Mandelbrot

Benoit Mandelbrot passed away on 14 October. The Guardian gives quite a good obituary. The Economist's is admirable and even includes some mathematics.

He was a character of hen's teeth rarity, a mathematician known far beyond the confines of academia. Fast computers became a routine tool of mathematical work during his career and he seized on the resulting possibilities for making abstract mathematics visible. His investigations were always rooted in the visible anyway, in questions like "How long is the coastline of Britain?" and the geometrical objects he studied opened up new possibilities for understanding the messy character of the world around us, for a "science of roughness" embracing clouds and coastlines. Mandelbrot set and fractals became almost household phrases and the beautiful images that reveal their properties turned up on tee-shirts, paperback covers, rock gig posters, ... they entered the vocabulary of popular culture (They also entered the lexicon of phrases used to legitimise sciencey sounding gibberish in other academic areas but we can't blame the man himself for that depressing outcome). Mandelbrot did not invent all the mathematical tools he exploited but he promoted their use, now routine in many sciences - in contrast to the suggestion in the Economist obituary that popular interest has drifted away again.

I wonder now why a topic so illuminating and so visually appealing hasn't cropped up more in DACE Science courses. Rex Whitehead once gave an excellent talk in a day school on Antichaos, prompted by a Channel 4 documentary and the Channel 4 Science Club (does anybody remember it?). Fractals certainly turn up in other topics, for the insight they give. Maybe it's time for another day school, maybe "Mandelbrot's legacy" - could be really cross-disciplinary, many sciences and creative arts too.

In 2005, World Year of Physics, we had a day school looking at Einstein's three 1905 papers and what followed from them. I spoke about his theory of Brownian motion, its importance in demonstrating the reality of molecules and its significance as a starting point for statistical physics, one road that leads to Mandelbrot. One feedback form voiced the view that too much time had been spent on this. These forms are of course anonymous but it turned out I know the person who made this comment and he was quite happy to repeat it to my face. He thought my talk was interesting and there was nothing wrong with it - but if we'd left it out there could have been more time spent on the topics he regarded as 'fundamental': cosmology, relativity, quantum mechanics. I think this is wrong! But I guess this is not an unusual view and it might make Mandelbrot's legacy a hard sell.

Any thoughts? I'd love to hear them.