Introduction: From Linear to Nonlinear Thinking

Abstract

The theory of nonlinear complex systems has become a successful problem solving approach in the natural sciences — from laser physics, quantum chaos, and metereology to molecular modeling in chemistry and computer-assisted simulations of cellular growth in biology. On the other hand, the social sciences are recognizing that the main problems of mankind are global, complex, nonlinear, and often random, too. Local changes in the ecological, economic, or political system can cause a global crisis. Linear thinking and the belief that the whole is only the sum of its parts are evidently obsolete. One of the most exciting topics of present scientific and public interest is the idea that even our mind is governed by the nonlinear dynamics of complex systems. If this thesis of computational neuroscience is correct, then indeed we have a powerful mathematical strategy to handle the interdisciplinary problems of the natural sciences, social sciences, and the humanities. But one of the main insights of this book is the following: Handling problems does not always mean computing and determining the future. In the case of randomness, we can understand the dynamical reasons, but there is no chance of forecasting. Understanding complex dynamics is often more important for our practical behavior than computing definite solutions, especially when it is impossible to do so.