## Bigger Than ChaosMany 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. |

### What people are saying - Write a review

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 |

403 | |

### Other editions - View all

Bigger than Chaos: Understanding Complexity through Probability Michael Strevens Limited preview - 2009 |