Musings On Mandelbrotian vs Gaussian Aspects of the Universe

(Image from: blogs.warwick.ac.uk)

In a previous blog entry, I mentioned how Nassim Nicholas Taleb's book, The Black Swan, made me angry as I read it, even though I agreed with it. I am just re-reading the real meat of the book, where the author contends that Gaussian distribution and the bell curve does a huge disservice to man. The world is not bell curve average, but rather Mandelbrotian, as in Benoit Mandelbrot's classical work on fractals.

I must admit that I am an early adopter of the ideas of Benoit Mandelbrot, and his epic book "The Fractal Geometry of Nature" has been in my personal library since 1985.

My mind keeps going over Taleb's ideas. At first I thought that he was thinking too deeply of a simply self-evident thing. After all, experts get to know more and more about less and less until they know everything about nothing. And then I thought that Taleb was capitalising on a meme that turns out to be an incredible moneymaker for him. And that is possibly true as well.

I had just read something that Taleb further refined his ideas such that anything dealing with gravity behaves in a Gaussian fashion and the exclusion set (which is everything else) is Mandelbrotian.

So on this fine morning on the first of November of this year, I have come up with some musings of Mandelbrotian vs Gaussian aspects of the world.

1) Suppose that you are a Gaussian dogmatist, and your Gaussian beliefs have a sort of high degree of correlation to the curve, as metaphorically depicted below in the modified graphic. Reality is the underlying fractal, and the red bell curve is how you believe the world works. There is enough of a degree of correlation to make it work for you except in three areas (the really dark blue areas behind the red line). But since you tend to ignore these areas and live in the Platonic fold, the curve is "good enough" for you.

The really big outlier is the area by the yellow arrow. This is the outlier that whipsaws you out of the market and makes you lose your retirement money. This is the outlier that puts you on the Air France flight that disappears over the ocean. This is the Black Swan.

BUT, can it really be an outlier or a Black Swan, or unpredictable, given the underlying fractal?

Can one know the underlying fractal geometry that caused that?

I was talking with a risk manager of the biggest bank in these islands after a rather nice dinner that the Lovely One cooked. It was Julia Child's recipe for Boeuf Bourgignon. He told me that he doesn't buy into Talib's ideas because the Gaussian curve works fine for him and the ultimate proof is that the bank makes money every day.

That got me to thinking. Can there be a quantum element whereby events in life have a duality of Gaussian and Mandelbrotian. Just like quantum physics where light behaves as a particle or a wave depending on how you measure it, can events in our histories be either Gaussian or Mandelbrotian? Can Richard Feynman's The Sum of All Histories be applied here?

I don't have the mental discipline today to think these things through, or to put some mathematical rigor behind them. I just let these thing roll around in my head. I would think some more about these things, but I have to go swim in the ocean. Maybe I will have a moment of clarity as I swim the half mile of surf today.

I hope that the Great Pumpkin visited you last night.