SCIENCE

The roots of chaos

An exciting theory stirs the scientific world

DIANE BRADY November 19 1990
SCIENCE

The roots of chaos

An exciting theory stirs the scientific world

DIANE BRADY November 19 1990

The roots of chaos

SCIENCE

An exciting theory stirs the scientific world

According to modern science, the universe is ruled by fundamental laws, which are supposed to operate in an orderly way. But scientists also know that the consequences of these laws can be complex and often unpredictable. A sudden summer storm breaks out in the midst of calm weather. A normally functioning heart experiences a damaging spasm. The stock market unexpectedly plunges during a period of economic tranquillity. The common denominator in all of those developments is an outbreak of turbulence in a system. In recent years, a growing number of scientists have become fascinated by unpredictable events. Their name for the phenomenon is chaos, and they claim that chaos is probably intrinsic to most systems in the universe. Now, disciples of chaos theory are searching for ways to apply mathematical formulas that could enable them to predict chaotic events. If they succeed, the added knowledge could revolutionize scientists’ understanding of how the human body and other systems in the cosmos work.

Since scientists formulated chaos theory two decades ago, researchers in a wide variety of

disciplines have begun to use it as a tool for improving their understanding of subjects as widely separated as schizophrenia and population growth. John Outerbridge, an associate professor of physiology at Montreal’s McGill University, says that by using the approach, he can produce computer simulations of the way systems in the human body function. Meteorologists say that it is chaos that makes completely accurate weather forecasting impossible. But they also contend that by understanding the theory, they can gain a better knowledge of long-term weather patterns. For their part, economists are using chaos models to understand why unpredictable events so often upset business cycles. Said Peter Watson, a professor of physics at Carleton University in Ottawa: “We are realizing that chaos is the norm and not the exception in the universe.”

Indeed, proponents of the theory say that its potential for helping in the solution of scientific mysteries may be almost limitless. Some medical researchers now claim that the process by which AIDS undermines the human immune system is chaotic rather than predictable, and they add that that understanding may help them to find a cure for the disease. Eventually; says John Hubbard, a professor of mathematics at Cornell University in Ithaca, N.Y., applications from the chaos model may even enable scientists to understand how the genetic material deoxyribonucleic acid programs growth ir the human body. Said Outerbridge: “It’s very exciting and perplexing. We are now forced tc re-examine all of the things we thought were random or dismissed as unimportant.”

The approach challenges a basic assumptior

that has served as one foundation of Western science since Isaac Newton formulated his laws of motion during the 17th century. That is the conviction that nature operates in a predictable, cause-and-effect manner. On the basis of that world view, many scientists have assumed that if they knew about all of the major factors involved in an event, they could generally forecast the outcome. Indeed, Newtonian laws suggest that if scientists knew every factor, they could ultimately predict everything in the universe. But the development of computers enabled early chaos theorists to see that such an assumption was wrong.

Edward Lorenz, a meteorologist at the Massachusetts Institute of Technology in Cambridge in the early 1960s, used a computer to try to understand weather systems. By feeding information on temperatures, wind velocity and other data into the computer, Lorenz tried

to find ways of predicting long-range weather patterns. Then, he made a disturbing, and important, discovery. He found that a tiny variation in the data would not, as scientists had always believed, produce a small difference in the final result—it produced a markedly different weather pattern. Lorenz called that the Butterfly Effect, because, taken to the extreme, a butterfly flapping its wings in China could ultimately affect the weather across North America. James Gleick, an eminent science writer, stated in his 1987 book, Chaos, that, in a complex system, “errors and uncertainties multiply, cascading upward through a chain of turbulent features.”

