A black swan is an event that nobody expected, that changes a great deal, and that everybody explains afterwards. The phrase is a metaphor with a history, Nassim Taleb made it a term in 2007, and since then it has been used for almost every crisis. This chapter sorts the matter out: where the word comes from and what it requires, which events in history deserve it and for whom, the case of 11 September in detail, the mathematics behind the surprise, a test for your own event, and what a person or a firm can do about something that cannot be predicted.
For about sixteen hundred years the black swan was a figure of speech for something that does not exist. The Roman poet Juvenal, around the year 100, called a good wife a rare bird on earth, most like a black swan. Then, in January 1697, a Dutch expedition under Willem de Vlamingh sailed into a river in Western Australia and saw black swans on it. One sighting turned the proverb around: the sentence that all swans are white had been confirmed by every swan ever seen in Europe, and a single bird refuted it. This is the problem of induction, described by David Hume in 1748, illustrated with swans by John Stuart Mill in 1843 and made the centrepiece of Karl Popper's philosophy of science in 1934: no number of confirmations proves a general sentence, one counterexample breaks it.
Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable, 2007. An event is a black swan only if all three hold.
Nothing in the past pointed convincingly to its possibility. Not merely rare: it lay outside the range that the people concerned were considering at all.
A war, a crash, a technology, a pandemic. A rare event without consequences is a curiosity, not a black swan.
After the fact, people produce explanations that make it look predictable, even inevitable. This third property is the one most often forgotten, and it is the one that makes the other two so hard to see coming.
Taleb's own list of examples: the outbreak of the war of 1914, the rise of Hitler, the collapse of the Soviet Union, the spread of the internet, the crash of 1987, epidemics, fashions and art movements. Not all of them were bad; the internet was a black swan too.
The turkey's evidence, day by day. Every feeding raises its confidence that the farmer means well; the data have never been better than on the day before the last one. Schematic, after Taleb, who took the chicken from Bertrand Russell (1912).
A black swan is relative to the observer. For the turkey, day 1,001 is a black swan. For the farmer it is a date in the calendar. Nothing about the event itself decides which; what decides is who knew what. Keep that sentence for the third tab, because it answers the question who stages such events.
Since 2007 other animals have joined the black swan, each naming a different mix of foreseeability and size. Across: how foreseeable the event was. Up: how large its impact. Tap a number or a name for the definition. Positions are a way of ordering the terms, not a measurement.
The first misuse is inflation: every crisis gets called a black swan, which makes the term useless. Taleb himself refused it for the pandemic of 2020. In January 2020 he had co-written a note warning of the systemic risk of a new pathogen, and in March he said on television that Covid was a white swan, foreseeable and foreseen, which is why the failure to prepare was a choice. The second misuse is the excuse: the phrase is most popular with those who should have seen the event coming. The operator of Fukushima called the wave unforeseeable; its own engineers had calculated a wave of that height three years earlier. A bank's chief financial officer said in August 2007 that his models had seen twenty-five-standard-deviation moves several days in a row; the honest reading is not that the world had gone mad but that the model was wrong. Whenever somebody calls a loss a black swan, the first question is whether it was one for them, or only for their customers.
Which events in history were black swans? The honest answer is: for whom. The same day can be a plan for those who made it, a warning ignored for those who studied it, and a bolt from the blue for everybody else. The matrix below rates fourteen events for four observers. It is an assessment, not a measurement; the point is the pattern, not any single cell.
0 = expected or planned · 1 = warned, the signs were on the table · 2 = held improbable · 3 = unthinkable, outside what anyone considered. A dash means the column does not apply. Tap a row for what was known before and how it was explained afterwards.
Three things stand out. First, the column for experts is rarely dark: for almost every event somebody had described the possibility in writing, often years before. What was missing was not knowledge but imagination, attention or the will to pay for a precaution. Second, the column for those involved is light wherever the event was a decision: an embargo, an attack, an invasion. A black swan that somebody made is, for its makers, not a black swan. Third, the public column is dark almost throughout, and that is where the word lives. The only event in the list that was unthinkable for everybody, including the people who knew most, is the one that gave the term its name: the bird itself.
