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THE STRUCTURE OF INTELLIGENCE

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The Structure of Intelligence A New Mathematical Model of Mind

By Ben Goertzel

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Get any book for free on: www.Abika.com

THE STRUCTURE OF INTELLIGENCE

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The Structure of IntelligenceA New Mathematical Model of MindPaper Version published by Springer-Verlag, 1993

ContentsStructure of Intelligence File 1 Structure of Intelligence File 2 Structure of Intelligence File 3 Structure of Intelligence File 4 Structure of Intelligence File 5 Structure of Intelligence File 6 Structure of Intelligence File 7

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THE STRUCTURE OF INTELLIGENCE

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The Structure of Intelligence

The universe is a labyrinth made of labyrinths. Each leads to another. And wherever we cannot go ourselves, we reach with mathematics. -- Stanislaw Lem, Fiasco

Contents 0. INTRODUCTION 1 1

0.0 Psychology versus Complex Systems Science 0.1 Mind and Computation 0.2 Synopsis 4 7 9 3

0.3 Mathematics, Philosophy, Science 1. MIND AND COMPUTATION 1.0 Rules 9

1.1 Stochastic and Quantum Computation 1.2 Computational Complexity 14

12

1.3 Network, Program or Network of Programs? 2. OPTIMIZATION 2.0 Thought as Optimization 2.1 Monte Carlo and Multistart 2.2 Simulated Annealing 2.3 Multilevel Optimization 26 27 23 23 24

18

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THE STRUCTURE OF INTELLIGENCE

4 31 31 34

3. QUANTIFYING STRUCTURE 3.0 Algorithmic Complexity 3.1 Randomness 3.2 Pattern 3.3 Meaningful Complexity 3.4 Structural Complexity 38 47 50

4. INTELLIGENCE AND MIND 4.0 The Triarchic Theory of Intelligence 4.1 Intelligence as Flexible Optimization 4.2 Unpredictability 62

56 56 60

4.3 Intelligence as Flexible Optimization, Revisited 4.4 Mind and Behavior 5. INDUCTION 5.0 Justifying Induction 5.1 The Tendency to Take Habits 5.2 Toward General Induction Algorithm 5.3 Induction, Probability, and Intelligence 6. ANALOGY 77 68 68 70 73 76 66

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6.0 The Structure-Mapping Theory of Analogy 6.1 A Typology of Analogy 6.2 Analogy and Induction 6.3 Hierarchical Analogy 81 86 88

77

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THE STRUCTURE OF INTELLIGENCE

5 90 95 95 97 99

6.4 Structural Analogy in the Brain 7. LONG-TERM MEMORY 7.0 Structurally Associative Memory 7.1 Quillian Networks

7.2 Implications of Structurally Associative Memory 7.3 Image and Process 102

8. DEDUCTION

p.103

8.0 Deduction and Analogy in Mathematics 8.1 The Structure of Deduction 8.2 Paraconsistency 8.3 Deduction Cannot Stand Alone 9. PERCEPTION 9.0 The Perceptual Hierarchy 9.1 Probability Theory 9.2 The Maximum Entropy Principle 9.3 The Logic of Perception 10. MOTOR LEARNING 10.0 Generating Motions 10.1 Parameter Adaptation 10.2 The Motor Control Hierarchy 10.3 A Neural-Darwinist Perceptual-Motor Hierarchy 11. CONSCIOUSNESS AND COMPUTATION p.142 p.135 p.112

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11.0 Toward a Quantum Theory of Consciousness 11.1 Implications of the Quantum Theory of Consciousness 11.2 Consciousness and Emotion 12. THE MASTER NETWORK 12.0 The Structure of Intelligence 12.1 Design for a Thinking Machine APPENDIX 1: COMPONENTS OF THE MASTER NETWORK p.161 p.155

