Chaos - James Gleick [49]
Scholz remembered Mandelbrot’s name, and in 1978 he bought a profusely illustrated, bizarrely erudite, equation-studded book called Fractals: Form, Chance and Dimension. It was as if Mandelbrot had collected in one rambling volume everything he knew or suspected about the universe. Within a few years this book and its expanded and refined replacement, The Fractal Geometry of Nature, had sold more copies than any other book of high mathematics. Its style was abstruse and exasperating, by turns witty, literary, and opaque. Mandelbrot himself called it “a manifesto and a casebook.”
Like a few counterparts in a handful of other fields, particularly scientists who worked on the material parts of nature, Scholz spent several years trying to figure out what to do with this book. It was far from obvious. Fractals was, as Scholz put it, “not a how-to book but a gee-whiz book.” Scholz, however, happened to care deeply about surfaces, and surfaces were everywhere in this book. He found that he could not stop thinking about the promise of Mandelbrot’s ideas. He began to work out a way of using fractals to describe, classify, and measure the pieces of his scientific world.
He soon realized that he was not alone, although it was several more years before fractals conferences and seminars began multiplying. The unifying ideas of fractal geometry brought together scientists who thought their own observations were idiosyncratic and who had no systematic way of understanding them. The insights of fractal geometry helped scientists who study the way things meld together, the way they branch apart, or the way they shatter. It is a method of looking at materials—the microscopically jagged surfaces of metals, the tiny holes and channels of porous oil-bearing rock, the fragmented landscapes of an earthquake zone.
As Scholz saw it, it was the business of geophysicists to describe the surface of the earth, the surface whose intersection with the flat oceans makes coastlines. Within the top of the solid earth are surfaces of another kind, surfaces of cracks. Faults and fractures so dominate the structure of the earth’s surface that they become the key to any good description, more important on balance than the material they run through. The fractures crisscross the earth’s surface in three dimensions, creating what Scholz whimsically called the “schizosphere.” They control the flow of fluid through the ground—the flow of water, the flow of oil, and the flow of natural gas. They control the behavior of earthquakes. Understanding surfaces was paramount, yet Scholz believed that his profession was in a quandary. In truth, no framework existed.
Geophysicists looked at surfaces the way anyone would, as shapes. A surface might be flat. Or it might have a particular shape. You could look at the outline of a Volkswagen Beetle, for example, and draw that surface as a curve. The curve would be measurable in familiar Euclidean ways. You could fit an equation to it. But in Scholz’s description, you would only be looking at that surface through a narrow spectral band. It would be like looking at the universe through a red filter—you see what is happening at that particular wavelength of light, but you miss everything happening at the wavelengths of other colors, not to mention that vast range of activity at parts of the spectrum corresponding to infrared radiation or radio waves. The spectrum, in this analogy, corresponds to scale. To think of the surface of a Volkswagen in terms of its Euclidean shape is to see it only on the scale of an observer ten meters or one hundred meters away. What about an observer one kilometer away, or one hundred kilometers? What about an observer one millimeter away, or one micron?
Imagine tracing