Time, Space, and Number in Physics and Psychology Time, Space, and Number in Physics and Psychology William R. Uttal Arizona State University 2008 SLOAN PUBLISHING Cornwall-on-Hudson, NY 12520 http://www.sloanpublishing.com Library of Congress Control Number: 2007939517 Uttal, William R. Time, Space, and Number in Physics and Psychology / William R. Uttal. p. cm. Includes bibliographical refrences and index. ISBN 1-59738-015-6 ISBN-13: 978-159738015-7 Cover design by Amy Rosen 2008 by Sloan Publishing, LLC Sloan Publishing 220 Maple Road Cornwall-on-Hudson, NY 12520 All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Printed in the United States of America 10987654321 ISBN 1-59738-015-6 For Mitchan Books by William R. Uttal • Real Time Computers: Techniques and Applications in the Psychological Sciences • Generative Computer-Assisted Instruction (With Miriam Rogers, Ramelle Hieronymus, and Timothy Pasich) • Sensory Coding: Selected Readings (Editor) • The Psychobiology of Sensory Coding • Cellular Neurophysiology and Integration: An Interpretive Introduction • An Autocorrelation Theory of Form Detection • The Psychobiology of Mind • A Taxonomy of Visual Processes • Visual Form Detection in 3-Dimensional Space • Foundations of Psychobiology (with Daniel N. Robinson) • The Detection of Nonplanar Surfaces in Visual Space • The Perception of Dotted Forms • On Seeing Forms • The Swimmer: An Integrated Computational Model of a Perceptual Motor System (with Gary Bradshaw, Sriram Dayanand, Robb Lovell, Thomas Shepherd, Ramakrishna Kakarala, Kurt Skifsted, and Greg Tupper) • Toward a New Behaviorism: The Case Against Perceptual Reductionism • Computational Modeling of Vision: The Role of Combination (with Ramakrishna Kakarala, Sriram Dayanand, Thompas Shepherd, Jaggi Kalki, Charles Lunskis Jr., and Ning Liu) • The War Between Mentalism and Behaviorism: On the Accessibility of Mental Processses • The New Phrenology: On the Localization of Cognitiive Processes in the Brain • A Behaviorist Looks at Form Recognition • Psychomyths: Sources of Artifacts and Mispresentations in Scientific Cognitive Neuroscience • Dualism: The Original Sin of Cognitivism • Neural Theories of Mind: Why the Mind-Brain Problem May Never Be Solved. • Human Factors in the Courtroom: Mythology vesus Science • The Immeasurable Mind: The Real Science of Psychology • Time Space, and Number in Physics and Psychology Contents Preface ix 1 Time, Space, and Number in Physics 1 2 Cardinality, Measurability, and Quantifiability of 38 Psychological Phenomena 3 Psychological Paradoxes in Time and Space 70 4 Statistics and Mathematics in Psychology and Physics 109 5 General Conclusion: How Cognitive Inaccessibility 147 Influences the Great Controversies of Psychology Bibliography 167 Author Index 179 Subject Index 185 vii Preface The crux of the debate between behaviorism and mentalist cognitivism focuses on the issue of accessibility. Cognitivists believe that mental mechanisms and pro- cesses are accessible, and that their inner workings can be inferred from experi- mental observations of behavior, or, to a lesser and more controversial extent, from introspection. Behaviorists, to the contrary, believe that mental processes and mechanisms are inaccessible, and that nothing important about them can be in- ferred from even the most cleverly designed empirical studies or insightful intro- spections. Behaviorists argue, therefore, that publicly observable behavior should be the central focus of psychology, whereas cognitivists contend that understand- ing the mind is an achievable goal. It is clear that the conundrum of accessibility permeates much of modern psy- chological thinking. Nevertheless, the issue is rarely discussed overtly, and the controversy remains unresolved. Which side of the debate one falls on depends on some of the most fundamental and usually unspoken assumptions and prejudices of each individual psychological scientist. One argument that is repeatedly raised by cognitivists and others is that even though mental processes are not directly accessible, this should not be an impene- trable barrier to unraveling the nature of the inner mental processes and mecha- nisms. Inference works for other sciences, so why not psychology? For example, the absence of direct accessibility, it has been pointed out by such scholars as the eminent physicist David Hestenes of Arizona State University, does not deter ix x Preface modern physical science from producing powerful theories of the nature of distant or microscopic matter that is equally invulnerable to direct examination. Great dis- tances or ultramicroscopic size still leave traces of their physical properties in observations that are subject to measurement, and