Tyler Cowen has a nice review in Slate (actually, a slice & summation) of Nassim Nicholas Taleb's most recent book, The Black Swan: The Impact of the Highly Improbable. Taleb's discursive and meandering narrative delves mostly into the domains of economics, statistics and psychology, so Cowen is in a good place to tackle his argument. Myself, I was intrigued by the jeremiad against the Gaussian and Poisson distributions. Like Michael Stastny I think Taleb goes a bit too far. Nevertheless, I have to wonder about the fact that though we model characteristics like IQ as a bell curved Gassian distribution, the tails are invariably fat. That is, beyond 2 or 3 standard deviations above or below the norm there start to be many more individual as an empirical matter who exhibit a particular value then the distribution would predict. One might make the case that in those north of 3 standard deviations are particularly important in shaping the path which our species takes through history. In evolutionary biology R.A. Fisher long promoted a gradualist paradigm predicated on the substitution of alleles of small effect which resulted in minimal deviation of a character's central tendency over a short period of time, but, as I have noted recent work implies that a large role maybe played by mutations of large effect. Veritable genetic "Black Swans." The eminent evolutionary geneticist James F. Crow told me last year that "...Nature seems to follow least-squares principles." Taleb would surely beg to differ, and no doubt emphasize the ubiquity of non-linearity and the enormous biological import of the rare anomalous deviation from the regression line.
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Taleb is best known as a brilliant options trader and theorist. He wrote the bible on Dynamic Hedging. (Trust me this book still gives me nightmares). And in that arena the distribution of short-term returns is definitely fat-tailed. I think it's colored his perceptions about everything else.
Reminds me a bit of Soros... has a similar tendency to universalize from finance to metaphysics. Enjoyed his earlier philosophical effort, "Fooled by Randomness" though. I'll read "Black Swan" sometime if my local city library gets it.
Benoit Mandelbrot, the fractal guy, wrote a very interesting book called "The (Mis)behavior of Markets". It's worth a look. It turns out that some of Mandelbrot's first developments of his ideas were in a discussion of cotton futures.
mandelbrot plays a big role in the black swan. in short, taleb believes that reality is more 'mandelbrotian than gaussian.'
Hmm, for scalar-valued characteristics, e.g. height, with single-peaked norms of reaction (at least to the more common factors) I'd expect the distribution to be lognormal rather than normal. Should be easy enough to test that hypothesis given raw data (e.g. compare Anderson-Darling test on original data versus log-transformed data). Lognormal gives a longer high tail with equivalent sigma.
Seems like this should be addressed in the literature - is it?
If IQ (or its measurement) is a complex trait (observation), a power-law relationship would presumably fatten the tails. (Which I presume Mandelbrot points to, as power-laws and fractals are related.) It would be interesting to see if that can be implied, or at least recovered, from genetics. Perhaps a subject for a post for laymen dummies?
OTOH statistics of tails is precarious.
Oh, and incidentally Cosma Shalizi has coauthored a paper on "statistical techniques for making accurate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic [and] how to tell whether the data follow a power-law distribution at all", and blogs about it.
Little Dickie Richard Silverstein is to Islamofascist terrorists and jihadis as Monica was to Bill!!