Reality Rules, 2 volume set, combined

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Reality Rules: I The Fundamentals

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1 The Ways of Modelmaking: Natural Systems and Formal Mathematical Representations 1
1. A Theory of Models 1
2. States, Observables and Natural Systems 4
3. Equations of State 7
4. Equivalent Descriptions and the Fundamental Question of Modeling 10
5. Bifurcations and Catastrophes 17
6. Complexity 21
7. Error and Surprise 23
8. Formal Systems 25
9. Modeling Relations 28
Discussion Questions 35
Problems 40
Notes and References 44
2 Catastrophes, Dynamics and Life: The Singularities of Ecological and Natural Resource Systems 53
1. The Classification Problem 53
2. Smooth Functions and Critical Points 57
3. Structural Stabiliy and Genericity 60
4. Morse's Lemma and Theorem 66
5. The Splitting Lemma and Corank 70
6. Determinacy and Codimension 71
7. Unfoldings 74
8. The Thorn Classification Theorem 78
9. Electric Power Generation 81
10. Bifurcations and Catastrophes 83
11. Harvesting Processes 87
12. Estimation of Catastrophe Manifolds 92
13. Forest Insect Pest Control 95
14. The Catastrophe Controversy 99
15. Mappings 103
16. Dynamical Systems, Flows and Attractors 107
17. Bifurcation of Vector Fields 114
18. Stochastic Stability and the Classification of Vector Fields 120
Discussion Questions 125
Problems 136
Notes and References 149
3 Pattern and The Emergence of Living Forms: Cellular Automata and Discrete Dynamics 161
1. Discrete Dynamical Systems 161
2. Cellular Automata: The Basics 164
3. One-Dimensional Cellular Automata 170
4. Local Properties of One-Dimensional Automata 178
5. Global Properties of One-Dimensional Automata 182
6. Algebraic Properties of Additive Cellular Automata 186
7. Languages: Formal and Natural 189
8. DNA Sequences and Cellular Automata 195
9. L-Systems and the Growth of Plants 200
10. The Game of Life 203
11. A Cellular Automaton Model of Vertebrate Skin Patterns 209
12. Self-Reproducing Automata 211
13. Artificial Life 216
14. Cellular Automata-Extensions and Generalizations 222
Discussion Questions 224
Problems 234
Notes and References 241
4 Order in Chaos: Variety and Pattern in the Flow of Fluids, Populations and Money 250
1. The Circle-10 System 250
2. Deterministic Mechanisms and Stochastic Behavior 255
3. Quasi-periodic Trajectories and the KAM Theorem 259
4. A Philosophical Digression: Randomness and Determinism in Dynamical System Modeling 263
5. Scalar Maps and the \l"Period-3\r" Theorem 267
6. Snap- Back Repellors and Multi-Dimensional Chaos 272
7. Tests for Chaos 275
8. Economic Chaos 288
9. Beer, Bears, Bulls and Chaos 293
10. Population Fluctuations 304
11. Continuous Chaos and the Lorenz Attractor 306
12. Poincare Maps and Strange At tractors 310
13. Chaos and the Problem of Turbulence 318
14. Turbulent Behavior in the Spread of Disease 323
15. Self-Similarity and Fractals 326
16. Fractals and Domains of At traction 335
Discussion Questions 340
Problems 345
Notes and References 358
Index 373

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Reality Rules: II The Frontier

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5 Strategies for Survival: Competition, Games and the Theory of Evolution 1
1. Evolutionary Epistemology 1
2. the Neo-Darwinian Paradigm 3
3. Genetic vs. Phenotypic Change 6
4. Game Theory \em the Basics 10
5. A Typology of Mixed-Motive Games 14
6. Replicators, Hypercycles and Selection 20
7. Equilibrium Properties of Replicator Systems 23
8. Perseverance of Species in Replicator Systems 26
9. Classification of Replicator Systems 29
10. Game Theory and Replicator Systems 31
11. Desert Plant Root Systems and ESS 33
12. ESS vs. Optimality 36
13. Flowering Times for Plants under Competition 38
14. Sociobiology 41
15. The Evolution of Cooperation 49
Discussion Questions 55
Problems 64
Notes and References 77
6 The Analytical Engine: A System-theoretic View of Brains, Minds and Mechanisms 88
1. Brains and Minds 88
2. Input/Output Relations and Control Systems 89
3. Behavioral vs. Cognitive Psychology 90
4. Stimulus-Response Patterns and External System Models 92
5. Cognitive States and Internal Models 93
6. Realizations and Canonical Models 94
7. Linear Systems and Canonical Realizations 96
8. The Ho Realization Algorithm 107
9. Partial Realizations 111
10. Approximate Modeling and Inexact Data 113
11. The State-Space X 115
12. The Cognitive Theorem 119
13. Memory and Behavior 120
14. Thoughts and Group Invariants 121
15. Linearity? 128
16. Reachability of Bilinear Systems 129
Discussion Questions 130
Problems 135
Notes and References 140
7 Taming Nature and Man: Control, Anticipation and Adaptation in Social and Biological Processes 148
1. Classical Optimal Control Theory 148
2. The Minimum Principle and Open-Loop Control 152
3. Feedback Control and Dynamic Programming 156
4. Anticipatory Systems 166
5. Perfect Subsystems and Global Failures 172
6. A Taxonomy of Adaptive Systems 175
7. Metabolism-Repair Systems 178
8. Linear (M, R)-Systems: Repair 183
9. Linear (M, R)-Systems: Replication 193
10. Cellular Networks and Manufacturing Processes 196
Discussion Questions 201
Problems 206
Notes and References 223
8 The Geometry of Human Affairs: Connective Structure in Art, Literature and Games of Chance 229
1. Geometric Paradigms 229
2. Sets and Relations 230
3. Covers and Hierarchies 231
4. Complexes, Connections and Traffic 236
5. Structure Vectors and Eccentricity 242
6. Complexity and Complexes 249
7. The Art of M. C. Escher 251
8. Connective Structure in the Work of Piet Mondrian 255
9. Chance and Surprise 259
10. Simplicial Complexes and Dynamical Systems 263
Discussion Questions 266
Problems 273
Notes and References 280
9 The Mystique of Mechanism: Computation, Complexity and the Limits to Reason 287
1. Computing the Cosmos 287
2. Algorithms and Programs 289
3. Computation and Reality 297
4. Formalization and Hilbert's Program 303
5. The Undecidable and the Incomplete 308
6. Complexity, Programs and Numbers 314
7. The Randomness of Arithmetic 319
8. P and NP: the \l"Easy\r" and the \l"Impossible\r" 325
9. Numerical Analysis, Complexity and Information 332
10. Chaos, Godel and Truth 343
11. The Rules of the Game 349
Discussion Questions 355
Problems 367
Notes and References 370
10 How Do We Know?: Myths, Models and Paradigms in the Creation of Beliefs 379
1. Ordering the Cosmos 379
2. Models and Theories 381
3. Paradigms, Revolutions and Normal Science 385
4. Explanations vs. Descriptions 387
5. \l"Good\r" Models and \l"Bad\r" 389
6. Validation and Falsification 391
7. Competition among Models 392
8. Science and Pseudoscience 394
9. Science, Religion and the Nature of Belief Systems 398
Discussion Questions 400
Problems 402
Notes and References 402
Index 409