The Theroy of Chaos

Where Chaos begins, classical science ends. Ever since physicists have inquired into the laws of nature, the have not begun to explore irregular side of nature, the erratic and discontinuous side, that have always puzzled scientists. They did not attempt to understand disorder in the atmosphere, the turbulent sea, the oscillations of the heart and brain, and the fluctuations of wildlife populations. All of these things were taken for granted until in the 1970's some American and European scientists began to investigate the randomness of nature.

They were physicists, biologists, chemists and mathematicians but they were all seeking one thing: connections between different kinds of irregularity. "Physiologists found a surprising order in the chaos that develops in the human heart, the prime cause of a sudden, unexplained death. Ecologists explored the rise and fall of gypsy moth populations. Economists dug out old stock price data and tried a new kind of analysis. The insights that emerged led directly into the natural world- the shapes of clouds, the paths of lightning, the microscopic intertwining of blood vessels, the galactic clustering of stars." (Gleick, 1987)

The man most responsible for coming up with the Chaos theory was Mitchell Feigenbaum, who was one of a handful of scientists at Los Alamos, New Mexico when he first started thinking about Chaos. Feigenbaum was a little known scientist from New York, with only one published work to his name. He was working on nothing very important, like quasi periodicity, in which he and only he had 26 hour days instead of the usual 24. He gave that up because he could not bear to wake up to setting sun, which happened periodically. He spent most of time watching clouds from the hiking trails above the laboratory. To him could represented a side of nature that the mainstream of physics had passed by, a side that was fuzzy and detailed, and structured yet unpredictable. He thought about these things quietly, without producing any work.

After he started looking, chaos seemed to be everywhere. A flag snaps back and forth in the wind. A dripping faucet changes from a steady pattern to a random one. A rising column of smoke disappears into random swirls. "Chaos breaks across the lines that separate scientific disciplines. Because it is a science of the global nature of systems, it has brought together thinkers from fields that have been widely separated...Chaos poses problems that defy accepted ways of working in science. It makes strong claims about the universal behavior of complexity. The first Chaos theorists, the scientists who set the discipline in motion, shared certain sensibilities. They had an eye for pattern, especially pattern that appeared on different scales at the same time. They had a taste for randomness and complexity, for jagged edges and sudden leaps. Believers in chaos-- and they sometimes call themselves believers, or converts, or evangelists--speculate about determinism and free will, about evolution, about the nature of conscious intelligence. They feel theat they are turning back a trend in science towards reductionism, the analysis of systems in terms of their constituent parts: quarks, chromosomes, or neutrons. They believe that they are looking for the whole."(Gleick, 1987)

The Chaos Theory is also called Nonlinear Dynamics, or the Complexity theory. They all mean the same thing though- a scientific discipline which is based on the study of nonlinear systems. To understand the Complexity theory people must understand the two words, nonlinear and system, to appreciate the nature of the science. A system can best be defined as the understanding of the relationship between things which interact. For example, a pile of stones is a system which interacts based upon how they are piled. If they are piled out of balance, the interaction results in their movement until they find a condition under which they are in balance. A group of stones which do not touch one another are not a system, because there is no interaction. A system can be modeled. Which means another system which supposedly replicates the behavior ofthe original system can be created. Theoretically, one can take a second group of stones which are the same weight, shape, and density of the first group, pile them in the same way as the first group, and predict that they will fall into a new configuration that is the same as the first group. Or a mathematical representation can be made of the stones through application of Newton's law of gravity, to predict how future piles of the same type - and of different types of stones - will interact. Mathematical modeling is the key, but not the only modeling process used for systems.

The word nonlinear has to do with understanding mathematical models used to describe systems. Before the growth of interest in nonlinear systems, most models were analyzed as though they were linear systems meaning that when the mathematical formulas representing the behavior of the systems were put into a graph form, the results looked like a straight line. Newton used calculus as a mathematical method for showing change in systems within the context of straight lines. And statistics is a process of converting what is usually nonlinear data into a linear format for analysis.

Linear systems are the classic scientific system and have been used for hundreds of years, they are not complex, and they are easy to work with because they are very predictable. For example, you would consider a factory a linear system. If more inventory is added to the factory, or more employees are hired, it would stand to reason that more pieces produced by the factory by a significant amount. By changing what goes into a system we should be able to tell what comes out of it. But as any factory manager knows, factories don't actually work that way. If the amount of people, the inventory, or whatever other variable is changed in the factory you would get widely differing results on a day to day basis from what was predicted. That is because a factory is a complex nonlinear system, like most systems found in nature.

When most natural systems are modeled, their mathematical representations do not produce straight lines on graphs, and that the system outputs are extremely difficult to predict. Before the chaos theory was developed, most scientists studied nature and other random things using linear systems. Starting with the work of Sir Isaac Newton, physics has provided a process for modeling nature, and the mathematical equations associated with it have all been linear. When a study resulted in strange answers, when a prediction usually came true but not this one