from those measurements the otherwise inaccessible properties can be inferred or derived. Thus, for example, it is possible to determine the age of, or distance to, a star by the pattern of elec- tromagnetic radiation (e.g., the red shift) that does make its way to earth. Simi- larly, the invisible structure of an elementary physical particle can be deduced from the behavior of its constituent parts when they are ejected from a disinte- grating atomic nucleus. Cognitivists and other reductively oriented scientists then confront behavior- ists with the challenge: If physics can work so successfully with their kind of inac- cessibility to make such enormous theoretical progress, then why not psychology? Why then, this argument goes, should psychology be inhibited from the powerful tool of deductive inference any more than is physical science, just because we can- not directly examine its targets of inquiry? If this argument is correct, the door is open to a kind of cognitive reductionism in which the inaccessible mental pro- cesses and mechanisms can be analyzed and parsed into fundamental components or modules, causes identified, and interactions detailed. This is a powerful strategy that has served the physical sciences well. Behaviorism would then have to admit that it is only an incomplete, truncated approach to psychological knowledge and retire, if somewhat ungracefully in the style of most obsolescent psychological theories, from the field. If the analogy between the properties of physical and psychological activities and dimensions is not, however, correct, then cognitivism would have to admit that it has set out on an impossible and intractable quest in its search for inner pro- cesses and mechanisms. One would imagine that its retreat would be equally un- graceful. Given the strong intellectual and emotional hold that either approach to psychological science has on its supporters, it is unlikely that a complete surrender of either school of thought will occur in the short run. Indeed, we might have to wait for a generational change, as we did during the last century of psychological history, for a comparable change in thinking. The nature and comparability of physical and psychological inaccessibility, therefore, represent a formidable problem that has extreme importance in the de- velopment of psychological science. Indeed, this complex issue has troubled me for some years. In an earlier work (Uttal, 2007) I went so far as to express my doubts about this argument in the following way: However, I must also admit that this is one of the most difficult challenges faced by any exclusively behaviorist approach, and I am not utterly convinced that phys- ics and psychology can be compared in this regard. (p.83) This concern set me off on a quest that culminates in this present book. The question asked here is: Are the properties of psychological and physical space and time sufficiently alike to require us to admit that inference works as well for psy- Preface xi chology as for physics? The answer proposed here to this rhetorical question is that there are major discrepancies between the properties of the respective subject mat- ters that make the analogy of comparable inaccessibilities a false one. An impor- tant corollary of this proposed answer is that the argument that the two fields are equally capable of overcoming their respective inaccessibility barriers is incor- rect. As we see later, the main reason for this difference is that physical inference is supported by the general Cosmological Principle, which implies that the laws of the physical universe are the same everywhere, but psychology has no equivalent unifying principle. The arguments that I present here to support these ideas are based on the differ- ences between the dimensions of time, space, and number as they are observed in physics and psychology, respectively. The bases of these arguments are primarily empirical. We do know quite a bit about time and space in both psychological and physical phenomenology and are becoming increasingly aware of the differences between them. Why, another version of the overarching question asks, has psychology been so recalcitrant to conventional mathematical analyses? Why should this science have been so incapable of being consolidated into broad, all-encompassing mathemati- cal theories like those of Newton, Einstein, Bohr, and Heisenberg? Why, in other words, has psychology been so incapable of being fused into a pyramidal theory in which an increasingly small number of unifying concepts or laws describe an in- creasingly large number of empirical phenomena, observations, and findings? In- stead, even its most ardent supporters agree that today’s psychology is