity with which the physical space can be described, it is appropriate to ask how this space translates perceptually, and how the perceptual space may then be used in turn to mediate activities such as similarity judgment or identification. From time to time in their article, however, the authors referred to a class of stimuli that seem to pose a quite different set of issues when it comes to uncovering the nature of psychological perceptual space and how this is used to influence behavior. Human faces are but one example of the more naturalistic kinds of forms that humans evolved to perceive and recognize. What messages can be gained from this chapter, and the literature on which it draws, for understanding the perceptual dimensions which we use in judging faces, or other complex everyday objects and sounds? The issues reviewed in Townsend's and Thomas' chapter are timely, as notions of a psychological similarity space for faces have been increasingly dominant in recent years. Researchers have moved from charting the cognitive processes of facial identification (e.g., Bruce & Young, 1986; Young & Bruce, 1991) to exploring the perceptual "front end" on which the later cognitive activities are based. Research on facial distinctiveness (e.g., Valentine, 1991) and on caricature (Rhodes, Brennan, & Carey, 1987) has been explicit in suggesting that faces can be located in a "space" of facial variation, which underlies both perception and memory for faces. The idea is that the more extreme and isolated is the location of a face

Pattern Similarity

345

within this space, the easier it will be to identify. Moreover, the caricature hypothesis suggests, and is supported by evidence, that a face can be made artificially more distinctive by making it more deviant from the norm. To date, the geometrical approach to ”face space” has been unashamedly Euclidean. For example, Valentine (1991) assumes a Euclidean space ”for simplicity,” awaiting evidence of a more appropriate geometrical model. Rhodes et al. (1987) develop a model of caricature in which a face can be made more distinctive by exaggerating its difference from the ”average” face. The ”difference” which is exaggerated is the location of each of a large set of x, y coordinates of key points on contrast contours, and the exaggeration is obtained by simple multiplication of these x, y distances by a caricaturing parameter, which can be positive or negative. Moreover, resulting caricatures are expressed as percentages according to the value of this parameter and ordered linearly as values of the independent variable (degree of caricature). We believe that a number of problems of interpretation of results arise from this approach and we would like to see investigators in this field take issues of geometry and scaling much more seriously. This is particularly because the results are so intriguing and provocative, for example Benson and Perrett’s (1991) extension from line-drawn to photographic caricatures, where they appear to be able to produce caricatured images which look more like people than the original, veridical images! Another area where related issues arise lies in methods based upon principal components analysis (PCA) of the variations in intensity (gray) levels from one face image to another. Some of these approaches have in recent years proved rather interesting (e.g., Turk & Pentland, 1991; see Bruce, Burton, & Craw, 1992, for an overview) since they seem to provide a potential model for face ”space” from which the underlying “dimensions” will emerge simply from the statistical variation of different images of faces. However, the PCA methodology rests on the assumption that the data represent points in a linear space. As a result, all published work using PCA requires images to be carefully normalized, in terms of size and location of the face within the image and in terms of viewpoint. There is considerable scope for the development of more sophisticated models of space, including notions of a face manifold embedded within a higher-order space, to underpin this methodology (I. Craw, personal communication). Can we make progress by more basic empirical work to uncover the nature of the similarity space for faces? The problem is that it is very difficult to uncover the possible form or dimensionality of such a space without making assumptions about the answer, as we do not properly understand the possible physical dimensions of variation which may be manipulated

346

J. T. T d a n d R . D.Thumas

or revealed in our mappings. What are the physical properties of faces that correspond to the frequency or intensity of a pure tone? Can we make progress here by studying the effect of manipulations made upon face images to judgments made of them? At present, we think not. To date, there has been an assumption that manipulating the distance or size of ”features” in the picture plane of the facial image represents a legitimate operation on the “stimulus,” whose effect on perception can then be judged. However, an increase or decrease in the number of pixels separating the eyes in a picture of a face corresponds to nothing whatsoever in the physical space of faces, since faces are not flat patterns with 2 0 distances separating their “features” but are actually bumpy surfaces. The pixels separating the eyes in a picture of a face convey, in their pattern of lightness and darkness, information about the protuberance and shape of the bridge of the nose. Altering their separation in the picture (i.e., x, y) plane may have the effect of making the nose bridge appear to recede or protrude more in the depth (i.e., the z plane). In recent years we have been arguing that a proper psychophysics of face perception must take account of the nature of the objects of face perception, and we have been trying to develop a methodology in which we examine perception as a function of changes to surface shape rather than picture layout (e.g., Bruce, Burton, Doyle, & Dench, 1989; Bruce, Burton, Hanna, et al., 1992; Bruce, Coombes, & Richards, 1993). However, this in itself poses problems since we must then develop the appropriate geometry to describe the face surface, and find ways of relating changes expressed in these geometrical terms to perceptual similarity, a difficult problem which we have only just begun to address in a highly simplistic way (Bruce, Coombes, & Richards, 1993). Perhaps we can sidestep the issues by using multi-dimensional scaling of similarity judgments made to faces, to uncover the perceptual structures ”directly” without manipulating the physical shapes of faces at all? Unfortunately many such studies have made use of schematic or highly simplified faces, artificially constructed and manipulated along artificial dimensions, thus raising the same issues addressed above (e.g., Sergent, 1984). Some investigators have used real faces, but have had to interpret the resulting similarity space in terms of proposed underlying dimensions (Shepherd, Davies, & Ellis, 1981). The results of such studies are highly dependent on the size and heterogeneity of the set of faces whose similarities are assessed. Although studies of real faces seem consistently to pull out dimensions related to overall age, face shape and hair length (for male faces), they have not yet yielded any finer scale information than that. This is presumably because resulting dimensions must be interpreted in terms of underlying face structureand we have already seen that we do not properly understand that.

Pattern Similarity

347

The complexity and (assumed) high dimensionality of faces makes the task of assessing similarities rather formidable for the observer. In this case, an alternative approach would be to try to understand the physical basis of a related variable, facial distinctiveness, which observers seem moderately comfortable with. In recent work (Bruce, Burton, & Dench, 1993) we have tried to relate psychological dimensions such as the measured memorability, or rated distinctiveness, of faces, to their objectively measured "eccentricity" in terms of their physical deviation from normal measurements. Reassuringly, there does seem to be a reasonable correlation between psychological distinctiveness and physical eccentricity, at least provided faces are both measured and judged without hair visible. However, although such studies avoid the need to manipulate faces, all the same problems that we discussed above are inherent in attempts to measure faces in terms of the spatial layout of features in the picture plane. In our study we tried to reduce these problems by including measurements of the surface protuberance as well as simple "20" layout, but again only in the most simplistic way. Are these problems peculiar to faces? (It has often proved convenient, when face perception proves tricky, to dismiss it as "special" and move on!). It is certainly the case that we must keep the different uses made of facial information clearly in mind when we consider what makes faces similar or dissimilar to one another. We may judge two different variations of the same face as very dissimilar one to another if the task is expression-based, but as very similar if the task is identity-based, for example. An ordinary-looking person can pull an extraordinary face. Few other materials are complicated by their multiple uses in social perception. However, faces are not the only class of objects within which we can make fine discriminations on the basis of extended experience, and all the problems we discussed above apply even if we restrict ourselves to the similarity space of full-face images of faces wearing neutral expressions. We recognize makes of car, breeds of dog, our own cars, our own dogs, as effortlessly as faces, given appropriate motivation and experience. For such complex stimuli the same questions arise of how we begin to study the basis of such perceptual judgments without making simplifying assumptions that beg the very questions we seek to answer. Townsend and Thomas: Bruce and Burton raise a number of provocative issues in their insightful commentary, and provide several key references to face perception literature that relate to our chapter. Their emphasis seems to be on the spatial aspects of object perception. Bruce and Burton believe that faces and other naturalistic objects pose different sets of issues than simple psychophysical stimuli. We agree that they pose more

348

1.T. TaonsendandR.D. Thomas

complex issues but we are not convinced they differ in kind from those confronting the early psychophysicists. Basically, psychologists would seem to be interested in attributes of the stimuli that are employed by observers, how these attributes are transformed, including the Gestalt itself, and how these all interrelate to various psychological facets of behavior. Naturalistic perception is more complex because observers have an extremely large number of ”features” from which to choose in everyday situations. And, they very likely store and use holistic (and possibly hologramatic) Gestalts of frequently encountered objects like faces. Much of our own interest relates to high dimensional objects like faces, but we had to set the stage for discussion of such phenomena within the context of simpler objects. Bruce and Burton question the validity of “studying the effect of manipulations made upon face images to judgments made of them ...” (p. 346). Part of the difficulty is that two dimensional variation may be having unknown or at least uncontrolled three dimensional effects, in many studies. However, this would not by itself appear to scuttle the general methodology itself so much as impugn ineffectual application. We have not yet acquired a couple of the intriguing ”in press” references alluded to by the commentators but they seem to be quite compatible with the general milieu and format provided in our chapter. This may be the case with the ”... notions of a face manifold embedded with a higher-order space...” (p. 345), and with ”... we examine perception as a function of changes to surface shape rather than picture layout! (p. 346) (e.g., Bruce et al., 1989, 1992). In our view, certain tasks likely elicit the full infinite (i.e., so large as to effectively be modeled by an infinite space) dimensionality inherent in objects like faces. Such tasks as a familiarity judgment regarding a face from a random crowd probably employ a similarity matching process that integrates over all of the available facial surface as well as hair color and the like. Another candidate for high dimensionality would be a same-different task. Although on any single trial, a certain region of the face or particular feature may suffice to distinguish two different faces, it seems probable that the entire facial surfaces and full set of characteristics may be compared in an unlimited capacity parallel fashion. On the other hand, a teacher meeting a new classroom full of students for the first time may utilize a few features to discriminate similar faces, in a limited capacity parallel or even serial fashion, until learning permits more efficient strategies. Of course, as noted in our paper, most “features” in natural visual stimuli will in reality be of higher dimension. Thus, the visible nose is itself a two dimensional manifold, so that the space of noses is an infinite dimensional manifold.

Pattern Stinrlarily

349

Bruce and Burton and their colleagues have shown us it is possible to make valuable strides in regions formerly eschewed as "too complex," such as face perception. We believe that the concepts discussed in our chapter may aid in approaching some of the goals resident in such domains. David LaBerge (Department of Cognitive Sciences, University of California, Irvine, CA): Townsend and Thomas use the notion of object similarity to take the reader on a guided tour of a wide variety of mathematical structures that have been used in modeling object perception. The major areas of research, heretofore operating relatively independently, have provided formal structures for the psychological scaling of similarity: the foundational approach that deals with assumptions about properties of scales, multidimensional scaling that uncovers hidden structures in data, and processing-models that attempt to describe how particular tasks (e.g., identification, categorization, recognition) are carried out by the observer. In view of the central role of similarity in these three research domains, and in view of the unsolved questions about how similarity operates in a variety of perceptual tasks and conditions, the authors urge investigators in these three domains to combine their efforts to forge a general quantitative theory of similarity. The similarity orderings of an array of objects are typically modeled by representing each object as a point or a (probabilistic) distribution of points within a space, and the particular topology assumed for the space enables similarity values to be derived for pairs of objects. Sometimes the similarity space is used simply to provide a means of efficiently predicting data from judgment tasks, and in these cases multidimensional scaling techniques can extract from a given set of data the smallest number of dimensions required to represent the similarity orderings. At other times the similarity space is regarded as a model of an (internal) psychological space, and as such it provides a means of viewing how a given collection of objects might be represented in the cognitive system. When one takes the second view, one easily slips into the more general issue of considering how internal spaces are structured. In the authors' words, "The similarity judgment format is intended only to provide a milieu for the raising of critical issues concerning psychological spaces, ..." (p. 300). It is to this broader issue that the present set of comments is directed. The researcher who is poised to embark on the modeling of a psychological space would seem to be blessed with a reach store of mathematical structures to choose from, and the present chapter offers a fairly extensive glimpse into the range of alternative structures that have seen recent use. However, one might claim that there is an inherent disadvantage in

350

J. T. Townsendand R. D.Thomas

having a large number of alternative mathematical models at hand that could satisfy a given set of psychological (or engineering) constraints (in the form of theory and/or data), and therefore additional constraints would be of benefit in narrowing the range of alternative models. Put otherwise, when a psychological space is treated in a "black box" fashion, with inputs and outputs providing the primary constraints, then the number of ways of modeling the "space" inside the black box given a particular set of input/output relations can be enormous. But if one chooses to look inside the box, one may discern structural characteristics that will usefully constrain candidate models. Recently there has been a startling increase in the rate of new information regarding the anatomy and physiology of neural systems. Some of these findings are directly relevant to the way that we conceive of internal representational spaces and challenge the common belief that receptive fields of neurons and the topographies of networks are fixed. Probably the most well-known and vivid example of an internal representation is the map of the body surface. The typical textbook illustrations of brain maps of the body surface have fostered the notion that somatosensory cortex faithfully preserves spatial and temporal characteristics of cutaneous receptors. However, recent studies have shown that the cortical somatosensory map changes after repeated tactile stimulation (Whitsel et al., 1989) and after peripheral deafferentiation (Merzenich et al., 1983). Apparently the structure of the circuitry underlying a receptive field of a cell cluster in the cortical body map involves an excitatory center and an inhibitory surround. The receptive field of a cell or a small cluster of cells is measured by stimulating the body surface (e.g., with a camel's hair brush) and determining the surface locations that change the firing rate of that cell or cell-cluster. If a drug (bicuculline) is then injected into the cortical area to inhibit the inhibitory cells, the receptive field is found to have expanded dramatically. The basis for the expanded receptive field is attributed to the wide distribution of excitatory fibers whose extremities are normally inhibited by the overlying inhibitory fibers. The effect of inhibiting the inhibitory elements is to "unmask" the widespread projections of excitatory elements. Hence, the structure of the representational space for body locations apparently involves a broad projection of excitatory cells whose responses are locally "sculpted" by an overlying inhibitory network. Presumably, this knowledge of circuitry could be used to construct a corresponding model of stimulus generalization (perhaps along the lines of the neural network models of Shepard and Kannappan, 1991, and Staddon and Reid, 1990) of body location, which, among other things, might predict behavioral outcomes of new and perhaps more dynamic psychological task conditions suggested by the model.

The authors mention very briefly the issue of how percepts are represented in a psychological space. Typically a percept or a stimulus object has been represented in psychological space as a point, but it has been represented also as a probabilistic distribution of points. While these two ways of coding a stimulus may be appropriate for the kind of mathematical structures the authors review for the triad of foundational measurement, multidimensional scaling, and process models, in the larger issue of internal spaces, it would seem useful in model building to know how objects, attributes, and locations appear to be coded in the brain. The area of the brain containing cells that are sensitive to discrimination and identification of objects is the inferotemporal cortex. Recent studies have shown that information sufficient for measuring discrimination capacity is not available in single neurons but only in ensembles (populations) of neurons (e.g., Gochin et al., 1992). In this cortical area the coded information about a stimulation is apparently carried independently by members of an ensemble, rather than redundantly or interactively (Gawne, Eskander, & Richmond, 1992). Other systems that have been shown to employ population coding are odor-identification cells of the olfactory bulb (Freeman & Skarda, 1985), eye-movement cells of the superior colliculus (Sparks & Mays, 1986), the limb-movement cells of the motor cortex (Georgopoulos, Swartz, & Keller, 19861, and forelimb-movement cells in the cerebellum (Pellionisz & Bloedel, 1991). It is possible for an ensemble of cells to code stimulus inputs or response outputs deterministically or probabilistically, depending on the amount of noise in the system. In contrast to the multidimensional scaling efforts that find the minimum number of dimensions required to represent similarity orderings among a set of objects or attributes, the neural-inspired modeling of internal spaces may require a tolerance for a large number of dimensions accompanied with a search for appropriate mathematical methods for dealing with them. A related example of a mathematical model of neural internalization is given by Pellionisz and Llinas (1985), in which each neural fiber is treated as a dimension and the firing rates are treated as the dimensional values. External objects are represented first in the peripheral sensory coordinate system by a point vector (representing the electrical activity in each incoming fiber), and this sensory vector is transformed into a vector in an internal space where meaningful operations can be performed on it. A special mathematical problem arises in this transformation from an external to an internal space, because the two spaces do not in general have the same number of dimensions; that is, the number of fibers entering an internal space may be larger or smaller than the number of fibers leaving it. The type of mathematical transformation that is inde-

352

1.T. Townsendand R. D.Thomas

pendent of coordinate properties is the tensor, and Pellionisz and Llinas developed a tensor network theory to describe the functions of neural circuits mathematically. It has been said that the growth of structural knowledge of neural circuits has outpaced the growth of the kinds of mathematical tools needed for adequate study of how the neural circuits might function. The modeling by Pellionisz and Llinas perhaps may be regarded as an effort to redress this imbalance. It is desirable, from considerations of theoretical simplicity as well as efficiency of production, that the information in the (internal) representational space be invariant across a variety of tasks (e.g., identification, categorization, recognition, similarity scaling); that is, we wish the representational space to be process-independent. However, as pointed out by the authors, attention apparently can induce a transformation on the similarity orderings in a space. Consider a set of objects mapped into a similarity space based on the data obtained from an identification task. Can one use this mapping to predict performance in a categorization task, particularly under exemplar models of categorization, in which the classification of an object depends upon its similarity to objects in other categories? Apparently cross-task performance is successful for integral-dimension stimuli (for which dimensions are not readily singled out by attention), but not for separable-dimension stimuli (in which the dimensions can be relatively easily singled-out by attention). Following the earlier lead of Shepard (Shepard, Hovland, & Jenkins, 1961; Shepard & Chang, 1963), Nosofsky (1984,1986) formulated a model of categorization in which each dimension of the similarity space is weighted such that a large attentional weight serves to “stretch” the space along the dimension while a small attentional weight serves to “shrink” the space along the dimension. Thus, on this view, the similarity spacings in a cognitive space involving separable dimensions are not invariant under changes in selective attention to particular dimensions. Variations in selective attention can occur not only across tasks, but also within a task. The notion that attention can operate on a space by stretching or shrinking the space along a dimension may be extended to the more general notion that at least for some object or location spaces, attention distorts the space only in the neighborhood of its current focus. In particular, attention could be viewed as a local change of the space inside and outside the area of attentional focus. A mechanism that could effect this kind of local distortion on a cortical map of spatial locations is the thalamic circuit (Nicolelis, Lin, Woodward, & Chapin, 1993), and a recent study (LaBerge, Carter, & Brown, 1992) that simulated operations of this circuit in a shape-identification task showed that information flow increased in the focal area of attention relative to its surround. Since every

Pattern Simllarify

353

area of the cortex is reciprocally connected to a particular thalamic nucleus containing this particular type of circuit (a cortical column typically extends downward to include its corresponding thalamic “column”), it would seem that activity in any cortical map (induced from external, bottom-up sources or from internal, top-down sources) involves this kind of local distortion of its space. The structural separation of the cortical map from its thalamic modulatory mechanism could encourage the hypothesis that the cortical map itself (during its base-rate state of cell firings) is relatively task-independent, and that task-related processes (e.g., selective attention) operate through its corresponding thalamic circuitry to produce momentary distortions in the cortical map. Townsend and Thomas have amply demonstrated the richness of mathematical structures that are available to model psychological space, with an emphasis on the common role of similarity scaling across research domains including foundational measurement, multidimensional scaling methods, and certain cognitive process models. The present commentary serves mainly to suggest how neurobiological findings may provide helpful constraints on the choice of structures that give rise to the topologies that could represent an internal space. Townsend and Thomas: LaBerge has keenly selected a domain of consideration which received little attention in our chapter, that of consideration of neural structure in model building and theorization. Our scant material on that subject was supplemented, at the urging of the Editor of this volume, by a few more remarks in the Conclusion on the outlook for reductionism and theory construction in general. This material was added after LaBerge had received the chapter, but in any case, really doesn’t affect his commentary. Basically, LaBerge argues that knowledge of the physiology may aid in constraining the large number of theoretical entities that are capable of producing a corpus of input-output data, to a dramatically reduced set of alternatives. As our remarks in the chapter indicate, we are entirely comfortable with this proposal. More generally, the recent fast progress in neuroscience is helping to guide many of us from day-to-day in our conception of information processing systems underlying perception and cognition. On the other hand, it does seem that the specific goal of restraining the size of explanatory classes capable of handling well-known cognitive phenomena, is largely still in the form of a promissory note. We have not seen very many cases, for example, where an issue concerning two competing cognitive hypotheses has been decisively settled by physiological data. Rather, the primary contribution of neurophysiology has been in

1. T. T d a n d R. D. Thomas

354

finding the circuitry probably responsible for cognitive processes already pretty well accepted. Even the famous Hubel and Wiesel feature work has not ruled out more continuous and global models of processing, in most researcher‘s minds. Another benefaction from neuroscience has been the proliferation of specified brain regions jointly responsible for certain task elements. On the one hand, this has supported at least a weak form of modularity and on the other, has challenged both physiologists as well as psychologists to fully account for the many ”centers” contributing to certain task performance. All this being said, the future looks promising for a more sophisticated brand of interaction of neurological data with behavioral phenomena and theoretical structures. LaBerge and colleagues own recent work is striking in this regard. For instance, LaBerge, Carter, and Brown (19921, have employed current information about the visual pathways, especially vis-avis thalamus, to construct simulations of attentional models which obey both contemporary neural tenets as well as the general assumptions of LaBerge’s model of visual attention. In our view, this kind of work could be valuable in conjunction with the quantitative tools discussed in our chapter, in building and testing more accurate theories of form cognition and similarity relations therein.

REFERENCES ALGOM, D., & COHEN-RAZ, L. (1987). Sensory and cognitive factors in the processing of visual velocity. Iournal of Experimental Psychology: Human Perception and Performance, 13, 3-13. ANDERSON, J. R. (1990). The adaptive character of thought. Hillsdale, NJ: Erlbaum. ASHBY, F. G. (1982) Deriving exact predictions from the cascade model. Psychological Review, 89, 599-607. ASHBY, F. G. (1989). Stochastic general recognition theory. In D. Vickers & P. L. Smith (Eds.), Human information processing: Measures, mechanisms, and models (pp. 435-457). Amsterdam: Elsevier. ASHBY, F. G. (Ed.) (1992). Multidimensional models of perception and cognition. Hillsdale, NJ: Erlbaum. ASHBY, F. G., & GOTT, R. E. (1988). Decision rules in the perception and categorization of multidimensional stimuli. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 33-53.

Pafiern simllmity

355

ASHBY, F. G, & LEE, W. W. (1991). Predicting similarity and categorization from identification. Journal of Experimental Psychology: General, 120, 150-172. ASHBY, F. G., & MADDOX, W. T. (1990). Integrating information from separable psychological dimensions. Journal of Experimental Psychology: Human Perception and Performance, 16, 598-612. ASHBY, F. G., & PERRIN, N. A. (1988). Toward a unified theory of similarity and recognition. Psychological Review, 95, 124-150. ASHBY, F. G., & TOWNSEND, J. T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154-1 79. AUSLANDER, L., & MACKENZIE, R. E. (1977). Introduction to differentiable manifolds. New York Dover. BACHEM, S. (1954). Time factors in relative and absolute pitch determination. Journal of the Acoustical Society of America, 26, 751-753. BANKS, W.P. (1977). Encoding and processing of symbolic information in comparative judgments. In G. H. Bower (Ed.), The psychology of learning and motivation (vol. 11, pp. 101-159). New York: Academic Press. BEALS, R., & KRANTZ, D. H., (1967). Metrics and geodesics induced by order relations. Mathematische Zeitschrift, 101, 285-298. BEALS, R., KRANTZ, D. H., & TVERSKY, A. (1968). Foundations of multidimensional scaling. Psychological Review, 75, 127-142. BELTRAMI, E. (1987). Mathematics for dynamic modeling. San Diego: Academic Press. BENNETT, B. M., HOFFMAN, D. D., & PRAKASH, C. (1989). Observer mechanics. San Diego, CA: Academic Press. BENSON, P. J., & PERRETT, D. I. (1991). Perception and recognition of photographic quality facial caricatures: implications for the recognition of natural images. European journal of Cognitive Psychology, 3, 105-135. [VB&MB] BENTLER, P. M., & WEEKS, D. G. (1978). Restricted multidimensional scaling models. journal of Mathematical Psychology, 17, 138-151. BIEDERMAN, I. (1987). Recognition-by-components: A theory of human image understanding. Psychological Review, 94, 115-147. BINGHAM, G. P. (1987a). Dynamical systems and event perception: A working paper, parts 1-11, 201, 4-14. BINGHAM, G. P. (198%). Kinematic form and scaling: Further investigations and the visual perception of lifted weight. Journal of Experimental Psychology: Human Perception and Performance, 13, 155-177. BINGHAM, G. P. (1991a). The identification problem in visual event perception part I : Rate structures in optic flow and the degrees of freedom problem (Research Report No. 52, Indiana University Cognitive Science Research Report Series). Bloomington, IN: Indiana University.

