Twentieth century science will always be remembered for Einstein's theory of relativity and the advent of studies in quantum mechanics. Both are considered breakthroughs for the demands they put on scientists to reconsider their premises.

And now there is the science of chaos. Or is there? While both natural and social scientists have become excited about the prospect of a new breakthrough in scientific method, there are those skeptical of chaos theory's novelty. They argue that chaos has always been a part of scientific inquiry. But it has often been overlooked.

Historically, science has sought to create a list of unbreakable laws that explain how anything and everything in the universe operates and interacts. Chaos is commonly thought of as a state in which chance is supreme --a state of utter confusion. But scientists have avoided studying anything which seemed patternless or random.

The laws of science can seem indisputable. While unstable phenomena have challenged these doctrines, scientists have been reluctant to incorporate them into their research. This bias against acknowledging instability has caused many theoreticians to exclude the examination of chaotic action from their conventional approaches to scientific inquiry. But some scientists have seen beyond the bias. The breakthrough in the popularity of chaos study was made by meteorologist Edward Lorenz of the Massachusetts Institute of Technology. In the early 1960s, he was working on a computer simulation of global weather systems. He created a reasonable facsimile of atmospheric conditions with a few simple equations and variables, such as temperature and wind direction, entered as numbers. Lorenz found that entering the same input variables into the computer produced identical output variables each time he ran the program.

As James Gleick, author of Chaos: Making a New Science tells it, Lorenz one day ran the program by entering values that he thought had been output at the halfway point of an earlier run. Entering the same variables, even at a point in the middle of the program, should still have produced the results that Lorenz had seen so often before.

But in fact, Lorenz entered rounded approximations of the actual values. For one series, he entered 0.506 rather than 0.506127. He never imagined that his approximation would make any difference in the program's outcome.

But it did.

In the early part of the run, the weather pastern resembled the pastern with which he was familiar. Before long, though, he noticed that the program was following a new pattern, one that had begun to diverge drastically from the original one. Over time, this new pattern lost all semblance of its predicted form. The difference between the original numbers and Lorenz's approximations, although very small, had produced huge changes in the end result. Gleick said, "Given a particular starting point, the weather would unfold exactly the same way each time. Given a slightly different starting point, the weather should unfold in a slightly different way." "A small numerical error was like a small puff of wind --surely the small puffs faded or canceled each other out before they could change important, large-scale features of the weather. Yet in Lorenz's particular system of equations, small errors proved catastrophic," he said.

In meteorology, this was like say-ing that a butterfly fluttering its wings in Beijing today might create conditions that would bring a hurricane down on Wash-ington D.C. next month. While commonly referred to as "the butterfly effect," this phenomenon is more precisely called "sensitive dependence on initial condi-tions." This new understanding forecasted doom for future advances in weather prediction. Coupled with the Heisenberg uncertainty principle, which states that it is impossible to take an exact measurement at an exact time and that errors are therefore common, the Butterfly Effect suggests that accurate weather forecasting for a period of more than five or six days is practically impossible.

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Meteorologists can now view the flow of water in gulf streams, atmospheric storm systems such as the greet red spot on Jupiter, heat convection through a cup of hot coffee, and even the flow of rush hour traffic in terms of chaotic motion.

All of these phenomena are examples of turbulence. And understanding turbulence is as easy as understanding a dripping faucet.

A slowly dripping faucet will drip in a regular, steady pattern. Drip by drip, one may measure the time between each release of a parcel of water. As the flow is allowed to increase, the time interval between drips decreases. Eventually, the dripping becomes erratic, hardly the patterned flow it had once been. The difference between the patterned flow and the unpatterned flow is a matter of chaos.

We humans, because we cannot keep track of an infinite number of variables all at once, can no more predict the voyage of one drip of water through a faucet than we can the significance of a Chinese butterfly for Hurricane Hugo. The development of computers, however, has allowed science further insight into what the Butterfly Effect is all about. Because computers allow their users to enter data and see the results of millions of calcula-tions upon those data more quickly than ever before, and with the recent develop-ment of high resolution graphics, scientists can now view problems and model solu-tions in ways previously undreamed.

Chaotic states, when graphed on a computer, can produce some very interesting results. It was probably Edward Lorenz himself who saw the first graphic construction of chaos.

In 1963, Lorenz viewed what has come to be called the Lorenz Attractor. An attractor is any point around which solutions to a function revolve. The equilibrium point for a pendulum is an attractor. The graph of the Lorenz attractor is based upon simple components, as James Gleick describes:

"Three equations, with three variables, completely described the motion of this system. Lorenz's computer printed out the changing values of the three variables. The three numbers rose and then fell as imaginary time intervals ticked by. To make a picture from the data, Lorenz used each set of three numbers as coordinates to specify the location of a point in three dimensional space. Thus the sequence of numbers produced a sequence of points tracing a continuous path, a record of the system's behavior."

