Exploring CHAOS. Mathematicians search for keys to randomness
Santa Cruz, Calif.
DESPITE the commonly held scientific conceit that nature is always orderly, symmetrical, and often predictable, most people know better. Human affairs reflect nature and both seem to have a disturbing propensity for chaos. Now a growing number of mathematicians, social scientists, and reluctant physicists are recognizing the truth in Henry Miller's aphorism: ``Chaos is the score upon which reality is written.'' They think that even in chaos there may be a pattern that lends itself to exploration and perhaps, eventually, to a better understanding of the real world. From chaos may also come an understanding of the weather, of chemistry, of war and peace. Mathematicians are also trying to determine what role chaos might play in the Strategic Defense Initiative, in which thousands of things would have to work together simultaneously.Skip to next paragraph
Subscribe Today to the Monitor
``This subject, I believe, is critically important for our future. Scientists have to have this information,'' says Ralph Abraham of the University of California at Santa Cruz. Professor Abraham is a pioneer in the mathematical study of chaos, or ``dynamic systems theory,'' as it is frequently called.
A bespectacled, bearded, slightly rumpled but unabashedly idealistic man, he has a clear goal: ``Our goal is to save the world from itself, do good, and have a good time,'' he says.
For years, however, many scientists did not want the information that dynamic systems mathematicians had to offer. Chaos theory bothered their aesthetics, even though life kept reminding them they could be wrong.
For instance, it is possible with some degree of sureness to predict the weather for the next 12 hours or so. But that is almost as far as meteorologists today can take it. The farther ahead one tries to forecast, the more variables enter the picture, and the result becomes increasingly unpredictable.
What meteorologists confront is chaos.
Physicists, who may be the most sensitive to the need for order in the universe, tended to reject the concept of chaos as a physical state. The notion that nature provided for seemingly total randomness was apparently philosophically unacceptable.
That left physicists with at least one major problem -- turbulence. Think of the wake behind a speeding boat, or the roiling air along an aircraft fuselage. Those patterns could not be quantified, compartmentalized, or predicted with any degree of accuracy.
``Everything in the universe was orderly, provided they [the physicists] put on the blinders, and looked at what they could understand,'' Abraham says. ``Turbulence they couldn't understand, so turbulence had to be excluded from mathematical physics.''
The physicists did what may have seemed the only logical thing in that case: They gave turbulence to the engineers to worry about. Engineers called it ``fluid dynamics.''
But in 1962, Edward Lorenz of the Massachusetts Institute of Technology discovered ``chaotic attractors.'' He found that nature tends to be attracted to certain states in mathematically describable ways even in the midst of chaos. The idea that it rarely snows in July in most places in the Northern Hemisphere is an example of an attractor: an attraction to summertime weather in the summer. That, Lorenz said, can be stated mathematically.
``An `attractor' is where you end up if you just start the system and wait a long time,'' Abraham explains.