A few days ago, I finished reading *The Black Swan* by Nicholas Taleb, which goes in-depth on topics such as judgment under uncertainty and the issues relating to unrealistic models which deliberately ignore unlikely but possibly highly influential phenomena in order to stay simple. Taleb emphatically argues against the use of the Gaussian bell curve, or the GIF (“great intellectual fraud”), as he likes to call it, pointing out that it forecasts events several standard deviations from the norm as extremely unlikely. He points out that an event 4 SD away is twice as likely as 4.15 SD, and that “the precipitous decline in odds of encountering something is what allows you to ignore outliers. Only one curve can deliver this decline, and it is the bell curve (and its nonscalable siblings). Nassim instead expounds scalable “Mandelbrotian” curves, which, like all things Mandelbrotian, are fractal – The speed of the decrease of odds as one moves from the mean is constant, not declining. So the odds of having a net worth of over 8 million pounds is 1 in 4,000, for higher than 16 million pounds it’s one in 16,000, for 32 it’s 1 in 64,000, etc. So not only does the Mandelbrotian curve put more importance on outliers (“Black Swans”, or unpredictable but highly influential events such as stock market crashes that Gaussian models miss), but any small portion of the graph resembles the larger curve in a fractal sort of way.

## Black Swans, the “Ludic Fallacy”, and Bayesian inference

June 28, 2011
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