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### Summary

### Summary

Many complex systems - from immensely complicated ecosystems to minute assemblages of molecules - surprise us with their simple behaviour. 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 micro-behaviour generate stable, predictable macro-behaviour?

### Reviews 1

### Choice Review

In this ambitious reformulation of the probabilistic descriptions of stability (equilibrium, quasi-equilibrium, or quasi-determinate evolution) of collective systems, Strevens, a philosopher at Stanford (where he maintains a Web site featuring appendixes to this volume), has fairly rigorously defined a set of problems of micro state-macro state relations focusing on the inevitably "simple behavior" of "complex systems" that meet appropriate stochastic criteria. Examples of "Epa" ("enion" probability analysis) include a close (Markovian) study of the equilibrium of two-dimensional gas, descriptive models of homeostatic eco- and bio-systems and reformulations of philosophical issues in statistical mechanics, complexity theory, chaotic or nonlinear dynamics, ergodic theory, and related areas. The latter subjects are illuminated by the oft-cited classic by Lawrence Sklar, Physics and Chance (CH, Jun'94). Strevens adroitly bypasses many philosophical questions, e.g., the status of "emergent" qualitative domains, by eschewing the "metaphysics" of probability in favor of its "physics." This is accomplished by limiting his model situations where microsystem (enion) probabilities are independent of each other, conditioned only by macrosystem initial conditions. Whether this is too procrustean to be useful for a general theory of simplicity will require careful consideration. For collections in philosophy of science and those sciences relying on statistical and probabilistic inferences. ^BSumming Up: Highly recommended. Upper-division undergraduates through faculty. P. D. Skiff Bard College

### Table of Contents

Note to the Reader |

1 The Simple Behavior of Complex Systems |

1.1 Simplicity in Complex Systems |

1.2 Enion Probability Analysis |

1.3 Towards an Understanding of Enion Probabilities |

2 The Physics of Complex Probability |

2.1 Complex Probability Quantified |

2.2 Microconstant Probability |

2.3 The Interpretation of IC-Variable Distributions |

2.4 Probabilistic Networks |

2.5 Standard IC-Variables |

2.6 Complex Probability and Probabilistic Laws |

2.7 Effective and Critical IC-Values |

2.A The Method of Arbitrary Functions |

2.B More on the Tossed Coin |

2.C Proofs |

3 The Independence of Complex Probabilities |

3.1 Stochastic Independence and Selection Rules |

3.2 Probabilities of Composite Events |

3.3 Causal Independence |

3.4 Microconstancy and Independence |

3.5 The Probabilistic Patterns Explained |

3.6 Causally Coupled Experiments |

3.7 Chains of Linked IC-Values |

3.A Conditional Probability |

3.B Proofs |

4 The Simple Behavior of Complex Systems Explained |

4.1 Representing Complex Systems |

4.2 Enion Probabilities and Their Experiments |

4.3 The Structure of Microdynamics |

4.4 Microconstancy and Independence of Enion Probabilities |

4.5 Independence of Microdynamic Probabilities |

4.6 Aggregation of Enion Probabilities |

4.7 Grand Conditions for Simple Macrolevel Behavior |

4.8 Statistical Physics |

4.9 Population Ecology |

5 Implications for the Philosophy of the Higher-Level Sciences |

5.1 Reduction 5.2 Higher-Level Laws |

5.3 Causal Relevance |

5.4 The Social Sciences |

5.5 The Mathematics of Complex Systems |

5.6 Are There Simple Probabilities? |

Notes |

Glossary |

References |

Index |