|
While many pure and applied mathematicians advanced these trends, it is Benoit B. 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 visualised 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 statistically 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 visualisation 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".
Visualisation 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 Centre. He has also been a visiting professor and guest lecturer at many universities.
|
