Tuesday, December 4, 2012

The Mandelbrot Conundrum.

Way back in the 1970s, the great scientist, thinker and IBM Fellow Benoit Mandelbrot arrived at the idea of Fractals. I'd be lying if I understood what Fractals are. That said their influence on the world of mathematics, physics, geography, biology, physical sciences and economics has been considerable.

Fractals are based on the notion that the closer you look at something, the more complicated it appears. In a famous example, Mandelbrot looked at the coast of England. How long the coast line depends on how closely one looks. On a map, the coast may look smooth, but zooming in will reveal "jagged lines that add up to a longer coast."

When Mandelbrot presented his book to his Uncle Szolem (also a famous scientist) Szolem asked Benoit, "...What kind of book is it? For whom have you been writing?" Benoit answered, "I don't know but I hope it will create a readership for itself, perhaps even a large one." At that point Benoit's cousin Jacques interjected and said to Szolem, "When you write a book, you always know exactly who's going to read it, right?" To which Szolem replied, "Yes, there are about fifteen people in the world who read everything I write. That is enough."

I don't dabble much in science. But it seems to me that this discussion among Mandelbrots is the essential crux of our business.

Many of us, like Benoit, create work that we hope will attract an audience. We throw our work on broadcast channels and hope it gets found.

Others know exactly whom they are creating work for. And it might just be a few people. But that's ok. They're a few very important people.

Of course what the Mandelbrot's didn't discuss was the interplay between something broad (and unaccountable) and something extremely narrow. Do they build, in some way, on each other. Would Benoit's more accessible, more popular work create young mathematicians who would eventually be open to Szolem's work?

I think the narrow and the broad, as is the case of Szolem and Benoit, are cousins. They are related and important to each other.

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