Chaos Theory
Uploaded by tyson_626 on Feb 03, 2005
Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part. There were still many facets of the universe that were an enigma to physicists. Mathematicians could indeed illustrate patterns in nature but there were many aspects of Mother Nature that remained a mystery to Physicists and Mathematicians alike. Mathematics is an integral part of physics. It provides an order and a guide to thinking; it shows the relationship between many physical phenomenons. The error in mathematics until that point was linearity. “Clouds are not spheres, mountains are not cones, bark is not smooth, nor does lightning travel in a straight line.” - Benoit Mandlebrot. Was it not beyond reason that a process, which is dictated by that regularity, could master a world that shows almost no predictability whatsoever? A new science and a new kind of mathematics were developed that could show the universe’s idiosyncrasies. This new amalgam of mathematics and physics takes the order of linearity and shows how it relates to the unpredictability of the world around us. It is called Chaos Theory.
The secular definition of chaos can be misleading when the word is used in a scientific context. As defined by Webster’s dictionary chaos is total disorder. That may lead one to believe that chaos theory is indeed the study of total disorder, which it truly is not. In 1986 at a prestigious conference on Chaos another definition for chaos was introduced. It is stochastic behavior occurring in a deterministic set. This definition of chaos was hesitantly brought forth. The scientists, mathematicians and intellectuals present were hesitant to define a concept they did not truly understand yet. They left the scientific community with a rather cryptic and oxymoronic definition of chaos. Deterministic sets behave by precise unbreakable law. Stochastic behavior is the opposite of deterministic it has no finite laws, it is totally dependant upon chance. The dissected definition of chaos is lawless behavior that is ruled entirely by law. (Stewart 16-17)
The principles of Chaos Theory are...