Can 11 September 2001 be a black swan? Taleb uses it as his opening example, and by his three criteria it is one: outside what almost anybody considered, enormous in its effects, and explained ever since. But the observer question applies here more sharply than anywhere. For the nineteen men on the planes and those who sent them it was a plan two years in the making. For the intelligence services it was a warning not acted on. For the public and the markets it was the black swan of the century. The same morning, three different animals.
Nineteen members of al-Qaida hijacked four airliners; two were flown into the towers of the World Trade Center, one into the Pentagon, the fourth crashed in Pennsylvania after passengers fought back. 2,977 people were killed. The plot had been brought to Osama bin Laden by Khalid Sheikh Mohammed in 1996 and approved in 1999. The public record consists of the 9/11 Commission Report of July 2004, the reports of the National Institute of Standards and Technology on the towers (2005) and on Building 7 (2008), the trials, and the intelligence files declassified since, most recently 71 documents released by the CIA on the twenty-fifth anniversary in September 2026.
Not a hidden history. Every item below was in the record before the day, most of it in public.
A bomb in the garage of the World Trade Center kills six. The organiser, Ramzi Yousef, is a nephew of Khalid Sheikh Mohammed.
Algerian hijackers seize Air France flight 8969; French authorities conclude they intended to bring the aircraft down over Paris. Special forces storm the plane in Marseille.
The Bojinka plot is uncovered in Manila: bombs on a dozen airliners, and, in the confession of one plotter, a plan to fly a plane into the headquarters of the CIA.
Al-Qaida bombs the American embassies in Nairobi and Dar es Salaam, 224 dead. Bin Laden is indicted. A CIA report of 10 September 1998, released only in 2026, says he intends to fly an aircraft loaded with explosives into an American city.
A report for the Library of Congress on the psychology of terrorism names, as a scenario, suicide pilots crashing an aircraft into the Pentagon, the CIA or the White House.
A boat bomb hits the destroyer USS Cole in Aden, seventeen dead.
The summer of warnings: the CIA director later said the system was blinking red, and at least eighteen presidential briefings that year mentioned bin Laden. In July an FBI agent in Phoenix asks whether al-Qaida is sending students to American flight schools. On 6 August the President's daily brief is titled Bin Ladin Determined To Strike in US and mentions preparations for hijackings. On 16 August Zacarias Moussaoui is arrested after a flight school in Minnesota grows suspicious of a student who wants to fly a jumbo jet.
The Commission's verdict of 2004: the most important failure was one of imagination. Aircraft as weapons had been imagined, hijackings had been imagined, al-Qaida in the country had been imagined; the combination had not been taken seriously enough to lock a cockpit door. Taleb's remark on this: had the risk been reasonably conceivable on 10 September, the attack would not have happened, and the official who had quietly made it impossible would never have been thanked.
Share naming al-Qaida and share naming the American government, 16,063 respondents in 17 countries, July and August 2008 (WorldPublicOpinion.org, University of Maryland). Across all 17 countries 7 per cent named Israel and one in four did not know. Turkey: 36 per cent named the American government; Egypt: 43 per cent named Israel; Jordan: 11 per cent al-Qaida, 31 per cent Israel.
In the United States, a Scripps Howard poll of 2006 found 36 per cent who thought it somewhat or very likely that federal officials had either taken part in the attacks or knowingly let them happen; a Zogby poll of 2007 found 4.8 per cent who believed the government had actively planned or assisted them. The distance between the two figures is the distance between suspicion of a cover-up and belief in staging.
Nineteen identified hijackers, their training and travel, the money trail, the planners' own claims of responsibility, the Commission's report, the NIST investigations of the collapses, and thousands of pages of intelligence released since, including the 28 pages on Saudi contacts in 2016. Where the record has gaps, they concern who helped from outside and what the agencies missed, not who flew the planes.
