8.1.2 Who Is This Guy, Anyway?
While many pure and applied mathematicians advanced these trends, it is
Benoit Mandelbrot above all who saw what they had in common and pulled
the threads together into the new discipline.
He was born in Warsaw in 1924, and moved to France in 1935. In a time
when French mathematical training was strongly analytic, he visualized
problems whenever possible, so that he could attack them in geometric
terms. He attended the Ecole Polytechnique, then Caltech, where he
encountered the tangled motions of fluid turbulence.
In 1958 he joined IBM, where he began a mathematical analysis of
electronic "noise" -- and began to perceive a structure in it, a
hierarchy of fluctuations of all sizes, that could not be explained by
existing statistical methods. Through the years that followed, one
seemingly unrelated problem after another was drawn into the growing
body of ideas he would come to call fractal geometry.
As computers gained more graphic capabilities, the skills of his mind's
eye were reinforced by visualization on display screens and plotters.
Again and again, fractal models produced results -- series of flood
heights, or cotton prices -- that experts said looked like "the real
thing."
Visualization was extended to the physical world as well. In a
provocative essay titled "How Long Is the Coast of Britain?" Mandelbrot
noted that the answer depends on the scale at which one measures: it
grows longer and longer as one takes into account every bay and inlet,
every stone, every grain of sand. And he codified the "self-similarity"
characteristic of many fractal shapes -- the reappearance of
geometrically similar features at all scales.
First in isolated papers and lectures, then in two editions of his
seminal book, he argued that many of science's traditional mathematical
models are ill-suited to natural forms and processes: in fact, that many
of the "pathological" shapes mathematicians had discovered generations
before are useful approximations of tree bark and lung tissue, clouds
and galaxies.
Mandelbrot was named an IBM Fellow in 1974, and continues to work at the
IBM Watson Research Center. He has also been a visiting professor and
guest lecturer at many universities.