Bruce M. Bennett

Chetan Prakash

PREFACE

*Observer Mechanics* is an inquiry into the
subject
of perception. It suggests an approach to the study of perception that
attempts to be both rigorous and general. A central thesis of *Observer
Mechanics* is that every perceptual capacity (e.g., stereovision,
auditory
localization, sentence parsing, haptic recognition, and so on) can be
described
as an instance of a single formal structure: viz., an "observer."
The first two chapters of *Observer Mechanics* develop this
structure,
resulting in a formal definition of an observer. The third chapter
considers
the relationship between observers and Turing machines. The fourth
chapter
discusses the semantics of observers. The next three chapters present a
formal framework in which to describe an observer and its objects of
perception,
and then develop on this framework a perceptual dynamics. Using this
dynamics,
chapter eight defines conditions in which an observer may be said to
perceive
truly. Chapter nine discusses how stabilities in perceptual dynamics
might
permit the genesis of higher level observers. Chapter ten comments on
the
relationship between the formalisms of quantum mechanics and observer
mechanics.
Finally, the epilogue discusses the philosophical context and
implications
of observer mechanics.

We want the ideas and principles in *Observer
Mechanics*
to be accessible to a wide audience; this dictates a rather informal
style.
On the other hand, we want to introduce a new formalism; this requires
a fairly technical language and thereby restricts the audience. We have
been advised to do one or the other, but not to attempt both. We have
chosen,
perhaps foolishly, to ignore this advice. We want to communicate to the
nonmathematical reader as well as to the mathematical reader without
seriously
offending the sensibilities of either. Here, in outline, is how we have
attempted this.

In chapters one through six, when mathematics is necessary to develop a point, we intersperse liberal explanations for nonmathematical readers. Chapters two, five, and six each have a section presenting basic mathematical notation and terminology. We intend these sections to be helpful references for readers having many different levels of mathematical sophistication. Chapters seven through ten are primarily mathematical; they are intended to give rigor to the intuitive discussions of the first six chapters.

For convenience in reference, we number in one
sequence
all definitions, terminology, figures, equations, propositions, and
theorems.
For example, "Definition **5**--2.1" refers to the first numbered
item in section two of chapter five. Figures are numbered in sequence
with
all other numbered items. For instance, a figure immediately following
Proposition **6**--3.8 would be numbered "Figure **6**--3.9,"
even if it were the first figure in the third section of chapter six.
At
the top of each page we display the chapter and section. For instance,
a page in section three of chapter four would have the display "**4**--3."

For suggestions and critical comments we thank N. Ahuja, G. Andersen, J. Arpaia, R. Black, M. Braunstein, V. Brown, R. Carmona, T. Cornsweet, D. Estlund, D. Glaser, C. Glymour, H. Hironaka, D. P. Hoffman, L. Hoffman, X. Hu, T. Indow, G. Iverson, A. Jepson, R. Kakarala, M. Kinsbourne, P. Kube, D. Laberge, Le D.-T., V. Lefebvre, A. Lewis, E. Matthei, L. Narens, A. Nelson, J. Nicola, R. Olson, D. Revuz, S. Richman, R. Reilly, J. Sarli, W. Savage, B. Skyrms, D. Smith, B. Teissier, W. Uttal, D. Van Essen, P. Williams, P. Woodruff, and J. Yellott. We thank especially J. Koenderink, H. Resnikoff, and W. Richards for reading substantial portions of the manuscript and for making many suggestions. We thank A. Mendez, J. Nicola, and J. Sinek for proofreading and J. Beusmans for writing a computer simulation of the participator dynamics.

Work on this book was supported in part by National Science Foundation grants IST-8413560 and IRI-8700924, and by Office of Naval Research contracts N00014-85-K-0529 and N00014-88-K-0354. We are grateful for their support.

PREFACE xi

1. Introduction 1

2. Principles 4

3. Bug observer 11

4. Biological motion observer 14

CHAPTER 2. DEFINITION OF OBSERVER

1. Mathematical notation and terminology 20

2. Definition of observer 23

3. Ideal observers 27

4. Noise 29

5. Examples of observers 30

6. Transduction 41

7. Theory neutrality of observation 46

CHAPTER 3. PERCEPTION AND COMPUTATION

1. Turing observers 53

2. Turing simulation 55

3. Discretization 57

4. Effective simulation: The algebraic case 60

1. Observer/world interface: Introduction 64

2. Scenarios 66

3. Meaning and truth conditions 69

4. Extended semantics 72

5. Hierarchical analytic strategies and nondualism 75

CHAPTER 5. REFLEXIVE FRAMEWORKS

1. Mathematical notation and terminology 79

2. Definition of reflexive observer framework 81

3. Channeling on reflexive frameworks 86

4. Formal examples of reflexive frameworks 88

5. Symmetric observer frameworks 92

6. Example: Instantaneous rotation 97

CHAPTER 6. INTRODUCTION TO DYNAMICS

1. Mathematical notation and terminology 108

2. Fundamentals of dynamics 110

3. Kinematics of a single participator 122

4. Kinematics of pairs 123

5. True perception among pairs 127

6. An example 131

1. Some fundamentals 139

2. The *t*-distribution 144

3. Augmented dynamics 147

4. Augmented dynamics and standard dynamics 151

5. Descent of Markov chains 157

6. Summary of formulae 165

CHAPTER 8. PERCEPTIONS AND REALITIES

1. Introduction 167

2. Relativization 168

3. Diagrammatic representation of descent conditions 171

4. Trace chains and their descent 174

5. Compatibility of multiple descents 183

6. Matching perception to reality 191

CHAPTER 9. TOWARDS SPECIALIZATION

1. Introduction to specialization 198

2. Hierarchical analytic strategies revisited 201

3. Framework specialization 205

4. On Ullman's incremental rigidity procedure 212

5. Chain-bundle specialization 219

CHAPTER 10. RELATION TO QUANTUM MECHANICS

1. Quantum systems and imprimitivity 231

2. Cocycles and bundles 240

3. Canonical linearization 252

EPILOGUE 256

REFERENCES 269

INDEX 276

NOTATION INDEX 283

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