356

1.T. Taonsendand R. D. Thomas

BINGHAM, G. P. (1991b). The identification problem in visual perception part II. Dynamics and orientation (Research Report No. 53, Indiana University Cognitive Science Research Report Series). Bloomington, IN: Indiana University. BIRNBAUM, M. H. (1974). Using contextual effects to derive psychophysical scales. Perception & Psychophysics, 15, 89-96. BIRNBAUM, M. H. (1982). Controversies in psychological measurement. In B. Wedener (Ed.), Social attitudes and psychophysical measurement (pp. 401-485). Hillsdale, NJ: Erlbaum. BLUMENTHAL, L. M. (1950). Theory and applications of distance geometry. New York: Chelsea. BOOTHBY, W. M. (1986). An introduction to differentiable manifolds and Riemannian geometry. Orlando, FL: Academic Press. BRUCE, V. (1988). Recognizing faces. Hillsdale, NJ: Erlbaum. BRUCE, V., BURTON, A. M., & CRAW, I. (1992). Modelling face recognition. Philosophical Transactions of the Royal Society of London, B335, 121-128. [VB&MB] BRUCE, V., BURTON, A. M., & DENCH, N. (1993). What’s distinctive about a distinctive face? Quarterly Iournal of Experimental Psychology, in press. [VB&MBl BRUCE, V., BURTON, A. M., DOYLE, T., & DENCH, N. (1989). Further experiments on the perception of growth in three dimensions. Perception & Psychophysics, 46, 528-536. [VB&MBl BRUCE, V., BURTON, A. M., HANNA, E., HEALEY, .P, MASON, O., COOMBES, A., FRIGHT, R., & LINNEY, A. (1992). Sex discrimination: how do we tell the difference between male and female faces? Perception, in press. [VB&MBl BRUCE, V., COOMBES, A., & RICHARDS, R. (1993). Describing the shapes of faces using surface primitives. Image and Vision Computing, in press. [VB&MBI BRUCE, V., & YOUNG, A. W. (1986). Understanding face recognition. British journal of Psychology, 77, 305-327. [VB&MBl BUFFART, H., & LEEUWENBERG, E. (1983). Structural information theory. In H. G. Geissler, H .F . J. M. Buffart, E. L. J. Leeuwenberg, & V. Sarris (Eds.), Modern issues in perception (pp. 48-72). Berlin: VEB Deutscher Verlag der Wissenschaften. BUNDESEN, C. (1990). A theory of visual attention. Psychological Review, 97, 523-547. BURTON, G., & TURVEY, M. T. (1990). Perceiving the lengths of rods that are held but not wielded. Ecological Psychology, 2, 295-324. BUSEMAN, H. (1955). The geometry of geodesics. New York: Academic Press.

Pattern simrlmity

357

BUSEMEYER, J. R., & TOWNSEND, J. T. (1989). Decision field theory: a dynamic-cognitive approach to decision making (Report No. 89-7, Purdue Mathematical Psychology Program Technical Report Series). West Lafayette, IN: Purdue University. BUSEMEYER, J. R., & TOWNSEND, J. T. (1992). Fundamental derivations from decision field theory. Mathematical Social Sciences, 23, 255-282. CAELLI, T., HOFFMAN, W. C., & LINDMAN, H. (1978a). Apparent motion: Self excited oscillations induced by retarded neuronal flows. In E. L. J. Leeuwenberg & H. F. J. M. Buffart (eds.), Formal theories of visual perception (pp. 103-116). Chichester: Halsted Press. CAELLI, T., HOFFMAN, W. C., & LINDMAN, H. (1978b). Subjective Lorentz transformations and the perception of motion. Journal of Optical Society of America, 68, 402-411. CARLTON, E. H., & SHEPARD, R. N. (1990a). Psychologically simple motions as geodesic paths. I. Asymmetric objects. Journal of Mathematical Psychology, 34, 127-188. CARLTON, E. H., & SHEPARD, R. N. (1990b). Psychologically simple motions as geodesic paths. 11. Symmetric objects. Journal of Mathemati~ a Psychology, l 34, 189-228. CARROLL, J. D., ARABIE, P. (1980). Multidimensional scaling. Annual Review of Psychology, 31, 607-649. CARVELLAS, T., & SCHNEIDER, B. (1972). Direct estimation of multidimensional tonal dissimilarity. Journal of the Acoustical Society of America, 51, 1839-1848. CECH, C. G., & SHOBEN, E. J. (1985). Context effects in symbolic magnitude comparisons. Journal of Experimentaf Psychology: Learning, Memory, 19Cognition, 11,299-315. CHEN, M., & CHEN, K. C. (1982). A transformational analysis of form recognition under plane isometries. Journal of Mathematical Psychology, 26, 237-251. CHEN, M., & CHEN, K. C. (1987). A group model of form recognition under plane similarity transformations. Journal of Mathematical Psychology, 31, 321-337. CLIFF, N. (1992). Abstract measurement theory and the revolution that never happened. Psychological Science, 3, 186-190. CUTTING, J. E. (1991). Four ways to reject directed perception. Ecological Psychology, 3, 25-34. CUTTING, J. E., PROFFIIT, D. R., & KOZLOWSKI, L. T. (1978). A biomechanical invariant for gate perception. Journal of Experimental Psychology: Human Perception and Performance, 4, 357-372.

358

J. T. Townsend and R. D. Thomas

DEUTSCH, D. (1973). Octave generalization of specific interference effects in memory for tonal pitch. Perception 6 Psychophysics, 13, 271275. ENNIS, D. M., & MULLEN, K. (1986a). A mutivariate model for discrimination methods. Iournal of Mathematical Psychology, 30, 206-219. ENNIS, D. M., & MULLEN, K. (1986b). Theoretical aspects of sensory discrimination. Chemical senses, 11, 513-522. ENNIS, D. M., & MULLEN, K. (1992). A general probabilistic model for triad discrimination, preferential choice, and two-alternative identification. In F. G. Ashby (Ed.), Mu1 tidimensional probabilistic models of perception and cognition (pp. 115-122). Hillsdale, NJ: Erlbaum. ENNIS, D. M., PALEN, J. J., & MULLEN, K. (1988). A multidimensional stochastic theory of similarity. Journal of Mathematical Psychology, 32,449-465. ERIKSEN, C. W., & MURPHY, T. D. (1987). Movement of attentional focus across the visual field: A critical look at the evidence. Perception 6 Psychophysics, 43, 299-305. FALMAGNE, J. C. (1992). Measurement theory and the research psychologist. Psychological Science, 3, 88-93. FISHBURN, P. C. (1982). The foundations of expected utility. Dordracht, Holland: Reidel. FLETCHER, H., & MUNSON, W. A. (1933). Loudness: Its definition, measurement, and calculation. Journal of Acoustical Society of America, 5, 82-108. FREEMAN, W. J., & SKARDA, C. A. (1985). Spatial EEG patterns, nonlinear dynamics and perception: The neo-Sherringtonian view. Brain Research Reviews, 10, 147-175. [DLI FUKANAGA, K. (1990). Introduction to statistical pattern recognition. San Diego, CA: Academic Press. GARNER, W. R. (1954). Context effects and the validity of loudness scales. Journal of Experimental Psychology, 48, 218-224. GARNER, W. R. (1974). The processing of information and structure. New York: Wiley. GARNER, W. R., & FELFOLDY, G. L. (1970). Integrality of stimulus dimensions in various types of information processing. Cognitive Psychology, 1, 225-241. GAWNE, T. J., ESKANDER, E. N., & RICHMOND, B. J. (1992). The heterogeneity of adjacent neurons in inferior temporal cortex. Society of Neuroscience Abstracts, IS, 147. [DLI GEORGOPOULOS, A. P., SWARTZ, A. B., & KELLER, R. E. (1986). Neuronal population coding of movement direction. Science, 233,1416-1419. [DLI

Pattern similarity

359

GIBSON, J. J. (1986). The ecological approach to visual perception. Hillsdale, NJ: Erlbaum. GOCHIN, P. M., COLOMBO, M., DORFMAN, G. A., GERSTEIN, G. L., & GROSS, C. G. (1992). Neural ensemble measurement of stimulus selectivity in inferior temporal cortex. Society of Neuroscience Abstracts, 18,147. [DLI GREGSON, R. (1988). Nonlinear psychophysical dynamics. Hillsdale, NJ: Erlbaum. HOFFMAN, D. D., & BENNETT, B. M. (1985). Inferring the relative three dimensional positions of two moving points. Journal of the Optical Society of America, 2, 350-353. HOFFMAN, D. D., & BENNETT, B. M. (1986). The computation of structure from fixed-axis motion: Rigid structures. Biological Cybernetics, 54, 71-83. HOFFMAN, W. C. (1966). The Lie algebra of visual perception. Journal of Mathematical Psychology, 3, 65-98. HOLMAN, E. W. (1978). Completely nonmetric multidimensional scaling. Journal of Mathematical Psychology, 18, 39-51. HOLMAN, E. W. (1979). Monotonic models for asymmetric proximities. Journal of Mathematical Psychology, 20, 1-15. HOLYOAK, K., & MAH, W. A. (1981). Semantic congruity in symbolic comparisons: Evidence against an expectancy hypothesis. Memory t2 Cognition, 9, 197-204. HOLYOAK, K., & MAH, W. A. (1982). Cognitive reference points in judgments of symbolic magnitude. Cognitive Psychology, 14, 328-352. HUMMEL, J. E., & BIEDERMAN, I. (1992). Dynamic binding in a neural network for shape recognition. Psychological Review, 99, 480-517. HUREWICZ, W., & WALLMAN, H. (1941) Dimension theory. Princeton, NJ: Princeton University Press. HYMAN, R., & WELL, A. (1967). Judgments of similarity and spatial models. Perception t2 Psychophysics, 2, 233-248. IMAI, S. (1992). Fundamentals of cognitive judgments of pattern. In H. G. Geissler, S. W. Link, & J. T. Townsend (Eds.), Cognition, information processing, and psychophysics: Basic issues (pp. 225-265). Hillsdale, NJ: Erlbaum. JAMES, I. M. (1987). Topological and uniform spaces. New York: SpringerVerlag. JOHANSSON, G. (1950). Configurations in event perception. Uppsala: Almqvist & Wiksell. JOHANSSON, G. (1973). Visual perception of biological motion and a model for its analysis. Perception 19Psychophysics, 14, 201-211.

360

J. T. Townsendand R. D. Thomas

KADLEC, H., & TOWNSEND, J. T. (1992a). Implications of marginal and conditional detection parameters for separabilities and independence of perceptual dimensions. Journal of Mathematical Psychology, 36, 325-374. KADLEC, H., & TOWNSEND, J. T. (1992b). Signal detection analyses of dimensional interactions. In F. G. Ashby (Ed.), Multidimensional probabilistic models of perception and cognition (pp. 181-227). Hillsdale, NJ: Erlbaum. KELLY, L. M. (1951). Distance sets. Canadian Journal of Mathematics, 3, 187-194. KELLY, L. M., & NORDHAUS, E. A. (1951). Distance sets in metric spaces. Transactions of the American Mathematical Society, 71, 440456. KILLEEN, P. R. (1992). Mechanics of the animate. Journal of the Experimental Analysis of Behavior, 57, 429-463. KINCHLA, R. (1974). Detecting target elements in multi-element arrays: A confusability model. Perception & Psychophysics, 15, 410-419. KOENDERINK, J. J. (1990). Solid Shape. Cambridge, MA: MIT Press. KOFFKA, K. (1935). Principles of Gestalt psychology. New York: Harcourt, Brace. KOHONEN, T. (1989). Self-organization and associative memory. Berlin: Springer. KOPPERMAN, R. (1988). All topologies come from generalized metrics. The American Mathematical Monthly, 95, 89-97. KRANTZ, D. H., LUCE, R. D., SUPPES, P., & TVERSKY, A. (1971). Foundations of measurement: Additive and polynomial representations (vol. 1). New York: Academic Press. KRANTZ, D. H., & TVERSKY, A. (1975). Similarity of rectangles: An analysis of subjective similarity. Journal of Mathematical Psychology, 12, 4-34. KRUEGER, L. E. (1989). Reconciling Fechner and Stevens: Toward a unified psychophysical law. Behavioral and Brain Sciences, 12, 251-320. KRUMHANSL, C. L., & KESSLER, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review, 89, 334-368. KRUSCHKE, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning. Psychological Review, 99, 22-44. KRUSKAL, J. B., & WISH, M. (1978). Multidimensional Scaling. Beverly Hills, CA: Sage. LABERGE, D., & BROWN, V. (1989). Theory of attentional operations in shape identification. Psychological Review, 96, 101-124.

Paftern simrlarity

361

LABERGE, D., CARTER, M., & BROWN, V. (1992). A network simulation of thalamic circuit operations in selective attention. Neural Computation, 4,318-331. [DLI LAMING, D. (1991). Reconciling Fechner and Stevens? Behavioral and Brain Sciences, 14, 188-191. LAPPIN, J. S. (1990). Perceiving the metric structure of environmental objects from motion and stereopsis. In R. Warren & A. H. Wertheim (Eds.) The perception and control of self-motion (pp. 541-578). Hillsdale, NJ: Erlbaum. LAPPIN, J. S., & LOVE, S. R. (1992). Planar motion permits perception of metric structure in stereopsis. Perception 6 Psychophysics, 51, 86-102. LAPPIN, J., & WASON, T. D. (1989). The perception of geometrical structure from congruence. In S. R. Ellis & M. K. Kaiser (Eds.), Spatial display and spatial instruments (pp. 18.1-18.15). NASA Conference Publication 10032. LEE, D. N. (1980). The optic flow field: The foundations of vision. Philosophical Transactions of the Royal Society of London, B290, 169-179. LEYTON, M. (1986a). A theory of information structure. I. General principles. Iournal of Mathematical Psychology, 30, 103-160. LEYTON, M. (1986b). A theory of information structure. 11. A theory of perceptual organization. Iournal of Mathematical Psychology, 30, 257305. LICKLIDER, J. C. R. (1951). Basic correlates of the auditory stimulus. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 985-1039). New York: Wiley. LIGHTHILL, M. J. (1958). Fourier analysis and generalized functions. London: Cambridge University Press. LINDMAN, H., & CAELLI, T. (1978). Constant curvature Riemannian scaling. Journal of Mathematical Psychology, 17, 89-109. LUCE, R. D. (1963). Detection and recognition. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (pp. 103189). New York Wiley. LUCE, R. D., KRANTZ, D. H., SUPPES, P., & TVERSKY, A. (1990). Foundations of measurement: Represen tation, axiomatization, and invariance (vol. 3). San Diego, CA: Academic Press. LUENBERGER, D. G. (1979). Introduction to dynamic systems: Theory, models, 6 Applications. New York: Wiley. MARKS, L. E. (1992). The contingency of perceptual processing: Context modifies equal-loudness relations. Psychological Science, 3, 285-291. MARLEY, A. A. J. (1992). Measurement, models, and autonomous agents. Psychological Review, 3, 93-96.

362

J.T. Townsendand R. D. Thomas

MASSARO, D. W. (1987). Speech perception by ear and by eye: A Paradigm for psychological inquiry. Hillsdale, NJ: Erlbaum. MASSARO, D. W. (in press). Information processing models: Microscopes of the mind. In M. R. Rosenzweig & L. W. Porter (Eds.), Annual Review of Psychology. MCCLELLAND, J. L. (1979). On the time relations of mental processes: An examination of systems of processes in cascade. Psychological Review, 86, 287-330. MEDIN, D. L., & SCHAFFER, M. M. (1978). Context theory of classification learning. Psychological Review, 85, 207-238. MERZENICH, M. M., KAAS, J. H., WALL, J. T., NELSON, R. J., SUR, M., & FELLEMAN, D. J. (1983). Topographic reorganization of somatosensory cortical areas 3b and 1 in adult monkeys following restricted deafferentiation, Neuroscience, 8, 33-55. [DLI MEYER, M. (1904). On the attributes of the sensations. Psychological Review, 11, 83-103. MEYER, M. (1914). Review of G. Rev&, "Ziir Grundleguncy der Tonpsychologie." Psychological Bulletin, 11, 349-352. MORGAN, C. T., & GARNER, W. R. (1947). Further measurements of the relation of pitch to intensity. American Psychologist, 2,433. MUNKRES, J. R. (1976). Topology: A first course. Englewood Cliffs, NJ: Prentice-Hall. MUNSELL, A. H. (1915). Atlas of the Munsell color system. Maldin, MA: Wadsworth, Howland. NARENS, L., & LUCE, R. D. (1990). Three aspects of the effectiveness of mathematics in science. In R. E. Mickens (Ed.), Mathematics and science (pp. 122-135). Singapore: World Scientific Publishing Company. NAVON, D. (1977). Forest before trees: The precedence of global features in visual perception. Cognitive Psychology, 9, 353-383. NEWELL, A. (1990). Unified theories of cognition. Cambridge, MA: Harvard University Press. NEWHALL, S. M., NICKERSON, D., & JUDD, D. B. (1943). Final report of the 0. S. A. subcommittee on spacing of the Munsell colors. Journal of the Optical Society of America, 33, 385-418. NICOLELIS, M. A. L., LIN, C. S., WOODWARD, D. J., & CHAPIN, J. K. (1993). Dynamic and distributed properties of many-neuron ensembles in the ventral posterior medial (VPM) thalamus of awake rats. Proceedings of the National Academy of Sciences, in press. [DLI NILSSON, N. J. (1965). Learning machines: Foundations of trainable pattern classifying systems. New York: McGraw-Hill. NOETHER, E., & CAVAILLES, J. (1937). Briefwechsel Cantor-Dedekind. Berlin: Hermann.

Pattern Similarity

363

NORMAN, J. F., & LAPPIN, J. S. (1992). The detection of surface curvatures defined by optical motion. Perception 6 Psychophysics, 51, 386396. NORMAN, J. F., & TODD, J. T. (1992). The visual perception of three dimensional form. In G. A. Carpenter & S. Grossberg (Eds.), Neural networks for vision and image processing (pp. 94-110). Cambridge, MA: MIT Press. NOSOFSKY, R. M. (1984). Choice, similarity, and the context theory of classification. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 104-114. NOSOFSKY, R. M. (1985). Overall similarity and the identification of separable-dimension stimuli: a choice model analysis. Perception 6 Psychophysics, 38, 415-432. NOSOFSKY, R. M. (1986). Attention, similarity, and the identificationcategorization relationship. journal of Experimental Psychology: General, 115, 39-57. NOSOFSKY, R. M. (1987). Attention and learning processes in the identification and categorization of integral stimuli. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 87-108. NOSOFSKY, R. M. (1990). Relations between exemplar-similarity and likelihood models of classification. Journal of Mathematical Psychology, 34,393-418. NOSOFSKY, R. M. (1991). Stimulus bias, asymmetric similarity, and classification. Cognitive Psychology, 23, 94-140. NOSOFSKY, R. M. (1992). Similarity scaling and cognitive process models. Annual Review of Psychology, 43, 25-53. NOSOFSKY, R. M., KRUSCHKE, J. K., & MCKINLEY, S. C. (1992). Combining exemplar-based category representations and connectionist learning rules. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 211-233. ONEILL, B. (1966). Elementary differential geometry. Orlando, FL: Academic Press. PALMER, S. E. (1989). Reference frames in the perception of shape and orientation. In B. Shepp & S. Ballesteros (Eds.), Object perception: Structure and process (pp. 121-163). Hillsdale, NJ: Erlbaum. PALMER, S. E. (1992). Reference frames in the perception of spatial structure. In H. G. Geissler, S. W. Link, & J. T. Townsend (Eds.), Cognition, information processing, and psychophysics: Basic issues (pp. 141-174). Hillsdale, NJ: Erlbaum. PALMER, S. E., SIMONE, E. J., & KUBE, P. (1988). Reference frame effects on shape perception in two versus three dimensions. Perception, 17, 147-163.

364

I. T. Townsendand R. D. Thomas

PAPOULIS, A. (1965). Probability, random variables, and stochastic processes. New York: McGraw-Hill. PARDUCCI, A. (1965). Category judgment: A range-frequency model. Psychological Review, 72, 407-418. PARDUCCI, A. (1992). Elaborations upon psychophysical contexts for judgment: Implications of cognitive models. In H. G. Geissler, S. W. Link, & J. T. Townsend (Eds.), Cognition, inforination processing, and psychophysics: Basic issues. (pp. 207-223) Hillsdale, NJ: Erlbaum. PEANO, G. (1890). Sur une courbe, qui remplit une aire plane. Mathematischen Annalen, 36, 157-160. PELLIONISZ, A. J., & BLOEDEL, J. R. (1991). Functional geometry of Purkinje cell population responses as revealed by neurocomputer analysis of multi-unit recordings. Society for Neuroscience Abstracts, 17, 920. [DLI PELLIONISZ, A. J., & LLINAS, R. (1985). Tensor network theory of the metaorganization of functional geometries in the CNS. Neuroscience, 16,245-273. [DL] PETZOLD, P. (1992). Contexts effects in judgments of attributes: An information-integration approach. In H. G. Geissler, S. W. Link, & J. T. Townsend (Eds.), C o g n i t i o n , information processing, and psychophysics: Basic issues (pp. 175-205). Hillsdale, NJ: Erlbaum. POMERANTZ, J. R., (1981). Perceptual organization in information processing. In M. Kubovy & J. R. Pomerantz (Eds.), Perceptual organization (pp. 141-180). Hillsdale, NJ: Erlbaum. REVES, G. (1913). Ziir grundleguncy der tonpsychologie. Leipzig: Feit. RHODES, G., BRENNAN, S., & CAREY, S. (1987) Identification and ratings of caricatures: Implications for mental representations of faces. Cognitive Psychology, 19, 473-497. [VB&MBl ROBERTS, F. (1979). Measurement theory with applications to decisionmaking, utility, and the social sciences. Reading, MA: Addison-Wesley. ROBINSON, D. W., & DADSON, R. S. (1956). A redetermination of the equal-loudness relations for pure tones. British Iournal of Applied Physics, 7, 166-181. ROSENBAUM, D. A. (1975). Perception and extrapolation of velocity and acceleration. Iournal of Experimental Psychology: Human Perception and Performance, 1, 305-403. RUCKMICK, C. A. (1929). A new classification of tonal qualities. Psychological Review, 36, 172-180. SERGENT, J. (1984). An investigation into component and configural processes underlying face perception. British Iournal of Psychology, 75, 221-242. [VB&MB]

Pattern simllmity

365

SHAW, G. L. (1988). Local and global interpretation of moving images. London: Pittman. SHEPARD, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 22, 325-345. SHEPARD, R. N. (1964a). Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology, 1/54-87. SHEPARD, R. N. (1964b). Circularity in judgments of relative pitch. lournu1 of the Acoustical Society of America, 36, 2345-2353. SHEPARD, R. N. (1965). Approximation to uniform gradients of generalization by monotone transformations of scale. In D. I. Mostofsky (Ed.), Stimulus generalization (pp. 94-1 10). Stanford, CA: Stanford University Press. SHEPARD, R. N. (1982). Geometrical approximations to the structure of musical pitch. Psychological Review, 89, 305-333. SHEPARD, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 1317-1323. SHEPARD, R. N., & CHANG, J. J. (1963). Stimulus generalization in the learning of classifications. Journal of Experimen tal Psychology, 65, 94102. [DL] SHEPARD, R. N., & COOPER, L. A. (1982). Mental images and their transformations. Cambridge, MA: MIT Press/Bradford. SHEPARD, R. N., HOVLAND, C. I., & JENKINS, H. M. (1961). Learning and memorization of classifications. Psychological Monographs, 75, 141. [DL] SHEPARD, R. N., & KANNAPPAN, S. (1991). Toward a connectionist implementation of a theory of generalization. In R. Lippman, J. Moody, & D. Touretzky (Eds.), Advances in neural information processing systems (vol. 3, pp. 665-671). San Mateo, CA: Morgan Kaufman. [DLI SHEPHERD, J., DAVIES, G., & ELLIS, H. (1981). Studies of cue saliency. In G. Davies, H. Ellis & J. Shepherd (Eds.), Perceiving and Remembering Faces (pp. 105-131). London: Academic Press. [VB&MBl SHIFFRIN, R. M. (1988). Attention. In R. C. Atkinson, R. J. Herrnstein, G. Lindzey, & R. D. Luce (Eds.), Steven’s Handbook of experimental psychology: Learning and cognition (vol. 2). New York: Wiley. SHIN, H. J., & NOSOFSKY, R. M. (1992). Similarity-scaling studies of dot-pattern classification and recognition. Journal of Experimental Psychology: General, 121, 278-304. SPARKS, D. L., & MAYS, L. E. (1986). Translation of sensory signals into commands for control of saccadic eye movements: Role of the superior colliculus. Annual Review of Neuroscience, 9, 118-171. [DLI

366

j . T.T d a n d R . D. Thomas

SPERLING, G. & DOSHER, 8. A. (1986). Strategy and optimization in human information processing. In K. R. Boff, L. Kaufman, and J. P. Thomas (Eds.), Handbook of perception and human performance: Sensory Processes and Perception (vol. 1, pp. 2.1-2.65). New York: Wiley. SPIVAK, M. (1979). A Comprehensive introduction to differential geometry. Wilmington, DE: Publish or Perish. STADDON, J. E. R., & REID, A. K., (1990). On the dynamics of generalization. Psychological Review, 97, 576-578. [DL] STEVENS, S. S. (1935). The relation of pitch to intensity. journal of the Acoustical Society of America, 6, 150-154. STEVENS, S. S. (1951). Mathematics, measurement, and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 149). New York: Wiley. STEVENS, S. S., & DAVIS, H. (1938). Hearing, its psychology and physiology. New York: Wiley. SUPPES, P., KRANTZ, D. H., LUCE, R. D., & TVERSKY, A. (1989). Foundations of measurement: Geometrical, threshold, and probabilistic representations (vol. 2). San Diego, CA: Academic Press. TODD, J. T., & REICHEL, F. D. (1989). Ordinal structure in the visual perception and cognition of smoothly curved surfaces. Psychological Review, 96, 643-657. TOWNSEND, J. T. (1971). Theoretical analysis of an alphabetic confusion matrix. Perception & Psychophysics, 9, 40-50. TOWNSEND, J. T. (1981). Some characteristics of visual whole report behavior. Acta Psychologica, 47, 149-173. TOWNSEND, J. T. (1990a). Serial vs. parallel processing: Sometimes they look like Tweedledum and Tweedledee but they can (and should) be distinguished. Psychological Science, 1, 46-54. TOWNSEND, J. T. (1990b). Truth and consequences of ordinal differences in statistical distributions: Toward a theory of hierarchical inference. Psychological Bulletin, 108, 551-567. TOWNSEND, J. T. (1992a). Chaos theory: A brief tutorial and discussion. In A. F. Healy, S. M. Kosslyn, & R. M. Shiffrin (Eds.), From learning theory to connectionist theory: Essays in honor of William K. Esfes. (vol. 1, pp. 65-96). Hillsdale, NJ: Erlbaum. TOWNSEND, J. T. (1992b). Don’t be phased by PHASER: Beginning exploration of a cyclical motivational system. Behavior, Research Methods, Instruments, & Computers, 24, 219-227. TOWNSEND, J. T. (1992~).On the proper scales for reaction time. In H. G. Geissler, S. W. Link, & J. T. Townsend (Eds.), Cognition, information processing, and psychophysics: Basic issues (pp. 105-120). Hillsdale, NJ: Erlbaum.

