(2005-02-28) Mandelbrot Edge

Benoit Mandelbrot at EdgeOrg. A recent, important turn in my life occurred when I realized that something that I have long been stating in footnotes should be put on the marquee. I have engaged myself, without realizing it, in undertaking a theory of roughness (Texture). Think of color, pitch, heaviness, and hotness. Each is the topic of a branch of Physics. Chemistry is filled with acids, sugars, and alcohols; all are concepts derived from sensory perceptions. Roughness is just as important as all those other raw sensations, but was not studied for its own sake... Do I claim that everything that is not smooth is Fractal? That fractals suffice to solve every problem of science? Not in the least. What I'm asserting very strongly is that, when some real thing is found to be un smooth, the next mathematical model to try is fractal or multi fractal. A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals. Since roughness is everywhere, fractals - although they do not apply to everything - are present everywhere. And very often the same techniques apply in areas that, by every other account except geometric structure, are separate.