Chaos - James Gleick [55]
So the fourth stage was this: What do people in these branches of mathematics think about your work? (They don’t care, because it doesn’t add to the mathematics. In fact, they are surprised that their ideas represent nature.)
In the end, the word fractal came to stand for a way of describing, calculating, and thinking about shapes that are irregular and fragmented, jagged and broken-up—shapes from the crystalline curves of snowflakes to the discontinuous dusts of galaxies. A fractal curve implies an organizing structure that lies hidden among the hideous complication of such shapes. High school students could understand fractals and play with them; they were as primary as the elements of Euclid. Simple computer programs to draw fractal pictures made the rounds of personal computer hobbyists.
Mandelbrot found his most enthusiastic acceptance among applied scientists working with oil or rock or metals, particularly in corporate research centers. By the middle of the 1980s, vast numbers of scientists at Exxon’s huge research facility, for example, worked on fractal problems. At General Electric, fractals became an organizing principle in the study of polymers and also—though this work was conducted secretly—in problems of nuclear reactor safety. In Hollywood, fractals found their most whimsical application in the creation of phenomenally realistic landscapes, earthly and extraterrestrial, in special effects for movies.
The patterns that people like Robert May and James Yorke discovered in the early 1970s, with their complex boundaries between orderly and chaotic behavior, had unsuspected regularities that could only be described in terms of the relation of large scales to small. The structures that provided the key to nonlinear dynamics proved to be fractal. And on the most immediate practical level, fractal geometry also provided a set of tools that were taken up by physicists, chemists, seismologists, metallurgists, probability theorists and physiologists. These researchers were convinced, and they tried to convince others, that Mandelbrot’s new geometry was nature’s own.
They made an irrefutable impact on orthodox mathematics and physics as well, but Mandelbrot himself never gained the full respect of those communities. Even so, they had to acknowledge him. One mathematician told friends that he had awakened one night still shaking from a nightmare. In this dream, the mathematician was dead, and suddenly heard the unmistakable voice of God. “You know,” He remarked, “there really was something to that Mandelbrot.”
THE NOTION OF SELF-SIMILARITY strikes ancient chords in our culture. An old strain in Western thought honors the idea. Leibniz imagined that a drop of water contained a whole teeming universe, containing, in turn, water drops and new universes within. “To see the world in a grain of sand,” Blake wrote, and often scientists were predisposed to see it. When sperm were first discovered, each was thought to be a homunculus, a human, tiny but fully formed.
But self-similarity withered as a scientific principle, for a good reason. It did not fit the facts. Sperm are not merely scaled-down humans—they are far more interesting than that—and the process of ontogenetic development is far more interesting than mere enlargement. The early sense of self-similarity as an organizing principle came from the limitations on the human experience of scale. How else to imagine the very great and very small, the very fast and very slow, but as extensions of the known?
The myth died hard as the human vision was extended by telescopes and microscopes. The first discoveries were realizations that each change of scale brought new phenomena and new kinds of behavior. For modern particle physicists, the process