Nicholas Naseem Taleb’s book Fooled by Randomness argued that there is a human tendency to recognise false patterns and attribute causes in random processes.  The style was informed by a wide range of reading, full of anecdotes, irretrievably opinionated.  You would expect the war stories and the strength of views, from a trader and hedge fund manager, but not the erudition.

       Taleb’s new book develops a theme from that earlier book.  Everyone substantially underestimates the significance of extreme events in contemplating the future.  Taleb calls these extreme events black swans, not imagined till they are seen.

       Taleb writes of two worlds:  Mediocristan and Extremistan.  The mathematics of Mediocristan is the algebra of classical statistics and probability theory.  Distributions are normal, curves are bell-shaped.  A carpet looks like a brush if you lie face down on it, with every tuft distinguishable and of different length;  at a distance, a carpet looks like – well, a carpet.  Individual variation averages out.

       The mathematics of Extremistan is the fractal geometry described by Benoit Mandelbrot.  Distributions follow a power law. 

The pictorial representation of Extremistan is a rugged landscape looks rugged whether you see it close up, or from a distance, just as a snowflake which has the same shape whatever the degree of magnification.

       The law of large numbers applies in Mediocristan.  No single event matters, only accumulations and agglomerations.  But in Extremistan every observation can make a large difference to the overall outcome.  For risk analysis, it matters a lot whether you are in Mediocristan, the province of standard statistics texts, or Extremistan, the territory of newer theories associated with chaos and complexity. 

Taleb claims that there are too many extreme events in securities markets for such markets to be located in Mediocristan.  The black swan of October 1987, when the Dow Jones index fell by around 20% was the first trigger for his personal reassessment. The event was simply outside the realms of possibility in classical statistics.

       Taleb would first substitute power laws and the mathematics of extreme statistics for the reassurance of normal distributions.  But this still gives more credence to economists and financial analysts than he will allow.  Probabilities can only be defined, predictions can only be made, if the events that are the subject of the probabilities and predictions can be described.  Donald Rumsfeld’s famously distinguished known unknowns and unknown unknowns.  Statistics, old and new, deals with known unknowns.  Taleb’s world is determined by unknown unknowns – black swans.

       No-one, he explains, can predict the invention of the wheel, or measure the probability that the wheel will be invented, because if you could do either of these things you would already have invented the wheel. The invention of the wheel was a black swan and through black swans the world has progressed. 

It is simply meaningless to ask what was, on September 10, the probability that the events of September 11 would occur.  Meaningless because knowledge of such possible events would dramatically affect the likelihood that they would occur:  meaningless because the probability that the exact sequence of events that took place the following day would occur is, like the probability of any particular and specific historic sequence of events, vanishingly small.  The best we might do is ask what the probability of an incident like 9/11 would be: but that question immediately dissolves into a fruitless discussion of what is meant by like.

       9/11 was a one-off event, never to be repeated, yet followed, often, by other black swans.  And these black swans defy prediction. Taleb laughs at a correspondent who, impressed by the argument, asks what are the ten most likely black swans?   To pose the question is completely to miss the point.

       Taleb does not only live in Extremistan when it comes to statistics.  With few exceptions, the writers he quotes, the fellow professionals he describes, are either knaves or fools, and mostly fools.  Taleb’s writing is self-indulgent – full of irrelevances, asides, and colloquialisms: the book reads like the conversation of a voluble raconteur rather than a tightly argued thesis.  But it is hugely enjoyable, compelling to read at one sitting, yet easy to dip into: there are stimulating, and often original, observations –  generally well taken – are to be found on every page.

       Yet beneath Taleb’s rage and his mockery are deadly serious issues.  The risk management models in widespread use today exclude, essentially by design, the very events against which they claim to protect the businesses that employ them.  These models import a spurious veneer of technical sophistication, the result of the simultaneous development of modern finance theory and information technology.  Quantitative analysts have lulled regulators and corporate executives into an illusory sense of security.  Beware the black swan.