Pattern Similarity

367

TOWNSEND, J. T., & ASHBY, F. G. (1982). Experimental test of contemporary mathematical models of visual letter recognition. Journal of Experimental Psychology: Human Perception and Performance, 8, 834864. TOWNSEND, J. T., & ASHBY, F. G. (1983). Stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press. TOWNSEND, J. T., & ASHBY, F. G. (1984). Measurement scales and statistics: The misconception misconceived. Psychological Bulletin, 96, 394-401. TOWNSEND, J. T., & BUSEMEYER, J. (1989). Approach-avoidance: return to dynamic decision behavior. In D. Izawa (Ed.), Current issues in cognitive processes: Tulane Flowerree Symposium on Cognition (pp. 107-133). Hillsdale, NJ: Erlbaum. TOWNSEND, J. T., & KADLEC, H. (1990). Mathematics and psychology. In R. E. Mickens (Ed.), Mathematics and science (pp. 223-248). Singapore: World Scientific Publishing Company. TOWNSEND, J. T., & LANDON, D. E. (1983). Mathematical models of recognition and confusion in psychology. Mathematical Social Sciences, 4, 25-71. TURK, M., & PENTLAND, A. (1991). Eigenfaces for recognition. Journal of Cognitive Neuroscience, 3, 71-86. [VB&MBl TVERSKY, A. (1977). Features of similarity. Psychological Review, 84, 327-352. TVERSKY, A,, & KRANTZ, D. H. (1970). The dimensional representation and the metric structure of similarity data. Journal of Mathematical Psychology, 7, 572-596. ULLMAN, S. (1979). The interpretation of visual motion. Cambridge, MA: MIT Press. U'ITAL, W. R. (1988). On seeing forms. Hillsdale, NJ: Erlbaum. UTTAL, W. R. (1992). The swimmer. Hillsdale, NJ: Erlbaum. VALENTINE, T. (1988). Upside-down faces: A review of the effect of inversion upon face recognition. British Journal of Psychology, 79, 471491. VALENTINE, T. (1991). A unified account of the effects of distinctiveness, inversion and race in face recognition. Quarterly Journal of Experimental Psychology, 43A, 161-204. [VB&MB] VAN DER HEIJDEN, A. H. C. (1975). Some evidence for a limited capacity parallel self-terminating process for simple visual search tasks. Acta Psychologica, 39, 21-41. VAN LEEUWEN, C. (1992). Drawing inferences from representation structure: In defense of a formal theory of representations. In H. G. Geissler,

363

1.T. TawnsendandR. D. Thomas

S. W. Link, & J. T. Townsend (Eds.), Cognition, information processing, and psychophysics: Basic issues (pp. 91-103). Hillsdale, NJ: Erlbaum. WARREN, W. H. (1977). Visual information for object identity and apparent movement. Percept ion & Psychophysics, 21, 264-268. WHITSEL, B. L., FAVOROV, O., TOMMERDHAL, M., DIAMOND, M., JULIANO, S., & KELLY, D. G. (1989). Dynamic processes governing the somatosensory cortical response to natural stimulation. In J. S. Lund (Ed.), Sensory processing in the mammalian brain (pp. 84-116). New York: Oxford University Press. [DLI YOUNG, A. W., & BRUCE, V. (1991). Perceptual categories and the computation of "Grandmother." European Iournal of Cognitive Psychology, 3, 5-49. [VB&MB] YOUNG, F. W. (1975). Methods for describing ordinal data with cardinal models. Iournal of Mathematical Psychology, 12, 416-436. ZACHMANAGLOU, E. C., & THOE, D. W. (1976). Introduction to partial differential equations with applications. Baltimore, MD: Williams & Wilkins. ZAGORSKI, M. A. (1973). A topological test of metric models of stimulus similarity. (Report No. 73-10, Indiana University Mathematical Psychology Program Technical Report Series). Bloomington, IN: Indiana University. ZAGORSKI, M. A. (1975). Perceptual independence of pitch and loudness in a signal detection experiment: A processing model for 2ATFC (2ITFC) experiments. Perception b Psychophysics, 17, 525-531. ZAGORSKI, M. A. (1978). Noncombination of pitch and loudness in multidimensional scaling. Iournal of the Acoustical Society of America, 63, 273-274.

Foundations of Perceptual Theory S.C. Masin (Editor) 0 1993 Elsevier Science Publishers B.V. All rights reserved.

369

PERCEPTUAL VARIABILITY AS A FUNDAMENTAL AXIOM OF PERCEPTUAL SCIENCE F . Gregory Ashby and W . William Lee

Department of Psychology University of California, Santa Barbara, California

ABSTRACT Theories in perception frequently have a short life because they try to account for the results of one particular experimental paradigm instead of trying to model some fundamental truth about perception. This essay proposes one such truth, namely that there is trial-by-trial variability in all perceptual representations. First, the evidence is reviewed that suggests one must take variability into account when building a model of perceptual processing. Next, the implications and constraints that this axiom imposes on perceptual theories are examined. These include: (1) the decision problem that must be solved in any task that requires an organism to emit a response is functionally equivalent to classification, (2) perceived similarity is a secondary, rather than a fundamental construct, and (3) lateral interactions between neural channels evolved specifically to improve classification performance in the face of inherent perceptual variability.

Models of perception are frequently short-lived. They are usually either replaced by a newer model that accounts for a larger percentage of variance in the relevant data, or else they are just forgotten as the experimental paradigm for which they were devised falls out of fashion. One reason for their transience is that, in many cases, the models were designed specifically to account for the data collected from one particular experimental paradigm. Such models do not usually generalize well; that

370

F. G. Ashbyand W.W. Lee

is, if some, often very minor, aspect of the experiment is changed then the performance of the model collapses. An alternative method for developing new theories and models is to begin with simple axioms or self-evident truths about the topic of interest and then to examine the logical consequences of these axioms. Apparently, this was the tack taken by Einstein when he developed the special theory of relativity. In fact, the prevailing opinion is that when writing his 1905 paper that outlined the special theory, he was essentially unaware of the critical Michelson-Morley experiment (Holton, 1969). Instead, the principle features of the theory were developed by thinking hard about some simple thought experiments. There is no reason why this general approach to theory construction will not work in perception. Specifically, we propose that a general theory of perception should begin by trying to axiomatize the relevant fundamental truths. Of course, an attempt to formulate a complete list of such axioms is far beyond the scope of this essay. Instead, we will propose only what we consider to be one such axiom. The remainder of the essay will examine the implications that this axiom has for modern perceptual theory. The axiom of interest can be stated as follows.

Axiom of Perceptual Variability: There is trial-by-trial variability in the perceptual information obtained from every object or event. In other words, the percept changes even if the stimulus does not. There are many causes of such variability. The most well known include changes in the proximal stimulus that are due to the observer moving, the object moving, or the viewing conditions changing. As an animal runs across a rocky field, the image of the horizon bounces erratically on the animal’s retina, yet the percept is of a steady fixed field. To a large extent, such effects are predictable and therefore, they can be corrected or at least anticipated by the perceptual system. Although failures do sometimes occur, perception of an object or one of its attributes remains constant or invariant over a huge number of changes in the proximal stimulus (Gibson, 1979). In fact, the study of perceptual constancies is a major area of current perceptual theory. If one accepts the Axiom of Perceptual Variability then the search for such constancies is a fundamental problem of perception. The study of perceptual constancy is well documented and so will not be discussed further. However, note that the Axiom of Perceptual Variability is not restricted to situations in which the observer moves, the object moves, or the viewing conditions change. Instead, it asserts that variability will occur even if the observer, the object, and the viewing conditions are fixed. It is in this case that the axiom is most controversial and that

Perceptual Variability

371

its implications for perceptual theory are least understood. Consequently, this is the case considered here. In the case of threshold level stimuli and fixed viewing conditions, the Axiom of Perceptual Variability dates back to Fechner (1866; see also Link, 1992) and forms the cornerstone of signal detection theory (Green & Swets, 1966; Peterson, Birdsall, & Fox, 1954). However, with the high contrast stimuli used in many perceptual tasks, the axiom might appear more controversial. There are reasons however, why even in this case, variability in the percept is expected. First, physical stimuli are intrinsically variable. For example, it is well known that the number of photons emitted by a light source of constant intensity and constant duration varies probabilistically from trial-to-trial. In fact, the number of photons emitted has a Poisson distribution (Geisler, 1989; Wyszecki & Stiles, 1967). In a Poisson distribution, the mean equals the variance, so the standard deviation of the number of photons reaching the cornea increases as the square root of the luminance of the light source. As a result, intense stimuli are more variable than threshold level stimuli. If the stimulus varies from trial-to-trial then we expect the percept to vary from trial-to-trial. Thus, one cause of variability in the percept is stimulus noise. A second source of variability occurs after the stimulus enters the sensory system but before transduction occurs. We refer to this as perireceptor noise. For example, in vision, some light is scattered or absorbed as it passes through the lens and the aqueous and vitreous humors. In addition, because of the discrete distribution of photoreceptors on the retinal surface, some light will pass through the retina and be absorbed in the pigment epithelium. In fact, it has been estimated that somewhere between 67% and 89% of the photons that strike the cornea are never absorbed by a photoreceptor (Barlow, 1977). These two sources of perireceptor noise occur in all sensory systems. Table 1 summarizes these effects for vision, audition, and the chemical senses. The third and final source of variability in perceptual information is due to spontaneous activity within the central nervous system. Such activity is present at all levels of sensory and perceptual processing. For example, spontaneous isomerization of photopigment occurs frequently enough to be called "dark light" (Barlow, 1956, 1957) and ganglion cells in optic nerve sometimes have spontaneous firing rates as high as 100 spikes per second (e.g., Levine & Shefner, 1991; Robson, 1975). On the other hand, spontaneous firing rates differ greatly at different levels of processing. For example, spontaneous firing rates within the striate cortex are many times lower than in the optic nerve (e.g., Robson, 1975). Thus, although neural noise must necessarily increase as the sensory signal passes deeper into the cortex, it is a mistake to assume spontaneous activity levels are due en-

F. G. Ashbyand W. W. lee

372

tirely to unavoidable noise. In the presence of strong lateral inhibition, a high spontaneous rate extends the dynamic range of the neural channel because it allows for the possibility of negative as well as positive signals (i.e., a signal is negative if it i s below the resting level). Even so, variability tends to increase with firing rate, so the cost of a high resting level i s increased neural noise.

Table 1. Examples of how variability is introduced into perceptual processing before neural transduction occurs.

STIMULUS NOISE (Physical fluctuations inMODALITY trinsic to the stimulus Presentation Process 1

Vision

Poisson nature of light; variation in magnetic/ gravitational fields?

Audition

Variation in power source that is producing the sound; variation in humidity, barometric pressure, temperature, and wind conditions

Olfaction and Taste

Variation in molecular concentration of stimulus solution; Poisson distribution of molecules thrown across sensory surface

PERIRECEPTOR NOISE (Variation due to preneural events) Variation in pupil sue; variation in scatter and absorption as light passes through the cornea, the iris, the lens, and the aqueous and vitreous humors; discrete distribution of photoreceptors on the retinal surface Variation in the action of the ossicles; variation in the elasticity of the tympanic and basilar membranes and the oval and round windows; variation in mucous levels in sinus cavities Variation in the levels and chemical composition of olfactory mucosa and saliva; variation in binding affinities between stimulus and receptor molecules (e.g., caused by temperature variations); discrete distribution of receptors on the sensory surface

Perceptual Variability

373

These three types of variability all contribute to what might be called perceptual noise. Although such effects are undeniable, they are ignored by many perceptual theories because perceptual noise is not likely to affect the outcome of the tasks that the theories were proposed to explain. For example, when classifying pieces of fruit as apples or oranges, trialby-trial variability in perceived color (i.e., in hue) is unlikely to lead to a categorization error. As a result, most categorization theories ignore perceptual noise (for an exception, see Ashby, 1992a; Ashby & Lee, 1991,1992; Ashby & Maddox, 1993; Maddox & Ashby, 1993).

CLASSIFICATION AS A FUNDAMENTAL PERCEPTUAL PROCESS Even if perceptual noise does not affect the outcome of a perceptual task, the existence of such noise has profound effects on the nature of perceptual decision processes. For example, consider the difference between perceptual categorization and identification. In categorization, many stimuli are assigned the same response. There are many objects that we label ’%blue.” In identification, each stimulus has a unique response. There is only one person we identify as our spouse. In the presence of perceptual noise, the decision problem in a categorization task is identical to the decision problem in an identification task. In both cases, the subject must learn the many different percepts that are associated with each response. As a consequence, a theory of identification that acknowledges perceptual variability needs no extra structure to account for categorization. Conversely, a theory that postulates uniquely different decision processes for identification and categorization is almost surely wrong. In fact, this argument can be taken further. The Axiom of Perceptual Variability states that no matter what the stimulus, the resulting percept will have trial-by-trial variability. Thus, in any task that requires the subject to emit a response, trial-by-trial perceptual variability will force the subject to associate each response alternative with many different perceptual states. As a consequence, virtually all perceptual decision problems reduce to classification. Therefore, the problem of determining how an organism comes to classify perceptual states must be one of the fundamental problems of perception. A number of alternative algorithms might be used to solve this classification problem. Current research on human subjects rejects many, but not all, viable classification algorithms. For example, prototype models predict that the organism classifies a percept by comparing its similarity to the prototypical percept associated with each alternative category

374

F. G. Ashby and W. W. Lee

(Posner & Keele, 1968, 1970; Reed, 1972; Rosch, 1973). Prototype models are now known to be incapable of accounting for the diversity found in human categorization performance. For example, in contrast to the predictions of prototype theory, humans are sensitive to intra-category variability and correlation (Ashby & Gott, 1988; Ashby & Maddox, 1990,1992; Medin & Schwanenflugel, 1981; Shin & Nosofsky, 1992). At present, however, several alternatives cannot be rejected. Two of these have performed particularly well. Exemplar models assume that the organism selects a category label by first performing a global match between the percept and the memory representation of every percept of each relevant category (Brooks, 1978; Estes, 1986; Hintzman, 1986; Medin & Schaffer, 1978; Nosofsky, 1986).In contrast, decision bound models assume that the organism establishes the boundary conditions between percepts associated with competing categories. The resulting boundaries effectively partition the perceptual space into response regions. On each trial, the organism determines in which region the percept falls and then emits the associated response (Ashby, 1992a; Ashby & Lee, 1991, 1992; Ashby & Maddox, 1993; Green & Swets, 1967; Maddox & Ashby, 1993). Exemplar and decision bound models both have provided good to excellent accounts of a wide variety of categorization data. In their only direct comparisons, decision bound models have outperformed exemplar models (Ashby & Lee, 1991; Maddox & Ashby, 1993), but not nearly enough analyses have been completed to reject the exemplar approach. Although the Axiom of Perceptual Variability cannot resolve the debate between decision bound and exemplar models, it does offer some broad suggestions about what the correct theory of classification might look like. First, note that the axiom applies to all biological organisms.' As such, even the simplest organisms must be proficient at classification or else they will not survive long enough to reproduce. In fact, when the first central nervous system began to evolve, survival depended heavily on the organism's ability to identify nutrients and hospitable environments, and soon thereafter, predators, and perhaps, members of its cohort. Organisms able to perform these tasks accurately were favored in the sense that they were more likely to survive long enough to reproduce. Thus, there was a tremendous evolutionary pressure that favored organisms adept at classification. Modern evolutionary theory asserts that all animals evolved from the same common ancestor (e.g., Darnell, Lodish, & Baltimore, 1990). In fact, it applies to all physical systems. For example, quantum mechanics establishes the impossibility of constructing a physical classification device that circumvents the Poisson nature of light.

Percephd Variability

375

For example, the nucleotide sequences of human and chimpanzee DNA are compatible in 97.5%of the positions. Humans even show a 58% agreement with lemurs (Stebbins, 1982). Thus, it seems likely that the classification strategies used by all animals evolved from a common ancestral strategy. If so, then it is plausible that the fundamental nature of classification is the same for all animals and that the main difference across the phylogenetic scale is in the degree to which this basic strategy has been elaborated. These arguments suggest that when evaluating a theory of human classification, it is important to consider whether the theory is at least reasonably compatible with the known neurobiology of lower animals. For example, exemplar theories of classification assume that a separate memory trace exists for every percept that has ever been associated with each category (although the theory does not necessarily assume that the organism consciously recalls each trace). In humans, there is no good reason to doubt this assumption. However, as one moves down the phylogenetic scale, the assumption seems more and more implausible. One expects simple animals to have only a limited memory capacity. Even so, simple animals can perform some complex categorizations. For example, when a recently inseminated female mouse sniffs the urine of a strange male mouse, implantation and pregnancy are prevented (Bruce, 1959; Parkes & Bruce, 1962). This cannot be simply a genetically encoded reflexive action, because there is no way to encode genetically the odor of a future mate. Clearly then, the female’s olfactory experience with urine is essential to this phenomenon. On the other hand, the fact that her experience with urine affects her ability to recognize unfamiliar male urine, does not mean that a separate memory trace exists of her every encounter with urine. How could a decision bound model solve this problem more efficiently? One possibility is that each percept elicits a certain cycle of neural activity. Each category or response alternative is associated with some equilibrium state of brain activity. The set of all initial percepts or brain states that eventually settle at the same equilibrium state is called the basin of attraction for the category associated with that equilibrium state. Experience shapes the basin of attraction but specific memory traces need not be stored. In fact, on any single trial, classification may proceed almost automatically. In conclusion, we are not so much arguing against exemplar theories as we are arguing for the need to consider the entire animal kingdom when evaluating theories of human classification.

376

F. G. Ashbyand W. W. Lee

IS SIMILARITY A FUNDAMENTAL CONSTRUCT IN PERCEPTION? The classification of perceptual states and of brain states in general, must be the fundamental problem of perceptual decision-making. In contrast, few theories of decision processes in perception treat it as such. Instead, the most popular notion is that perceived similarity is the fundamental construct. The list of similarity-based models of perceptual decision-making includes: multidimensional scaling (Kruskal, 1964a, 1964b, Shepard, 1962a, 1962b; Torgerson, 1958; Young & Householder, 1938), the most popular exemplar-based models of categorization (i.e., the context model and the generalized context model; Medin & Schaffer, 1978; Nosofsky, 1986), and the MDS-choice model of identification (Shepard, 1957). In each of these models, the most primitive and immediate computation is of the perceived similarity between a pair of stimuli or of the similarities between the single stimulus and each member of the stimulus ensemble. The probability of the various response alternatives is then assumed to be some function of these primitive-level similarities. In the absence of trial-by-trial perceptual variability, similaritybased models are straight-forward and compelling. For example, identification confusion probabilities are assumed to be a function of the similarities between the presented stimulus and each member of the stimulus ensemble. In other words, on each trial the subject is assumed to compute the similarity between the stimulus and the memory representation of each stimulus alternative. The greater the similarity to some alternative, the more likely that alternative will be selected for response. The great majority of these models explicitly assume that there is no trial-by-trial perceptual variability. In the presence of such variability, the concept of perceived similarity becomes problematic. First, if each stimulus is associated with many percepts, then what memory representation does one choose for the similarity computation? There are several possibilities. One is to choose the prototypical representation. Another is to select a representation at random from the set of all percepts that were associated with that stimulus. In either case, similarity becomes a random variable because the percept associated with the presented stimulus varies from trial to trial. Similarity models of this type have been investigated by Zinnes and Mackay (1992), Ennis, Palen, and Mullen (1988), and De Soete and Carroll (1992). The problem with this approach is that the resulting models are relatively insensitive to the covariance structure of the distribution of percepts associated with an individual stimulus (Ennis & Ashby, 1993). For example, suppose the percepts associated with a set of stimuli are mediated by two separate neural

Perceptual Variability

377

channels, so that the resulting perceptual representation is two dimensional. If there is lateral inhibition between these two channels then there will be a resulting negative correlation between the outputs of the two channels across trials when the same stimulus is presented (Ashby, 1989). The optimal classification device, that is, the device that assigns responses to percepts in the most accurate possible manner, is extremely sensitive to such correlation, in the sense that the optimal categorization rule changes when the correlation changes (Ashby & Gott, 1988). As a consequence, predicted accuracy of the optimal classifier depends heavily on the magnitude of the perceptual correlation. In contrast, probabilistic similarity models predict that identification accuracy is much less sensitive to changes in the covariance structure of the perceptual distributions (Ennis & Ashby, 1993). The optimal classifier is sensitive to the covariance structure of the perceptual distributions, but, of course, humans might be relatively insensitive. Unfortunately, at this point, there exists little data that is relevant to this issue. Even so, there are several reasons why we might expect humans to display more sensitivity to covariance structure than predicted by the probabilistic similarity models. First, there is good evidence that in categorization tasks, humans are nearly as sensitive to the covariance structure of the contrasting categories as the optimal classifier (Ashby & Gott, 1988; Ashby & Maddox, 1990, 1992). Since the decision problem in categorization is similar to the decision problem in identification, it is reasonable to suppose that sensitivity to category covariance structure will generalize to sensitivity to perceptual covariance structure. Second, evolutionary arguments support such sensitivity. The ability to categorize and identify environmentally meaningful objects and events accurately is fundamentally important for survival. It makes sense that evolutionary pressures would favor animals that were better at these tasks. Attending to correlational information improves categorization and identification accuracy, so we expect humans to display such sensitivity. One way, and perhaps the only way, for similarity models to exhibit sensitivity to covariance structure is to assume that the subject compares the percept of the presented stimulus to the entire distribution of percepts that have been associated with each stimulus alternative (Ashby & Maddox, 1993; Nosofsky, 1990). Note that such a model predicts that to identify your brother: 1)you must access every percept you have ever had of every person you have ever seen, 2) for each of these people, you must somehow compute a similarity between the current percept and the set of all stored percepts, and 3) you must compare all the resulting similarity values. Although, at present, we have no data that allows us to reject this

378

F. G. Ashby and W.W.Lae

possibility, a simple argument of parsimony must cause us to seriously question its validity. A related question is to ask how the organism computes the similarity between a pair of perceptual states. The most popular theories of perceptual similarity assume that similarity is inversely related to psychological distance. Thus, in these theories, the fundamental construct is actually distance, rather than similarity. So, how does an organism compute distance between perceptual states? The distance formula used in most similarity theories (i.e., the Minkowski metric) requires some fairly complex computation and the answer to this question is not obvious. Perhaps an even more important question, however, is why would evolution select this method for solving the perceptual classification problem? One possibility is because perceived similarity is a construct that is useful for tasks other than identification and categorization. For example, a popular perceptual task is to ask subjects to rate the pairwise similarity of stimuli on an n-point scale. If similarity is a fundamental construct then this should be a natural and easy task for subjects, whereas if classification is fundamental then subjects should have difficulty with the similarity rating task. There are a number of reasons to think that subjects find the similarity rating task to be more difficult than identification. Ashby and Lee (1991) compared the two tasks directly. In their experiment two subjects first participated in an identification task and then in a similarity rating task. The same nine stimuli were used in both experiments (circles that varied in size and in orientation of a radial line). In the identification task, each stimulus was presented approximately 165 times (after learning) and in the similarity rating task, each pair of stimuli was presented approximately 22 times. The similarity ratings were considerably noisier than the identification responses. For example, on trials when stimulus 1 was presented in both stimulus positions, Subject 1 gave similarity ratings that ranged from 1 to 10 (on a 10-point scale) and Subject 2 gave ratings that ranged from 4 to 10. When the most dissimilar pair was presented (Stimuli 1 and 91, the ratings ranged from 1 to 7 for Subject 1and from 1 to 8 for Subject 2. In contrast, during identification, Subject 1 never confused this pair of stimuli and Subject 2 confused this pair only once in 258 trials. There is good reason for the inconsistent performance in the similarity rating task. Every day, a human identifies or categorizes hundreds of objects and events. On the other hand, most people have very little experience producing a number that measures the degree to which they perceive a pair of objects to be similar. Certainly the ability to produce such a number does not objectively improve an organism’s prospects for survival. In

Perceptual Variability

379

addition, unlike identification, with similarity ratings there is no correct response, so subjects cannot be given feedback and hence are without direction. In summary, although many current perceptual theories treat perceived similarity as a fundamental construct, we know of no data that supports this hypothesis. In addition, at a theoretical level, the hypothesis faces a number of difficulties. First is the problem of finding a plausible neurological model that computes Minkowski distance. Second, as described above, the Axiom of Perceptual Variability causes extreme conceptual difficulties for the hypothesis.

