Foundations of complex-system theories


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Complex behavior can occur in any system made up of large numbers of interacting constituents, be they atoms in a solid, cells in a living organism, or consumers in a national economy. Scientific theories about this behavior typically involve many assumptions and approximations. Foundations of Complex-system Theories analyzes and compares, for the first time, the key ideas and general methods used in studying complexity in the physical, biological, and social sciences. It highlights the features common to the three areas, clarifies conceptual confusions, and provides a nontechnical introduction to how we understand and deal with complexity.

The book begins with a description of the nature of complexity. The author then examines a range of important concepts: situated individuals, composite systems, collective phenomena, emergent properties, chaotic dynamics, stochastic processes. Each topic is illustrated by extended examples from statistical physics, evolutionary biology, and economics. What the sciences investigate are very different, but how the sciences address their topics has certain general commonality, which illustrates, among other things, the general structure of our theoretical reason.

Besides the three sciences, the book also examines several mathematical theories widely used in complexity research: nonlinear and chaotic dynamics, the calculus of probability and stochastic processes. It lays out the conceptual structures of these mathematics and explains what make them so powerful. By exposing the common conceptual foundation of deterministic dynamics and stochastic processes, it refutes both the doctrines of determinisim and chance.

This detailed yet nontechnical book will appeal to anyone who wants to know more about complex systems. It will also be of great interest to philosophers engaged in scientific methodology and specialists studying complexity in the physical, biological, and social sciences.

Contents

1. Introduction: § 1. Synthetic Microanalysis of Complex Systems; § 2. Topics, Theories, Categories; § 3. Economics, Evolutionary Biology, Statistical Physics

PART I. EQUILIBRIUM

2. Theories of Composite Systems: § 4. The World in Many Levels of Description; § 5. Deductive Construction of Small Systems; § 6. Synthetic Microanalysis of Large Systems; § 7. Idealization, Approximation, Model; § 8. Federal Versus Imperial Unity of Science; § 9. Equilibrium and Optimization
3. Individuals: Systems and Constituents: § 10. An Individual and Its Possibilities; § 11. The Integrity of the Topic of Statistical Mechanics; § 12. The Unit of Evolution and the Unit of Selection; § 13. Economic Individuals as Ideal Optimizers
4. Situated Individuals and the Situation: § 14. Independent-Individual Approximations; § 15. Single Particles in the Self-Consistent Field; § 16. Price Takers in the Competitive Market; § 17. Fitness, Adaptation, and the Environment
5. Interacting Individuals and Collective Phenomena: § 18. Intermediate Layers of Structure and Individuals; § 19. Collective Excitations and Their Coupling; § 20. Economic Institutions and Industrial Organization; § 21. Population Structure and the Evolution of Altruism
6. Macro Individuals and Emergent Properties: § 22. Emergent Characters of the System as a Whole; § 23. Self-Organization in Phase Transition; § 24. Adaptive-Organization of Biological Systems; § 25. Inflation, Unemployment, and Their Microfoundation

PART II. DYNAMICS

7. The Temporality of Dynamic Systems: § 26. Temporality and Possibility; § 27. Endurance Versus Composition; § 28. Past, Present, Future
8. The Complexity of Deterministic Dynamics: § 29. Deterministic Dynamical Systems; § 30. Stability, Instability, Bifurcation; § 31. Chaos and Predictability; § 32. Uniting Deterministic and Stochastic Concepts; § 33. The Foundation of Statistical Mechanics; § 34. Causality but not Determinism
9. Stochastic Processes: § 35. The Calculus of Probability and Stochastic; § 36. Stochastic and Deterministic Models of Business Cycles; § 37. The Survival of the Fittest or the Luckiest?; § 38. Causality and Randomness in Statistical Mechanics; § 39. Probability but not Tychism
10. Directionality, History, Expectation: § 40. Causality and Temporally Asymmetry; § 41. Natural History and Its Abuse; § 42. Dynamic Optimization, Expectation, Uncertainty
11. Epilogue: § 43. A Look Backward and Forward
Notes
Bibliography

Foundations of Complex-
System Theories:
In Economics,
Evolutionary Biology,
and Statistical Physics

Sunny Y Auyang
Cambridge University Press

1998
ISBN 0-521-77826-3
$ 29.95 paperback
418 pages