Benoit Mandelbrot died last week. As a mathematician he may have as much impact as any number cruncher since maybe Euclid, who gave us regular old geometry, or Charles Babbage, who laid the groundwork for the modern computer, or folks like Euler and Hilbert and Gauss just famous monster geniuses of numbers. Mandelbrot’s genius was in having the vision to fuse a simple abstract notion about geometry with the power of the computer. Good old Euclid shows us how lines and points and surfaces behave in space and the immutable laws that seem to keep them in a state of perpetual orderliness. Mandelbrot thinks of mathematical objects as having a history. They are the product of millions of calculations that determine their size and space. Shapes, for instance, are histories of repeated computations that together constitute complex surfaces or they replicate complex processes like life itself. Mandelbrot’s fractals are capable of modeling all kinds of complicated phenomena. They are the key to creating simulations with rich computer graphics so essential for everything from video games to movie special effects to weather and planetary scale climate simulators.
On my wall as a kid I had a timeline for the history of mathematics. It was published by IBM, whose computers back in the 1960s were just beginning to depict complicated phenomena and didn’t have much in the way of graphics. But Mandelbrot was quietly figuring out ways of turning the computational crank rapidly enough to allow his fractals to take flight and become what we see in the rich graphics of the movie "Avatar" or to simulate the chaos in complex systems like the financial markets. They are beautiful and complex and imprecise but completely mathematical.
The towering achievement of Mandelbrot is the set named for him. The recursive function Z/Z squared plus C repeated endlessly produces a pattern that at first was shocking, then shockingly familiar because it looked like something alive. Not the Mandelbrot set is a symbol of how the computer has changed out view of complexity and chaos. We may still fear it. It may still be elusive if we try to predict its outcomes. But because of Benoit Mandelbrot we can actually see it.
Here’s to Benny and the Sets…..