APPENDIX 2: AUTOMATA NETWORKS

p.164 p.166

APPENDIX 3: A QUICK REVIEW OF BOOLEAN LOGIC

0 Introduction 0.0 Psychology versus Complex Systems Science Over the last century, psychology has become much less of an art and much more of a science. Philosophical speculation is out; data collection is in. In many ways this has been a very positive trend. Cognitive science (Mandler, 1985) has given us scientific analyses of a variety of intelligent behaviors: short-term memory, language processing, vision processing, etc. And thanks to molecular psychology (Franklin, 1985), we now have a rudimentary understanding of the chemical processes underlying personality and mental illness. However, there is a growing feeling -- particularly among non-psychologists (see e.g. Sommerhoff, 1990) -- that, with the new emphasis on data collection, something important has been lost. Very little attention is paid to the question of how it all fits together. The early psychologists, and the classical philosophers of mind, were concerned with the general nature of mentality as much as with the mechanisms underlying specific phenomena. But the new, scientific psychology has made disappointingly little progress toward the resolution of these more general questions. One way to deal with this complaint is to dismiss the questions themselves. After all, one might argue, a scientific psychology cannot be expected to deal with fuzzy philosophical questions that probably have little empirical significance. It is interesting that behaviorists and cognitive scientists tend to be in agreement regarding the question of the overall structure of the mind. Behaviorists believe that it is meaningless to speak about the structures and processes underlying

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behavior -- on any level, general or specific. And many cognitive scientists believe that the mind is a hodge-podge of special-case algorithms, pieced together without any overarching structure. Marvin Minsky has summarized this position nicely in his Society of Mind (1986). It is not a priori absurd to ask for general, philosophical ideas that interlink with experimental details. Psychologists tend to become annoyed when their discipline is compared unfavorably with physics -- and indeed, the comparisonis unfair. Experimental physicists have many advantages over experimental psychologists. But the facts cannot be ignored. Physics talks about the properties of baseballs, semiconductors and solar systems, but also about the fundamental nature of matter and space, and about the origin of the cosmos. The physics of baseball is much more closely connected to experimental data than is the physics of the first three minutes after the Big Bang -- but there is a continuum of theory between these two extremes, bound together by a common philosophy and a common set of tools. It seems that contemporary psychology simply lacks the necessary tools to confront comprehensive questions about the nature of mind and behavior. That is why, although many of the topics considered in the following pages are classic psychological topics, ideas from the psychological literature are used only occasionally. It seems to me that the key to understanding the mind lies not in contemporary psychology, but rather in a newly emerging field which I will call -- for lack of a better name -- "complex systems science." Here "complex" does not mean "complicated", but rather something like "full of diverse, intricate, interacting structures". The basic idea is that complex systems are systems which -- like immune systems, ecosystems, societies, bodies and minds -- have the capacity to organize themselves. At present, complex systems science is not nearly so well developed as psychology, let alone physics. It is not a tightly-knit body of theorems, hypotheses, definitions and methods, but rather a loose collection of ideas, observations and techniques. Therefore it is not possible to "apply" complex systems science to the mind in the same way that one would apply physics or psychology to something. But complex systems science is valuable nonetheless. It provides a rudimentary language for dealing with those phenomena which are unique to complex, self-organizing systems. And I suggest that it is precisely these aspects of mentality which contemporary psychology leaves out. More specifically, the ideas of the following chapters are connected with four "complex systems" theories, intuitively and/or in detail. These are: the theory of pattern (Goertzel, 1991), algorithmic information theory (Chaitin, 1987), the theory of multiextremal optimization (Weisbuch, 1991; Dixon and Szego, 1978; Goertzel, 1989), and the theory of automata networks (Derrida, 1987; Weisbuch, 1991). The theory of pattern provides a general yet rigorous way of talking about concepts such as structure, intelligence, complexity and mind. But although it is mathematically precise, it is extremely abstract. By connecting the theory of pattern with algorithmic information theory one turns an abstract mathematical analysis of mind into a concrete, computational analysis of mind. This should make clear the limited sense in which the present theory of mind is computational, a point which will be elaborated below. Most of the ideas to be presented are not tied to any particular model of computation, but they are discussed in terms of Boolean automata for sake of concreteness and simplicity.

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Pattern and algorithmic complexity give us a rigorous framework for discussing various aspects of intelligence. The theory of multiextremaloptimization, which is closely tied to the abstract theory of evolution (Kauffman, 1969; Langton, 1988), gives us a way of understanding some of the actual processes by which intelligences recognize and manipulating patterns. Perception, control, thought and memory may all be understood as multiextremal optimization problems; and recent theoretical and computational results about multiextremal optimization may be interpreted in this context. And, finally, the theory of automata networks -- discussed in Appendix 2 -- gives a context for our general model of mind, which will be called the "master network". The master network is not merely a network of simple elements, nor a computer progr