The theories run from the government knowingly standing aside to the towers being brought down with explosives, Building 7 being the usual exhibit. A study at the University of Alaska Fairbanks (2020), financed by a group of the theory's supporters, concluded that fire alone could not have collapsed Building 7; it stands against the NIST investigation and has not changed the assessment of the engineering profession.
No explosive residue, no witnesses to a demolition, no document, no participant in twenty-five years, in the one country where such a secret would have had the most people able to sell it. What the theories do have is a motive: the wars, the Patriot Act, the security budgets. Benefit is not authorship. That a fire brigade grows after a fire does not mean it lit the fire.
Three mechanisms, each measured. Proportionality bias: people expect big events to have big causes, and nineteen men with box cutters feel too small an explanation for the fall of two towers (Leman and Cinnirella, 2007). The narrative fallacy, Taleb's third criterion at work: once the outcome is known, the mind assembles the warnings into a story in which somebody must have known, and then into one in which somebody must have wanted. Hindsight bias: after the event, people remember having judged it more likely than they did (Fischhoff, 1975), so the failure to prevent it looks like a decision. Add the observer rule from the first tab: the event was in fact planned, by somebody; the argument is only about by whom. That is why the question who stages black swans has a precise answer. Nobody stages a black swan. Whoever stages an event has a plan; for everybody else the same event may be a black swan. Surprise is therefore no evidence of staging in either direction. What counts is what a staging leaves behind, and history shows what that looks like.
The category exists. These are the cases with archives, participants or official studies behind them.
Officers of Japan's Kwantung Army blow up a stretch of their own railway near Mukden and blame Chinese troops; the pretext for the occupation of Manchuria. Admitted by participants after the war and established at the Tokyo trials.
The fire of 27 February gave the new government the emergency decree that ended civil liberties. Whether Marinus van der Lubbe acted alone or with help from the regime is still disputed among historians; the use made of the fire is not.
On 31 August SS men in Polish uniforms stage an attack on the German radio station at Gleiwitz; the next morning Germany invades Poland. Described by the SS officer in charge at Nuremberg in 1945.
The American Joint Chiefs of Staff propose staged attacks, including on their own citizens, to justify an invasion of Cuba. Rejected by the Kennedy administration; the document was declassified in 1997. The proposal is real, the operation never happened.
The clash of 2 August was real; the second attack reported for 4 August did not happen. The intelligence was presented, an NSA historian concluded in a study declassified in 2005, so as to keep decision makers from the complete picture. Congress passed the resolution that opened the Vietnam War on 7 August. McNamara in 2003: it did not happen.
A state stages a small event as the pretext for a large decision already taken; the staging is exposed within years by archives, trials or its own participants; and the event was never a black swan for its authors, only for its audience. None of the cases required a secret held by thousands for decades, and none involved the state attacking its own capital with its own aircraft.
Why are we surprised so often by events that, taken together, are not rare at all? Because most of our tools assume a world in which extremes are impossible. Taleb divides the world into two provinces. In Mediocristan, quantities are bounded and no single observation changes the total: heights, weights, calories. In Extremistan, one observation can dwarf all the others: wealth, book sales, city sizes, war deaths, market moves. The bell curve is at home in the first province and a stranger in the second.
Height, weight, the yield of a field, a baker's daily takings.
Add one person to a thousand and the average barely moves; the tallest man ever was under three metres.
The bell curve works; a five-sigma event is a once-in-history event.
Wealth, city sizes, book sales, pandemics, wars, daily market returns.
Add one person to a thousand and, if it is the right person, the average doubles.
Fat tails: the extreme is not rare, it is the part that matters, and the past underestimates it.
Two distributions with the same width: the normal curve (dashed) and a Student t distribution whose tail thickness you set with the slider. Small ν means fat tails; above 30 the two are nearly identical. Empirical studies put daily stock returns near ν ≈ 3 (Gabaix and others, 2003). Model, not data.
Only the tail, from 3σ outwards, on its own scale. This is where the two worlds part.
