Probabilistic reasoning and the science of complexity

Stimulated by curiosity as well as by necessity, we undertake studies of various phenomena and the processes that seem to produce them. Our initial explanations of the process by which some phenomenon is produced may often be oversimplified or possibly entirely mistaken. But, as our research continues we begin to recognize more elements of this process and the manner in which they appear to interact in producing the phenomenon of interest. In other words, as discovery lurches forward we begin to capture more of what we might regard as complexities or subtleties involving these elements and their interactions. In the last decade or so there has been growing interest in the study of complexity itself; Research in what has been called the science of complexity [Waldrop, 1992, 9; Casti,1994, 269-274] has brought together persons from many disciplines who, in the past, might not have been so congenial to the thought of collaborating. At present there are various accounts of what complexity means and how it emerges. In some studies it is observed that simple processes can produce complex phenomena; in others, it is observed that what we often regard as simple phenomena are the result of complex processes. But these observations are not new by any means. Years ago Poincare observed [1905, 147]: If we study the history of science we see produced two phenomena which are, so to speak, each the inverse of the other. Sometimes it is simplicity which is hidden under what is apparently complex; sometimes, on the contrary, it is simplicity which is apparent, and which conceals extremely complex realities.