From instability to intelligence. Complexity and predictability in nonlinear dynamics.

So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some- thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi- bility in thermodynamics, the phenomena of chaos and turbulence in clas- sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de- scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al- ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.