Throughout history, educational methods and theories have mirrored the beliefs of the times about the workings of the human mind. As our technology has grown, our understandings of the universe and its abstract happenings have also. In order to fully understand these new discoveries we must continually develop new formulas. Not only do these formulas and ideas help us solve complex math problems, but they also lead to new insights in both the natural world and the human body. In addition to insights, these new ideas create more problems to be solved, in a never-ending process of le

Gleick, James Chaos: Making a New Science New York: Penguin Books, Copyright 1997

Internet Document: http://library.advanced.org/12170 Visited March 12, 1997

"Given a system of arbitrarily many mass points that attract each other according to Newton's Laws, try to find, under the assumption that no two points ever collide, a representation of the coordinates of each point as a series in a variable that is some known function of time and for all whose values the series converge uniformly."

"He was a mathematician, but he relied upon the formulation of shapes in his head to solve problems, rather than the traditional algebraic approaches. Although this ostracized him from his colleagues, Mandelbrot's unique ability proved invaluable."

heory is order - not simply order but the very essence of order. While it is true that the chaos theory says that minor fluctuations can cause huge fluctuations: "It is a theory describing the complex and unpredictable motion or dynamics of systems that are sensitive to their initial conditions," one of the main concepts is that while impossible to exactly predict the state of a system, it is usually possible to model the overall behavior of the system.

Chaos theory is among the youngest of the sciences, and has rocketed from its obscure roots in the seventies to become one of the most fascinating fields in existence. It is at the forefront of much research on many medical fields. Chaos science promises to continue to yield absorbing scientific information, which may shape the face of science in the future. Not only will it have an impact on science, but it also points to a new direction in thinking that is more natural, albeit much more complex. These changes are far down the road, but not as far as most would imagine. This report has just scratched the surface to the uses and benefits that chaos may someday provide. Although its still just in its infancy many people are already comparing its effects on science to quantum physics and relativity. Only time will tell if it really will change our lives and beliefs so drastically.

While he worked at IBM, Mandelbrot was asked to figure out a problem that was occurring in data transfer. Whenever large electronics transmissions were being sent, electronic noise would sometimes interfere with the data. This noise created many errors. Mandelbrot saw that the interference appeared only in clusters, with many errors at once followed by very few. Mandelbrot's observation and further examination led him to the discovery that on any scale of time magnification of the errors, the proportion of error-free transmission to error-filled transmission stays constant. His explanation was an exact reiteration of the Cantor Set, an earlier discovery by George Cantor, a nineteenth century mathematician. The Set is constructed in this manner:

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Approximate Pages = 10 (250 words per page double spaced)