That stream of uncertainty is what scientists now call chaos. But at the root of their theory is a conviction, based on computer calculations, that there is a kind of order within disorder. One of the most important findings in that area emerged in 1975, when Mitchell Feigenbaum, a physicist working at the Los Alamos National Laboratory in New Mexico, used a hand calcu-

lator to discover a set of formulas that seemed to demonstrate that all complex systems break down into chaos at the same points along a transition scale. Using so-called populations of data as models for all complex orders, Feigenbaum discovered that, even in chaotic systems, a short-lived equilibrium develops around a point called an “attractor.”

Then, as change continues within the model, the attractor splits in two, creating more change within the system. Feigenbaum discovered a series of ratios, now known as “Feigenbaum numbers,” that enabled him to calculate the point at which the attractors would divide. Since then, theorists have discovered that Feigenbaum numbers can be used as a key to understanding systems as disparate as electrical circuitry and business cycles.

Chaos theory has even given birth to its own eerily beautiful art form, in which both scientists and artists use computer graphics to

create symbolic representations of chaos. The often breathtaking images are based on shapes called “fractals”—irregular, often multidimensional patterns that simulate shapes occurring in nature. The architect of the new geometry was Benoit Mandelbrot, a mathematician who coined the word “fractal” while he was working at the Thomas J. Watson Research Center in Yorktown Heights, N.Y., during the mid-1970s.

In the system that Mandelbrot developed, fractals are the computer-generated shapes that can be created from a set of simple equations that represent the chaotic patterns or randomness in nature. One classic model is known as the Mandelbrot Set. It resembles an ornate, spiked Christmas-tree ornament. When a computer operator enlarges details of the picture, the resulting image reveals an infinite array of similar patterns. Said Mandelbrot to Maclean’s last week: “It makes us understand that marvellous complexity can emerge from such simple math.” He added:

“Fractals bring chaos closer to the common person.”

Now, fractal-based images are becoming a popular art form. Several computer software firms have translated the Mandelbrot Set into programs that illustrators and computer experts can manipulate on their own screens. Said Leslie Titze, a Toronto-based designer who created the MandelZoom program for Apple Computer Inc.: “It’s a jumping-off point for inspiration and a great way to waste time.” He added, “We’re just beginning to explore the textures and shapes that fractals will enable us to see.” Another admirer of fractals is Toronto computer graphic artist Christine Partridge, who says that “some images really evoke spooky ideas of magic.”

Still, some scientists dispute the contention that chaos theory represents a dramatically new way of looking at scientific issues. They say that turbulence has always been an acknowledged part of the natural order. While most admit that the chaos model is significant, they say that its impact can easily be exaggerated. Said Leon Glass, a professor of physiology at McGill: “It seems we can predict when some chaotic reactions should occur. The theory certainly helps, but it is just one step towards interpreting situations.” For his part, Rashmi Desai, a University of Toronto physics professor who is applying chaos theory to his work, said that the French mathematician Jules Henri Poincaré first pointed to some of the principal elements of chaos theory over a period of several years around the turn of the century. At that time, he claimed that seemingly remote events, like the death of a planet in a remote galaxy, could lead to enormous I changes elsewhere in the universe. As

well, Poincaré was aware that chaotic g patterns contained stable patterns. Said ï Desai: “Sometimes, we discover something that was known to other people 100 1/1 years ago. The difference is that we are better able to explain it.”

But proponents of chaos theory insist that it will eventually lead to a basically new view of the universe. In the fields of theology and moral philosophy, some experts argue that chaos theory offers an answer to the debate over how free will can exist in a deterministic universe—a conundrum that has perplexed theologians for thousands of years. As well, some scientists and artists say that by making a place for unpredictability in natural law, chaos theory can have a liberating effect on human thought. Said Carleton’s Watson: “It’s one of these things that will slowly drift into the subconscious and alter the way we think.” Added William Sienkiewicz, a Connecticutbased artist who is illustrating a series of comic books with themes inspired by chaos theory: “There’s a poetry to the belief that any slight movement can shake up the whole structure.” Clearly, by challenging so many long-held assumptions, the theory has already introduced an element of chaos into scientific thought.

DIANE BRADY