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.

      Note to the Reader


   1  The Simple Behavior of Complex Systems
         1.1 Simplicityin Complex Systems 2
         1.2 Enion Probability Analysis 12
         1.3 Towards an Understanding of Enion Probabilities 27


   2  The Physics of Complex Probability
         2.1 Complex Probability Quantified  39
         2.2 Microconstant Probability  47
         2.3 The Interpretation of IC-Variable Distributions  70
         2.4 Probabilistic Networks  73
         2.5 Standard IC-Variables 81
         2.6 Complex Probability and Probabilistic Laws 96
         2.7 Effective and Critical IC-Values  101
         2.A TheMethod ofArbitraryFunctions  118
         2.B More on the Tossed Coin  122
         2.C Proofs 127

   3  The Independence of Complex Probabilities
         3.1 Stochastic Independence and Selection Rules 140
         3.2 Probabilities of Composite Events 141
         3.3 Causal Independence  145
         3.4 Microconstancy and Independence  150
         3.5 The Probabilistic Patterns Explained  161
         3.6 Causally Coupled Experiments  163
         3.7 Chains of Linked IC-Values  178
         3.A Conditional Probability 213
         3.B Proofs 214






4 The Simple Behavior of Complex Systems Explained
     4.1 Representing Complex Systems 250
     4.2 Enion Probabilities and Their Experiments 251
     4.3 The Structure of Microdynamics 253
     4.4 Microconstancy and Independence of Enion Probabilities 263
     4.5 Independence of Microdynamic Probabilities 275
     4.6 Aggregation of Enion Probabilities 286
     4.7 Grand Conditions for Simple Macrolevel Behavior 292
     4.8 Statistical Physics 293
     4.9 Population Ecology 319

5 Implications for the Philosophy of the Higher-Level Sciences
      5.1 Reduction 333
      5.2 Higher-Level Laws 339
      5.3 Causal Relevance 346
      5.4 The Social Sciences 351
      5.5 The Mathematics of Complex Systems 355
      5.6 Are There Simple Probabilities? 357

   Notes
   Glossary
   References
   Index