Bigger Than Chaos

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Harvard University Press, 2003 - Mathematics - 413 pages
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Many complex systems--from immensely complicated ecosystems to minute assemblages of molecules--surprise us with their simple behavior. Consider, for instance, the snowflake, in which a great number of water molecules arrange themselves in patterns with six-way symmetry. How is it that molecules moving seemingly at random become organized according to the simple, six-fold rule? How do the comings, goings, meetings, and eatings of individual animals add up to the simple dynamics of ecosystem populations? More generally, how does complex and seemingly capricious microbehavior generate stable, predictable macrobehavior?

In this book, Michael Strevens aims to explain how simplicity can coexist with, indeed be caused by, the tangled interconnections between a complex system's many parts. At the center of Strevens's explanation is the notion of probability and, more particularly, probabilistic independence. By examining the foundations of statistical reasoning about complex systems such as gases, ecosystems, and certain social systems, Strevens provides an understanding of how simplicity emerges from complexity. Along the way, he draws lessons concerning the low-level explanation of high-level phenomena and the basis for introducing probabilistic concepts into physical theory.

 

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p 312, hard sphere RW:
- MB proba results of each molecule taking a RW through position & velocity.
- impact angle distribution induces the RW
- standard MB proba with molecular chaos hypothesis [43]

Contents

The Simple Behavior of Complex Systems
1
11 Simplicity in Complex Systems
2
12 Enion Probability Analysis
12
13 Towards an Understanding of Enion Probabilities
27
The Physics of Complex Probability
38
21 Complex Probability Quantified
39
22 Microconstant Probability
47
23 The Interpretation of ICVariable Distributions
70
3A Conditional Probability
213
3B Proofs
214
The Simple Behavior of Complex Systems Explained
249
41 Representing Complex Systems
250
42 Enion Probabilities and Their Experiments
251
43 The Structure of Microdynamics
253
44 Microconstancy and Independence of Enion Probabilities
263
45 Independence of Microdynamic Probabilities
275

24 Probabilistic Networks
73
25 Standard ICVariables
81
26 Complex Probability and Probabilistic Laws
96
27 Effective and Critical ICValues
101
2A The Method of Arbitrary Functions
118
2B More on the Tossed Coin
122
2C Proofs
127
The Independence of Complex Probabilities
139
31 Stochastic Independence and Selection Rules
140
32 Probabilities of Composite Events
141
33 Causal Independence
145
34 Microconstancy and Independence
150
35 The Probabilistic Patterns Explained
161
36 Causally Coupled Experiments
163
37 Chains of Linked ICValues
178
46 Aggregation of Enion Probabilities
286
47 Grand Conditions for Simple Macrolevel Behavior
292
48 Statistical Physics
293
49 Population Ecology
319
Implications for the Philosophy of the HigherLevel Sciences
333
52 HigherLevel Laws
339
53 Causal Relevance
346
54 The Social Sciences
351
55 The Mathematics of Complex Systems
355
Notes
363
Glossary
387
References
397
Index
403
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Michael Strevens is Professor of Philosophy at New York University.

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