Although the graph is bounded and appears to have some order, at no point does the graph ever repeat itself. It is impossible to predict at what points the graph will stop spinning, turn around, and start going the other way. The chaos can be visibly seen on a computer screen.

Since Lorenz first viewed the image of his attractor, experts across a myriad of disciplines have made their own graphs of chaotic systems. Environmental zoologists have used computers to study population growth and decline. Economists have charted economic boom and recession.

Likewise, medical doctors now map the complex geography of the human body on a computer screen. Arrhythmia, which accounts for hundreds of thousands of deaths each year, is a disorder characterized by the failure of nodes in the heart to emit at regular intervals electrical impulses which stimulate the heart to contract. During arrhythmia, the timing of those impulses becomes chaotic. In severe cases, the heart may go into ventricular fibrillation, during which the heart "beat" resembles an erratic flutter. And according to Dr. John Kennedy of the Davison Health Center, the randomness of the heartbeat takes away the heart's "mechanical advantage," leading to improper flow of blood and eventually death.

Prediction has been extremely difficult in charting when a heart may go into fibrillation. But now doctors are teaming up with mathematicians to develop new methods of prediction based upon close analysis of the chaotic patterns evident on a patient's electrocardiogram (EKG).

But according to Chemistry professor David Beveridge, in some cases chaos is good for the body. Whereas a healthy heart beats at a regular rate, a healthy brain operates erratically.

"A healthy person's brain waves are in a chaotic pastern. But medical scientists have discovered that under the influence of cocaine, a person's EEG (electroencephalogram) develops a highly regular pattern," said Beveridge.

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At the core of all these graphings, computer simulations, and predictions are the fundamentals of mathematics. Equations and formulas stand at the root of the basic principles and laws of all sciences. Therefore, chaos theory may really be nothing but mathematics in disguise.

"It is an exploitation of some kind of math which provides interesting results," said Physics professor Ralph Baierlein. "Math itself is interdisciplinary, so it's no small wonder that chaos shows up in astronomy, economics, biology, etcetera," he said.

According to Ethan Coven, all of the graphic representation being done through mathematics is based on a lot of approximation. The Mandelbrot Set is one example.

Gleick has said that the Mandelbrot Set is considered the most complex object in mathematics by its admirers. But in fact, to create the Mandelbrot image, one needs only to define a set of points on the basis of a few simple equations. These equations serve as guidelines for determining which points are in the Mandelbrot Set and which are not. This determination is based upon whether or not the answer to each equation is infinite. Before there were computerized graphics, Mandelbrot plotted points with colored magic markers on a huge sheet of paper. He could calculate points in the set manually. He could not display an image of the set itself on a computer in the detail he can today. But even the new "high tech" computer representation of the Mandelbrot Set is imperfect. Because computers cannot determine which answers to each equation are infinite, it must work with very high numbers which serve as approximations of infinity. Even high numbers, however, are poor representations of infinity. This makes questionable the image of the Mandelbrot Set we see.

Indeed, Coven says that we must ask ourselves, "Is this (the image of the Mandelbrot Set) an accurate picture? If not, is it a picture of anything at all?" Until the existence of these representations can be mathematically proven, he said, all we have are a bunch of pretty pictures.

"Some of the kinds of questions that mathematicians ask are changed by computers ' said Coven. "The computer is useful for coming up with questions, questions which for the most part, the computer is incapable of answering."

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New horizons are not only crop-ping up in such fields as medicine and mathematics. Social scientists, too, are developing their own ideas about chaos and its usefulness.

James Gleick has said that all of science is mathematical at heart. "If it wasn't for these sets of mathematical techniques, which can be very boring, there would be no science," Gleick explained.

But social scientists only use mathematics to a limited extent. Their brand of chaos, sometimes spoken of in terms of spontaneous order, self-regulation, de-centralization, or organismic order, uses non-mathematical laws based on empirical observation to define rather than predict.

Chaos as an imprecise phenomena is something with which social scientists are very familiar. Assistant Professor of Government Giulio Gallarotti said, "We [social scientists] are always considering sensitivity to initial conditions because we're always looking for explanations. We're trying to explain causation."

Gallarotti said that social scientists, unlike natural scientists, study groups of people, organizations, and countries rather than inanimate matter. He said that inanimate matter includes those things that behave regularly because they do not have any free will. Because human beings and the groups they form act arbitrarily according to individual free will, social science is less exact than natural science, he said.

Social science has empirical laws, Gallarotti said. They do not always hold. "We can't always predict something. We can do a pretty good job, but we're not always right. If you can explain more than fifty percent variability, that's usually good for a social scientist. We aspire, however, to universal laws because that's science," he said.

