Discovering method in madness - the scientific uses of chaos
Chaos: Making a new science, by James Gleick. New York: Viking. 354 pp. $19.95. Science attempts to describe nature. For generations, those descriptions have been in terms of equations giving well-determined answers. Now a new description is emerging, which still involves equations. But the way those equations are understood, and when or if the answer is determined, is undergoing a dramatic change.
Researchers are looking at some of their results and finding chaos. As usual in scientific development, common words are adopted into the scientific literature with more precise definitions. Chaos is the word that has been adopted to define this new way of looking at things, this new insight into the nature of solutions of well-used and familiar equations. As James Gleick describes it, ``Chaos has become not just theory but also method, not just a canon of beliefs but also a way of doing science.''
Gleick begins with the problem of weather prediction. For physicists who believe that all you need to do is provide a physicist with the initial conditions and an understood mechanism to completely define the future state of the system, weather prediction was just a complicated, but doable problem. As computers became larger and faster, the possibility of accurate numerical weather prediction was just a question of effort. There were problems, of course; there were many complex effects involved, there was a need for many kinds of initial data such as temperatures, pressures, and the locations of mountains, rivers, and lakes, but conceptually at least, numerical weather prediction should yield to the diligence of researchers and the advances in computing technology. Unfortunately, each attempt on larger and larger scales failed.
Gleick's first chapter, entitled ``The Butterfly Effect,'' introduces some of the difficulties with numerical weather prediction. Maddeningly small differences in the input would result in very different predictions of the future weather. Gleick describes Edward Lorentz's first glimpse of chaos. Lorentz just could not believe that a butterfly landing on a flower in Australia would affect the weather in Chicago. So he constructed a simple system of equations that retained some of the characteristics of the big, complex weather-prediction computer programs. Inside Laurentz's computer, the temperatures rose and fell, winds changed directions, cyclones spun on a digitized world, imitating weather patterns on the nightly news.
He ran this program on and on, watching the weather in his computer vary. This simple system had the advantage of not being subject to the uncertainties of a real physical system. Repeating an interesting section again, he noticed that the results of the second run differed markedly from the first run even though the initial conditions were almost the same. Soon he had constructed very simple systems that had the apparently conflicting properties of being deterministic (that is, exact equations described the behavior of the parts) and having results that were unpredictable. In a word the equations produced chaos.
Gleick describes the situation: ``In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes. But chaos meant that such points were everywhere. They were pervasive. In systems like weather, sensitive dependence on initial conditions was an inescapable consequence of the way small scales intertwined with large.
``His colleagues were astonished that Lorentz had mimicked both aperiodicity and sensitive dependence on initial conditions in his toy version of the weather; 12 equations calculated over and over again with ruthless mechanical efficiency. How could such richness, such unpredictability - such chaos - arise from a simple deterministic system?''
On one level Gleick describes the history of a new and exciting development in the science: how people discovered new insights in weather prediction; how science is done, the frustrations and joys of fighting established ideas and conventions, and the histories of ideas.
On a different level this is a story of how one idea - chaos - has been discovered and practiced in a wide variety of fields. Thinkers in biology, physics, economics, medicine, mathematics, art, and architecture have found chaos in this new science sense in their fields.
On still another level, Gleick explains a beautiful and universal theory, without resorting to the language and equations of the mathematician and specialist. Through simple examples in a variety of fields, the nature of this new science emerges. The philosophical and physical impact of this ``new science'' of chaos is likely to affect humans in deep and profound ways.
Although the details may escape us in fields other than our own, ``Chaos'' is an important book for today's thinkers. It may even set your own work on new directions, dusting off those problems that before were unapproachable. Readers of this book may find themselves joining ecologist William Schaffner, who to quote Gleick, ``could not work in the old way any more.''
Paul A.Robinson Jr. is a staff scientist at the Jet Propulsion Laboratory in Pasadena, Calif.