Lynn Arthur Steen

Order from Chaos

One of the greatest achievements of 20th-century mathematics is the exploitation of random or stochastic models to bring intellectual order out of apparently chaotic natural processes. From statistical mechanics to human behavior, the hypothesis of randomness has made possible greater accuracy in predicting the course of events than did even the full elaboration of Newtonian mechanics. This shift away from pure determinism as an explanation of natural events has had major technical and intellectual repercussions, and still hides some significant unsolved problems on the interface of mathematics, science and philosophy. In recent years several major results in theoretical probability have shed new light on many of these problems, offering not only better understanding of random processes but also new tools for future research. One of the most important advances is the proof that entropy provides a complete classification of independent random processes, as well as the discovery of a whole class of nondeterministic processes that cannot