Nassim Nicholas Taleb uses the term Black Swan to identify significant unexpected events. Holling made some similar points from a different perspective in his 1973 paper on resilience and his 1986 paper the resilience of terrestrial ecosystems; local surprise and global change. In on the interdisciplinary Edge Taleb writes on Learning to expect the unexpected and defines what he means by Black Swans:

A black swan is an outlier, an event that lies beyond the realm of normal expectations. Most people expect all swans to be white because that’s what their experience tells them; a black swan is by definition a surprise. Nevertheless, people tend to concoct explanations for them after the fact, which makes them appear more predictable, and less random, than they are. Our minds are designed to retain, for efficient storage, past information that fits into a compressed narrative. This distortion, called the hindsight bias, prevents us from adequately learning from the past.

From my perspective, Black swans occur when there are significant mismatches between the models people use to understand the world and the subsquent expectations that those models produce and observations. In other words, black swans are model errors – something that I’ve written (Peterson, Carpetner & Brock et al 2003) in the context of ecological management.

In Wired Magazine article Black Swans: expect the unexpected economic writer James Surowiecki talks to Nassim Nicholas Taleb.

From Wall Street to Washington, we’re constantly being told that the future can be forecast, that the world is knowable, and that risk can be measured and managed. Nassim Nicholas Taleb is having none of this. In his new book, The Black Swan, the finance guru and author of the surprise hit Fooled by Randomness argues that history is dominated not by the predictable but by the highly improbable — disruptive, unforeseeable events that Taleb calls Black Swans. The effects of wars, market crashes, and radical technological innovations are magnified precisely because they confound our expectations of the universe as an orderly place. In a world of Black Swans, the first step is understanding just how much we will never understand.—

Wired: If Black Swans are the crucial determining events in history, why do we think we can predict anything at all?
Taleb: After they happen, in retrospect, we think that Black Swans were predictable. We think that if we can explain why something happened in the past, we can explain what will happen in the future.

But with better models and more computational power, won’t we get better at predicting Black Swans?
We know from chaos theory that even if you had a perfect model of the world, you’d need infinite precision in order to predict future events. With sociopolitical or economic phenomena, we don’t have anything like that. And things are getting worse, not better, because the growing complexity of the world dwarfs any improvement in sophistication or computational power.

So what do we do? If we can’t forecast the really important things, how do we act?
You need to ask, “If the Black Swan hits me, will it help me or hurt me?” You cannot figure out the probability of a Black Swan hitting. But if you’re in a business that’s prone to negative Black Swans, like catastrophe insurance, I advise you not to take your forecasting seriously — and to think about getting into a different business. You don’t want to be a sucker. What you want are situations where you can have as much of the good uncertainty as possible, where nothing too bad can happen to you, and where you have what I call free options. All of technology, really, is about maximizing free options. It’s like venture capital: Most of the money you make is from things you weren’t looking for. But you find them only if you search.

Nassim Nicholas Taleb was also profiled by Malcolm Gladwell in the New Yorker in 2002 . There his work at his trading firm describes how his trading focuses on the fat tails of probability distributions:

Nassim Taleb and his team at Empirica are quants. But they reject the quant orthodoxy, because they don’t believe that things like the stock market behave in the way that physical phenomena like mortality statistics do. Physical events, whether death rates or poker games, are the predictable function of a limited and stable set of factors, and tend to follow what statisticians call a “normal distribution,” a bell curve. But do the ups and downs of the market follow a bell curve? The economist Eugene Fama once studied stock prices and pointed out that if they followed a normal distribution you’d expect a really big jump, what he specified as a movement five standard deviations from the mean, once every seven thousand years. In fact, jumps of that magnitude happen in the stock market every three or four years, because investors don’t behave with any kind of statistical orderliness. They change their mind. They do stupid things. They copy each other. They panic. Fama concluded that if you charted the ups and downs of the stock market the graph would have a “fat tail,”meaning that at the upper and lower ends of the distribution there would be many more outlying events than statisticians used to modelling the physical world would have imagined.

In the summer of 1997, Taleb predicted that hedge funds like Long Term Capital Management were headed for trouble, because they did not understand this notion of fat tails. Just a year later, L.T.C.M. sold an extraordinary number of options, because its computer models told it that the markets ought to be calming down. And what happened? The Russian government defaulted on its bonds; the markets went crazy; and in a matter of weeks L.T.C.M. was finished. Spitznagel, Taleb’s head trader, says that he recently heard one of the former top executives of L.T.C.M. give a lecture in which he defended the gamble that the fund had made. “What he said was, Look, when I drive home every night in the fall I see all these leaves scattered around the base of the trees,?” Spitznagel recounts. “There is a statistical distribution that governs the way they fall, and I can be pretty accurate in figuring out what that distribution is going to be. But one day I came home and the leaves were in little piles. Does that falsify my theory that there are statistical rules governing how leaves fall? No. It was a man-made event.” In other words, the Russians, by defaulting on their bonds, did something that they were not supposed to do, a once-in-a-lifetime, rule-breaking event. But this, to Taleb, is just the point: in the markets, unlike in the physical universe, the rules of the game can be changed. Central banks can decide to default on government-backed securities.

According to the article, a simplified version of Taleb’s trading strategy is based on expecting the unexpected – betting that the markets underestimates extreme events – and being resilience to catastrophe. Gladwell’s article continues:

Taleb likes to quote David Hume: “No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion.” Because L.T.C.M. had never seen a black swan in Russia, it thought no Russian black swans existed. Taleb, by contrast, has constructed a trading philosophy predicated entirely on the existence of black swans. on the possibility of some random, unexpected event sweeping the markets. He never sells options, then. He only buys them. He’s never the one who can lose a great deal of money if G.M. stock suddenly plunges. Nor does he ever bet on the market moving in one direction or another. That would require Taleb to assume that he understands the market, and he doesn’t. He hasn’t Warren Buffett’s confidence. So he buys options on both sides, on the possibility of the market moving both up and down. And he doesn’t bet on minor fluctuations in the market. Why bother? If everyone else is vastly underestimating the possibility of rare events, then an option on G.M. at, say, forty dollars is going to be undervalued. So Taleb buys out-of-the-money options by the truckload.