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CHAOS THEORY
by Jennifer LeBlanc (1996)
Chaos is a misnomer. Chaos theory cannot explain the mess on your desk. Dr.
Alan Hastings, head of the environmental studies division at the University of
California at Davis defines it as "the complex dynamics found in simple
patterns." Chaos theory is a relatively new, nonlinear way of looking at
problems that have plagued scientists for centuries: population changes,
turbulence, irregular heartbeats and other apparently disordered systems.
Chaos theory was developed mostly by mathematicians and physicists but also received help from research problems in ecology, economics, physiology and epidemiology. It has been a bridge for scientific communication between these apparently unrelated fields. For example, Dr. Hastings and his doctoral
student, Kevin Higgins, used the mathematics of chaos theory to understand
Dungeness crab population changes. They used a simplified computer model to
study patterns of population change over 10 000 years.
Contrary to their expectations, the population did not settle on any
equilibrium value. This means yearly variations in Dungeness crabs may be due to chaotic forces within the population, rather than previously suspected
external forces, such as environmental changes. This result also shows
variability is the norm in some populations, not the exception.
Chaotic systems all share one characteristic  they are extremely sensitive to initial conditions and therefore, the final results are unpredictable. Edward Lorenz, a meteorologist working at MIT in the 1960s was one of the first to recognize this characteristic while playing with a simplified weather computer model. He designed this toy weather' model hoping to find recognizable patterns that would eventually lead to longterm weather forecasting.
One day, wanting to review some intermediate results but not wanting to start all over, he stopped the program, input the intermediate numbers from the printout, and restarted it. Soon the computer showed radically different
weather than it had previously. Lorenz knew the only difference had been that
the printout produced numbers with three decimal places whereas the program normally calculated with six decimal place precision.
Newtonian physical laws would predict that such small differences would produce only small final variations. However, Newtonian laws apply to linear systems. From his unusual results, Lorenz hypothesized that weather was a nonlinear, chaotic system. Through further work, he confirmed this hypothesis and found that, in chaotic systems, tiny initial differences become magnified over time to produce dramatically different final results.
Lorenz once explained his work on chaotic systems in terms of the effect of a
butterfly flapping its wings in Brazil. The butterfly could alter local wind
patterns and as these changes became magnified over time and space, they could
play a role in the formation of a tornado in Texas. This explanation led to
the popular term, the "Butterfly Effect," to describe the behavior of chaotic
systems. Such conclusions forced Lorenz to abandon his dream of longterm
weather forecasting and his results remain true today  weather predictions are rarely good for much longer than a week.
Chaos theory has been described in bold terms. Chaos proponents talk of
revolution, conversion', a paradigm shift. Evangelical statements are rife.
It is not a field lacking in passion or ego.
Others researchers have predicted the death of chaos. Chaos theoreticians
predicted itwould become the elusive Theory of Everything and because it
hasn't, some have pronounced the entire science dead. Dr. Hastings
emphatically says, "No." Chaos theory remains as a useful model to ecologists
and other scientists. Their study, using chaos as a model, showed the
unpredictable nature of population changes and will have an impact on resource management in the future. Other scientists are looking to chaos theory to explain turbulence, the nemesis of physicists and engineers.
Chaos theory has also given us fractal geometry, the visual representation of
chaos theory. Fractals give the world a language and an explanation for the exquisite forms found in Nature. Chaos theory and fractal geometry have squarely turned mathematics around to face the problems and the beauty of the real world.
Sources and Contacts Used
 Gleick, James, "Chaos," in The World Treasury of Physics, Astronomy and
Mathematics, ed.
 Timothy Ferris (Boston: Little, Brown and Company, 1991).
 Gleick, James. Chaos: Making a New Science. New York: Viking, 1987.
 Hastings, Alan. Interview by author. Davis, CA, 6 October 1995.
 Hazen, Robert M. and James Trefil, Science Matters: Achieving Scientific
Literacy (New York: Doubleday, 1991), 1819.
 Mandelbrot, Benoit B., "How Long is the Coast of Britain?" in The World
Treasury of Physics,
 Astronomy and Mathematics, ed. Timothy Ferris (Boston: Little, Brown and
Company, 1991).
 McGuire, Michael. An Eye for Fractals. Redwood City: AddisonWesley, 1991.
 Morton, Carol Cruzan, "Beyond Chaos: Ecological Systems Show Further
Uncertainty," UCDavis News, Thursday, 24 February 1994. (University of
California at Davis News Service Office, Mrak Hall, Davis, CA, 95616)
 Morton, Carol Cruzan. Interview by author. Davis, CA, 5 October 1995.
 Trefil, James, "Chaos," in 1001 Things Everyone should know about Science (New York: Doubleday, 1992), 183185.
 Yoon, Carol Kaesuk, "Boom and Bust May Be the Norm in Nature," New York Times, Tuesday, 15 March 1994, sec 2, p.7.