Gallarotti pointed out that neither natural science nor social science has laws for everything. Chaos is present in both sciences. "Natural science cannot model turbulence, and social science cannot model social revolution."

But social scientists, according to Gallarotti, have found what he calls "periodicity" in social phenomena that suggests an empirical pattern. He gave the example of the Kondratieff theory in economics which purports that from 1790 to 1940, it is possible to distinguish three periods of expansion and contraction in economic activity.

"It's kind of like clockwork," said Gallarotti. "It's periodic, but we don't know why. That's what makes it chaotic. [The cycles] happen for different reasons, but they happen," he said. In a paper he presented this past summer to a panel at the annual meeting of the American Political Science Association, Gallarotti said, "knowledge of even the most complicated social systems can be founded on systematic understanding...contrary to a widely held belief then, there is a discernible order in social systems which can be modeled."

The ability to make models to describe natural phenomena is one of the things that makes social studies scientific, Gallarotti said. "We have a lot in common with the natural sciences. We study different things, but we have the same scientific approach. Scientists of both types use controlled experiments and have a systematic understanding of phenomena," he said.

Gallarotti said he thinks mathematics can be used in some cases to construct social scientific models. Econometrics, for example, focuses on the use of mathematics of forecasting changes in the stock market and the business cycle. "The forecast is based on mathematics, but it [the forecast] cannot be perfect. We can't ever know if we could find a perfect model.

But according to Economics Professor Richard Adelstein, while mathemat-ics is a powerful language, it is not always useful to social scientists. "I think mathematics may not be a sufficiently rich language to discuss phenomena like chaos. I think there are more things in the world than can be described by numbers."

"As far as I can tell, [chaotic phenomena] seem to be quantified in mathematical models. There are things that cannot be made into numbers. Here we talk about aspects of organization rather than aspects of quantity," Adelstein said. "Not all science needs to be reduced to mathematics. It is possible to look at these things in a scientific way without mathematics."

Adelstein claims that this ap-plies to both the natural and the social sciences. As an example, he noted the biological organization of a species. "The way we differentiate a zebra from a horse has to do with qualitative differences.

Evolution draws out qualities in species. It's a sort of continuous variation across forms of life. Our minds are able to make distinctions and notice patterns and there-fore make meaningful definitions," he said.

And Adelstein said that evolu-tion theory, while written within the framework of the natural sciences, can be use-fully applied to the social sciences. "I don't believe that distinguishing characteristics of English common law can be reduced to numbers any more than zebra characteristics can," Adelstein said.

Adelstein said he thought the fundamental concern with sensitivity of marginal changes in initial conditions is important for both the study of spontaneously ordered social phenomena such a species or social institutions and chaotic phenomena studied by natural scientists.

Gallarotti said the chaotic development of social institutions can be understood in terms of "invisible-hand explanations." That method for understanding social organization was first put forward by Adam Smith in 1776 in his The Wealth of Nations.

"How is it that groups of people, organizations, and countries, can find themselves in systems that work without a lot of people thinking about the system itself? When you think of it logically, it's chaos."

Gallarotti explained that capitalist markets work upon the basis of individual freedom in the marketplace. He said that these markets exist without being organized by anyone in particular. "Everybody does what they want to do in their own way. How is it that we can all provide for ourselves the things we need without thinking about the system as a whole?"

Gallarotti said that socialists try to organize the system according to rules set down by a small group of people. "In socialist economies, you have certain people thinking about the economy as a whole. They set a goal for the system. They plan out how much toilet paper will be used in one year, who will get what food and how much, how much everybody will be paid."

But according to Gallarotti, a capitalist market will produce what is needed by members of the market on its own. "Why are there enough doctors? Because of competition. Why is there competition? Because the people are free to do what they want. There are forces that you cannot see, such as competition and ideology, that coordinate these things," he said.

Gallarotti said, "We [social scientists] are especially interested in chaos because the social sciences have a lot of seeming disorder, and we're looking for order in that. There are systematic relations in an unsystematic world, and as scientists we're trying to model that order just as natural scientists do."

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There is an ongoing debate between natural and social scientists concerning the very nature of chaos itself, and how it should be defined. To the natural scientist, chaotic phenomena implies an underlying mathematical substructure (e.g. the Lorenz Attractor). To the social scientist, chaotic phenomena is explained in non-mathematical terms (e.g. Invisible Hand Theory).

But just because certain phenomena in various fields superficially appears to be "chaotic" (in a state of utter confusion), that does not necessarily identify a single property which transcends the natural-social science border. Scientists are free to pursue their own directions of interest, but they should be cautious in hastily drawing general conclusions regarding potentially incomparable modes of thought.