On 19 October 1987 the Dow Jones fell 22.6 per cent in one session and the S&P 500 20.5 per cent. With a usual daily swing of about one per cent that is a move of roughly twenty standard deviations, which under the bell curve should occur less than once in the lifetime of the universe. On 16 March 2020 the S&P 500 fell 12 per cent, a twelve-sigma day by the same measure. In August 2007 the chief financial officer of Goldman Sachs told the Financial Times that his firm had seen twenty-five-standard-deviation moves several days in a row. None of these days was impossible; the model that called them impossible was wrong. Under fat tails with ν near 3, a five-sigma day comes round about once a year, and the tiles above show the arithmetic for the tail you have set.
Five conditions under which the tail grows. None of them requires anybody to plan anything.
Wherever one unit can serve millions at no extra cost, outcomes concentrate: a book, a song, a platform, a virus. The winner takes almost everything, and the average tells you nothing about the next case.
Charles Perrow's normal accidents: in systems that are both complex and tightly coupled, small failures interact in ways nobody designed, and the accident is a property of the system, not of any operator. Three Mile Island, Chernobyl, a supply chain with one canal.
Strategies that earn a little every day and lose everything once, picking up pennies in front of a steamroller, look excellent for years. The loss is not improbable; it is deferred, and the record of the good years is the evidence for the turkey.
Hyman Minsky's rule: stability breeds instability. Every quiet year lowers the price of risk and raises the debt taken on against it, until a small shock is enough. The Minsky moment is the turkey's day 1,001 for an economy.
One strait for a fifth of the world's oil, one canal for a tenth of its trade, one island for most of its advanced chips, one supplier for a firm's key part. Efficiency removes the redundancy that would have made the shock a nuisance instead of an event.
Whether the frequency of black swans has grown is not settled. Systems are more connected than in 1900, which favours cascades; they are also better measured, which favours warnings. Both are true at once, and the chapter takes no side.
The two questions that get confused in the word: whether somebody decided the event, and whether the rest of us saw it coming. Placement by assessment.
An announced war, a rate decision, a referendum with the polls at fifty-fifty. Decisions by actors, and no surprise to anyone who watched.
11 September for the public, the oil embargo of 1973, 24 February 2022 for most of Europe. A plan for the makers, a black swan for everybody else. This is the only cell in which the word staged has a meaning.
The wave at Fukushima, the mortgage crisis for those who read the numbers, a pandemic for epidemiologists. Nobody decided them, and the warnings were on file: grey rhinos.
The crash of 1987, the swan of 1697, a new technology, an asteroid. Nobody made it and nobody saw it. The black swan in the strict sense.
Take an event that hit you, your firm or your country: a lost customer, a burst pipe, a lockdown, a competitor that appeared from nowhere. Four questions decide which animal it was, and the last of them decides for whom. The sliders describe your view before the event; the answers say whether it was a black swan for you, and whether it was one for anybody.
Answer as you would have on the day before, not as you would today.
Your event as a dot among the animals of the first tab. Foreseeability is the mirror of the first slider; impact is the second.
The first two sliders are Taleb's first two criteria. The third is his third, and it is a trap: the higher you set it, the more likely you are looking at the event through the story written afterwards, which is why the test asks for your view of the day before. The fourth slider is the observer question. An event can be unthinkable for you and well documented for others; then it was a black swan for you and a grey rhino for them, and the useful lesson is not that the world is random but that you were not reading the right pages. Only when the fourth slider stays low, when nobody had described it, is it a black swan for everybody. Those are rarer than the word suggests, and the chronicle in the second tab has exactly one.
A black swan cannot be predicted; that is its definition. What can be shaped is what it finds when it arrives. Taleb's advice is not to forecast better but to become less fragile, and his measure of fragility is simple: does a larger shock hurt more than proportionally, or less? The chart shows the three shapes, and the rules below are the ones that follow from them.
Gain or loss against the size of a disturbance, schematic after Taleb (Antifragile, 2012). Fragile: losses accelerate. Robust: losses stay small and linear. Antifragile: small shocks cost a little, large variation pays. Move the slider to compare the three at one shock size.