LATERAL INTERACTION AND PERCEPTUAL VARIABILITY In a previous section, we argued that evolutionary pressures would favor proficient classification strategies all along the phylogenetic scale. In this section, we consider evolution as an active process. Specifically, we consider how the presence of perceptual variability might have affected the way in which the evolutionary process shaped the modern central nervous system. In the ideal brain, there would be no perceptual variability, because only in the absence of variability is error-free classification possible (i.e., when there is some physical difference between the stimuli). Unfortunately, however, we saw in an earlier section that this goal is unattainable. For example, quantum mechanics tells us that light itself is inherently variable, so variability is present in an image even before it reaches the eye. Obviously, evolution cannot change the fundamental character of light, so no matter how a brain evolves, the Axiom of Perceptual Variability must still hold. In addition, no biological system can operate in a noise-free fashion. For example, consider the initial neural events that occur during vision. When a molecule of the rod photopigment rhodopsin absorbs a photon, it activates about 100 molecules of a G protein called transducin ( T ) that forms a complex with guanosine diphosphate (GDP). Activation causes the GDP to be exchanged for guanosine triphosphate (GTP). Each T.GTP complex then activates a phosphodiesterase that catalyzes the hydrolysis of cyclic guanosine monophosphate (cGMP). The loss of the cGMP causes sodium channels to close, which hyperpolarizes the cell. Each T.GTP complex eventually hydrolyzes about lo00 molecules of cGMP, so a single photon leads to the hydrolysis of at least 100,OOO cGMP molecules (Kosower, 1991). Clearly, it is unreasonable to expect such a huge amplification process to operate in an error-free fashion. Rather, we expect the

380

F. G. Ashby and W. W. Lee

number of cGMP molecules that are hydrolyzed by a single photon to be a random variable, with a mean of approximately 100,000, but almost surely, with a very large variance. Thus, perceptual variability is inevitable even within the first cell of the central nervous system. In a primitive nervous system, we expect few neurons and few connections between neurons. In particular, in the simplest nervous system, separate neural channels would be unconnected, and thus operate independently. Now, consider a situation in which an organism must discriminate between two similar objects (e.g., food sources) constructed of components that stimulate two neural channels. Because of perceptual variability, perfect performance is impossible. The question of interest, however, is whether any feasible changes in this nervous system can be made that will improve the discriminability of these two objects. Clearly, one possibility is to increase the difference between the mean channel outputs and a second is to decrease the channel variabilities. It turns out, however, that other, more subtle changes, can also influence classification accuracy. To see this, note that because the channels are unconnected, their outputs will be statistically independent (Ashby, 1989). In this case, we say that the stimulus components are perceived independently, or equivalently, that perceptual independence is satisfied (Ashby & Townsend, 1986). Given such conditions, the following theorem shows that discrimination can be improved by introducing a correlation between the channel outputs. Theorem 1. Consider a discrimination problem between two objects, A and B. Suppose that on each trial, the percept associated with either object can be represented by the ordered pair (XI, x2), where XI designates the output of neural channel 1 and x2 designates the output of neural channel 2. Suppose XI and x2 have a bivariate normal distribution and that the mean output when object A is presented is (PA, P A ) and the mean output when object B is presented is &, PB). Let p be the correlation between the outputs of the two channels. Under these conditions, the accuracy of the optimal classifier monotonically increases as the correlation coefficient p decreases from 0 to -1.

Proof: Let of represent the variance on channel i (for i = 1,2) and let p = pg -PA. Ashby (1992b, p. 31) showed that under these conditions, the accuracy of the optimal classifier monotonically increases with

Perceptual Variability

381

Differentiating with respect to p leads to

Accuracy monotonically increases as p decreases from 0 to -1 if and only if a(2,) / dp < 0 for all p < 0. Note that this derivative is negative if and only if

The right side is always positive and the left side is negative throughout the interval of interest. Thus, this inequality holds for all -1 < p < 0.

Thus, evolutionary pressures might favor organisms in which the outputs of separate neural channels are correlated. As already noted, with unconnected channels, the outputs are expected to be statistically independent. Correlations will occur, however, in the presence of lateral interactions between the channels. In particular, with lateral inhibition, the channel outputs should be negatively correlated (Ashby, 1989). On the other hand, lateral inhibition will affect more than just the channel correlations. A s the inhibition of Channel 1 on Channel 2 increases, both the mean and variance of the Channel 2 output should decrease. With respect to classification accuracy, therefore, the effects of lateral inhibition on the output variances and correlations should improve accuracy, whereas the effect on the means is to degrade performance. Therefore, to determine whether lateral inhibition increases the classification accuracy of the optimal classifier, a model is needed of a simple sensory system. All biological sensory systems can be viewed as a cascading series of neural channels. Figure 1 is a schematic diagram illustrating a system with a series of two sets of channels. Within each level, two or more channels operate in parallel. The vector u contains the values of the stimulus on the relevant physical dimensions along which it varies. The random vector e , represents the preneural stimulus noise (e.g., photon flux). The vectors y1 and y2 contain the outputs of each channel within levels 1 and 2, respectively, and the vectors epl and ep2 represent perceptual noise that is added to the channel outputs between levels. We assume that the three noise vectors are mutually independent and that each has a

382

F. G. Ashbyand W.W.h

multivariate normal distribution with mean vector 0 and covariance matrix Cs,&,,, and Cp2, respectively.

Figure 1. A simple multilevel model of a sensory system.

To see how lateral interactions between channels at the same level affect such a system, requires a model of channel operations within each level. The simplest such model is linear and assumes each channel output is just a weighted sum of the inputs. Consider a task in which an organism must discriminate between response terminated stimuli p and q, each constructed from the same two physical dimensions. Suppose that within each level, neural channel 1 is tuned to physical dimension 1 and channel 2 is tuned to dimension 2. Let A,, B,, and C, be 2 x 2 matrices of constants and let t represent time. Then the linear channel model assumes that the output of the two channels at level 1 at timg t on trials when stimulus i (i = p or q ) is presented can be described by the equations:

The state vector x,(t) describes the direct output of the channels. If the matrix C, is not diagonal, then the output vector of level 1, denoted by ylW, is a mixture of the direct channel outputs. The most natural interpretation of the C, mixture matrix is that it represents a decision-level integration of the signals (Ashby, 1989). The elements of the B, matrix describe the degree to which the tuning curves of the two channels overlap. The channels are separable if the B, matrix is diagonal (Ashby, 1989). Finally, the coefficients of the A, matrix measure the interactions between the channels. A positive coefficient indicates excitation and a negative coefficient indicates inhibition. The elements of the main diagonal represent self-feedback and the off-diagonal elements are measures of lateral interaction.

Percephl Variability

383

Similarly, the output of the two channels at level 2 is described by the equations:

Finally, the y3 vector in Figure 1 is equal to:

Theorem 2 describes the effects of the Ak, Bk, and Ck (for k = 1 or 2) matrices on the classification accuracy of the optimal classifier. Theorem 2. The matrices Ak, Bk, and Ck (for k = 1 or 2) affect the accuracy of the optimal classifier if and only if noise is added downstream. If epl and ep2 are both zero then classification accuracy is invariant with respect to changes in any of the matrices. If epl is nonzero but ep2 is zero, then accuracy depends on the coefficients of the matrices A], BI, and C I but not on the coefficients of Az, B2, and Cz. Proof: We assume that the optimal classifier bases its response on the equilibrium state of the system. The equilibrium state for the output of level k satisfies

Y3 = Y2 + 5 2 .

Since the noise vectors each have multivariate normal distributions, each equilibrium state is multivariate normally distributed. The three mean vectors are given by

F.G.AshbyandW. W.Lee

384

and the three covariance matrices (which do not depend on which stimulus is presented) are

XI= C1 (I - Al)-' B1& BI'[(I - A])-']' Cl'

-

Z2 = C2 (1 A,$'

B2 El +

&' [(I - Az)-'I' C2'

The accuracy of the optimal classifier is monotonic with (Ashby, 1992b): 2& = [Ep(y3)- Eq(y3)1&-' [EP(y3)- Eq(y3)l' = [Ep(yz) - E&)1

(Zz + h 2 1 - I [Ep(y2)- E&2)1'

which is a function of all six interaction matrices (i.e., Ak, Bk, and ck, for = 0 and 2ph reduces to

k = 1 and 2). If ep2 = 0 then &2

2,~h= (up- us)'B,' [(I - AI)-']' CI' El + %I)-' CI (I - A])-' B1 (9 -us) which does not depend on A2, B2, or C2. Finally, if epl also is zero, then 2ph simplifies to

which does not depend on any of Ak, Bk, or cb for k = 1 and 2.

Theorem 2 states that lateral interactions only affect the classification accuracy of the optimal classifier if noise is added downstream. In other words, if there is no perceptual noise then there is no need for lateral interactions, even in the presence of stimulus noise. Parsimony suggests that a nervous system with few interconnections is simpler than one with many interconnections. These facts suggest that lateral interactions evolved specifically as a method for increasing classification accuracy in the face of inherent perceptual noise? The Theorem 2 result is stated for linear channels, but we suspect that it holds for a much larger class of systems. A linear system performs a linear transformation of the input variables. Theorem 2 states that there is no linear transformation that will improve the performance of the optimal classifier when no noise is added downstream. The idea is that a linear transformation cannot add information to the input, it merely transforms it in a one-to-one fashion. The optimal classifier, therefore, would See Cornsweet (1970) for an alternative discussion of the evolutionary benefits of lateral inhibition.

Percephl Variability

385

perform as well classifying the inputs as classifying the outputs. Seen in this way, it is plausible to expect Theorem 2 to also hold for any nonlinear system that performs a one-to-one transformation of the input vector. If noise is added downstream then lateral interactions will affect classification accuracy, even in a linear system. For example, one simple way to do this is through self-excitation on each channel. Essentially, recurrent excitation increases the gain on the channel, with the result that the output is amplified. However, any noise added downstream is not amplified by this process, so the resulting signal-to-noise ratio increases.

CONCLUSIONS After a bit of reflection, the Axiom of Perceptual Variability might seem obvious, perhaps trivially so. Yet it has important implications for perceptual science. First, it identifies some fundamental problems to solve (e.g., determining how an organism classifies perceptual states). Second, it constrains or challenges current theories of perception (e.g., similaritybased theories). Finally, it can be used to better understand the structure of the modem central nervous system. We believe that enduring theories of perception will emerge only after other simple axioms are proposed and their consequences examined. In this essay, one simple axiom was considered in isolation. If the Axiom of Perceptual Variability were combined with other perceptual axioms, or with other accepted scientific theories, then many other implications might be derived.

Acknowledgment. This research was supported in part by National Science Foundation Grant DBS92-09411 to F. Gregory Ashby.

DISCUSSION David H. Brainard (Department of Psychology, U n i v e r s i t y of California, Santa Barbara, C A ) : Ashby and Lee argue that a successful theory of perception must contend with certain invariants that are common to a wide variety of perceptual tasks. In this, they share Shepard’s wellknown hypothesis that our perceptual systems have evolved so that they internalize invariant properties of physical laws (e.g., Shepard, 1987). Ashby and Lee, however, emphasize a different sort of invariant. They note that because of variability, the mapping between object properties and sense organ data is inherently one-to-many. They suggest that to un-

386

F. G.Ashbyand W.W.lee

derstand perception, it is necessary to analyze the implications of this perceptual variability and how our perceptual systems cope with it. Ashby and Lee’s view is not controversial among psychophysicists who study low level perceptual processes. Understanding the implications of perceptual variability is at the heart of the widely-accepted theory of signal detection (e.g., Green & Swets, 1966). More recently, Geisler and his colleagues have developed sequential ideal observer calculations that determine the limits on performance imposed by perceptual variability that arises early in the visual pathways. These calculations provide a theoretically sound null model and have helped identify those aspects of human performance that remain to be explained after known variability has been taken into account (e.g., Geisler, 1989). More controversial is the proposition that variability remains an important consideration for the study of higher level processes. Ashby and Lee’s argument is primarily one of parsimony. They note that models based on the assumption that the perceptual representation is variable provide a unified framework for understanding a) the performance of humans on different tasks (p. 3731, b) the performance of different species (pp. 374-3751, and c) the organization of the neural mechanisms underlying behavior (pp. 379-385). I find these arguments quite compelling. One might reasonably ask, however, whether a rigorous approach that begins with considerations of variability may be pursued successfully for tasks more complex than the detection and discrimination of simple stimuli. The recent literature suggests an affirmative answer. In the rest of this commentary I provide a brief review. A generalization of the notion of perceptual variability is the notion of information loss. Consider two stimuli. Suppose that in the absence of variability, presenting each stimulus results in a distinct set of perceptual responses. In this case, the stimuli should be distinguishable by the perceptual system. In the presence of variability, however, there may be sets of sense organ data that could have arisen from either stimulus. When this is possible, the organism cannot be sure which stimulus was presented; the variability reduces the information available to distinguish the stimuli. The information loss occurs because variability causes the mapping between stimuli and perceptual responses to be many-to-one. Variability is not the only possible source of information loss. The sense organs are not sensitive to all physical differences between stimuli. For example, the retinal image is a two-dimensional projection of the threedimensional physical world. Thus two different three-dimensional objects can result in identical images on the retinas. Other analogous examples include spatial sampling by the photoreceptor mosaic and the trichromacy of human color vision. This type of information loss may also be character-

Perceptual Variability

387

ized by the fact that it results in a many-to-one mapping between stimuli and sense organ data. In the remainder of this commentary I will use the phrase information loss rather than the phrase perceptual variability. Marr (19821, in what might be considered the manifesto of computational vision, argued that it is always important to analyze how information loss (in the general sense defined above) limits performance in a given perceptual task. He called this a computational analysis. In the last decade, such computational analyses have served to sharpen the experimental questions asked by visual psychophysicists. Of note for present purposes is the fact that computational analyses have provided novel insights into long-standing problems in high level perception, such as color constancy and the perception of shape. (See Landy & Movshon, 1991, for a number of examples.) Ideal observer calculations are a particularly rigorous type of computational analysis. In an ideal observer calculation, the statistical properties of the stimuli, the perceptual information loss, the subject’s task, and the subject’s goal as he performs the task are all specified explicitly. The principles of statistical decision theory (e.g., Duda & Hart, 1973) are then used to compute an upper bound for performance. This upper bound is used as a null model and the focus of subsequent theorizing is the deviation between human and ideal performance. Ideal observer calculations actually predate Marr considerably. The theory of signal detection itself is a perfect example of an ideal observer analysis. In mature form, ideal observer analyses are now an important tool used by psychophysicists to understand low level perceptual processes (e.g., Geisler, 1989). The application of ideal observer analyses to high level tasks is more recent. Barlow (1980), however, was able to compute ideal performance for the detection of symmetry in random dot patterns. His paper illustrates how interesting psychological models can emerge from attempts to explain the deviation between human and ideal performance. Other high level tasks that have recently proved amenable to ideal observer analyses include visual search (ravel, Econopouly, & Landy 1992), categorization and identification (Ashby & Lee, 1990, and object recognition (Liu, Kersten, & Knill, 1992). In the literature I have mentioned so far, the underlying principle is that an ideal observer calculation can pinpoint what information is lost in perceptual processing. I conclude by noting a second important principle that emerges naturally from ideal observer analyses. As mentioned above, the calculation of ideal observer performance requires specification of the goal that the subject is striving to attain; computed ideal performance will vary depending on this goal. Consider, for example, the classic signal detection analysis of a yes-no task. Depending on how the subject decides to trade off hits and false alarms, different performance will be observed

388

F. G. Ashbyand W. W. Lee

(Green & Swets, 1966).Subject strategy is conceptually quite different from information loss in perceptual processing. The ideal observer analysis reveals this difference. It also provides guidance about how to design experiments that allow the two types of factors to be identified from the data. Such guidance is not typically available from an approach that ignores information loss. Recent work shows that the role of subject strategy grows in importance as higher level tasks are considered (e.g., Sperling & Dosher, 1986). This in turn suggests that perceptual theory for high level tasks should indeed include a careful consideration of the implications of information loss.

Ashby and Lee: Brainard makes several insightful remarks. First, he points out that perceptual variability is only one of the many ways stimulus information gets lost during perceptual processing; he calls this generalized notion “information loss.” Of course, it is not technically a loss of information since noise increases entropy, but it is a loss in the sense that the noise causes a loss of the ability to identify the stimulus (without error). Thus, the notion of information loss is extremely important. An interesting exercise, therefore, might be to rewrite our Axiom of Perceptual Variability in terms of information loss. We suspect that a number of other interesting implications for perceptual science could be drawn from this more general axiom. Another important issue Brainard raised is whether our notion of perceptual variability and the use of ideal observer analysis are relevant for “higher level” tasks. For ”low level” tasks, ideal observer analysis has been especially useful because it has shown that certain aspects of human performance compare favorably with an ideal observer who is operating under the same sources of information loss as the human observer (e.g., photon flux, optical blur, the discrete nature of the photoreceptor mosaic; e.g., see Geisler, 1989). However, for tasks involving more complex stimuli (and/or decision processes), an ideal observer analysis is both more difficult and less likely to succeed. First, the increased complexity of the task makes it more likely that high level cortical processing plays a dominant role. Second, many more response strategies are possible with complex tasks (and a complete ideal observer analysis should examine the effects of each of these). Traditionally, ideal observer analyses have modeled only stimulus noise, perireceptor noise, the decision rule, and perhaps neural noise introduced before the first or second synapse. In complex tasks, these noise sources will account only for a modest percentage of the total variance in the data. In spite of these facts, an ideal observer analysis that includes a specific attempt to model all known sources of noise is still

P e r c q t d Varhbilify

389

useful. We describe a number of reasons why in our reply to Ennis’s commentary. Daniel M. Ennis (Philip Morris Research Cenfer, Richmond, V A ) : In 1907, “Student” showed that when a uniformly mixed liquid containing yeast cells or blood corpuscles (particles) was poured over a surface composed of many small areas, the number of particles per area closely follows a Poisson distribution. Rutherford and Geiger (1910) also showed that the number of particles emitted by a radioactive source in particular time periods could be modeled using the Poisson distribution. In this chapter, Ashby and Lee note that variation prior to signal transduction (stimulus noise) combined with variation in the reception apparatus (perireceptor noise) and variation post transduction (neural noise) are ubiquitous. They argue that these sources of variation all contribute to perceptual noise. Ennis and Mullen (1992) proposed a specific model that describes how stimulus and neural noise lead to variation in the percept. In the case of chemosensory stimulation, it is easy to see how “Student’s’’ result would be directly applicable to a dilute, uniformly mixed, solution of a chemical poured over the surface of a tongue on/in which millions of taste neurons reside. The same comment might be made about the olfactory epithelium with respect to volatile odorant effects. Even if the neural mechanism operated identically from moment to moment, stimulus variation would ensure that the same stimulus would not be identical from moment to moment. These facts are sufficient justification for the position that probabilistic models are highly likely to be useful in the study of perceptual processes. Ashby and Lee suggest that the evolution of lateral interactions occurred as a result of the need for developing nervous systems to cope with perceptual variability. Theoretically, the manipulation of perceptual correlations has both positive and negative effects on mental performance (Ennis & Ashby, 1993)and it would be interesting if this manipulation was a tool in improving classification accuracy. Ashby and Lee do not really explain how neural noise is generated and their account of the G-protein transduction mechanism does not necessarily imply anything about variation. The role played by stimulus and/or neural noise in shaping the development of signal generation and integration mechanisms is important. In Crick’s recent autobiography (1988), he makes the point that evolution does not always favor the optimum or most efficient processes, but those that are good enough. The processes that exist in biological systems today are ones that happened to work well enough to justify their existence. There also may be irrelevant mechanisms that have not been expunged because there was no advantage to doing so (like some files in my computer

390

F. G. Ashbyand W.W.Lee

directories). Before discussing similarity, identification, and categorization models it is worth making a few general points. To a neurochemist, concepts like perceptual spaces, Minkowski metrics, decision boundaries, decision rules, perceptual distributions, and so forth are not particularly meaningful. Like all ideas in science, these are just constructs that may lose their value if taken too literally and too seriously. So far, very little structural or chemical meaning has been developed for these constructs. With respect to bridging deterministic and probabilistic models of identification, Shepard’s (1957, 1987) model of similarity based on a monotonic function of distance between two stimulus representations was extended (Ennis, Palen, & Mullen, 1988; Ennis, 1988b; Ennis & Johnson, 1993) to the case in which this distance is a random variable, changing from trial to trial, but following a particular distribution. Some discussion of these ideas occurred when an attempt was made to explain the paradoxical results (with respect to Shepard’s general thesis about the similarity function and distance metric) of Nosofsky with confusable stimuli (Nosofsky, 1986; Ennis, 1988a; Nosofsky, 1988; Shepard, 1988). In these discussions, it became clear that an exemplar model of identification becomes essentially an exemplar model of categorization when probabilistic assumptions are made because stimuli are associated with distributions (a category of infinite size). It is not necessary to assume that all of the category exemplars are stored in memory and used to make categorization judgments. A random sample may be taken of one or more representations to make a decision about a particular probe. If all the exemplars are not stored, then how are the parameters of these distributions stored? How can a random sample be drawn from a distribution unless some mechanism exists to learn about and encode the distribution’s essential features? If we assume that subjects do not learn about the properties of distributions, but variables that define response regions (as Ashby and Lee suggest), then how are these response regions defined structurally and biochemically? Ashby and Lee mention that decision boundary models of categorization are more sensitive to perceptual dependence than some distance-based models involving similarity as a kernel (Ennis & Ashby, 1993). The insensitivity to perceptual dependence seems to be particularly notable with the exponential decay similarity function of city-block distance. This is important because this similarity function appears to be the most likely candidate among alternatives of this type for separable dimension stimuli (Shepard, 1987). However, there are degrees of sensitivity and it would be an overstatement to say that all distance-based similarity or identification probabilistic models are insensitive to perceptual dependence. The decision boundary models of identification studied by Ennis and Ashby (1993) were more responsive to perceptual dependence than the distance-

P e r c w Variability

391

based identification models that they evaluated, but perhaps some of these models are good enough. Nevertheless, it seems unlikely that the city-block, exponential decay model can be justified because of its extreme insensitivity. If identification and generalization decisions of sentient organisms were based on this model, then it seems unlikely that perceptual dependence would be used as a tool to improve performance. One would then have to conclude that lateral inhibition was not developed to manipulate perceptual dependence with the goal of improving performance. Categorization is certainly an important mental activity and the development of categorization models that have neurochemical and neurobiological significance would be extremely important. Decision boundary models may emerge, as the link between cognitive science and neural mechanisms is developed. This would be a relief from the present necessity to justify them entirely on the basis of model fitting to behavioral data. One thing does seem clear: Perceptual variability plays a role in decision making. It may also have played an evolutionary role in the development of nervous systems.

