Information, Sensation and Perception

Transcription

1 Information, Sensation and Perception Kenneth H. Norwich Institute of Biomedical Engineering Department of Physiology, and Department of Physics University of Toronto Toronto, Ontario, Canada Copyright 2003 Kenneth H. Norwich Published on the Internet by Biopsychology.org, 2003 Esteban Barrull Published originally by Academic Press, Inc. A Division of Harcourt Brace & Company San Diego, California

2 Copyright 2003 Kenneth H. Norwich Published on the Internet by Biopsychology.org, 2003 Esteban Barrull Library of Congress Cataloging-in-Publication Data Published originally by Academic Press, Norwich, Kenneth H. Information, Sensation, and Perception / Kenneth H. Norwich Includes index. ISBN I. Title. BF311.N dc CIP

3 To my wife, Barbara, Supportive from t = 0

4 Preface...ix 1 Introduction...1 Perception... 1 The Meaning and Import of Unification of the Laws of Science... 4 Laws of Conservation and Laws of Mechanism... 6 Notes... 6 References Perception as a Choice among Alternatives...8 Perception: Undefined... 8 Information: Defined... 9 Information and Perception The Gist of the Entropic Theory of Perception Notes References The Empirical Laws of Sensation and Perception...15 The Law of Sensation Adaptation The Weber Fraction The Analogs Threshold Effects: The Laws of Blondel and Rey, of Hughes, and of Bloch and Charpentier Simple Reaction Time The Poulton-Teghtsoonian Law A Very Approximate Law of Olfactory Thresholds The Ferry-Porter Law and Talbot's Law Notes References iv

5 v 4 Information of Events with Discrete Outcomes: Methods of Communication Theory and Psychology...34 Picking up the Thread A Channel of Communication The Noisy Channel I The Noisy Channel II Summary The Bottom Line Appendix: The Equivalence of Equations (4.21) and (4.33) Notes References Information of Events with Discrete Outcomes: Applications in Communications Science and in Psychology...50 Communications Science Psychology: Categorical Judgments The Conceptual Basis for the Application of Information Theory as Developed in the 1950s References Information of Events with Discrete Outcomes: Methods of Physics...58 Orientation The First Law of Thermodynamics The Second Law of Thermodynamics The Carnot Cycle/Engine The Clausius Inequality Physical Entropy The Principle of Increase of Physical Entropy The Laboratory Measure of Physical Entropy Change Summary of Section on Classical Thermodynamics Statistical Mechanics: m-space and Phase Points Macrostates and Microstates The Basic Assumption of Statistical Mechanics Physical Entropy and Disorder Applications of Entropy Change in Chemistry The Purpose of This Chapter Notes References The Information of Events with Continuous Outcomes...72 Probability Density The Differential Entropy of a Probability Density Function The Absolute Entropy Convolution Applications in Perceptual Studies Notes References... 80

6 vi 8 The Entropy of the Normal Distribution...81 Introduction Convolution of Two Gaussians Information More on the Interpretation of the Information from Continuous Sources The Central Limit Theorem Analog Channels Appendix: Convolution of Two Gaussian Functions References Modeling the H-Function...88 The Sensory Receptor as a Quantum Detector Sampling the Stimulus Population The Reference Signal Relationship between Variance and Mean The Entropy Function Population vs. Sample Variance Maximum H as Potential Information The Sensory Neuron as Metachannel F at the Threshold Information-Free Approach Conservation Laws and Unification Appendix: The Parable of the Supermarket Notes References Derivation of the Law of Sensation The Dual Forms of the Empirical Law of Sensation: Fechner's and Stevens' Laws Derivation of the Law of Sensation from the Entropy Equation Objections to a Common Law of Sensation Objections to the Entropic Formulation of the Law of Sensation Other Endeavors to Unify the Two Forms of the Law of Sensation Numerical Evaluation of the Constants k, y, and n Measurements of Total Numbers of Action Potentials The Perceptual Variable Unification History Notes References Sensory Adaptation The Entropic Interpretation of Adaptation Information, Receptors, and Categorical Judgments Experimental Tests of the Entropic Theory of Adaptation Experimental Tests of the Entropic Theory: Combined Stimulus Intensity and Adaptation Magical Numbers from the Law of Sensation Numero, Numero, Wherefore Art Thou Numero?

7 vii Audition: The Technique of Simultaneous Dichotic Loudness Balance (SDLB) Concluding Remarks Notes References Differential Thresholds, Weber Fractions, and JND s The Analogs The Weber Fraction Derivation of the Poulton-Teghtsoonian Law Information per Stimulus from Weber Fractions Invariants in Measuring Differential Thresholds On the Physical Meaning of I The Terminal, Rising Portion of the Weber Fraction Curve H as Threshold Working toward a Common Set of Parameters Prediction: Effects of Adaptation on Equal Loudness Contours Summary Notes References Simple Reaction Times and the Blondel-Rey Law Introduction Derivation of an Equation Giving Simple Reaction Time as a Function of Stimulus Intensity Derivation of One of the Empirical Equations of H. Piéron The Constant H for Simple Reaction Time Evaluation of the Informational Equation for Simple Reaction Time The Informational Basis of Reaction Times Compiling a Common Set of Parameters for Taste of Sodium Chloride The Laws of Blondel and Rey, of Hughes, and of Bloch and Charpentier The Blondel-Rey Law and the Ferry-Porter Law Brightness Enhancement Olfactory Thresholds Conclusions Appendix: Changing the Units of the Parameter β Notes References Odds and n s, and the Magical Number Log (2π) Bits of Information Retrospective: The Genealogy of F = kh F Just Above Threshold for Detection: Distinction between F(Psychophysical) and F(Neural) Expanding the Horizons beyond "Intensity" and "Duration" The Exponent n The Exponent n at Various Auditory Frequencies An Intensity-Frequency Formulation of the Entropy Equation for Audition De-adaptation The "Magical" Number 7: Whence and Why? A Brief History of the "Complete" Law of Sensation

8 viii Notes References Boltzmann and Berkeley Boltzmann: F = kh and S = -k B H B George Berkeley: The Relativity of Perception Appendix: The Near-equivalence of H B and H I Notes References Physiological Consequences of the Relativity of Perception Perception of the States of Matter: A Personal Reminiscence Origin of the Entropy Theory Generation of Signals by the Perceptual Unit: The Discrete Model Generation of Signals by the Perceptual Unit: The Continuous Model Notes References Extrapolations and Speculations Reality The Perceptual Unit Illusions: The Necker Cube as Entropic Multivibrator Cochlear Implants The Relativity of Existence The Evolution of Evolution The Anthropic Principle Quantum Theory and Perception Summary Notes References Glossary of Symbols...206