Chaos - James Gleick [50]
Or imagine looking at the Volkswagen from closer and closer, zooming in with magnifying glass and microscope. At first the surface seems to get smoother, as the roundness of bumpers and hood passes out of view. But then the microscopic surface of the steel turns out to be bumpy itself, in an apparently random way. It seems chaotic.
Scholz found that fractal geometry provided a powerful way of describing the particular bumpiness of the earth’s surface, and metallurgists found the same for the surfaces of different kinds of steel. The fractal dimension of a metal’s surface, for example, often provides information that corresponds to the metal’s strength. And the fractal dimension of the earth’s surface provides clues to its important qualities as well. Scholz thought about a classic geological formation, a talus slope on a mountainside. From a distance it is a Euclidean shape, dimension two. As a geologist approaches, though, he finds himself walking not so much on it as in it—the talus has resolved itself into boulders the size of cars. Its effective dimension has become about 2.7, because the rock surfaces hook over and wrap around and nearly fill three-dimensional space, like the surface of a sponge.
Fractal descriptions found immediate application in a series of problems connected to the properties of surfaces in contact with one another. The contact between tire treads and concrete is such a problem. So is contact in machine joints, or electrical contact. Contacts between surfaces have properties quite independent of the materials involved. They are properties that turn out to depend on the fractal quality of the bumps upon bumps upon bumps. One simple but powerful consequence of the fractal geometry of surfaces is that surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that. Even in rock under enormous pressure, at some sufficiently small scale it becomes clear that gaps remain, allowing fluid to flow. To Scholz, it is the Humpty-Dumpty Effect. It is why two pieces of a broken teacup can never be rejoined, even though they appear to fit together at some gross scale. At a smaller scale, irregular bumps are failing to coincide.
Scholz became known in his field as one of a few people taking up fractal techniques. He knew that some of his colleagues viewed this small group as freaks. If he used the word fractal in the title of a paper, he felt that he was regarded either as being admirably current or not-so–admirably on a bandwagon. Even the writing of papers forced difficult decisions, between writing for a small audience of fractal aficionados or writing for a broader geophysical audience that would need explanations of the basic concepts. Still, Scholz considered the tools of fractal geometry indispensable.
“It’s a single model that allows us to cope with the range of changing dimensions of the earth,” he said. “It gives you mathematical and geometrical tools to describe and make predictions. Once you get over the hump, and you understand the paradigm, you can start actually measuring things and thinking about things in a new way. You see them differently. You have a new vision. It’s not the same as the old vision at all—it’s much broader.”
HOW BIG IS IT? How long does it last? These are the most basic questions a scientist can ask about a thing. They are so basic to the way people conceptualize the world that it is not easy to see that they imply a certain bias. They suggest that size and duration, qualities that depend on scale, are qualities with meaning, qualities that can help describe an object or classify it. When a biologist describes a human being, or a physicist describes a quark, how big and how long are indeed appropriate questions. In their gross physical structure, animals are very