Ashby and Lee: In his comment, Ennis makes a number of interesting and relevant points. In particular, he points to the need for theories that specifically model the various noise sources described in our essay. He notes that in the case of stimulus noise, a great deal is already known about what such models should look like. In fact, we have proposed a method for estimating the amount of stimulus information that is available along the relevant physical dimensions in complex visual stimuli (Lee & Ashby, 1991). Ennis also briefly describes an attempt to construct a model that specifically accounts for stimulus and perceptual noise (Ennis & Mullen, 1992). Models of this kind are likely to play an increasingly important role in perceptual science. They have a number of advantages over traditional models, even over those that specifically account for variability in the percept. First, of course, in tasks where stimulus noise leads to response errors, a model that specifically accounts for stimulus noise reduces the unexplained variation in the resulting data. This allows more powerful models of sensory and perceptual processing to be constructed and tested. Second, stimulus noise distributions provide an anchor for perceptual noise distributions. Perceptual noise distributions may be interpreted as the distribution of information available to the subject's decision (i.e., classification) process. According to this interpretation, the information processing performed by the subject's sensory and perceptual systems transforms the stimulus noise distributions into perceptual noise distributions. Given separate estimates of the stimulus noise and perceptual noise dis-

392

F. G. Ashbyand W. W. Lee

tributions, it might therefore be possible to determine the transformations that are performed during sensory and perceptual processing. Hopefully, these transformations will constrain severely the set of potential sensory and perceptual architectures. For example, if the stimulus noise distributions are treated as inputs to some unknown connectionist network, then knowledge that the outputs of the network are the perceptual noise distributions should make it possible to identify a canonical class of potential network architectures. A third benefit of models that separately model stimulus noise and perceptual noise is that they allow stimulus and perceptual effects to be separated. For example, suppose that a particular perceptual noise distribution indicates a statistical dependence between a pair of perceptual dimensions. Currently, this result, known as perceptual dependence (Ashby & Townsend, 1986), is interpreted as implying some sort of interaction (e.g., lateral inhibition) between the sensory/perceptual channels associated with the two dimensions. Now consider what a study of the relevant stimulus noise distribution can add to this inference. First, suppose that the information available along the two physical dimensions is statistically independent. This knowledge implies that the dependence exhibited in the perceptual noise distribution arose within the sensory/perceptual systems. However, suppose the information available along the two physical dimensions is statistically dependent. In this case, it is incorrect to infer a sensory/perceptual interaction. In fact, it is possible that the statistical dependence present in the stimulus is carried through the sensory /perceptual systems along independent neural pathways. Therefore, before concluding that a finding of perceptual dependence has anything to say about sensory or perceptual processing, it is vital to know that such interactions are not present within the stimulus itself.

Sergio C. Masin (Department of General Psychology, University of Padua, Padua, Italy): Undoubtedly, perceptual science deals with perception as well as perceptual performance. Ashby and Lee elegantly discussed variability in perceptual performance, that is, in categorization, identification, similarity evaluation, detection, and discrimination. When considered in relation to perceptual performance, the Axiom of Perceptual Variability seems incontrovertibly true. Therefore, I agree with Ashby and Lee that this axiom identifies the fundamental problem of “how an organism classifies perceptual states.” However, in my opinion the Axiom of Perceptual Variability does not apply to perception. For example, notwithstanding the variability of perceptual information, in ordinary illumination and viewing conditions

Perceptual Variability

393

there is no variation in seen attributes of passively viewed static objects. It would be most interesting if Ashby and Lee give us their opinion on this apparent lack of generality of the Axiom of Perceptual Variability.

Ashby and Lee: Masin asks an interesting question about variability in the conscious percept. Specifically, if variability in the neural state is as important and prevalent as we claim, why do our conscious percepts of passively viewed static objects appear to be intact and noise-free? Why do we not experience all this variability? Our essay made no mention of consciousness, so to begin we need to state explicitly where in the sequence of perceptual processing we think that consciousness arises. This is a difficult task, because in no way are we claiming to possess a rigorous theory of consciousness. Nevertheless, we believe that, in general, the conscious percept will be the outcome of the classification decision process. In this sense, we agree with the constructivists (e.g., Hochberg, 1970; Rock, 1983; see, also Barlow, 1980) who argue that the proximal stimulus is often ambiguous, so the task of the perceptual system is to actively select an interpretation (i.e., a likely distal stimulus) that is consistent with the available sensory information. Changes in viewing conditions that leave the conscious percept invariant imply that this selection process is one of classification. To this, we add the argument that stimulus, perireceptor, and neural noise guarantee that the selection process is a classification problem even in high contrast, static viewing conditions. Of course, correlating the onset of conscious awareness with the perceptual classification decision does not explain why our conscious percepts seem to be noise-free. It is still possible that the various noise sources that we described could cause the classification process to continually contradict itself. This, in turn, would introduce instability to the conscious percepts. We believe, however, that such instability does not occur because it has no adaptive value. In fact, in many cases, it is associated with a significant adaptive disutility. As argued in our essay, classification is a fundamental perceptual process that must occur in any instance requiring an overt response from an organism. When an animal classifies a shadowy form in its periphery as a predator, it initiates a sequence of actions that facilitate escape. Variability in the conscious percept could cause the animal to doubt the object is really a predator, and thereby lead to inaction. In countless instances, survival requires a quick response. Thus, there is considerable adaptive value in selecting a conscious percept and then acting upon it as quickly as possible. Such actions are facilitated by well formed, noise-free conscious percepts.

F. G. Ashbyand W.W.Lae

394

A somewhat different situation occurs when a stimulus object is under continual view. At least with familiar objects, classification will occur quickly and in many such instances, no special actions will be required from the organism. In this case, there is no apparent adaptive disutility associated with variability in the conscious percept. However, the same perceptual machinery must be used in this case as in the last. Thus, the conscious percept will again be the output of the classification process. As such, variability in the conscious percept will occur only if the classification decision changes during continued viewing. In the great majority of instances, however, continued viewing merely reinforces the earlier classification decision. There are occasional exceptions. Consider, for example, the Necker Cube. There are two prominent classification alternatives; that the cube points up or down. Because the evidence is ambiguous, continuous viewing provides support for first one then the other hypothesis. The classification decision therefore flips back and forth and the conscious percept changes in an apparently random fashion. The process of classification is one of assigning a single category label to any of a large set of neural states. By its nature it is a process that corrects, or attempts to correct, for neural, perireceptor, and stimulus noise. Given that such a correction has been made, why allow the noise back into the conscious percept?

REFERENCES ASHBY, F. G. (1989). Stochastic general recognition theory. In D. Vickers & P. L. Smith (Eds.), Human information processing: Measures, mechanisms, and models. (pp. 435-457). Amsterdam: Elsevier. ASHBY, F. G. (1992a). Multidimensional models of categorization. In F. G. Ashby (Ed.), Multidimensional models of perception and cognition (pp. 449-483). Hillsdale, NJ: Erlbaum. ASHBY, F. G. (1992b). Multivariate probability distributions. In F. G. Ashby (Ed.), Multidimensional models of perception and cognition (pp. 1-34). Hillsdale, NJ: Erlbaum. ASHBY, F. G., & GOTT, R. E. (1988). Decision rules in the perception and categorization of multidimensional stimuli. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 33-53. ASHBY, F. G., & LEE, W. W. (1991). Predicting similarity and categorization from identification. Journal of Experimental Psychology: General, 120, 150-172.

Percqdd Variability

395

ASHBY, F. G., & LEE, W. W. (1992). On the relationship among identification, similarity, and categorization: Reply to Nosofsky and Smith (1992). Journal of Experimental Psychology: General, 121, 385-393. ASHBY, F. G., & MADDOX, W. T. (1990). Integrating information from separable psychological dimensions. Journal of Experimental Psychology: Human Perception and Performance, 16, 598-612. ASHBY, F. G., & MADDOX, W. T. (1992). Complex decision rules in categorization: Contrasting novice and experienced performance, Journal of Experimental Psychology: Human Perception and Performance, 18, 5071 ASHBY, F. G., & MADDOX, W. T. (1993). Relations between prototype, exemplar, and decision bound models of categorization, Iournal of Mathematical Psychology, in press. ASHBY, F. G., & TOWNSEND, J. T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154-179. BARLOW, H. B. (1956). Retinal noise and absolute threshold. Iournal of the Optical Society of America, 46, 634-639. BARLOW, H. B. (1957). Increment thresholds at low intensities considered as signal /noise discrimination. Iournal of Physiology, 136, 469-488. BARLOW, H. B. (1977). Retinal and central factors in human vision limited by noise. In H. B. Barlow & P. Fatt (Eds.), Vertebrate Phoforeception (pp. 337-358). New York Academic Press. BARLOW, H. B. (1980). The absolute efficiency of perceptual decisions. Philosophical Transactions of the Royal Society of London, B290, 71-82. [DHBI BROOKS, L. (1978). Nonanalytic concept formation and memory for instances. In E. Rosch, & B. B. Lloyd (Eds.), Cognition and categorization (pp. 169-211). Hillsdale, NJ: Erlbaum. BRUCE, H. M. (1959). An exteroceptive block to pregnancy in the mouse. Nature, 184, 105. CORNSWEET, T. N. (1970). Visual perception. Orlando, FL: Harcourt Brace Jovanovich. CRICK, F. (1988). What mad pursuit: A personal view of scientific discovery. New York Basic Books. [DMEI DARNELL, J., LODISH, H., & BALTIMORE, D. (1990). Molecular cell biology. New York: Freeman. DE SOETE, G., & CARROLL, J. D. (1992). Probabilistic multidimensional models of pairwise choice data. In F. G. Ashby (Ed.), Multidimensional models of perception and cognition (pp. 61-88). Hillsdale, NJ: Erlbaum. DUDA, R. 0. & HART, P. E. (1973). Pattern classification and scene analysis. New York: Wiley. [DHB]

3%

F. G. Ashbyand W. W. Lee

ENNIS, D. M. (1988a). Confusable and discriminable stimuli: Comments on Nosofsky (1986) and Shepard (1986). Iournal of Experimental Psychology: General, 117, 408-411. [DMEI ENNIS, D. M. (1988b). Technical comment: Toward a universal law of generalization. Science, 242, 944. [Comment on Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237,1317-1323.1 [DMEI ENNIS, D. M., & ASHBY, F. G. (1993). The relative sensitivities of samedifferent and identification judgment models to perceptual dependence. Psychomet rika, in press. ENNIS, D. M., & JOHNSON, N. L. (1993). Thurstone-Shepard similarity models as special cases of moment generating functions. Iournal of Mathematical Psychology, in press. [DMEI ENNIS, D. M., & MULLEN, K. (1992). Probabilistic psychophysics with noisy stimuli. Mathematical Social Sciences, 23, 221-234. [DMEI ENNIS, D. M., PALEN, J. J., & MULLEN, K. (1988). A multidimensional stochastic theory of similarity. Iournal of Mathematical Psychology, 32,449-465. ESTES, W. K. (1986). Array models for category learning. Cognitive Psychology, 18, 500-549. FECHNER, G. T. (1860). Elements of psychophysics. Leipzig: Breitkopf & Hartel. GEISLER, W. S. (1989). Sequential ideal-observer analysis of visual discriminations. Psychological Review, 96, 267-314. GIBSON, J. J. (1979). The senses considered as perceptual systems. Boston: Houghton-Mifflin. GREEN, D. M., & SWETS, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley. HINTZMAN, D. L. (1986). ”Schema abstraction” in a multiple-trace memory model. Psychological Review, 93, 41 1-428. HOCHBERG, J. E. (1970). Attention, organization, and consciousness. In D. I. Mostofsky (Ed.), Attention: Contemporary theory and analysis (pp. 99-124). New York: Appleton-Century-Crofts. HOLTON, G. (1969). Einstein and the crucial experiment. American lournu1 of Physics, 37, 968-982. KOSOWER, E. M. (1991). Molecular mechanisms for sensory signals. Princeton, NJ: Princeton University KRUSKAL, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1-27. KRUSKAL, J. B. (1964b). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.

P e r c w Variability

397

LANDY, M. S. & MOVSHON, J. A. (1991). Cornputational models of visual processing. Cambridge, MA: MIT Press. [DHBI LEE, W. W., & ASHBY, F. G. (1991, August). Ideal Observer Analysis of Multidimensional Stimuli in Identification. Paper presented at the Twenty-fourth Annual Ma thematical Psychology Meetings, Bloomington, IN. LEVINE, M. W., & SHEFNER, J. M. (1991). Fundamentals of sensation and perception. Pacific Grove, CA: Brooks/Cole. LINK, S. W. (1992). The wave theory of difference and similarity. Hillsdale, NJ: Erlbaum. LIU, Z., KERSTEN, D., 6% KNILL, D. C. (1992). Object classification for human and ideal observers. Investigative Ophthalmology and Visual Science, Supplement 33,825. [DHB] MADDOX, W. T., & ASHBY, F. G. (1993). Comparing decision bound and exemplar models of categorization. Perception b Psychophysics, in press. MARR, D. (1982).Vision:A computational investigation into the human representation and processing of visual information. San Francisco: Freeman. [DHB] MEDIN, D. L., & SCHAFFER, M. M. (1978). Context theory of classification learning. Psychological Review, 85, 207-238. MEDIN, D. L., & SCHWANENFLUGEL, P. J. (1981). Linear separability in classification learning. Journal of Experimental Psychology: Human Learning and Memory, 1, 335-368. NOSOFSKY, R. M. (1986). Attention, similarity, and the identificationcategorization relationship. Journal of Experimental Psychology: General, 115, 39-57. NOSOFSKY, R. M. (1988). On exemplar-based representations: Comment on Ennis (1988). Journal of Experimental Psychology: General, 117, 412414. [DME] NOSOFSKY, R. M. (1990). Relations between exemplar-similarity and likelihood models of classification. Journal of Mathematical Psychology, 34, 393-418. PARKES, A. S., & BRUCE, H. M. (1962). Pregnancy-block of female mice placed in boxes soiled by males. Journal of Reproduction and Fertility, 4, 303-308.

PAVEL, M., ECONOPOULY, J., & LANDY, M. S. (1992). The psychophysics of rapid visual search. Investigative Ophthalmology and Visual Science, Supplement 33, 1355. [DHBI PETERSON, W. W., BIRDSALL, T. G., & FOX, W. C. (1954). The theory of signal detectability. Transactions of the IRE Professional Group on Information Theory, PGIT-4,171-212.

398

F. G. Ashby and W. W. Lae

POSNER, M. I., & KEELE, S. W. (1968). On the genesis of abstract ideas. Journal of Experimental Psychology, 77, 353-363. POSNER, M. I., & KEELE, S. W. (1970). Retention of abstract ideas. Journu1 of Experimental Psychology, 83, 304-308. REED, S. K. (1972). Pattern recognition and categorization. Cognitive Psychology, 3, 382-407. ROBSON, J. G. (1975). Receptive fields: Neural representation of the spatial and intensive attributes of the visual image. Handbook of Perception, 5, 81-116. ROCK, I. (1983). The logic of perception. Cambridge, MA: MIT Press. ROSCH, E. (1973). Natural categories. Cognitive Psychology, 4, 328-350. RUTHERFORD, E. & GEIGER, H. (1910). The probability variations in the distribution of a particles. Philosophical Magazine, 6th Series, 20, 698-704. [DME] SHEPARD, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 22, 325-345. SHEPARD, R. N. (1962a). The analysis of proximities: Multidimensional scaling with an unknown distance function I. Psychometrika, 27, 125140. SHEPARD, R. N. (1962b). The analysis of proximities: Multidimensional scaling with an unknown distance function 11. Psychornetrika, 27, 219246. SHEPARD, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 1317-1323. [DHB/DMEl SHEPARD, R. N. (1988). Time and distance in generalization and discrimination: Comment on Ennis (1988). Iournal of Experimental Psychology: General, 117,415-416. [DMEI SHIN, H. J., & NOSOFSKY, R. M. (1992). Similarity-scaling studies of dot-pattern classification and recognition. Journal of Experimental Psychology: General, 121, 278-304. SPERLING, G. & DOSHER, B. A. (1986). Strategy and optimization in human information processing. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.), Handbook of Perception and Performance (ch. 2). New York: Wiley. [DHB] STEBBINS, G. L. (1982). Darwin to DNA, molecules to humanity. San Francisco: Freeman. "STUDENT" (1907). On the error of counting with a haemacytometer, Biornetrika, 5, 351-360. [DMEI TORGERSON, W. S. (1958). Theory and methods of scaling. New York: Wiley.

Perceptual Variability

399

WYSZECKI, G., & STILES, W. S. (1967). Color science: Concepts and methods, quantitative data and formulas. New York: Wiley. YOUNG, G., & HOUSEHOLDER, A. S. (1938). Discussion of a set of points in terms of their mutual distances. Psychometrika, 3, 19-21. ZINNES, J. L., & MACKAY, D. B. (1992). A probabilistic multidimensional scaling approach: Properties and procedures. In F. G. Ashby (Ed.), Multidimensional models of perception and cognition (pp. 35-60). Hillsdale, NJ: Erlbaum.

This Page Intentionally Left Blank

401

AUTHOR INDEX A Abrahamsen, A. A., 157,176 Agazzi, E., 190,196 Algom, D., 329,354 Allemang, D., 263,292 Allman, J. M., 8,40,291-292 Allport, D. A., 200,217 Ames, A., Jr., 126,176 Anderson, C. H., 8,42,289,296 Anderson, J. R., 303,354 Anderson, N. H., 62,71 Anderson, R., 289,296 Anstis, S. M., 284,294 Appelle, S., 241,254 Arabie, P., 300,357 Aristotle, 242 Armstrong, E., 40 Ashby, F. G., 300-301,309,317-318,331332,334-335,338,354355,358,360,367, 369,373-374,376-378,380-382,384390, 392-393,394-397,399 Atkinson, R. C., 365 Auslander, L., 324,355 Austin, J. L., 248,254 Autrum, H., 98,108 Avenarius, R., 43 Ayer, A. J., 52, 72

B Bachem, S., 315,355 Bacon, F., 16,20 Badler, N. I., 255 Bahill, A. T., 240,260 Baird, J. C., 152,176,180 Balakrishnan, J. D., 63 Ballard, D., 282,287,292-293 Ballesteros, S., 363 Baltimore, D., 374,395 Banaji, M. R., 90,108 Banks, W. P., 305,355 Barac-Cikoja, D., 236,254 Barlow, H., 227-229 Barlow, H. B., 371,387,393,395 Bartlett, F. C., 89,108,295 Beals, R., 303,308,336,355 Bechtel, W., 157,176 Becker, D., 129,181 Bell, J. S., 67, 72 Belousov, 8. B., 210

Beltrami, E., 317,328,355 Bennett, 8. M., 21,40,318,328,355,359 Benson, P. J., 345,355 Bentler, P. M., 340,355 Benussi, V., 202 Bergman, R, 234,254 Berkeley, G., In,176 Berne, R. M., 110 Berridge, K., 33,35-36 Berson, E., 152,181 Biederman, I., 331,355,359 Bingham, G. P., 239,254,317,329,343,356 Birdsall, T. G., 371,397 Birnbaum, M. H., 305,356 Bischof, N., 156,176 Blakemore, C., 294 Blank, A. A., 321 Block, R. A., 218 Bloedel, J. R., 351,364 Blum, G. S., 117,179 Blumenthal, L. M., 308,356 Boff, K. R., 218,366,398 Bohr, N., 27 Bolyai, J., 321 Bonner, J., 77,108 Boothby, W. M., 324,356 Bootsma, R. J., 240,254,259 Boring, E. G., 201,203-201,216-217,257 Bower, G. H., 355 Bozzi, P., 183,194195,197,207,210,217 Braddick, O., 292 Bradshaw, G., 19,42 Brainard, D. H., 385,388 Braren, P. A., 236,249,256 Brennan, S., 344,364 Brentano, F., 198,201-203,216 Brewster, D., 171,177 Brooks, L., 374,395 Brooks, R., 279-281,287,290,292 Brouwer, L. E. J., 309 Brown, V., 329,331,352,354,360-361 Bruce, H. M., 375,395 Bruce, V., 327,344-349,356,368 Bruner, J. S., 39 Brunswik, E., 23&237,254 Buffart, H., 327,356-357 Bundesen, C., 329,331,356 Burigana, L., 155, 167-168 Burke, L., 209,217-218

402

Author Index

Burton, A. M., 344-349,356 Burton, G., 236,243,254,303,318,356 Bury, R. G., 196 Buseman, H., 308,356 Busemeyer, J. R., 317,357,367 Bush, R. R., 361 Butterworth, G., 197,218 Bylander, T., 263,292

Crick, F., 290,389,395 Crooks, L. E., 234,236,257 Crowder, R. G., 90,108 Culicover, P., 41 Cummins, R., 96,108 Cutting, J. E., 24,41,101,108,231,235-240, 242-250,253-254,255256,259,303,318, 329,357

C Caelli, T., 178,328,357,361 Cantor, G., 309,362 Carello, C., 237,246247,258-259 Carey, S., 344,364 Carlson, V. R., 122,177 Carlton, E. H., 326,357 Carpenter, G. A., 363 Carroll, J. D., 300,357,376,395 Carter, M., 352,354,361 Carterette, E. C., 294 Carvellas, T., 334,357 Cassirer, E., 244 Cattell, J. M., 92,108 Cavaillks, J., 309,362 Cavanagh, P., 284,295 Cech, C. G., 305,357 Chan, T.-C., 236,255 Chandra, A., 264,266,274,295 Chang, J. J., 352,365 Chapanis, A., 78,108 Chapin, J. K., 352,362 Charpentier, A., 62,72 Cheal, M. L., 16,41 Chen, K. C., 327,357 Chen, M., 327,357 Christodoulakis, S., 282 Church, A., 265,281,293 Churchland, P., 10,13,42,283,290,293 Clauser, J. F., 67, 72 Cliff, N., 305,337,357 Cobb, S., 285,287-288,290,295 Cohen-Raz, L., 329,354 Colombo, M., 359 Comerford, J., 133,180 Cook, S., 268,293 Coombes, A., 346,356 Cooper, L.A., 326,365 Cooper, P., 41 Cornillon, M., 249 Cornsweet, T. N., 59,72,384,395 Costall, A., 197,228 Coxeter, H. S. M., 339 Crabus, H., 180 Craw, I., 345,356 Gescitelli, F., 109 Crestoni, L., 62, 73 Creutzfeldt, O., 217

D Da Silva, J. A., 116,122,146,155,175,177179 Dadson, R. S., 311F, 312,364 Darnell, J., 374,395 Darwin, C. R., 398 Davies, G., 346,365 Davis, H., 312,366 Davis, M., 272,293 Day, R. H., 160,177 Dayanand, S., 19,42 De Soete, G., 376,395 de Pomerai, D., 77,108 Dedekind, R., 362 Delboeuf, M. J., 199,217 Dench, N., 346347,356 Descartes, R., 16-17 Deubch, D., 314,358 Diamond, M., 368 Dichgans, J., 116,282 Diener, H. C., 116,281 Dodge, R., 235,256 Dodwell, P., 278 Dorfman, G. A., 359 Dosher, B. A., 329,366,388,398 Dowling, J., 271,293 Doyle, T., 346,356 Duda, R. O., 387,395 Duke-Elder, S. W., 287,293 Duncker, K., 100,108

