Benoit Mandelbrot (RIP) and the quest for a theory of really everything

By John Horgan

Benoit MandelbrotThe passing of the mathematician Benoit Mandelbrot has triggered in me a wave of nostalgia for the 1980s, when Mandelbrot and other researchers seemed to be creating a scientific revolution. They hoped that sophisticated new mathematical techniques, plus increasingly powerful computers, could help them fathom a wide range of complex, nonlinear phenomena—from brains and immune systems to economies and climate—that had resisted analysis by the reductionist methods of the past.
The journalist James Gleick brilliantly described this research in his 1987 bestseller Chaos: Making a New Science. Mandelbrot, an applied mathematician who dabbled in a wide variety of fields, was a hero of Gleick’s book. Beginning in the 1960s Mandelbrot realized that many real-world phenomena—clouds, snowflakes, coastlines, stock market fluctuations, brain tissue—have similar properties. They display "self-similarity," patterns that recur at smaller and smaller scales; and they have fuzzy boundaries.
Mandelbrot found that he could model these phenomena with mathematical objects that he called fractals. The name Mandelbrot setrefers to a property called fractional dimensionality: fractals are fuzzier than a line but never quite fill a plane. The most famous fractal is the Mandelbrot set, which is generated by repeatedly solving a simple mathematical function and plugging the answer back into it.
When plotted by a computer, the Mandelbrot set produces a very odd-looking object, resembling a warty snowman toppled on its side. As you look at the object with higher and higher resolution, you see that the snowman’s borders are as vague as the borders of a flame; that is what fractional dimensionality looks like. Certain patterns, such as the warty snowman, keep recurring at smaller scales with subtle variations.

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