Sunday, July 18, 2010

Mandelbrot! Mandelbrot! Mandelbrot!

In case you missed the reference, I was thinking of the Seinfeld episode entitled "The English Patient" where Jerry has to deal with the highly competitive 80-year-old fitness trainer and weightlifter Izzy Mandelbaum, and his son and father, and in particular the scene where three of them are lying in hospital beds, having had their backs go out on them, and they start chanting, Mandelbaum!  Mandelbaum!  Mandelbaum!  You can see the scene over on YouTube, I'd embed it but it's been disabled, so you just have to click here,  It's an edited compilation of all of the Mandelbaum scenes (the character being played by Lloyd Bridges), and the chant comes in around 3:50 into the video, and again around 6:10 in an excerpt from the episode entitled "The Blood."  It's not much, but somehow that chant stuck in my memory...

And based on his accomplishments alone,  I do believe a group chant of Mandelbrot!  Mandelbrot!  Mandelbrot! would be in order,  but all the more so based on his TED talk, which I recently screened for the first time in my Introduction to New Media class at Fordham University, and what a marvelous presentation it is.  Not only did it illustrate and explain concepts I had just gone over in discussing chaos and complexity (and fractals), but Mandelbrot himself was absolutely charming and endearing!  Here's what it says on the TED site:

At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated. 
You can find the full transcript of the talk over on the TED page:  Benoit Mandelbrot: Fractals and the art of roughness.  And there's a short bio that reads

Benoit Mandelbrot is the pioneer of fractals, a broad and powerful tool in the study of many forms of roughness, in nature and in humanity's works -- including even art.
A link to a separate profile page reveals the following:

Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they'd been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets -- which make up, let's face it, quite a lot of the world. Mandelbrot coined the term "fractal" to describe these objects, and set about sharing his insight with the world.

The Mandelbrot set (expressed as z² + c) was named in Mandelbrot's honor by Adrien Douady and John H. Hubbard. Its boundary can be magnified infinitely and yet remain magnificently complicated, and its elegant shape made it a poster child for the popular understanding of fractals. Led by Mandelbrot's enthusiastic work, fractal math has brought new insight to the study of pretty much everything, from the behavior of stocks to the distribution of stars in the universe.

And there is a link for Professor Mandelbrot's home page at Yale University.

Anyway, here is the man himself:

To sum it all up, Mandelbrot shows us that order can emerge out of chaos, and that enormous complexity can be generated on the basis of a very simple rule or procedure, as it is repeated and reiterated over and over again.  That itself is the simply point behind the complexity of fractal mathematics, and the natural world that it corresponds to.

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