E Ebbinghaus, H., 89-90,208 Eccles, J. C., 208,217 Econopouly, J., 387,397 Eddington, A. S., 55-56,72 Edwards, D. A,, 157,181 Einstein, A., 27,6&67,72,321,370,396 Ellis, H., 346,365 Ellis, S. R., 361 Ellis, S., 255 Emmert, E., 116,120,171,173 Empiricus, S., 195-196 Ennis, D. M., 300.301,358,376-377,389390,396-398 Epstein, W., 177,180 Erd&, P., 339 Eriksen, C. W., 329,358

Author Index Eskander, E. N., 351,358 Estes, W. K., 42,366,374,396 Eve, H. W., 229

F Falk, D., 40 Falmagne, J. C., 337,358 Farber, J. M., 62,73 Fatt, P., 395 Favorov, O., 368 Fechner, G. T., 16,360-361,371,396 Feldman, J., 282,293 Felfoldy, G. L., 335,358 Felleman, D. J., 8,42,292,293,362 Field, D., 249 Fineman, M., 116,180 Fishburn, P. C., 338,358 Fisher, C., 78,109 Flaherty, E. W., 129,281 Fletcher, H., 311F, 312,358 Fodor, J. A.,95,108,122,157,165,177 Foley, J. M., 143,177,321 Forbes, M., 109-110 Fourier, J., 2425,362 Fox, W. C., 371,397 Fraser, J., 46,48-49,53,63,67-68,70-71 Freeman, W. J., 21,25,41,351,358 Friedman, M. P., 294 Fright, R., 356 Fu, J., 249 Fujita, N., 146,179 Fukanaga, K., 332,358 Fukuda, M., 59,73 Fukusima, S. S., 146,177,179

G Galanter, E., 361 Galileo, G., 48 Garey, M., 264,266,293 Gamer, W. R., 66,72,242,256,258-259, 304,312,314,331,333-335,358,362 Gauss, C. F., 321 G a m e , T. J., 351,358 Geerts, C., 39 Geiger, H., 188,389,398 Geisler, W. S., 371,386-388,396 Geissler, H.-G., 356,359,363-364,363367 Gell-Mann, M., 15,41 Gemelli, A., 202 Georgopoulos, A. P., 351,358 Gergen, K., 39 Gerstein, G. L., 359 Gibson, E. J., 236,256 Gibson, J. J., 72,85-86,89,94,96,98,101102,105-108,153,156-157,165,172,177, 231-254,255-259,280,289,303,359,370, 396

403 Gilchrist, A., 62,72 Gilinsky, A. S., 116,177 Gochin, P. M., 351,359 Godbeer, G., 263,293 Gijdel, K., 9,37 Gogel, W. C., 61-62,72,113,115F, 116-117, 119-122,123F, l24,125F, 127F, 128-129, 132-133,137-139,142-143,144F,145, 147-149,152,154159,161-167,169-172, 174176,177-179,181 Goldmeier, E., 229 Goldsmith, T. H., 98,108 Goldstein, E. B., 255 Gopallaishnan, P., 270,293 Gott, R. E., 300,331,354,374,377,394 Gottlieb, G., 84,103,108 Green, D. M., 371,374,386,388,396 Gregory, R. L., 160,179,283,286,289-290, 293,295 Gregson, R., 317,359 Grelling, K., 166,279 Grene, M., 79,108 Grimson, E., 268,293 Grobstein, C., 105,109 Gross, C. G., 359 Grossberg, S., 363 Grosseteste, R., 16 Grunwald, A., 255 Gyr, J. W., 257 H Hall, G. S., 202 Halpern, B. P., 241,257 Hamilton, W., 39 Hanna, E., 346,356 Harnish, R. M., 41 Harr6, R., 39,241,257 Hams, C., 241,259 Harris-Warrick, R. M., 79,109 Hart, P. E., 387,395 Hatfield, G., 9>94,98,10>104,107, 109 Hay, J. C., 176,179 Healey, P., 356 Healy, A. F., 42,366 Heaviside, O., 338 Hebb, D. O., 37 Hech t, S., 58 Hegel, G. W. F., 198 Heidegger, M., 39 Heller, M. A., 254 Helmholtz, H. v., 63-67,72,207,221,224 225,227,229,244,257,272,280,286, 289,293 Henle, M., 229,251-252,258 Herrnstein, R. J., 365 Hershenson, M., 277-178 Higashiyama, A., 175,179

404 Hilbert, D., 273 Hildreth, E. C., 238,258 Hill, A. L., 116,180 Hillebrand, K., 229 Hintzman, D. L., 374,396 Hochberg, J. E., 62,72,173,179,247,249, 251,258,393,396 Hoffman, D. D., 21,40,318,328,355,359 Hoffman, W. C., 324,328,357,359 Holman, E. W., 318,340,359 Holton, G., 370,396 Holyoak, K., 305,359 Hook, S., 72,217 Hopfield, J. J., 263 Householder, A. S., 376,399 Hovland, C. I., 352,365 Howard, I. P., 171,179 Hubel, D. H., 287,354 Hudson, L., 234,257 Hull, C. L., 6,37,41 Hull, D., 109-110 Hummel, J. E., 331,359 Hurewicz, W., 309,359 Husserl, E., 198,202 Hyman, R., 335,359 I Imai,S., 327,359 Indow, T., 321 Intrilagator, J., 284,294 Ittelson, W. H., 116,171,179 Izawa, D., 367

J

Jackendoff, R., 208-209,217 James, I. M., 307,359 James, W., 86,109,199,217,224,229 Jammer, M., 56,72 Jenkins, H. M., 352,365 Johansson,G.,88,1(M107,109,328,359 Johnson, D., 264,266,293 Johnson, N. L., 390,396 Johnson, S. H., 236,256 Josephson,J., 263,292 Judd, D. B., 335,362 Judd, J. S., 263,273,293 Julesz, B., 284,285,293 Juliano, S., 368

K Kaas, J. H., 291-292,362 Kaamarek, L. K., 79,109 Kadlec, H., 300,310,318,331,360,367 Kahl, R., 229,257 Kaiser, M. K., 101,110,255,361 Kakarala, R., 19,42 Kalish, M., 236,260

Author Index Kanal, L., 270,293 Kanizsa, G.,30,41,88,109,122,164,179, 189,196,202,204,206,209,217 Kannappan, S., 350,365 Kant, I., 198 Karwan, N. E., 249 Kak, D., 204,217 Kaufman, L., 218,366,398 Kaufman, T. C., 78,110 Kaushall, P., 236,257 Kautz, H., 263,294 Keele, S. W., 373,398 Keller, R. E., 351,358 Kelly, D. G., 368 Kelly, L. M., 339,360 Kepes, G., 257 Kersten, D., 387,397 Kessler, E. J., 316,360 Khurana, B., 249 Kiesov, F., 202 Ween, P. R., 5,26-27'30-32,41,63,6&67, 317,360 Kilpahick, F. P., 116,176,179 Kinchla, R., 330,360 Kirousis, L., 263,294 Kirsh, D., 280,294 Klinger, A., 296 Knill, D. C., 387,397 Koch, S., 256 Koenderink, J. J., 324,360 Koffka, K., 62,72,198,201-202,204,217, 238,257-258,326,360 Kohler, W., 61,72,99-100,109,198,201202,204,207-208,210,217,221-227,229, 251,258 Kohonen, T., 331-332,360 Kollar, E. J., 78,109 Kopperman, R., 308,360 Kosower, E. M., 379,396 Kosslyin, S. M., 42 Kosslyn, S. M., 366 Kozaki, A., 59,73 Kozaki, T., 59,73 Kozlowski, L. T., 101,108,244,256,329, 357 Krantz, D. H.,300,303,308,316,336,338, 355,360-361,366-367 Krauskopf, J., 59,73 Kravitz, J. H., 176,181 Kristofferson, A. B., 199,217 Kroll, J., 241,259 Krueger, L. E., 305,360 Krumhansl, C. L., 316,360 Kruschke, J. K.,318,331,360,363 Kruskal, J. B., 300,360,376,396 Kube, P., 326,363 Kubovy, M., 203,218,241,364

Author Index L La Gournerie, J. de, 255 LaBerge, D., 329,331,349,352-354,360361 Lambert, J. H., 198 Laming, D., 304,361 Land, E. H., 26,41 Landon, D. E., 323,332,367 Landy, M. S., 387,397 Lappin, J. S., 324,328-329,361,363 Laties, G., 78,109 Lebesgue, H., 342 Lee, D. N., 236,258,329,361 Lee, W. W., 300-301,355,369,373374, 378,385-393,394395,397 Leeuwenberg, E., 327,356357 Leibniz, G. W. v., 1,190 Lenneberg, E., 241,258 Levesque, H., 263,295 Levin, D., 249 Levine, G., 32 Levine, M. W., 371,397 Levitan, I. B., 79,109 Lewin, K., 237,239 Lewis, D., 59,73 Leyton, M., 244,258,327,361 Liberman, A. M., 240,258 Licklider, J. C. R., 312,361 Lighthill, M. J., 338,361 Lin, C. S., 352,362 Lindman, H., 328,357,361 Lindzey, G., 257,365 Link,S. W., 21,41,359,363-364,366-367, 371,397 Linneus, C. v., 15 Linney, A., 356 Lippman, R., 365 Liu, Z., 387,397 Llinas, R., 351,364 Lloyd, B. B., 395 Lobachevski, N. I., 321 Lockhead, G. R., 67,70,73,255,258 Lodish, H., 374,395 Longo, O., 219 Loomis, J. M., 117,146,177-179 Lorentz, H. A., 357 Lorenz, K., 201,2U7,214,218 Lott, L. A., 176,180 Love, S. R., 329,361 Lovell, R., 19,42 Luccio, R., 194-195 Luce, R. D., 300,310,316,320,338,360362,365-366 Luenberger, D. G., 317,361 Lund, J. S., 368 Luneburg, R. K., 321 Lyon, D. R., 16,41

405 Lythgoe, J. N., 98,109 M MacCracken, P. J., 117,120,122,179 Mach, E., 43,50,61-62,73 Machamer, P. K., 229 Mackay, D. B., 376,399 MacKenzie, R. E., 324,355 MacLeod, R. B., 72,258 Macnamara, J., 245,258 Maddock, K., 286 Maddox, W. T., 335,355,373-374,377, 395,397 Mah, W. A., 305,359 Marder, E., 79 Mark, L. S., 236,239,258 Marks, L. E., 305,361 Marley, A. A. J., 337,361 Marr, D., 89,92,94,109,238,258,274,280, 282-287,289-292,294,387,397 Martin, K., 292,294 Mash, S.C., 43,45F, 47F, 51F, 59-60,6265,67-71’73’226227,249-253,392-393 Mason, O., 356 Massaro, D. W., 318,331,362 Mattingly, I. G., 240,258 Maunsell, J., 292,294 Mays, L. E., 351,365 McCarthy, J., 41 McClelland, J. L., 1441,317,362 McConkie, A. B., 62,73 McCready, D. W., Jr., 116,143,171-172, 180

McFarland, W. N., 98,109 McKinley, S. C., 331,363 Medin, D. L., 320,362,374,376,397 Meinong, A., 202 Mendelleev, D., 15 Menger, K., 309 Merleau-Ponty, M., 198 Mertz, D. L., 152,178 Merzenich, M. M., 350,362 Metelli, F., 57,60,73,164,180,202,209, 218 Metzger, W., 156,176,180,203-204,218 Meyer, M., 314,362 Michaels, C. F., 237,247,258 Michelson, A. A., 370 Michotte, A., 56,73,192,204,209,218 Mickens, R. E., 362,367 Millard, R. T., 236,244,255 Miller, J. G., 256 Minkowski, H., 301,314,321,378-379,390 Moody, J., 365 Moore, E. F., 19,41,207 Morgan, C. T., 312,362 Morley, E. W., 370

406 Moms, M. W., 236,260 Moms, P. E., 110 Mostofsky, D. I., 365,396 Movshon, J. A., 387,397 Mower, 0.H., 37 Mullen, K., 300,358,376,389-391,396 Mundy, J. L., 245,258 Munkres, J. R., 306,342,362 Munsell, A. H., 335,336F, 362 Munson, W. A., 311F, 312,358 Munz, F. W., 98,109 Murphy, T. D., 329,358 Musatti, C. L., 202

N Nadel, L., 41 Nakayama, K., 284286,294 Narens, L., 310,362 Navon, D., 330,362 Neander, K., 96,210 Necker, L. A., 46,64,68,394 Neisser, U., 86,90,98,101-102,104-107, 110,207,218,235,237,240,258 Nelson, R. J., 362 Newell, A., 16,19,41,300,362 Newhall, S. M., 335,362 Newman, N. J., 117,178 Newton, I., 321 Newton, R. E., 121,178 Niall, K. K., 245,258 Nickerson, D., 335,362 Nickerson, R., 259 Nicolelis, M. A. L., 352,362 Nicolis, G., 210,218 Nilsson, N. J., 332,362 Nisbett, R. E., 31,41 Noether, E., 309,362 Nordhaus, E. A., 339,360 Norman, D. A., 239,258 Norman, J. F., 324,363 Normann, R. A., 78,110 Nosofsky, R. M., 30@302,318,320,331, 334335,352,363,365,374,376-377' 390, 39.5-398 0

O'Neill, B., 324,363 Ono,H., 133,153,17@171,173-174,176, 2 80 P Palen, J. J., 300,358,376,390,396 Palmer, S. E., 326,363 Palmer, S., 244,258 Pamakrishnan, I., 270,294 Papadimkriou, C., 263,294 Papoulis, A., 332,364

Author Index Parducci, A., 305,364 Parkes, A. S., 375,397 Parks, T. E., 160,177 Parmley, W. W., 96,220 Pastore, N., 63,221,224,226,229 Pattee, H. H., 105,108,110 Patterson, R., 199,218 Pavel, M., 387,397 Pavlov, I. P., 37,83,110 Peano, G., 309,364 Pellionisz, A. J., 351,364 Pentland, A,, 345,367 Perrett, D. I., 345,355 Perrin, N. A., 300-301,331,355 Perrone, J. A., 238,259 Peterson, M. A., 128,180 Peterson, W. W., 371,397 Petzold, P., 305,364 Picard, C. E., 339 Piccinini, L., 207,218 Pick, H. L., Jr., 72,258 Pittenger, J. B., 236,245,259 Plato, 242 Plummer, D., 290 Podolsky, B., 66,72 Poincark, H., 244,259 Poisson, S.-D., 322,371,372T, 374,389 Polanyi, M., 80,91,110 Polyak, S., 98,110 Pomerank, J. R., 70,73,2@3,218,255,258, 301,364 Pons, T., 283,288,295 Porter, L. W., 362 Posner, M. I., 373,398 Post, R. B., 176,180 Potter, M. C., 241,259 Prakash, C., 21,40,318,355 Predebon, J., 122,175,180 Prentice, W. C. H., 173,180 Price, H. J., 78,111 Prigogine, I., 210,218 Proffitt, D. R.,75,93-94,97-103,108,210, 244-245,255-256,259,329,357 Pylyshyn, Z. W., 157,165,177

Q

Quastler, H., 218 R Rabbitt, P., 273,294 Raff, R. A., 78,110 Raffel, G., 234,257 Ramachandran, V. S., 28@284,286-288, 290-291,293-295 Ramsey, W., 109 Rao, V. M., 285,295 Rausch, E., 157,180

Author Index Reed, E. S., 234,259 Reed, S. K., 373,398 Regan, D. M., 177 Reichel, F. D., 234,236, 259,327,366 Reid, A. K., 350,366 Restle, F., 234,247,259 R ~ v ~G., s , 314,362,364 Rhodes, G., 344,364 Richards, R., 346,356 Richmond, B. J., 351,358 Rickert, M., 343 Riegle, M., 196 Riemann, G. F. B., 321 Rivest, J., 133,153, 280 Roberts, F., 338,364 Robinson, D. N., 3 6 , 3 9 4 Robinson, D. W., 311F, 312,364 Robson, J. G., 371,398 Rock, I., 116,124,154,165,173,280,182, 393,398

RogersRamachandran, D., 283,285,288, 295

Rorschach, H., 246 Rosch, E., 373,395,398 Rosen, N., 66,72 Rosenbaum, D. A., 329,364 Rosenblum, L. D., 239,246,254,259 Rosenzweig. M. R., 362 Royce, J., 257 Rozeboom, W., 257 Rubin, E., 76,120,204,218 Ruckmick, C. A., 315,364 Rumelhart, D. E., 10,41,109 Russell, B., 66,73,251,259 Rutherford, E., 389,398

S Saida, S., 133,153,180 Saldaiia, H. M., 246,259 Salthe, S. N., 79,94,110 Sams, V., 356 Sartre, J. P., 39 Savelsberg, G. J. P., 240,259 Schaffer, M. M., 320,362,374,376,397 Schiff, W., 254 Schlosberg, H., 116,181 Schmidt, R. C., 239,254 Schneider, B., 334,357 Schopenhauer, A., 221,223-225,229 Schrbdinger, E., 1 Schwanenflugel, P. J., 374,397 Schwartz, E. L., 296 Sejnowski, T. J., 10,13,41,283,290,293 Selman, B., 263-264,294-295 Sergent, J., 346,364 Shannon, C. E., 41,242,259 Shapiro, L., 98,110

407 Sharkey, T. J., 117,178 Shaw, G. L., 329,365 Shaw, R. E., 236,245,255,258,260 Shefner, J. M., 371,397 Shepard, R. N., 300,302-303,314316,320, 326,331,333,335,350,352,357,365, 376,385,390,396,398 Shepherd, J., 346,365 Shepherd, T., 19,42 Shepp, B., 363 Shiffrin, R. M., 42,329,365366 Shimojo, S., 284-286,294 Shimony, A., 67,72 Shin, H. J., 321,365,374,398 Shoben, E. J., 305,357 Shy, G. C.-W., 128,180 Sierpinski, W., 339 Simon, H. A., 83,105,210-111 Simone, E. J., 326,363 Simons, D., 249 Skarda,C. A.,21,25,42,351,358 Skifsted, K., 19,42 Skinner, B. F., 5,20,42-42 Smith, B., 179 Smith, J. E. K., 395 Smith, L. D., 20,42 Smith, P. L., 354,394 Solomon, H. Y., 101,111 Southall, J. P. C., 229,293 Sparks, D. L., 351,365 Sparrow, A. H., 78,211 Sperling, G., 329,366,388,398 Spivak, M., 324,366 Springer, K., 236,256 Staddon, J. E. R., 350,366 Stadler, M., 180 Stanton, L., 129, 282 Stassen, M., 343 Stebbins, G. L., 375,398 Stevens, K. N., 242,259 Stevens, S. S., 303,312,360-361,365-366 Stewart, M., 283,288,295 Stich, S., 95,109,111 Stier, D. M., 245,259 Stiles, W. S., 371,399 Stockmeyer, L., 264,266,274,295 Stoffregen, T., 243,259 Stroud, J. M., 199,218 Stucchi, N., 240,260 Student, 389,398 Stumpf, C., 202,204,228 Summons, E., 149,181 S U P ~ ~P., S 300,305,316,321,338,360-362, , 366 Sur,M., 362 Swanston, M. T., 122,143,152,154,170, 173-174,176,181

Author Index

408 Swartz, A. B., 351,358 Swets, J. A.,371,374,386,388,396 Sykes, R. N., 110 T Talbot, L., 96,110 Tdbot, W. H. F., 57-58 Tanimoto, S., 296 Tanner, M., 263,292 Ternus, J., 284 Thin&, G., 197,201,204,218 Thoe, D. W., 328,368 Thomas, J. P., 218,366,398 Thomas, R. D.,297,344,347,349,353 Tietz, J. D., 117,119-120,124, 128,137-139, 142,148-149,154,169-170,174,176,178179,181 Titchener, E. B., 202 Todd, J. T., 234,236,259,324,327,363,366 Tolman, E. C., 3940 Tommerdhal, M., 368 Torgerson, W. S., 376,398 Touretzky, D., 365 Townsend, J. T., 21,42,297,300,309-310, 317-318,323,329,331332,334,338,344, 347,349,353,355,357,359-360,363-364, 366368,380,392,395 Treisman, A., 274,295 Tsobos, J. K., 255,261,263,267,272,274, 278-279,281-282,289-290,295-296 Tudor-Hart, B., 60,73 Tupper, K., 19,42 Turing A., 265-266,270,272-273,281,296 Turk, M., 345,367 Turnbull, R. G., 229 Turvey, M. T., 101,111,236,239,243,254255,259,303,318,356 Tversky, A,, 300-301,303,308,316,336, 355,360-361,366-367 U

Uhr, L., 268,282,296 Ullman, S., 244,247,260,329,367 Underbrink, A. G., 78, I 1 1 Urysohn, P. S., 309 Uttal, W. R., 3,6-7,9,13-17,19,21-22,24, 27-28,33-39,42,207,218,300,330,367

Vickers, D., 354,394 Vidotto, G., 199,219 Vidyasagar, T., 285,295 Vishton, P., 249 Viviani, P., 240,260

w Wagner, M., 152,176 Walk, R., 236,256 Wall, J. T., 362 Wallach, H., l24,129,133,152,1R,l76, 181,284 Wallman, H., 309,359 Walls, G. L., 98,Z 11 Warren, R., 101,111,361 Warren, W. H., Jr., 101,121,236,238-239, 260,329,368 Wason, T. D., 328-329,361 Waterlow, S., 73 Watson, J. B., 5,42,280,296 Watb, R. G., 240,260 Weaver, W., 242,259 Wedener, B., 356 Weeks, D. G., 340,355 Well, A., 335,359 Wells, W. C., 171,181 Werblin, F. S., 79,110 Wertheim, A. H., 101,111,361 Wertheimer,M., 99,109,201,204-206,219 Whang, S., 239,260 Wheatstone, C., 284 Wheeler, D. D., 92,111 Whelan, S. M., 101,110 Whitehead, A. N., 223 Whiting, H. T. A., 240,259 Whitsel, B. L., 350,368 Wiesel, T. N., 287,354 Wilcox, S., 157,181 Williams, c. w., 73 Winograd, E., 101,110 Wish, M., 300,360 Wist, E. R., 116,149,181 Wittgenstein, L. J. J., 38 Woodward, D. J., 352,362 Wright, B., 109 Wright, L., %, 111 Wundt, W., 16,195,202,216 Wyszecki, G., 371,399

V Valente, C., 287-288,295 Valentine, T., 327,344,367 Vallortigara, G., 211,215-216 Van der Heijden, A. H. C., 329,367 Van Essen, D. C., 8,42,289,292,296 Van Leeuwen, C., 299,367 Van Wieringen, P.C. W., 240,254 Vicario, G. B., 197,199-210,212-215,219

Y Yashuhara, A., 272,296 Young, A. W., 344,356,368 Young, F. W., 340,368 Young, G., 376,399

2 Zachmanoglou, E. C., 328,368

Author Index Zagorski, M. A., 313-314,334,368 Zambianchi, E., 199,219 Zanforlin, M., 211,215216 Zeki, S., 291,296 Zhabotinski, A.M., 210 Zinnes, J. L., 376,399 Zipser, D., 289,296 Zisserman, A., 245,258 Zuckerman, C., 133,173,182

409

This Page Intentionally Left Blank

411

Ability, perceptual, 33, 97-98, 174-175, 240,277-278,313,374375,377,388, see also Skill Accommodation,80,135,142,152,165 Acoustics, 200 Action,31,38-39,67,10@101,106,191, 234,240-241,248-249,275,280-281, 372T. 393-394 e n d e d , 375 neural, 10,24 potential, 239 Activity, 213 cognitive, 344 focal level, 80, 87, 91 mental, 29-30,391 neural/brain, 8,23-24,33,38,91,102, 205,351,353,371,375 perceptual, 165 receptor, 78,90,99,102 system, 79,84,91,215 Acuity, temporal, 199 Adaptation, 59,77-80,94-96,98,176,241 Adequacy, 234,242,252 mechanistic, 87-90,100 Affordance, 85-87,101,239'242,245,248 AI,see Intelligence Alarm, false, 387 Algorithm, 10,25,261,264-273,278-279, 283,286,289,291,301-302,373 Analysis, 18,25,31,50,64,77, SO, 85,87, 92-93,95-%, 98,101-102,105, 107, 113,125-126,130F, 132-133,135, 137, 140,14lF, 148,15&159,172,202, 204205, 235, 252, 264, 329, 335, see also Level Burigana's, 168 categorical, 201 co-perceptual, 157,164-165 complexity, 262,270,282 computational, 387 computer,266 Cutting's, 249-250 etiological, 96 expected-case, 267-268 feature, 304 Fourier, 24 from below and above, 99-100 functional, 5,9697 geometric, 139 .

