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On the Physics of Perception ON THE PHYSICS OF PERCEPTION Willy Wong A thesis submitted in conformity with the requirements for the degree of DOCTOR OF PHILOSOPHY Graduate Department of Physics and Institute of Biomedical Engineering University of Toronto @ Copyright by Willy Wong 1997 National Library Bibliothèque nationale I*I of Canada du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395. rue Wellington OttawaON K1AON4 Ottawa ON KIA ON4 Canada Canada Your file Votre tëtemœ Our Ne Notre rdtdrence The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or seU reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la fome de microfiche/nlm, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantiai extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. On the Physics of Perception PhD 1997 Willy Wong, Department of Physics and hstitute for Biomedical Engineering University of Toronto Abst ract A single equation has been discovered governing the flow of information or entropy fiom a sensory stimulus (such as light or sound) to the organ of sensation (such as a rod or a hair cell) which can account for nearly all expenmental results recorded in sensory neurophysiology relating stimulus intensity and stimulus duration to biolog- ical response. This equation is capable of handling any time-varying single-stimulus input. The biological response is taken as the frequency of neural discharge. When this equation is extended to the psychophysical level, the theory is capable of unifymg many phenornena associated with thresholds. There may be no other sensory theory of comparable generality. The scope and limitations of the theory are discussed. Acknowledgment s 1 would like to take this opportunity to thank some of the people who have helped make t his t hesis possible. First of dl, I am greatly indebted to my supervisor, Prof. Ken Norwich, for his contribution to this work. This thesis represents a coilaborative effort between Prof. Nornrich and myself. 1 would like to thank my supervisory committee, Prof. Rashmi Desai, Prof. Sajeev .John and Prof. Ham Kunov for their many helpfiil suggestions, criticisms and com- ments regarding the research. This thesis would not be possible without their insight and expertise. In particular, 1 would like to acknowledge the generosity of Prof. Kuuov for grant- ing me the use of all materials and equiprnent in the Bioacoustics Laboratory at the Ins titute of Biomedical Engineering. His generosity is great ly appreciat ed. A special word of thanks to Prof. Alf Dolan, Prof. bfichael Menzinger (chemistry) and Prof. John Perz, members of my final examination committee. 1 am particularly gratefd to Prof. Perz for his methodical review of my thesis. 1 woiild also like to thank Prof. Lawrence Wmd af the University of Bntish Colimbia for his many helpfd suggestions and comments as extemal reviewer. This research was supported by fellowships fiom the University of Toronto and the ... Ill Governrnent of Ontario. Furthermore, much of the research was carried out with the aid of an NSERC operating gant to Prof. Ken Norwich. Words cannot elcpress the gratitude that 1 owe to my parents? Bing and James, and Auntie Helen for al1 their support and encouragement. 1 couldn't have gone this far withoiit you! To my lovely Etsuko... thank you so much for helping me grow iip, for showhg me that there is more to Me than just intellectual pursuits. And hdy, to Ken Norwich, a friend and teacher for nearly 7 years, you have inspired me in a way like no other scientist. 1 will forever remember your limitless creativity, honesty, generosity and patience. To yoii, Ken, 1 dedicate this thesis. Contents 1 Introduction 1 2 An Overview of Sensory Physiology and Psychology 5 1 The Sensory Systern.. - . 5 2 The Physiology of the Senses. 8 1.I Neira1 Adaptation. .. 8 2.1.1 Early Rise in the Adaptation Cwe. -8 2.1.2 Spontaneous Activity . 10 2.1.3 De-adaptation . 10 2.2 Driven Neural Response . 10 2.3 Empirical Laws Goveniing the Neural Response . 11 3 The Psychology of the Senses . 14 3.1 Psychophysical Adaptation . 14 3.2 Magnitude Estimation and the Law of Sensation.. 15 3.3 Threshold Phenornena . .. 18 3.3.1 Absolute Threshold . 18 3.3.2 Differential Threshold . 22 3.4 Simple Reaction Time . .26 4 AFinalNote ..............................................................31 5 Conclusions .............................................................. -32 3 The Sensory Entropy Theory 34 1 Classical Entropy Theory (pre-1993) ...................................... 