Abstract

About a decade ago the concept of chaos burst upon scientific community as a new paradigm for viewing the certain of the workings of nature and the structures of mathematics. It embodied two key concepts: (1) that certain systems that are classified as "chaotic", while completely determined by initial conditions and the laws of physics, are nevertheless so unstable as to be inherently unpredictable; and (2) that the behavior of chaotic systems is not arbitrarily random, but instead shows regularities, repeating patterns, and self-similarities. The new science of chaos thus staked out its territory in the middle ground between order and randomness, a ground that in the real world is occupied by systems ranging from energy levels in nuclei, to turbulence in plasmas, to the spread of gypsy moths, to weather patterns of Earth and Jupiter, to the stock and commodities markets