Alternate realities : mathematical models of nature and man

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Title Page Half Title Copyright Preface Credits Contents Chapter 1 - The Ways of Modelmaking: Natural Systems and Formal Mathmatical Representations 1. A Theory of Models 2. States, Observables and Natural Systems 3. Equations of State 4. Equivalent Descriptions and the Fundamental Question of Modeling 5. Bifurcations and Catastrophes 6. Complexity 7. Error and Surprise 8. Formal Systems 9. Modeling Relations Discussion Questions Problems and Exercises Notes and References Chapter 2 - Pattern and the Emergence of Living Forms: Cellular Automata and Discrete Dynamics 1. Discrete Dynamical Systems 2. Cellular Automata: The Basics 3. One-Dimensional Cellular Automata 4. Local Properties of One-Dimensional Automata 5. Global Properties of One-Dimensional Automata 6. Algebraic Properties of Additive Cellular Automata 7. Languages: Formal and Natural 8. DNA Sequences and Cellular Automata 9. L-Systems and the Growth of Plants 10. Planar Automata and the Game of Life 11. Self-Reproducing Automata 12. A Cellular Automaton Model of Vertebrate Skin Patterns 13. Cellular Automata — Extensions and Generalizations Discussion Questions Problems and Exercises Notes and References Chapter 3 - The Analytical Engine: A Newtonian View of Brains, Minds And Mechanisms 1. Brains and Minds 2. Input/Output Relations and Dynamical Control Systems 3. Behavioral vs. Cognitive Psychology 4. Stimulus-Response Patterns and External System Models 5. Cognitive States and Internal Models 6. Realizations and Canonical Models 7. Linear Systems and Canonical Realizations 8. A Realization Algorithm 9. Partial Realizations 1O. The State-Space 11. The Cognitive Theorem 12. Memory and Behavior 13. Thoughts and Group Invariants 14, Linearity? Discussion Questions Problems and Exercises Notes and References Chapter 4 - Catastrophes and Life: The Singularities of Ecological and Natural Resource Systems 1. Smoothness and Discontinuity 2. Smooth Functions and Critical Points 3. Structural Stability and Genericity 4. Morse’s Lemma and Theorem 5. The Splitting Lemma and Corank 6. Determinacy and Codimension 7. Unfoldings 8. The Thom Classification Theorem 9. Electric Power Generation 10. Bifurcations and Catastrophes 11. Harvesting Processes 12. Forest Insect Pest Control 13. Mappings 14. Bifurcation of Vector Fields Discussion Questions Problems and Exercises Notes and References Chapter 5 - Order in Cuaos: Turbulence And Pattern In The Flow Of Fluids, Populations And Money 1. Deterministic Mechanisms and Stochastic Behavior 2. Dynamical Systems, Flows and Attractors 3. Quasi-periodic Trajectories and the KAM Theorem 4. A Philosophical Digression: Randomness and Determinism in Dynamical System Modeling 5. Scalar Maps and the “Period-3” Theorem 6. Tests for Chaos 7. Snap-Back Repellors and High-Dimensional Chaos 8. Economic Chaos 9. Population Fluctuations 10. Continuous Chaos and the Lorenz Attractor 11. Poincaré Maps and Strange Attractors 12. Chaos and the Problem of Turbulence 13. Turbulent Behavior in the Spread of Disease Discussion Questions Problems and Exercises Notes and References Chapter 6 - Strategies for Survival: Competition, Games and the Theory Of Evolution 1. Evolutionary Epistemology 2. The Neo-Darwinian Paradigm 3. Genetic vs. Phenotypic Change 4. Game Theory—The Basics 5. A Typology of Mixed-Motive Games 6. Replicators, Hypercycles and Selection 7. Equilibrium Properties of Replicator Systems 8. Perseverance of Species in Replicator Systems 9. Classification of Replicator Systems 10. Game Theory and Replicator Systems 11. Desert Plant Root Systems and ESS 12. ESS vs. Optimality 13. Flowering Times for Plants under Competition 14. Sociobiology 15. The Evolution of Cooperation Discussion Questions Problems and Exercises Notes and References Chapter 7 - Taming Nature and Man: Control, Anticipation, and Adaptation in Social and Biological Processes 1. Classical Optimal Control Theory 2. The Maximum Principle and Open-Loop Control 3. Feedback Control and Dynamic Programming 4. Anticipatory Systems 5. Global Failures and Perfect Subsystems 6. A Taxonomy of Adaptive Systems 7. Metabolism-Repair Systems 8. Linear (M,R)-Systems: Repair 9. Linear (M,R)-Systems: Replication 10. Cellular Networks and Manufacturing Processes Discussion Questions Problems and Exercises Notes and References Chapter 8 - The Geometry of Human Affairs: Connective Structure in Art, Literature, and Games of Chance 1. Geometric Paradigms 2. Sets and Relations 3. Covers and Hierarchies 4, Complexes and Connections 5. Structure Vectors and Eccentricity 6. Complexity 7. The Art of M. C. Escher 8. Connective Structure in the Work of Mondrian 9. Chance and Surprise 10. Simplicial Complexes and Dynamical Systems Discussion Questions Problems and Exercises Notes and References Appendix Chapter 9 - How Do We Know?: Myths, Models, and Paradigms in The Creation of Beliefs 1. Ordering the Cosmos 2. Models and Theories 3. Paradigms, Revolutions and Normal Science 4. Explanations vs. Descriptions 5. Predictions, Simulations and Models 6. “Good” Models and “Bad” 7. Validation and Falsification 8. Competition Among Models 9. Science and Pseudoscience 0. Science, Religion and the Nature of Belief Systems Discussion Questions Problems and Exercises Notes and References Index