I

Gibson's, 101 ideal observer, 387-388 input-output, 19 in ternal-structure, 9 Johansson's, 1U7 linguistic, 233 mathematical, 26 MDS,335,338 mechanistic, 94-96 of behavior, 5 of existence, 55 of Kohler's assertion, 61 of reductionistic case, 297 of space and time, 54 of the Fraser pattern, 70 of visual search, 272 phenomenological, 199-200,204-205, 209,215 prinapal components,345 signal detection, 387, see nlso Detection structural, 9,156 tensor, 328 worst-case, 267-268 Angle, visual, 116, 123F, 127F, l43,144F, 161,164,171-172 Anisotropy, of visual field, 213 Antinomy, 44l5,49,208,231,310 Appearance, 26,7l, 155,188189,193, 204206,212,221,225,227 Apperception, 64 Apprehension, 235 Approach, 4'15, 17-18,21,25,32, 65, 82, 89,101,185,211,254, 264,269,283, 333, 376, 386, 388, see also MetatheOY '

Bacon's, 20 behaviorist, 6, 9-10, 19, 27, 280, 282 bottom-up, 274 chaotic, 15 cognitivist, 3,7, 193 computational, 282 descriptive, 39 ecological, 85-86,88-89,92, 94,101, 105-107,231-232,234,236-240,243, 245-246,248-250,252-253 exemplar, 374 Fourier, 24 Gestalt, 105,107

412 Gibson's, see ecological Gogel's, 159,162,171-172 hierarchical, 93, 103-104 holistic, 26-27 integrative, 92 mathematical, new, 27 mechanistic, 87-88, 92,9495, 102 multiple-variable, 18 neural network, 273 nonreductionist, 9-11 phenomenological, 39,197 propositional, 157 psychophysical, 28,38 reductionist, 34,7,101-102,205 scientific, 23,31,40 task-directed, 274 to neuroelectric data analysis, 25 to psychological similarity, 297, 299305,326,339-341,344-345,347,349 to science, pragmatic and experimental, 20 to theory construction, 370 Uttal's, 10 Array, optic(al), 101, 233, 242, 246,249250 Association, 10,166,208,224225,329 Attention, 242,278,320-321,329-331,333 334,352-354 Attribute, 18,26, 28,36,40, 158,302,312, 348, 351, 370, 393, see also Characteristic, Dimension, Property perceived, 43,52, 57, 61-63,68 Audition, 200,206,371,372T Aufforderungscharakter, 239 Awareness, 9,8586,173-174,393 Axiom, 162,198,206,209,301,321,325, 370,385 of perceptual variability, 369-371, 373-374,379,385,388,392-393 Barrier, between levels of inquiry, 3 between models and mechanisms, 28 of intrapersonal privacy, 31 to neurophysics of mind, 22,33 Becoming, experience of, 199 Behavior, 4-7, 8-14, 17-18, 20, 22-23, 25-

26,29-30,33,35-37,39-40,66,75-76,7a 83,8592,97,99-101,104, 128,202,214 215,245-246,261,268,270-272,279-281, 283,287,289,344,348 Behaviorism, 3-7, 9, 11-12, 20,26-27,3033,3740,202,214,279-281,290,333 Biochemistry, 23,298 Biology, 15-16,98,193,209,238,254,283 Biopsychology, 35-36

Sutject Index Black box, 9,22,31,183,185,191-192,350 Body, 43, 88,221-224 Boundary, 374,390 Brain, 7,Z-24,33-36, 51-52,57,61,100101,183-184,205,207-208,222,225,262, 271,275-278,285,299,302,317,323, 332,351,379 Card, folded, Mach's, 128 Categorization, 286,298-299,318,321, 332,349,352,373,375-378,387,390-392 Causality, 192, 223-224 Causation, moleculetemind, 34 C a w , 20,35,37-38,102,183,197,208 211,370-371 Channel, 334 ion, 79 neural, 369,372,377,380-385 perceptual, 392 sodium, 379 Characteristic, 114, 130F, 143, 155-157, 160463,166,334,339-340,348,350, see also Attribute, Dimension, Prop erty operating, 77-78,80,87,91 perceived, 114,13OF, 143,168 perceptual, 159-160 physical, 114, 130F, 303,314 Chemistry, 15-16,22-23,210,261,298 Choice, 64,82,95-96,163,184,188, 201202,205,353 Classification, 14,32, 188,352,369,373375,378-380,391,393-394 Classifier, minimum distance, 323,332 optimal, 377,380-381,383-384 Cognition, 8,113,121,153,171-173,244, 264,317,327,341,353-354 Cognitivism, 4,7,11,202,214 Color, 19,26,34, 53, 6@61,97-98,189-190, 194,204,241,285,291,316,329,348,373 Communication, 7,18,22,263,279 Comparison, 163,187,189,267,304,323, 325327,330,374 Completion, 71,209, see also Occlusion Complexity, 1516, 18,30,78,83,145, 162,

201,204,207,214,261-268,270-274,278, 281-282,289,291,326,344,347,388 Computation, 34,191,238,262,267,269, 273,280,284,286-287,289-292,332,376, 378 Condition, 57,63,77,79,97,115F, 117, 121-124, 133, 137-140,148, 152-153, 157,159-161,166,168-I70,173,175, 199-200, 2U3, 205,209,211,213-214, 216,232,235,243,250,265,268,282,

Subj&t Index 299,301,305-308,319,322-323,349, 351,370-371,372T, 380,392-393 boundary, 75,79-95,97-105,107,374 initiating, 75, 79-84, 86-87, 89-94, 97, 99-100,102,1W Conditioning, 83,93,95,280 Connection, 51,63,70-71,79,205,262,275, 277-278,287,380 perceptual, 62, see also Interrelation Consciousness, 9,86,208,224,329,393 Consistency, 142-143, 144F, 145, 154-155, 159-163, 167-168,324, see also Inconsis tency Constancy, perceptual, 186,194,370,387 Constraint, 10,20,25,28,31,3435,75-76, 80-81,83-84,89,91,94,102,105,167, 261-264,270-271,273,276,282-283,289291,302,306,318,340,350,353,369 Construct, 45,26,43,50-56,59-65,67-69, 212,214216,369,376,378379,390 Contemplation, 213,215 Content, explanatory, 13 immediate, 256 mental, 197-198, 200,208-209 perceptual, 158-159 Context, 5,65,69-70,79,82,87,92,9495, 99-100, 149, 152, 155, 157, 162, 187, 226,232,236,241,247-249,253-254, 3&305,312,314,323 controlled, 75,93 ecological, 86,88,93,97 everyday, 75, 85 historical, 7677, 92-93, 171, 223 perceptual, 300 physical, 97 psychophysical, 300 Continuity, 61,209,216,319 Continuum, picture-reality, 247 space-time, 97 Contour, 59-60,88,209,286,330,345 equal-loudness, 311F, 312-313 Control, 20,84,90,207,235236,240-241, 263,280,287 hierarchical, 90, 92 intelligent, 279 Convergence, of the eyes, 133,135,142, 153,165,289 Coordination, 66-67 Correlation, 37,63,174,323,332,334,347, 374,377,38031,389 Correspondence, 51,57,64,164,243,253, 309,318 anomalous, 287-288 binocular,288289 inter-case, 159

413 inter-level, 158 motion, 284-285 stereo, 284,286 Cosmology, 30,261-262 Coupling, perception-action, 240-241 perceptual, see Connection cube, ice, 52 n-sided, 309 Necker, 46,64,68,394 wire, 47-49,53,68-69,128 Cue, 17,117,120-122,124,126,131,134135,137-140,142,145, 148,151-152, 165,169-171,173-174,188,210,232233,248,286,289 cognitive, 122 pictorial, 88, 248 visual, 129,132,142,157,289 Cycle, 375 of neural activity, 375 perception-action, 240 perceptual, 86,102 Dalmatian dog, 286 Datum, 4,66,157-158,183,198 210,223, 228, see also Observable Deasion-making, 299,314,376,391 Decomposition, 87,97 Demonstration, 201-203,211,213-214, 216,292,301,321 Dependence, 166,192,212,302,331,335, 390-392, see also Independence Depth, 19,69,122-129,131,133-135,144145,148-150,152-153,164,169-170,174 175,232-234,285-286 Description, 9, 13-14, 19,29, 67,76, 81-84, 87,90-91,95,97,101,106,151,157,183l85,187,189,198-199,203-204,208,211, 213-214,221,225-227,266,273,299,318, 321 Design, experimental, 16-18, 29,63,96 Detection, 96,386387,392 signal, 300, see also Analysis, Theory Differentiation, 77, 84, 169 Dimension, 15,17-18,38,70,98,170,200, 205,233,261,273,291,301-302,304305,309-313,314,315F,316,320,322, 327-328,330,333-335,337,340,342343, 345-346, 348-349, 351-352, see also Attribute, Characteristic, Property integrk, 353-335 perceptual, 39,159,299,331,334,344, 392 physical, 40,54,65,77,253,303,310,

414

Sutject Index 313-314,321,335,337,344-345,381-

382,391-392 psychological, 184,253,301-304,336337,344.347 separable,.333,352 Dimensionality, 302,327,329-330,345, 347-348 Direction, 61,113-114,117,122,125F,126, 127F,l28,145,149,15OF,151,154,162, 167,170-171,173,175-176,245,284 Discrimination, 299-301,310-311,326327,330,347,351,380,386,392 Disease, 186,198,207 Disparity, binocular, 19,117,124,138, 145,149,165,169,174,285-286 Distance, perceived, 61,113-114, 116-123,127F, 128-133,134F,l35,136F,137-140, 141F,143-155,157-158,161-162,164165,167-176,187,221-223 city-block, 337,390 Euclidean, 315F,316,322,324 metric, 303 Minkowski, 379 psychological, 308,323,339,378 Distinctiveness, facial, 344, 347 Distribution, perceptual, 376377,390392 DNA,75-78,82-85,89,93,95,97,100,1W, 105-106,375 Dualism, 10,31,54,202 Duration, 105,199,371 Ecology, 76'79,235-237,239,248 Brunswik's, 237 Ecosystem, 79,102,200 Edge, occluding,233-234,250, see also Occlusion Edge-finding, 274 Effect, 18, 23, 9@91,96, 99,113-114, 118, 121-122,125F,137,140,145,149,164167,175,185,187,194,197,199-200, 208-211,213-215,234235,269,284 286,291,298,304405,322,333,337, 346,348,350,370-373,381,383,388389 cognitive, 147,154,175 decisional, 334,348 frequency, 305 Michotte, 192 perceptual, 147,154,216,334,392 physical, 48,250,253 semantic congruity,305 tandem, 139,141F word superiority, 92 Electrodynamics, quantum, 250

Emergence, of quality, 17,286 Emotion, 13-14,43,55,208 Empiricism, 4,7,20,30,333 Energy, 29-30,54,64-65,79,84,97,243 minimum, 64-65 Entity, 6,37,55,63, 76,79,85,87,9495, 97,99,104-105,213, 221,227,238, 250,338,353,see also Thing mental, 12 perceptual, 37 phenomenal, 222 physical, 25,76,223 psychological, 94 Entropy, 388 Environment, 64,67,69-71,75,7-80,82, 8487,89,91,93-98,101-102, 137,170, 235-238,240,247-248,268,277,289,303, 333,374 Epiphenomena, 235 Epistemology, 4,183,188,190 dualist, see Dualism Error, 201,211,251-252,310,313,373,388, 391 perceptual, 120,122-124,126-128,130F, 137,139,148-151,153,155,163,165167,170,176,236 Rylean, 253 Event, 5,13,19,24,27,33,51,56-57'90, 107,158,184,188,191,207,210,222, 228,236,238,242-243,246,251-253, 264,272,277-279, 329,370,3722377379 auditory, 200 construct, 52 internal, 5,12 mental, 10-11,26,30,38-40 perceptual, 188-189,206,279 physical, 106,128,167-169,225 Evolution, 10,15,21,98,1a3-104,107,212, 236-238,242,243,250,261,274,278, 280,282,378-379,389 Excitation, 91,224225,228,382,385 Existence, 5,9-10,12,23,27,30,33-34,55, 65,68,93,156,161,166,222,233,242, 373,389 Existentialism, 39 Exotropia, 287-288 Experience, 7-9,12,18,31-33,37,39,64, 75-76,80,82-83,85,87,89,93,99,122, 165,170,173-175,197-201,203-204,207209,211-216,221,243,283,304,339, 347,375 Experimentum crucis, 203 Explanation, 5,7-8,10, 13-14,16,31,4546,49-50,52-53,56,61,68,92,95,102,

124,126,128-129,143,149,155,161-162, 167,169,183,185,199-201,207,209,

415 211-216,250,261,263,272-273,281 Exploration, 46,85-87,102,156,234,236, 240-241,248-249 Extent, perceived, 125, 147, 168,171-173 Externality, 225, 227 Face, 222,245'286,326327,329-330,344348, see also Mask Fact, 13,44-50,53,65,67,89,99,128, 149, 157,162,185, 188-189, 191-195, 197-201, 205-209,211-216,225,252,279,285,287, 298,303,311-313,325,34@341,375,384, 387-389 Factor, 93,98,113-114,124,126,128,130F, 133,135,142-143,145,149,151-152,157, 167,175,268,318,342,388 Feature, 25,37-38,69-70,165,209,216, 221,310,327-330,334,340,3&348,390 Feeling, 12,55-56,280 Field, auditory, 206 gravitational, 76, 372T magnetic, 372T nasal, 227-228 phenomenal, 205 receptive, 205,278,287,350 visual, 122,148,205,209-210,213,227228,252,290,370 Flow, optic(al), 101,107,243 Force, 213,215 Forgetting, 197,211,216 Form, 6,8,15,28,34,83,88,106,322,324 330,332,341,344,393 Foundation, 238,261,278,281,304,321 for a psychology of perception, 37 for a taxonomy, 16 of computation, 273 of modeling perception, 297 of multidimensional scaling, 336 of perception, biological, 254 of perceptual science, 297 of the behaviorist point of view, 9 of Uttal's approach, 10 Frame, 157-164,166,285,326 Framework, 20,171,184,231,250,28@ 281,302,314,334,386 Function, 4,9,10,13,16,21-24,3436,7779,82-83,86,95-98,104-105,107,166, 200,238,279,285,290,317,340,352 Functionalism, 234,239 Ganzfeld, 65 Gene, 77-78 Generalization, octave, 314315

stimulus, 350 Geodesic, 308,326 Geometry, 30,143,156,161-163,242,244, 297,302-303,305-306,321,324325, 328-330,332-333,338,340,345-346 Euclidean, 163,170 non-Euclidean, 143,321 phenomenal, 61,113-117,121-122, 123F, 124, 125F, 127-129,142-143, 144F, 145, 148-155, 159-160,162-165, 167-174, 176 Gestalt, 348 Gestalttheorie, see Theory Golem, 193-195 Gradient, 148,170,233,242-244,249,252 Habit, 63,197,208,211 Hierarchy, 13, 91, 100, 102-103. 105-107, 263,284,309,341 Historv. 77-83. 85-87. 89-91,93-94.98-102 Hit, 3i7 Homeomorphism, 309-310,312-314,316, 319 Homunculus,279 Hue, 316-317,330,335,336F, 373 Hypothesis, 10,21,26,34,166,291,301, 313,327,353,394 apparent distance/pivot distance, 117 attention-optimization, 320 best bet, 126 caricature, 345 computational, 261-262,264 Helmholtzean, 207 motion-distance invariance, 115F, 116, 161 of cue equivalence, 176 of independent modules, 291-292 of similarity as a construct, 379 psychophysical, 243 reference frame, 326 Shepard's, 385 size-distance invariance, 116-117, 143147,153-155,161,171-172,175 that others have minds, 66 traveling moment, 199 Wallach's, 172 Identification, 25,92-93,208,251,300, 318,320,328,332,344,349,351-352, 373,376379,387,390-392 Identity, 32,43,45-50,65,169 Ideology, 33,186 Illusion, 19, 26,30,44,48-49, 70, 128, 142143,148,155,163-171,194,199,203, 242,318

416 Ames, 126 Fraser, 46,68,71 horizontal-vertical, 4.4, 45F, 68-69 moon, 172 Necker, 68, see also Cube of explaining/understanding, 7,13,23 of relevance, 23 of statistical theory testing, 25 theoretical, 36 two types Of, 169-171 Image, 2425,64,71, 92,101,149,150F, 151,156,186,246,265,273-274,277-278, 285289,345-348,370,379,386 Imagination, 19,65,70-71 Implementation, 262-263,267,271,273, 281,291 Impression, 204,224 Inaccessibility, 190-191 Inconsistency, 143,145,167,234,248-249, see also Consistency Independence, 16167,215,291,331,334, 380, see also Dependence Individuation, 95-97 Inference, unconscious, 64,227-228,272, 280 Information, 45,7,10,18,22-23,25,29, 36,38-39,47,66,68-71,75,77,8@81, 8485,88-92, 96, 101-102, 104, 106IW, 113,128-129,135,142,145, 148, 151,153-154,157,17@-171,232,234, 236,240,242-246,248-249,251-253, 266,284,287,299,302,314,317-319, 327,329-330,337,339-340,346347, 350-352,354,377,384,386388,391392 auditory, 285 Gibson's concept of, 241,245 perceptual, 30,69,244,248-249,253, 370-371,387,392 sensory, 113,393 visual, 89,106,142,240,285 Inhibition, lateral, 372, 377, 381, 384, 391-392 Input, 80-81,85,90-92, 105,185,191-192, 267-268,271,287-288,291-292,317-318, 323,331,350-351,353,382,384-385,392 Inquiry, 3,6,12,21,40,69,85,101,106, 202-203,205-206,208 Integrality, 314, 331, 333-334 Intelligence, artificial, 8, 195, 272, 326 Interaction, 15, 17-18, 22-23, 2526, 34, 63, 77-79,84,93,268,289-290,292,318, 334-335,337,341,354 lateral, 369, 379, 381-382, 384-385, 389, 392 perceptual, see Connection Interdependence,perceptual, see Connec-

Sutject Index tion Interrelation, perception-action, 234 perceptual, 143, 145-146, 148, 153-154, 161,168, seealso Connection Introspection, 184,203,208 Introspectionism,37,207 Invariance, 304,326,334 Invariant, 242-250,252,316,385 Isomorphism, 10 Judgment,21,122,124,175,208,240,300, 305,321,344,346348,390 Knowledge, 10,14,16,19,21-22,29,32, 51,90,96,98,104,151,154,175,184185,193,198,200.201,204,208,214-215, 286,291,298,324,328,338,340,342, 350,352-353,392 Law, 14,30,33,162,207,214,298 Emmert's, 116,120,171,173 empirical, 161 inverse square, 133,135,170 mechanistic, 90-92 natural, 310 of causality, 223-225 of interaction, 337 of mathematics, 4 of nature, 65,212 of thermodynamics, 9,260 optical, 154 perceptual, 155 phenomenal, 205 physical, 44,48,53,56,77,250,385 Talbot's, 57-58 Layout, 233-234,236'250,346348 Learning, 7,12,33,35,317-318,333,348, 378 perceptual, 170,329-330 Length, 316,346 perceived, 44-45,48,50,53,64,144, 212-213 uhvsical. 65,144,151,321 L&e[ 5-6, io, i2,23,27; 33-35,100-102, 105-1&, 153,165,252,274,280,291, 304-305,312-313,315F, 320,335,341, 345,371372,381-383 adaptation, 78, 94 focal, 75,79-85,87-92, 94, 103-104, 107 hierarchical, 107 of analysis, 22-23,75,79,81,88,94, 100,253-254,283,341 of data, 157-158, 162

417 of discourse,31,253,298 of inquiry, 3,12 of perception, 298 of privacy, 251 of processing,371 of reality, 253 Life, 75,86,89, 93,107,186187,191,208, 213,216,250-251,254,262 Light, 28,43,51,54,5&59,75,78-82,87, 94,96-99,104,193,225,227,233,249250,252-253,266,37l-372,374,379 Linguistics, 7,283 Linkage, 338 perception-action, 240-241 perceptual, see Connection Localization, 9,29,117,154 of functions, 22-24 of processes, 35-36 Logic, 31, SO, 84-85,127, 165,195,205,211, 291 Loss, information, 318,38&388 Loudness, 54,200,305,312-314,334-336, 344 Machine, Turing, 265-266,272-273 Macromodel, 21 Macrotheory, 341 Manifold, 248,324,328-329,345,348 Mask, face, 125F, 126,128129,286 Matchhg), 48,273,275,277,285-286, 323,332,374 Matches, metameric, 151 Materialism, 7, 10 Mathematics, 9,24-27,31,195,233,244, 272-273,298,302,305,308-310,337,344 Matter, 15, 29-30,48,95,97, 253,289 Measurement, 11,14,31,40,48,69,119120,131,146-147,156,169,172,184, 200,212,299,304,308-310,330,337, 347,351,353 Mechanics, 21,209-210,326 quantum, 21,30,54,56,67,374,379 Mechanism, 86,8-14,19,21,2824,28-30, 33-35,37,87,89,91,9495,97,101,187, 202,207-208,272,299,304,329,352-353, 386,389-391 Memory, 89-90,100-101,106,154,205, 208,213,234,265,267,270,299,302, 327,329,341,344,390 Metaphysics, monistic, 10-11 Metatheory, 231-232, 234, 248-251, see also Approach Method, 5, 9,11,26,28,38,119,146-147, 153,155,158,163-165,168,171-173, 197-198, 200-204,207-211, 213, 216, 253, 269,279,283,301,314,338,345,351,

353,370,378,384,391, see also Procedure Metric, 301-302,304,306-309,313-314, 317-319,322-323,325-328,332-335,337, 340,378,390 Micromodel, 21 Micropsia, 172 Microtheory, 14,19,163 Mind, 4,22-23,30,33,35-36,65-66,95, 191,208-209 Modality, sense, 63,241,290,372T, see also Sense Model, 5,8,13,15,19,21,25,28,31,34,40, 62,92,101,163,198-199,201,207, 211,213,262,273-277,279-280,290291,298,300-301,303-304,316,321, 327,330-334,337-341,345,349-354, 379,381382,36387,389-392 Anderson, 62 context, 376 generalized, 376 decision bound, 374375,390-391 exemplar, 352,374,376,390 helical, 315F, 316 LaBerge’s, 354 Marr’s, 92 MDS-choice, 376 Nosofsky’s, 300,32Cl321,334 of h n i s and colleagues, 300 of transparency, 57-60 perceptual, 21,43,62,300,305,369-370 physical, 54,145,168 process, 297-298,301,304,332434,337338,340,351,353 prototype, 373-374 Shepard’s, 320,390 similarity, 376377,390 MDS, 297 probabilistic, 377 Modularity, 284285,354 Modulation, 77-80,82,91,94-95,98 Module, 279,284-286,291-292,341 Monism, 5,1611,30-31,202,243 Mosaic (sensory),205,386,388 Motion, 28,34,61,88,100-102,106-107, 113-122, 124126, 128-133, 135, 137-140, 141F, 142,144-146,148151,153-156, 158,161-162,161,167-176,186,192,194, 209-210,216,231-234,252,273,284285, 291-292,324,328,340 Motivation, 34,197,347 Motive, 12,208 Movement, 34,39,46,48-49,52-55,63,69, SO,& l00,102,105,138,150F, 171-173, 201,204,209,234,238,288 Multidimensionality, 17-18, 29-30, 32

418

Sulject Index

Neobehaviorism, 11,26-27,30,32-33,3738,40 Neodualism, 10 Neopositivism, 188 Network, neural, 7,10-12,26,29, 52,79, 82,263,273,275,277,332,338,350,392 Neurobiology, 7,291-292,375 Neuroscience, 7,22-23,29,31,35-36,100, 205,280,288,298,353354 Noise, perceptual, 373,381,384,389,391392 NP-Completeness, 269

