Philosophical Society of Washington

The Theory of Chaos

James Yorke
University of Maryland


2196th Meeting Abstract
Friday, October 14, 2005 at 8:15 PM

Abstract:

Scientists were probably the last people to find out about chaos. Everyone knows our lives are all chaotic and unpredictable in the long run. The mother of a friend of mine once took a taxi, met the driver, and wound up marrying him. If she had taken a different taxi, my friend would never have existed. I often say that the most successful people are those who are good at plan B. Our predictions must be flexible. Franklin wrote the famous lines “For the want of a nail, the shoe was lost; for the want of a shoe the horse was lost; and for the want of a horse the rider was lost, being overtaken and slain by the enemy, all for the want of care about a horseshoe nail.” Others carried this story further so that losing the rider and his message lead to the loss of a battle, then a war, and finally a kingdom, all for the want of a horseshoe's nail. There is common science fiction theme of time travelers making small pivotal perturbations in the past that result in crucial changes in the present. In Ray Bradbury's 1952 short story, “A Sound of Thunder”, a time traveler goes back millions of years and accidentally steps on a butterfly, significantly changing the present day world.

Chaos is an area of science and mathematics that describes situations in which small changes can cascade into larger and larger long-term effects.

Of course scientists always knew that is chaotic, but few recognized until the last 30 years that scientific environments in which precise rules govern change can be quite unpredictable in the long run. It is not the complexity of our lives that cause chaos as much as the instability of our lives. Meteorologist Edward Lorenz, one of the founders of chaos theory, suggested in 1960 that the flap of a butterfly wing in Brazil might set off a tornado in Texas, implying that we can never know all the factors that determine our weather. At best we can only predict the details of the weather a few days ahead. Scientists have found that many situations are equally unstable. Computer models have greatly helped us understand how pervasive chaos is throughout science. Our group at the University of Maryland has aimed at telling scientists how to look for varieties of chaos, for specific phenomena common to many situations. But I continue to wonder, if nearly all scientists missed this pervasive phenomenon, what else might we all be missing now?

James A. Yorke

About the Author:

James A. Yorke earned his bachelors degree from Columbia University in 1963 and his doctoral degree in Mathematics from the University of Maryland in 1966. He stayed at the University of Maryland as a member of Institute for Physical Sciences and Technology (IPST). IPST was established in 1950 to perform interdisciplinary research in the sciences. Today he holds the title of Distinguished University Professor and also is a member of the Mathematics and Physics Departments.

He is perhaps best known to the general public for coining the mathematical term “chaos” with T.Y. Li in a 1975 paper “Period Three Implies Chaos”. “Chaos” is a mathematical concept in non-linear dynamics for systems that vary according to precise deterministic laws but appear to behave in random fashion. The objective of his chaos research is to describe those robust properties that are common in the dynamics of physical, biological, and chemical systems.

Professor Yorke has coauthored three books on chaos and a monograph on gonorrhea epidemiology, and supervised approximately 30 Ph.D. dissertations in the Depts. of Mathematics and Physics. Dr. Yorke's Curriculum Vitae lists of over 300 publications.


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