Chaos - James Gleick [39]
No matter how he plotted them, Houthakker could not make the changes in cotton prices fit the bell-shaped model. But they made a picture whose silhouette Mandelbrot was beginning to see in surprisingly disparate places. Unlike most mathematicians, he confronted problems by depending on his intuition about patterns and shapes. He mistrusted analysis, but he trusted his mental pictures. And he already had the idea that other laws, with different behavior, could govern random, stochastic phenomena. When he went back to the giant IBM research center in Yorktown Heights, New York, in the hills of northern Westchester County, he carried Houthakker’s cotton data in a box of computer cards. Then he sent to the Department of Agriculture in Washington for more, dating back to 1900.
THE BELL-SHAPED CURVE.
Like scientists in other fields, economists were crossing the threshold into the computer era, slowly realizing that they would have the power to collect and organize and manipulate information on a scale that had been unimaginable before. Not all kinds of information were available, though, and information that could be rounded up still had to be turned into some usable form. The keypunch era was just beginning, too. In the hard sciences, investigators found it easier to amass their thousands or millions of data points. Economists, like biologists, dealt with a world of willful living beings. Economists studied the most elusive creatures of all.
But at least the economists’ environment produced a constant supply of numbers. From Mandelbrot’s point of view, cotton prices made an ideal data source. The records were complete and they were old, dating back continuously a century or more. Cotton was a piece of the buying-and–selling universe with a centralized market—and therefore centralized record-keeping—because at the turn of the century all the South’s cotton flowed through the New York exchange on route to New England, and Liverpool’s prices were linked to New York’s as well.
Although economists had little to go on when it came to analyzing commodity prices or stock prices, that did not mean they lacked a fundamental viewpoint about how price changes worked. On the contrary, they shared certain articles of faith. One was a conviction that small, transient changes had nothing in common with large, long-term changes. Fast fluctuations come randomly. The small-scale ups and downs during a day’s transactions are just noise, unpredictable and uninteresting. Long-term changes, however, are a different species entirely. The broad swings of prices over months or years or decades are determined by deep macroeconomic forces, the trends of war or recession, forces that should in theory give way to understanding. On the one hand, the buzz of short-term fluctuation; on the other, the signal of long-term change.
As it happened, that dichotomy had no place in the picture of reality that Mandelbrot was developing. Instead of separating tiny changes from grand ones, his picture bound them together. He was looking for patterns not at one scale or another, but across every scale. It was far from obvious how to draw the picture he had in mind, but he knew there would have to be a kind of symmetry, not a symmetry of right and left or top and bottom but rather a symmetry of large scales and small.
Indeed, when Mandelbrot sifted the cotton-price data through IBM’s computers, he found the astonishing results he was seeking. The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was