Bigger Than Chaos : Understanding Complexity Through Probability

by STREVENS MICHAEL

• ISBN13: 9780674010420
• ISBN10: 0674010426
• Format: Hardcover
• Copyright: 2003-06-30
• Publisher: Harvard Univ Pr

Summary

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.

Table of Contents

Note to the Reader	xiii
1 The Simple Behavior of Complex Systems	1	(37)
1.1 Simplicity in Complex Systems	2	(10)
1.2 Enion Probability Analysis	12	(15)
1.3 Towards an Understanding of Enion Probabilities	27	(11)
2 The Physics of Complex Probability	38	(101)
2.1 Complex Probability Quantified	39	(8)
2.2 Microconstant Probability	47	(23)
2.3 The Interpretation of IC-Variable Distributions	70	(3)
2.4 Probabilistic Networks	73	(8)
2.5 Standard IC-Variables	81	(15)
2.6 Complex Probability and Probabilistic Laws	96	(5)
2.7 Effective and Critical IC-Values	101	(17)
2.A The Method of Arbitrary Functions	118	(4)
2.B More on the Tossed Coin	122	(5)
2.C Proofs	127	(12)
3 The Independence of Complex Probabilities	139	(110)
3.1 Stochastic Independence and Selection Rules	140	(1)
3.2 Probabilities of Composite Events	141	(4)
3.3 Causal Independence	145	(5)
3.4 Microconstancy and Independence	150	(11)
3.5 The Probabilistic Patterns Explained	161	(2)
3.6 Causally Coupled Experiments	163	(15)
3.7 Chains of Linked IC-Values	178	(35)
3.A Conditional Probability	213	(1)
3.B Proofs	214	(35)
4 The Simple Behavior of Complex Systems Explained	249	(84)
4.1 Representing Complex Systems	250	(1)
4.2 Enion Probabilities and Their Experiments	251	(2)
4.3 The Structure of Microdynamics	253	(10)
4.4 Microconstancy and Independence of Enion Probabilities	263	(12)
4.5 Independence of Microdynamic Probabilities	275	(11)
4.6 Aggregation of Enion Probabilities	286	(6)
4.7 Grand Conditions for Simple Macrolevel Behavior	292	(1)
4.8 Statistical Physics	293	(26)
4.9 Population Ecology	319	(14)
5 Implications for the Philosophy of the Higher-Level Sciences	333	(30)
5.1 Reduction	333	(6)
5.2 Higher-Level Laws	339	(7)
5.3 Causal Relevance	346	(5)
5.4 The Social Sciences	351	(4)
5.5 The Mathematics of Complex Systems	355	(2)
5.6 Are There Simple Probabilities?	357	(6)
Notes	363	(24)
Glossary	387	(10)
References	397	(6)
Index	403