I saw a Guardian Weekly review of The Black Swan by Nassim Nicholas Taleb which mentioned Taleb's reverence of Mandelbrot, thus leading me to purchase and read the book — ok, I read some, I skimmed some. :)
The central thesis is that wildly unexpected events occur, in finance and elsewhere, more frequently than suggested by a Gaussian or Normal distribution. In fact markets and many other phenomena are better described by power laws. Both Gaussian and Power Law distributions have long tails, but the tail of a power law distribution is fatter further out. That's what makes sales of books and other media on "the long tail" so profitable for Amazon.
Here's a quote from the author:
The Black Swan is about these unexpected events that end up controlling our lives, the world, the economy, history, everything. Before they happen we consider them close to impossible; after they happen we think that they were predictable and partake of a larger scheme. They are rare, but their impact is monstrous. My main problem is: Why we don't know that these events play such a large role. Why are we blind to them?
It's a book of anecdotes and we've all heard "the plural of anecdote is not data" but while a cute phrase, it's a faulty argument and furthermore there is data for financial markets and long tail markets. For an accessible version of the mathematics, read the Mandelbrot book I discussed in this post. But as a book of anecdotes, The Black Swan is a pleasant read and Taleb's primary point is well taken.