Stewart Brand

Taleb seems oddly innocent of "power law" behavior, in which Black Swans hold a much different position than "outlier," "tail," etc.—all Bell Curve denotations. In power law phenomena, nothing is far from typical, because nothing whatever is typical.

The violence/incident of terrorist incidents can be charted on a power law curve, not a Bell curve.

STEWART BRAND is cofounder and co-chairman of The Long Now Foundation and author of How Buildings Learn, and The Clock of the Long Now.

Nassim Taleb

Reply to Stewart Brand

I agree that, if we used the right distribution, nothing would be a Black Swan, but the inference about "power laws" is misguided, and I would like to go a little deeper into the discussion. Also, a "power law" is another name for what I referred to as Pareto's distribution in my discussion.

Black Swans come from an unexpected outcome conditional on the framework of analysis used, meaning one may be using the "wrong distribution". It is an epistemological problem. The right distribution can be: a) Any distribution for which we may not have had a sufficient sample to know the parameters (this can easily apply to some members of the Gaussian family, such as a Poisson process); b) A type-2 distribution, one for which there are no defined properties or "typical deviations". One brand of these was first proposed by Wilfredo Pareto with his power law. He made us conscious of such intractability, but we should be warned against blindly using his distribution to define intractable processes: most power laws can deliver a "typical" deviation (and are not type-2) ˆonly a few power laws, those with a specific parametrization (where the power exponent is lower than 2), belong to "wild" uncertainty.

Those who specialise in the statistical properties of large deviations and in their epistemology find it preferable to avoid the casual (and now journalistic) designation "power law" to characterize all manner of fat-tailed processes, particularly those for which we do not have ample sample size. We are experiencing enormous difficulties characterizing those, let alone calibrating them from nonphysical processes. The use of "power laws" for historical events (particularly terrorism) is a gross simplification: history is far more difficult to characterize than a collection of sandpiles; historical knowledge is not verifiable by experiments. As a skeptical empiricist I find it is far preferable to just plead ignorance in these situations and say "I don't know the distribution".

NASSIM TALEB, an essayist and mathematical trader who studies large-impact hard-to-predict rare events ("Black Swans") is the author of Fooled by Randomness.