Chaos - James Gleick [54]
It hardly matters. The face of genius need not always wear an Einstein’s saintlike mien. Yet for decades, Mandelbrot believes, he had to play games with his work. He had to couch original ideas in terms that would not give offense. He had to delete his visionary-sounding prefaces to get his articles published. When he wrote the first version of his book, published in French in 1975, he felt he was forced to pretend it contained nothing too startling. That was why he wrote the latest version explicitly as “a manifesto and a casebook.” He was coping with the politics of science.
THE COMPLEX BOUNDARIES OF NEWTON’S METHOD. The attracting pull of four points—in the four dark holes—creates “basins of attraction,” each a different color, with a complicated fractal boundary. The image represents the way Newton’s method for solving equations leads from different starting points to one of four possible solutions (in this case the equation is x4 - 1 = 0).
FRACTAL CLUSTERS. A random clustering of praticles generated by a computer produces a “percolation network,” one of many visual models inspired by factal geometry. Applied physicists discovered that such models imitate a variety of real-world processes, such as the formation of polymers and the diffusion of oil through factured rock. Each color in the percolation network represents a grouping that is connected throughout.
THE GREAT RED SPOT: REAL AND SIMULATED. The Voyager satellite revealed Jupiter’s surface is a seething, turbulent fluid, with horizontal bands of east-west flow. The Great Red Spot is seen from above the planet’s equator and also in a view looking down on the South Pole.
Computer graphics from Phillip Marcus’s simulation present the South Pole view. The color shows the direction of spin for particular pieces of fluid: pieces turning counterclockwise are red, and pieces turning clock-wise are blue. No matter what the staring configuration, clumps of blue tend to bread up, while the red tends ot merge into a single spot, stable and coherent amit the surrounding tumult.
“The politics affected the style in a sense which I later came to regret. I was saying, ‘It’s natural to…, It’s an interesting observation that….’ Now, in fact, it was anything but natural, and the interesting observation was in fact the result of very long investigations and search for proof and self-criticism. It had a philosophical and removed attitude which I felt was necessary to get it accepted. The politics was that, if I said I was proposing a radical departure, that would have been the end of the readers’ interest.
“Later on, I got back some such statements, people saying, ‘It is natural to observe…’ That was not what I had bargained for.”
Looking back, Mandelbrot saw that scientists in various disciplines responded to his approach in sadly predictable stages. The first stage was always the same: Who are you and why are you interested in our field? Second: How does it relate to what we have been doing, and why don’t you explain it on the basis of what we know? Third: Are you sure it’s standard mathematics? (Yes, I’m sure.) Then why don’t we know it? (Because it’s standard but very obscure.)
Mathematics differs from physics and other applied sciences in this respect. A branch of physics, once it becomes obsolete or unproductive, tends to be forever part of the past. It may be a historical curiosity, perhaps the source of some inspiration to a modern scientist, but dead physics is usually dead for good reason. Mathematics, by contrast, is full of channels and byways that seem to lead nowhere in one era and become major