Organism, 46, 13, 17-18,75-79,82-87,91, 94, %98,100,102,105,107,221-225, 274-279,283,303,369,373-375,378, 38@382,385-386,391-394 Organization, 12, 1415, 19,22-23,32,82, 85,92,105-106,166,203,214,279,386 Orientation,47,52,92, %, 113-114, 123F, 126,129,145,162,167,169,171,176, 212-213,233,242,286,303,326,378 oUtp~t,33-34,92,185,191-192,275,285, 287,289,291,339,350-351,377,380383,385,392,394

Object, 14,40,43,45,53-57,61-65,68,7071,76,86,97-98,101,107,114,116117, 120-121, 123F, 125-126, 129-133, 134F, 135, 136F, 137-140, 142-143, 144F, l46,147F, 148-149,151,155156,158,162-165,168-172,175,184, 186-187,189,192,204-206,208-209, 221-222,224,226,228-229,233-234, 237-244,248-253,265,278-279,285287,289,300,318,322-323,325-327, 330,340,346-349,351-352,370,373, 377378,380,386,393-394 construct, 52 dimensional, 310,348 direct, 188 everyday, 246,344 external, 40,63,351 familiar, 121-122, 172, 175,394 natural, 63 naturalistic, 347 perceived, 302 perceptual, 204,329 phenomenal, 222,225,252 physical, 167, 222-223, 228, 252-253 pictured, 129 reversible, 52 Objectification, 223 Observable, 1 8 3 185,18%189, 191-192, seealso Datum Occlusion, 209,233,284, see also Completion, Edge Occurrence,43,51-52,54-55,59,70-7l, 100,150,159,193,222 Olfaction, 372T Operation, 4,8,19,21,27,29,37,48,66, 83,92,94,171,265,267,271,274,317, 323-324,327,330-333,337,341,346, 351-351,382 Operator, cognitive, 4 Optics, 154,237 ecological, 242 Ordering, similarity, 301, 321, 349,351352

Pain, 43,52,241 Paradox, 172,183,185,187,192-193,221, 224,310,334,340-341 Parallax, 69, 117, 124, 133,153,234,289 Parsimony,4,31,62,65,172,176,378,384, 386 Percept, 12-14,30-31,38, 63-65, 76,113, 197,221,223-225,227-228,251-252,286, 301,318,322,328,331,344,351,370371,373-377,380,389,391,393-394 Perception, 1,4,7-8, 18,22,27,29-30,3334,37-38,62-66, 68-71,75-76,85-88, 90,92-95,97-98, 99-101, 103-107, 113-114,117,119,121-122,125F, 126, 128-129,130F, 132-133,135,137,140, 141F, 142,144,147-155,157,160,163165,167-176, 183-188,190-195,203206,210,213,222,224225,227-228, 231-236,238,240-246,248-254,261262,265,267,272-274,279-281'283, 285,287,290,292,297-300,303,305, 311-312,314,316,324,326329,331, 333-335,341,344,346349,353,369370,373,385-386,392 accurate, 242 act of, 63,246 ambulatory, 85 auditory, 311 biological, 261,282 correct, 69,125F, 127F, 153 definition of, 43,71,75,85 and awareness, 174 derived, 114, 145, 151-153, 167-169, 175-176 direct, 107,153,247,248,280 everyday, 88,93,107,235,247,251 haptic, 101 high level, 387 illusory, 63-64,125F, 126,165,169-170 indirect, 247 levels of, 298 natural, 89 naturalistic, 348

419 objective, 223 pattern, 297 picture, 246-248 veridical, 63,126,128-129,135,165, 169-170, 172 visual, 8,26-27,37, 85,104,106,142, 145,151,171,240,329 Performance, 19,31,187,262,267-268, 280,311,320,352,354,369-370,374, 378,380-381,384,38&389,391 mental, 389 perceptual, 392 Pamanence, 56,204 Persistence, 56 Perspective, 6-7’67, 7l,91-92,99,124, 127F, 138,145,245,251,280,290,292, 298,304,317,321,331,339 Phenomenologist, 39-40, 195,203-205, 208,212-213,216 Phenomenology, 39-40,197-198,201-203, 205-207,209-214,284,333 Phenomenon, 75,186,199,211,234,264, 287-288,298,305,315,317,321,329, 341,348,353-354’375 blindsight, 34,36 perceptual, 14,18,31-32,40,88, 113114, 126,128,149,152, 187-188,194, 199-201,205-206,209-214,216,223, 227-228,231,235236,251,254,298 physical, 201, 210-211, 250, 310 Philosopher, 36, 95,190, 198,222-224, 254,299 Philosophy, 7’17, 183-184,193,232,242, 248,279-280,333,337 Photon, 53,102,225,228,250,253,371, 379-380 Physics, 22,28,40,43,54,56,61, 67,70, 77,157,193,240,251,253,298,321, 331,337 e~ologi~al, 157,261-262,289 mental, 326 Physiognomy,330 Physiology, 5-6, 193,201,222,283,287, 290,350,353 Pick-up, information, 242,246,252 Picture, 52, 55,128,202,234,237,245-248, 322,346 Pitch,.200, 312-314,315F, 316,334336 Plurivocity, of the stimulus, 203 Position, 44-45,54-55, 83, 101,114,122, l25,127F, 128,131-132,140,151,154, 162,167,175,233,326,330 Positivism, 4,39 Potential, 78,8344,244,318 brain, stimulusevoked, 24 Practice, 189,195,270,279 Rediction, 20,34,43,4849,52-53,55-57,

61,63-65,67-68,70-71,151,215,250, 262,264,300,329,340,374 Present, specious, 199 Primacy, of the phenomena, 31 Principle, 15,99,102,225,278-279,281, 283-284,289,309,327,387 coding,323 computational,36 Gestalt, 326 gradient descent, 326 hill-climbing ,see gradient descent of behaviorist perceptual psychology, 30 of holistic perception, 27,37 of parsimony, 4,61 of perceptual psychology, 16 of statistical decision theory, 387 of unification, 205 mathematical/physical, 9, 22, 36 Privacy, intrapersonal, 11,31,38,251 Problem, 10,32,38,99,102-103,153,166, 202,2U7,211-213,215,232-234,237, 239,246,248-249,261-274,277-278, 281-284,289-291,299,301,305,326, 338,345-347‘370,375376,380,387 ancient, 232-233 boundary condition, 100 classification, 373,378,385,392-393 computational, 264,268,283-284 decision,369,373,377 Hilbert’s loth, 273 insideoutside, 221-227 intractable, 268-269, 274 mathematical, 351 mind-brain, 7’22-23,25,29,34,202, see also Relationbhip), Understanding new behaviorism as a solution of, 33 NP-complete, 268-269,278 of behavior/mental-state linkage, 13 of cognition,264 of computational mind, 209 of conditions, 122 of depth perception, 232-233 of derivational order, 162 of direct experience, 208 of economics, 32 of localizingfunctions, 24 of mental aberrations, 23 of neural interconnectivity, 36 of perceptual psychology, 32 of physical laws ruling past things, 56 of psychism, 202 of space perception, 231-232 of the belief that things persist, 56 of the existence of constructs, 55 of the identity of things, 43 of the level of analysis, 22

420 of the neurological model that computes Minkowski distance, 379 of the occurrenceof things, 43 of the relation between higher and lower level theories, 103 of the separation of cognitive and perceptual effects, 147,153 of the unreachable object of inquiry, 40 of two ecologies, 237 of visual search, 278 ontological, 38 privacy, 37 reductionistic, 298 representation, 36 similarity scaling, 305 tractable, 268 with applying electrophysiological techniques, 82 with Barlods "syllogism," 228 with definitions, 35 with invariants, 246247 with mathematics, 24 with one-to-one mappings, 243 with the characterization of dimensional interactions, 334 Problem-solving, 299 Procedure, 99,186,189,192,200,202,273, 288,320,323,326327, see also Method Ebbinghaus's, 89 hand-adjustment, 119 head-motion, 118-122,138,145147, 153-154,173-175 MDS,302,318,340 null-adjustment, 120 perceptual-alignment, 146, 147F phenomenological, 205,211 stepby-step, 266, 273 triangulation-by-pointing, 146 Process, 4,68,13,16,29-34,35,38,52, 103,107,113,124,126,129,142,148, 151,154,165,169-170,172,185,191195,197,199,201-203,205-209,211, 213-216,222-223,225226,235,268269,273-274,278,280,284,286-287, 289,299,301,303,331,339-340,342343,348,353,372T, 376,379,385-386, 388,391,39>394 cognitive, 7,9-11,21,29,31,34,121122,142-143,145,153,155,172,339, 344,354 mental, 4,7-12, 19, 22-25,29-31,38,280 neural, 6-9,23,221,225,341 perceptual, 16,29-30,32, 71, 128, 145, 153,155,172,194,302,304-305,373, 386-387,389,393 visual, 274, 285

Subject Index Processing, 90-92,101,191,206,262,264, 271,274,276,283-287,318,330,336337,354,371,388 information, 29,89,92,236,262,298, 304,331,391 perceptual, 85-89,369,371,372T, 387388,391-393 visual, 34,276,284-285,287,341 Property, 3,8,17,2526,28,34,36,4549, 52-54,63,76,79,86-87,94,97,99, 104,154,158160,164,166,194,205, 210-211,238,242-243,266,289,291, 301,304,306-309,313,315-316,32> 325,332,33536,342,349,352,385, 387, 390, see also Attribute, Characteristic, Dimension , 65 emergent,279 illusory, 48,53,63,65,70 molar, 13 perceived, 171 physical, 48,53,63,65,70-71,302,346 structural, 61 visual, 34 Protocol, 184-190,194 Protorasis, 274279 Proximity, 64,205,215,222 Psychism, 202,208 Psychoacoustics, 2 N Psychobiology,reductive, 7,37 Psychologist, 7,9, 15,31,36,64-66,90,97, 103,188,198,201,206-207,210-211, 215,222,231-232,244253,264,305, 308,338,344,348,354 cognitive, 11,297,302 e c ~ l ~ g i ~101,239,242-243,248 al, Gestalt, 2627,37, 99-102, 198,203, 214 perceptual, 10,28,32,251,253 phenomenological, 209 Psychology, 67,ll-12,1416,18,21,3233,35,38,40,95,98,191,197-199, 201-204,207-210,212-213, 215-216,

234235,239,245246,250,252,280, 300-301,310,317,321,324,332,337, 339, 342, see also Science cognitive, 29,191,235,302 Gestalt, 99-100,204, 234, 333 perceptual, 34, 7-9, 11,16,27-28,30, 32,37,39,95,232 phenomenological, 40,197 reductionist, see Reductionism Psychophysicist, 242243,248,284,348, 386387 Psychophysics, 16,26, 38-39,98, 201,216, 242,251,253,283,289-290,302,346 Psychophysiology, 201

421 Quality, 17, 25,201,224,241,243,271,327 Quanta, 1,199 Quantity, 79,152,271,309,327 Quarks, 15 Range, spectral or visual, 96,98 Rating, similarity, 300-301, 304,323,327, 330,340,378-379 Ratio, am,243 signal-tenoise, 323, 385 Rationalism, 7, 30 Rayon daction, 192 Reafference, 200,289 Realism, 254 critical, 156, 251-252 direct, 252 indirect, 251 naive, 251-252 philosophical, 65, 67 Reality, 1,5-6, 10, 19, 32, 45,49,157, 2U3204,2(n-208,211,215,245-250,253, 291,321-322,326,330 environmental, 156-158 external, 39 objective, 65, 67 of mental processes, 4,11,30,38 of neural mechanisms, 11 phenomenal, 205 physical, 2425, 67, 142, 153, 170 single, 43,53,56,61,63-64 unreal, 46 Reasoning, 35,66,154,263,272,280 Recognition,279,299300,318,327,349, 352 object, 98,387 of three-dimensional form, 106 pattern, 323,332 Reduction, 8,11,13-14,33,35,92,317 Reductionism, 3,5-7, 9,33,35,37-40,8182,353 cognitive, 4,6,8,28-29 critique of, Gestalt, 39 mechanistic, 93 neural, 4,6,8, 10,27,31 three classic arguments against, 13 Reference, external, 221,224225 Relationbhip), 5, 8, 14, 17-18, 22, 27-28, 32-33,38,58,63,76-77,80,95,98, la,l17,121,133,139,15OF, 153,158, 166,171,209,213,234,236,238,240, 243,302 brain-mind, 13, 22, 25, 29, see also Problem, Understanding Relativity, see Theory Relevance, 76,274

causal, 26,30 illusion of, 23 Report, 5,12-13,26,31,38,71, 121-122, 172,288 Representation, 13,2425,29,35,65,89, 156,168,186,188,280,291,300-3U3, 314316,320-321,323,325,339 internal, 280,325,327,350 memory, 327,374,376,390 mental, 302303 neural, 7,13,33 perceived, 168 perceptual, 10,369,377,386 physical, 143, 161, 168 psychological, 297,313,327 stimulus, 390 Research, 4,16,20,21-22,2425,36,38, 75,82,87,89-90,93,95,101,103,106107, 157, 183, 187-188, 197, 199-200, 202,208-209,211,215,234236,239240,251,269,272,298,302,304,308309,321,329,331,338,342,344,349, 373 perceptual, 17,27-28,76,85,1@3,107, 142,155,165,169,185,187,231,234, 253,285,299 Response, 4,6,10,12,14,17-18,30-31,79, 81-83,88,91,94,97,121,147,155, 170,173,185,187-188,270-271,273, 304,320,332,334,350,369,373-374, 376379,383,393 perceptual, 303,386 Retina, 51-52,57-58, 68,71,96-97, 149, 150F, 223,227-228,232-233,274,370371,386 Rotation, mental, 326 RSVP,241 Rule, decision,388,390 of perceptual organization, 203,214215 Scale, 75,79,84,102, 105-105,308-309, 314315,323,349,378 phylogenetic, 174,375,379 physical, 337 psychological, 300-301,305,338 Scaling, 281,304-305, 345,352-353 cognitive, 303 multidimensional,297,299,320,333, 36337,346,349,351,353,376 perceptual, 299 psychological, 299 psychophysical, 304,328,349 School, 4,12,16,299 Berlin, 201-202

422 empiricist, 7, 30 Gestalt psychology, 204 Marr, 283 rationalist, 30 Wiirzburg, 298 Science, 45,7-8,1417, 20,23,30, 32, 89, 99,187,195,198,202,205-2&,209211,213-216,235,241,283,298,310, 321,337,390, see also Psychology approach to, see Approach behavioral, 5, 15, 27, 338 biological, 14, 81 cognitive, 7,16,101,195,300,391 computer, 7 information(-processing), 29,185 of boundary conditions, 101 of mind, 11 perceptual, 3, 9-10,17,26-32,43,56, 61, 67,98-99, 155-157, 163-165, 171, 173,184,193-195,213,235,245, 250-251,297,369,385,388,391-392 new-behavioral, 26, 30 Killeen’s criteria for, 26-27 physical, 27,69,262 psychological, 22,201 Search, visual, 207,263, 272-274,278-279, 387 Seeing, 51,193,205 Segmentation, image, 284-286,290 Segregation, perceptual, 36,61,205 Selection, 65,95,97,188,238,302 Self, 12,129,175,226 Sensation, 4,43,63-65,67,200,204,207208,221,223-225,227,242,251,253 Sense, 63,67,186,223-224,231,234,242, 371, see also Modality Sensorium,326,339 Separability, 312, 314, 331, 333-337 Shading, 233,284286 Shape,25,88,101,113-114,145,162,1661&7,170,175,233,241,247,263,273, 284286.328.346.348,387 Signal, 23,. 28, 206,280-281,289,371-372, 382 Similarity, 32, 158, 164, 301, 297, 299-301, 303-305,310,313-314,315F, 316,318, 320,322-324,327-328,332-333,337,340342,344,36347,349,352,369,373, 375,377-379,390 Simulation, 134, 183, 193-195,262,265, 354 Singularity, 163-166, 243 Size, 62,86, 102, 105, 118114, 116, 120122, 126, 143-145,151-154, 161-162, 164,167,170-172,175,233,247,263, 281,303,326,330,335,345-346,372T, 378

Subject Index familiar, 121-123, 172 Skill, perceptual, 240, see also Ability Solipsism, 66 Space, 43,114,117,131-132,137,143,147, 154,164,167-168,170,221,224225, 231-234,237,247,252,289 auditory, 312 Euclidean, 308,315-316,322,324,326, 338-339,345 internal, 349-353 metric, 303,30&308,323,338,340 of noses, 348 perceived, 113,143,151,154155,160 perceptual, 162,289,311,314,329,335, 344,374,390 phenomenal, 155,162-163,206 physical, 54, 156, 161, 163,205,312, 314,331,335,344,346 psychological, 300-303,312-313,320, 335,338-339,344,349-351,353 uniform, 305-309,319-320,323 State, 12, 18,48,52,64,77, 79-80, 96, 156160,172,224,317,375,383 brain/neural, 11-13,23,31,183-185, 353,375-376‘393-394 inner, 5-6 intervening, 32 mental, 6,ll-13,23,30,202 perceptual, 373,376,378,385,392 physical, 93-94, 252 psychological, 95 Stationariness, 113, 129, 132, 135, 140, 145,148,169 Stereogram, 128,169,174,285 Stereopsis, 98, 284-286,324 Stimulation, 38,65,82,96,228,241,243, 284,350-351,389 Stimulus, 17-18,25,28,30,38,68,113-114, 116-120,122-126,131-133,134F, 135, 136F, 137-138,140,141F, l43,144F, 145l46,147F, 148-149,152,154155,160, 164,166-171,173,175-176,185-187,197, 200-203,205-206,211,232,235236,243244,252,265,284285,290,300-304, 310-311,314,320,325,327,333-336,341, 344,346-348,351-352,370-371,372T, 373,376-379’381382,384,386-393 Strategy, 276-277, 290-291,326-327, 348, 375,379,388 Stratification, object, 209, 216 Structuralism, 2W,333 Structure, 4, 24,10,12,75,77-78,80-81, 83-84,86-87,91,93-102, 105, 107, 199,210,225,233,238,244,26247, 273,280,282-285,302-305,307-309, 317-319,322,327-328,334,338,341, 346,349-351,353354,373,376,377,

SutjfTtIndex 385 hierarchical, 82, 90, 100, 1W107 internal, 9-10, 13, 19, 100, seealso Analysis Substance, 58-59,77-80,91,216,237-238 Substructure, of reality, 253 Subsystem, 79-80,82,304,317-318,341 Suggestion, 122,175 Suprasystem, 79,81-85,90-93 Surface, 57,60,78,85,87,92, 107, 148, 152, 164,186,189,205,209,216,221,233, 236237,239,242,247, 250,31lF, 312, 316,324325,330,346,348,350,371, 372T. 389 Syllogism, 228-229 Symmetry, 307,318,323,326,387 System, 4,6, 8, 13,15,19,24-25,28-30,3334,69-71, 75-99,101, 104-106, 155, 160-162,164,183-184,262-264,267268,271,274,276277,279-281,283, 301,303-304,308,317,319,327-329, 331,337,340-341,349-351,353,371, 374,379,381-385,389 nervous, 7'10, 12,22-23,29,37, 76,80, 82-83, 85, 87, 93,200-202,207, 222, 224226,371,374,379-380,384385, 389,391 perceptual, 69-70, 76,85-86, 89-91, 9395,97,142,154-155,165,194195, 206,212,236,238,245,252,279,314, 316,370,385-386,391-393 visual, 80,82, 96, 98, 107,139-140,142, 153-154,160,170-172,186,237-238, 267,271,274,276-277,280-281,283284,289-290,292,316,330 Tachistoscope, 235,246 Taste, 229,241,372T Taxonomy, 14-16,20 Technology, 21,27,87,236,239 Television, 49,54, 186,237 Tendency, equidistance, 117,148,152 specific-distance, 117, 121, 137, 170-171 Texture, 107,233,237,242-244'247 Theorem, 161,270,274,302,339,380,388 385 Bell's, 67 Cook's, 268 from automata theory, 9 Gael's, 9,37 Moore, second, 207 Theory, 46, 9, 12-16, 18-21,28-29,31,3738,67, 103,113,155-156,162,172, 185,188, 191,193-194,214,231,246, 249-250, 261-263,270-272,280-282,

423 289-291,298'305,324,337-338,341, 350,352-353,370,374' 385,391 categorization, 373 chaos, 9,21,25,29,37 classification, 374-375 complexity, 264-266,268,270,272-274, 278,281-282 computational, 19,238,261,273,280281,291 decision processes, 376 decision, statistical, 387 dynamic systems, 317 ecological, 8687,105-105,153,165,238 general recognition, 300-301,318,334 Gestalt, 105, 201-202 Gibson's, see ecological Gogel's, 113-176 Hecht's, 58 Helmholtz's, 227 Hull's, 6 identification, 373 integrative, 89, 107 learning, 39,234 of consciousness,395 of evolution, 7,15,103-104,107 of geons, 331 of how neurons encode mind, 23 of internal structure, 9 of mental process, 19 of mind, syntactic, 95 of perception, see perceptual causal, 43,52,55-57,68,222,225 of relativity, 54, 370 perceptual, 8-9,27, 31-32,85,93,98, 107,151,153,173,183,187,203,210, 226,231-232,238,243,246248,261262,271-272,280,291,297-299,341, 369-371,373,379,385,388 prototype, 374 Ramachandran's, see utilitarian signal detection, 300,371,386-387, see also Detection similarity, 297, 299,349,378,385 transactional, 126 transitoriness of, 16 unified, of cognition, 19 utilitarian, 280-281, 290 Thermodynamics, 9,37,264 Thesis, Church/Turing, 265,281 Shepard's, 390 Thing, perceived, 43,44-46,48-56,59, 6164,66,68,70,94,101,191-194,198, 204,210,212-214,238-240,251,253, see also Entity occurrence of, see Occurrence persistence of, see Permanence

424 Thinkin% 1,8,207,299 Though6 11,14,65,191,208,280,333 Tilt, 119F, 120,124,169 Time, 54,65,77,79-81,86,91-92,94,96-

97,101,105,151,157,199-200,206-207, 216,265,311-312,317,321-322,328,382 Topology, 297,302,304-308,315,321,324 325,330,349,353 Touch,68,119,138,168,204,224,241 Trace, memory, 375 Transducer, peripheral, 200 Transform, see Transformation Transformation, 4,13,19,87,97,223,243244,246247,252,268,291,302,304, 308,311-314,316-317,319-322,324,326 327,331,333,335,337-340,351-352, 384385,392 Transparency, 56F, 57-60,62,164,209,216 Trichromacy, 386 Trigonometry, 163 Understanding, 2&21,27-28,36-37,71,99, 183,185,200,205,223-224,232,250, 253,269,280,302,344,386 depth of, 18,23 from above, 99 illusion of, 23 of behavior, 33 of boundary conditions, 88 of illusions, 199 of neural mechanisms, 34-35 of perception, 101,139,171,273,283 synthetic, 33 of perceptual solutions, 254 of perceptual system's long-run behavior, 89 of procgses, 7,151 of psychological mechanism, 34 of the history of perceptual science, 6 of the implications of perceptual variability, 386 of the mind-brain relationship, 22-23, 35, see also Problem, Relation(ship) of the nature of the stimulus, 303 of the nature of the world, 20 of the neural encoding of mental prw cesses, 24 of the physiological basis of mental processes, 22 strong sense of, 34 Unit, 5,35, 102,158-159,164,205 Unitariness, 216 Universe, 54,76-77,261-262,266 Validity, 5, 52, 116, 120, 122, 167, 170,

Suheci Index 261,282,348,378 ecological, 85, 89-90, 100, 107, 236 Value, 85,87,93,99, 101,231, 234,302303,339,390,393 Variability, 87 perceptual, 369-374,376,379-380,385389,391-394 Variation, 12, 115, 166,205,302-303,310311,340,344-345,347-348,352,372T, 389,391,393 Vision, 8,15,26,28,63,68,82,89,98,145, 151,156157,160,165-166,200,204-205, 214,222,224,227,238,242,263-264, 267,273,280,282-288,290-291,321,371, 3nT, 379,387 Will, free, 30 Window, trapezoidal, 124,126, 127F, 128 World, 20, 151,191,193-195, 231,235-236, 238,242-243,26247'253,267-268, 271,280,283,288 external, 64,66.67,191 internal, 321 natural, 20,236237,289 outside, 66,187,232,321 perceived, 43,49-52,55-57, 61,65-68, 70-71,252 perceptual,30,43,167,184,187,190, 192,235 phenomenal, 155-157,160,162,208, 213,216,225-227,251 physical, 30,153,156-157,167,186, 210,223,251-252,339,386 physiological, 298 private, 190, 251 real, 43,6566,190,267,310,318 simulated, 153,157