35 1.1 Properties of the Classical Entropy Equation ....................... -37 1.2 Failures of the Classical Theory .................................... -40 2 hiversal Entropy Theory (1993-) .........................................41 2.1 Deriving the Universal Entropy Equation ..........................-41 2.2 Siimmary ............................................................48 4 Neural Explorations with the Universal Entropy Equation 50 1 Neural Adaptation .......................................................-50 2 Spontaneoiis Neiiral Activity .............................................. 51 3 Early Rise in the Adaptation Cime .......................................54 3.1 Correlated Receptor Samples ........................................ 54 3.2 Effects of Stimulus Rise Tirne on Adaptation .......................-55 4 NelualDe-adaptation ..................................................... 56 5 On the Relationship Between the Classical and the Universal Entropy Equation .........................................................58 6 Finther Experimental Validation of the Universal Entropy Equation ..... 58 6.1 Ailditory Neural Response ........................................... 59 vi 6.2 O t her Cases ........................................................ -60 7 Other Investigators ........................................................63 5 Uni&ing Threshold P henomena 64 1 Thresholds and the Neiiral Response .....................................-66 3 Introdiicing the Threshold Hypothesis ....................................67 3 Differential Thresholds and Weber Fractions .............................. 71 3.1 Deriving the Differential Threshold Equation ....................... -71 3.2 Implications of the Differential Threshold Equation ................ -72 3.3 Validating the Differential Threshold Equation ..................... -73 3.3.1 Visual Differential Thresholds . -73 3.3.2 Auditory DifFerential Thresholds ... 76 3.4 A Generalization of the Threshold Hypothesis ...................... 80 4 Absolute Thresholds ..................................................... -81 4.1 Bloch's Law: Part I ................................................-83 6 Simple Reaction Time 84 1 Deriving Piéron's Law ..................................................... 84 2 Implications of the Entropic Derivation of Piéron's Law .................. 88 2.1 Bloch's Law: Part II ................................................ -89 7 Speculating on the Psychophysical Response 91 vii Psychophysical Adaptation ................................................92 Magnitude Estimation .................................................... 96 2.1 The Measurements of Riesz .......................................... 96 2.2 Magnitude Estimation ...............................................98 8 Discussion 1 The Interna1 Signal. 61 ................................................... 101 2 A Common Set of Acoustical Parameters? ............................... 104 3 The Threshold Associated with Simple Reaction Time ..................-105 4 Two Remaining Points .................................................... 106 9 Conclusions 107 1 CreneralRemarks .........................................................107 3 Specific Remarks ........ .. ............................................... 108 2.1 Neurophysiologicd Phenornena .................................... -108 2.2 Psychophysical Phenornena ........................................-109 A 4 Mode1 of Equilibrium Receptor Memory 112 1 Physical Model ...........................................................112 2 Derivation of the Power Dependence of Receptor blernory ............... 114 B Deriving the Neural Response to a Double Step Input C Deriving the Differential Threshofd Equation for the Continuous Increment 121 D Deriving Eq. (59) E The Absolute Threshold of Human Hearing F MapIe Worksheets Bibliography Chapter Introduction The stiidy of the senses is a highly interdisciphary endeavour. A complete stiidy may involve a wide range of disciplines including mat hemat ics, philosophy, physics, physiology and psychology. In this thesis, 1 hope to present a unified and conceptual approach towards the iuiderstanding of fundamental sensory processes. My approach is primarily fcom the point of view of a physicist. Perhaps it is important to realize what this thesis is not about. The thesis is not about the detailed rnechanisms of sensory processes. That is,
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