Disorder, Dynamical Chaos and Structures

Abstract

Science, like life itself, often poses questions whose answers are so sophisticated and indefinite that one must either rely on the opinion established by the majority or refer to some article of “faith” rather than deductive knowledge. “Where does randomness come from?” “How does order arise from disorder?” These are perhaps the oldest questions of this kind. Anyone who has thought about the principles governing nature has surely faced such questions. Everyday life, as well as conventional learning in physics, has almost persuaded us that complex, irregular and intricate behavior is possible only in very complex systems and that the study of some of these very complex systems may be beyond the scope of physical theory. The vast multitude of molecules in a bottle filled with gas or a crowd of infuriated fans reacting to the news that a football match has been canceled suddenly, are both examples of complex systems. In such systems we usually fail to relate cause and effect uambigously—that is, we cannot predict the behavior of the system in detail and therefore conclude that it is random. Of course, there is always the hope that it might be possible to eliminate such seeming randomness and unpredictability if one had more precise knowledge about the system. Would having a detailed knowledge of the interaction among the elements of a complex system and comprehensive and precise information about their initial states allow one to make precise predictions about the system's behavior at large times, so that the system will not appear to be random? The answer is yes only if one believes in Laplacian determinism, which was one of the earliest dogmas of science.