A science called chaos

SCIENCE

David Lees

Ever since Isaac Newton formulated his laws of motion in the 17th century, scientists have studied the orderly, predictable universe he had described. And they have largely ignored the chaotic elements: the apparently random nature of leaves in the wind or the toss of a coin. Chaos was too much governed by chance to merit serious study. But in the late 1970s a littleknown U.S. physicist revealed the presence of startling patterns underlying chaos. Since then, “chaotic dynamics”—the study of how orderly systems become chaotic—has caught the imagination of scientists throughout the world. Today, researchers are applying it to fields as diverse as biology, meteorology and physics, and some predict that insights into chaos will ultimately change our understanding of nature as fundamentally as Newton’s laws did. Said Joseph Ford, chaos researcher and physicist at the Atlanta-based Georgia Institute of Technology: “Hu-

mans tend to see order instead of disorder. But it now turns out that all Newtonian systems are chaotic in a mathematical sense.”

Since the turn of the century mathematicians have known that simple equations which usually produce logical results can be manipulated to produce disorderly strings of numbers that are completely chaotic. Often, a tiny change in input will produce a staggering variation in the result. That phenomenon fascinated Mitchell Feigenbaum, who in the early 1970s was a physicist working at the Los Alamos National Laboratory in New Mexico. His colleagues considered Feigenbaum, then 29, to be a brilliant physicist but they questioned the apparent aimlessness and the lack of results of his research. At the time, Feigenbaum was working with equations that described the annual fluctuations in insect populations.

But Feigenbaum was less interested in entomology than in the way that the usually predictable results of the equations slid over the brink into chaos when he ran them through a computer. To his surprise he detected a pattern in the way the systems became chaotic. He assumed that the pattern related specifically to the equations he was studying, but when he applied it to equations that describe other systems he discovered

that the same patterns emerged. He devised a mathematical description of the way that initially orderly systems slip into chaos and discovered that it contained the same numbers in every case, whether they dealt with animal populations or the motion of fluids.

The concept that all facets of nature follow the same paths into disorder seemed so weird that scientific journals refused to publish Feigenbaum’s findings. But in 1979 an Italian researcher, who was experimenting with turbulence in fluids, achieved results that confirmed them. Since then, so-called “Feigenbaum numbers” and the theory that underlies them have been used to analyse and sometimes to predict dramatically erratic behavior, even when no one can understand that behavior. At the Institute for Non Linear Science, estabI lished this year at the University of California at San Diego, 40 researchers are involved in a variety of projects related to chaotic dynamics, seeking applications for the new discipline in the fields of oceanography, meteoreology, physics and even psychology. Said Feigenbaum: “Some new kind of science is being constructed.”

Leon Glass, a professor of physiology at McGill University in Montreal, was one of the first researchers to find a practical application for Feigenbaum’s theorems. In 1981 Glass and his colleagues observed that embryonic chicken hearts which were stimulated by pulses from microelectrodes often broke into irregular, chaotic rhythms. Those rhythms were similar to the erratic “arrhythmias” or fibrillations that are caused by breakdowns in the internal electrical system which normally cause the heart to contract regularly. Fibrillation is a major cause of death by heart attack. Glass realized that the patterns of chaos shown by the chicken hearts followed the mathematical model Feigenbaum had outlined.

By applying chaos theory Glass has made it possible to predict which stimulation frequencies will give rise to which arrhythmias. Said Glass: “Physicians have been trying to relate heart rhythms to heart disease since the turn of the century. What we are trying to do is offer mathematical insight into the genesis and classification of arrhythmias.” Glass, who has taken a sabbatical from McGill to pursue his research at the Institute for Non Linear Science, cautioned that his work has not yet yielded a cure to heart disease, but he is convinced that it is pointing the way. He added, “It is not absolutely certain you need to know all this theory to understand what is happening when people get sick, but I believe it will help.”

The patterns of chaos that Glass observed in the breakdown of a heartbeat are also present in the boom-and-bust

cycle of insect populations, according to University of Alberta mathematics professor Thomas Rogers. Rogers is using chaos theory to find a substitute for complicated equations which attempt to predict those populations. Like weather forecasts, the predictions are rarely realistic because the thousands of factors that they must consider cannot be built into linear equations. More precise advance knowledge of insect breeding patterns could have useful applications to agriculture. Said Rogers: “Chaos theory may have some very interesting and profound applications here.”

Under normal circumstances the population density of a species such as the spruce budworm is largely determined by its reproduction rate and by the availability of food. The insects increase in numbers from year to year until they become so numerous that the food supply fails and they die off. Normally, the up-and-down cycle is regular and predictable, but if the process is skewed by new variables, such as bad weather or insecticides, it becomes unstable. The addition of enough variables, however minute, ultimately makes the system chaotic. Rogers is currently investigating a way to apply chaos theory to those systems in the hope that insect or animal populations can be predicted, even when it is impossible to know all the factors that come into play. Said Rogers: “Instead of looking for complicated models for population behavior, there may be very simple models that show the same thing.” If he succeeds, he will have provided a mathematical solution to one of the most intractable problems in biology. Said Rogers: “Because mathematicians have thought about these things, I think it helps biologists to perceive their own problems more clearly.”

Despite their excitement over practical applications of the new discipline, scientists agree that the real importance of chaos theory lies in its overall challenge to the understanding of nature. Chaos raises the thought that because the universe does not necessarily move in an orderly, Newtonian fashion, it will ultimately defy human comprehension. Said Ford: “Initially, it will seem that the universe is this great disorderly thing and that the most we can do is kind of trivial.” But he added that scientists who have experimented with chaos are excited by its challenge. “Chaos is opportunity, it is richness, it gives us an infinity of choices,” he said. Chaos theory is even upsetting Einstein’s belief that God does not toy with the world. Said Ford: “In a sense, God does play dice with the universe, and if we can just find out how he loaded them and learn to play ourselves, then our opportunities are just staggering.”^