Exploring CHAOS. Mathematicians search for keys to randomness

By , Special to The Christian Science Monitor

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.

``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.

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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.

Nine years later, mathematicians demonstrated that chaotic attractors existed in turbulence. ``That made it theoretical physics again.''

Abraham sees his entry into the study of chaos as an accident of timing: He was in graduate school at the University of Michigan when much of this discipline was being created.

The early 1960s also was a time when mathematics and physics were reuniting after a centuries-long divorce. That was a good thing for Abraham because physicists generally had access to computers, mathematicians did not. Abraham could get computer time by begging and borrowing it from physicist friends.

Computers could take concepts that lived only in mathematicians' imaginations and turn them into visual images. Abraham's excitement still shows as he plays with the keyboard of his ISI machine (which he purchased with $40,000 of his own money), and tells how he now can show his wife and children what has been in his head for years.

``These are among the main functions of the computer revolution from the point of view of the history of science,'' he says, ``the rendering visible of mathematical objects. That made it possible to study chaos.''

Abraham says there are thousands of possible applications for this research besides weather forecasting. They include earthquake prediction, understanding certain biological phenomena, climatology, physics, and even the stock market. Indeed, there are some investors who claim to be using chaos theory on Wall Street with some success.

The discipline has attracted serious scientific efforts. Six campuses of the University of California system are doing research in chaos theory, and the Los Alamos Scientific Laboratory has a Center for Nonlinear Studies. One Nobel Prize winner in physics, Murray Gell-Mann, is helping to set up an institute just for this research that has found corporate backers, including International Business Machines Corporation and Mountain Bell.

Sometimes the research has involved trying to predict what will come next within a chaotic state; sometimes it is watching the natural fluctuations between chaos and order.

Peace and war is the topic being explored by several dynamic systems investigators. A number of researchers define peace as a state of oscillation, and believe that humankind has a natural tendency to slip from this situation into chaos -- into war. They have produced complex computer models that contain such variables as the amount of a nation's gross national product going into armaments, the ``paranoia'' of leaders, and economic conditions, all in hopes of understanding the phenomenon of war.

If it is understandable, they theorize, might it not also be possible to intervene in the process?

If that sounds something like the psycohistorians in Isaac Asimov's science-fiction classic ``The Foundation Trilogy,'' who could predict human history and were capable of altering it, Abraham is hardly bothered; he is an avid reader of science fiction.

In fact, Abraham is working on a study that will eventually require a supercomputer in which much of chaos theory would be combined to see if there is a possible overview, a chaotic attractor for chaotic attractors, a way to thoroughly comprehend -- or grok, as he puts it (borrowing a word from the novel of a neighbor, Robert Heinlein) -- reality.

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