from Interdisciplinary English by Loretta F. Kasper

© 1998

- Chaos theory is a mathematical theory that breaks down order into disorder. Chaos theory was first developed in the 1970's.
- A linear system is a system that follows a logical and regular pattern. Linear equations are easily solved because they measure things that are orderly.
- A swinging pendulum is an example of a linear system. It is linear because it follows a regular pattern.
- A nonlinear system is one that does not follow a logical or regular pattern and one that is depends a lot on the conditions at the beginning. Small changes disrupt the system. Nonlinear equations are difficult to solve because they measure events that are turbulent and do not follow a regular pattern.
- The weather is an example of a nonlinear system. Small changes in air pressure or wind speed lead to large and often unexpected changes in the weather.
- Chaos theory began with the work of Henri Poincare in the late 1800's. Poincare was trying to map out the orbits of the planets. Then in 1963, Edward Lorenz demonstrated that the earth's atmosphere was a chaotic system. Feigenbaum, in the 1970's, developed a mathematical principle called Feigenbaum's number that could be applied to many different chaotic systems.
- The surprising finding is that there is some logic and regularity to chaotic systems. Events within a chaotic system operate according to a predictable unpredictability.
- Scientists first learned about the order within the chaos through their work with computers.
- Iteration means repetition. You get an answer to an equation and then keep feeding it back into the computer over and over.
- Three principles of chaos theory are:
- Chaotic systems are deterministic--they are ruled by an equation that determines how they operate
- Chaotic systems are very sensitive to beginning conditions. Whatever they start with determines how they develop and behave.
- Chaotic systems are unpredictable. Although they operate according to some kind of "order," you never really know how they are going to behave.

- Chaotic systems are deterministic--they are ruled by an equation that determines how they operate