Probability and Dynamics

The notion of complexity as an object of scientific interest is relatively new. Prior to the 20 th century, the main concern was that of simplicity, with the implication that there existed an opposite pole of complexity. Thus there existed the insinuation that scientific epistemological perception was defined as a delicate balancing act. In some sense, this idea is anomalous to the whole modern scientific enterprise as developed from the 16 th century onward. Although the dictum has proved its usefulness as a support for many scientific theories, the last century witnessed a gradual concern for simplicity's complement. Classical dynamics describes processes in which the future can be derived from the past, and past can be traced from future by time inversion. For the treatment of the material, insight is emphasized rather than mathematical rigor with few exceptions. The implications of such a formulation are rarely considered because it usually works well. An important distinction in the discussions is the fact that mathematical and experimental (real) models do not necessarily coincide. This chapter provides a different perspective in the study of nonlinear dynamics with additional attention to biological and social systems.