Benoît Mandelbrot passed away from a pancreatic cancer, across the river here, in Cambridge on Friday. He was 85 and survived by his wife and two sons, one in Newton and one in Paris.
Nassim Taleb shut down his website in honor of his teacher and left this one aphorism: “Benoit Mandelbrot, 1924-2010 – A Greek among Romans”. With all due respect to Taleb, Benoît Mandelbrot was a Jew among Greeks, or actually a Jew among Jews. A litvak who was born in Warsaw, Mandelbrot grew up in Paris. I am already hearing comparisons between Mandelbrot and Einstein, and just like the people who make similar comparison between the Rogachever and Einstein, as a rule they have no first hand knowledge of either.
I am way out of my depth here but I want to highlight one aspect of his legacy. Benoît Mandelbrot maintains (1999 article) that his fractal geometry can map the price fluctuations in the stock market and specifically accounts for the extreme events. Hence it’s a better description for the market inherently prone to crashes. This view came to prominence after the dotcom crash and again during this recession. The view is in opposition to the formula driven economists who created the commonly used on Wall St. quantitative tools. In the opinion of Taleb and Mandelbrot these tools don’t properly account for the risk and hence actually lead to crashes. This is why Taleb is indignant that they and not Mandelbrot gotten all the Nobels. The entire “black swan” metaphor is used by Taleb to illustrate his teacher’s ideas about the inevitability of the extreme events.
The two distinct philosophical views. On one hand is the view that the extreme events are the “acts of God”, the aberrations and can be ignored statistically and philosophically. On the other hand is the view that the extreme events are inevitable and far more consequential than the “normal conditions”.
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From the perspective of probability, extreme events are likely and expected (see the Birthday Paradox). There is also a whole field of mathematics called “extreme value theory”, which looks at extreme events.
I don’t understand the theoretical component of the argument but I think Taleb and Mandelbrot are opposed to the very idea that you can quantify risk accurately.