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Dynamical Cognitive Science
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Dynamical Cognitive Science
A Bradford Book The MIT Press Cambridge, Massachusetts London, England
Lawrence M. Ward
( 2002 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times New Roman in 3B2 by Asco Typesetters, Hong Kong, and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Ward, Lawrence M. Dynamical cognitive science / Lawrence M. Ward. p. cm. ``A Bradford book''. Includes bibliographical references and index. ISBN 0-262-23217-0 (hc. : alk. paper) 1. Cognitive science. 2. Change (Psychology). 3. TimeÐPsychological aspects. I. Title. BF311 .W2695 2001 153Ðdc21 2001044336
Contents
Preface
xiii
Chapter 1 Magic, Ritual, and Dynamics
1
1.1
Magic and Ritual
1.2
Dynamics
2.1
The Serial Universe
1
4
Chapter 2 Sequence
9
9
2.2 The Problem of Serial Order in Behavior 11 2.3 13
Markovian Analysis of Behavior
3.1
The Dance of Life
3.2
Music and Rhythm
3.3
Rhythms in the Brain
4.1
Space-Time
4.2
The Arrow of Time
4.3
Measuring Time
Chapter 3 Rhythms of Behavior
17
17 19 20
Chapter 4 Time
25
25 28 30
vi
Contents
Chapter 5 Cognitive Processes and Time
35
5.1 Temporal Unfolding of Cognitive Behavior 35 5.2 40
Timing of Cognitive Behavior
5.3
Memory
41
6.1
Systems
46
6.2
General Systems Theory
6.3
Dynamical Systems Theory
7.1
The Mandala of Science
7.2
Formal Theories
7.3 59
Principle of Complementarity
8.1 61
Theories, Models, and Data
8.2
Statical Models
8.3
Dynamical Models
Chapter 6 Systems and General Systems Theory 45
48 50
Chapter 7 Science and Theory
53
53
56
Chapter 8 Dynamical versus Statical Models
61
62 64
8.4 Why We Need Both Statical and Dynamical Models 68 Chapter 9 Dynamical and Structural Models 71
9.1
Structural Models
9.2
Graph Theory
71
72
9.3 Interplay between Dynamical and Structural Models 78
Contents
vii
Chapter 10 Deterministic versus Stochastic Dynamical Models 81
10.1 Deterministic Models 10.2 Stochastic Models
81 84
10.3 Do We Need Both?
87
Chapter 11 Linear Time Series Analysis
89
11.1 Time Series and Noise 11.2 ARIMA ( p; d; q)
89
90
11.3 ARIMA Model of Time Estimation 94 11.4 Mixed Regression-ARIMA Model of Psychophysical Judgment 96 Chapter 12 Probability Theory and Stochastic Models 99
12.1 Dynamical Cognitive Science and Mathematics 99 12.2 Stochastic Processes: A Random Walk to Ruin 100 12.3 Critical Points in Stochastic Models 103 12.4 Ergodicity and the Markov Property 105
Chapter 13 Stochastic Models in Physics
107
13.1 The Master Equation 13.2 Quantum Physics
110
13.3 Complementarity Redux Chapter 14 Noise
115
14.1 What Is Noise?
107
115
113
viii
Contents 14.2 Probabilistic Descri