Forecasts of rare events fail by construction; the exposure to them can be measured. The question is not what will happen but what happens to you if it does. A firm that survives a 40 per cent drop in revenue for a year need not know which crisis will cause it.
Taleb's strategy: put most of what you have in things that cannot ruin you and a small part in things with unlimited upside, and nothing in the middle, where the risk is hidden and the reward is modest. Ninety per cent boring, ten per cent bold, zero per cent clever.
Nature gives you two kidneys. Every spare part, second supplier, cash reserve and idle capacity looks like waste in the good years and is the whole difference in the bad one. Optimisation removes exactly the slack that absorbs the shock.
Keep the right, not the obligation, to act: short contracts, reversible decisions, small experiments. An option gains from variation; a commitment loses from it. Whoever holds options is the one for whom the unexpected can be good news.
Before a decision, assume it has failed a year later and write the story of how (Gary Klein, 2007). Then let somebody whose job it is argue the other side. Neither finds black swans; both find the grey rhinos that were going to be called black swans afterwards.
Most of the damage in the chronicle came from events somebody had described. The cheapest precaution is to ask, once a year, which warnings on file you have decided not to read, and what it would cost to be wrong about each.
Prevention is invisible. The official who had made cockpit doors bulletproof in 2000 would have been remembered, if at all, as the one who cost the airlines money for nothing; the black swan he prevented would never have existed. That is why precaution is underpaid and forecasting overpaid, and why the person who warns is unpopular before the event and forgotten after it. For a firm the sum is the same as for a household: insurance against the tail costs a little every year and looks foolish in every year in which nothing happens. The funds that hedge tails report small losses in almost every month and very large gains in the crash month; the choice is not between paying and not paying but between paying a premium and paying the loss. And the last rule is the observer rule of the first tab, turned into practice. If an event that ruined you was a plan for somebody else, the lesson is not about chance. It is about who you were depending on, and what they knew that you did not.
The terms used in this chapter, each with the year and the person they come from where there is one.
An event that lies outside regular expectations, has an extreme impact, and is explained afterwards as if it had been predictable. Relative to the observer: a black swan for the turkey, a date for the farmer.
A rare event that is known to be possible and can be roughly modelled: earthquakes, pandemics, market crashes. Taleb's Mandelbrotian grey swan; not unthinkable, only underestimated.
An event that was foreseeable and foreseen. Taleb's word for the pandemic of 2020.
Michele Wucker's term for a highly probable, high-impact threat that is visible, charging, and neglected: the wave at Fukushima, the mortgage numbers of 2007, the pandemic exercises of 2019.
A cross between a black swan and the elephant in the room: an event predicted by experts, widely ignored, and treated as a black swan after it happens.
Didier Sornette's outliers beyond the power law: extreme events produced by a mechanism, a bubble or a phase transition, whose build-up can be diagnosed in advance. Where a black swan is blind chance, a dragon king has a signature.
Laurence Siegel's answer to the banks of 2008: an event that is everywhere in the data, to which one is wilfully blind. Not a black swan but a turkey that did not look up.
The two provinces: where no single observation changes the total, and where one observation can dwarf all the others. The bell curve belongs to the first; most of economic and social life to the second.
Distributions in which extreme values are far more frequent than the bell curve allows. Daily stock returns have a tail exponent near three: a move of ten standard deviations is not a once-in-the-universe event but a once-in-a-decade one.
No number of confirming observations proves a general statement; one counterexample refutes it. All swans are white, until one is not.
The habit of binding facts into a story with a cause, because a story is easier to remember than a list. The story arrives after the event and makes it look inevitable.
Once the outcome is known, people remember having thought it more likely than they did. The experimental basis of the third criterion.
The expectation that a big event needs a big cause. In their experiment, the same assassination attempt drew more conspiracy explanations when the victim died than when he survived.
Treating the uncertainty of life like the uncertainty of a casino, where the rules and the odds are known. The dice have known faces; the world does not.
What we do not see because it did not survive to be counted: the failed firms, the drowned sailors who also prayed, the crises that were prevented. The record overstates success and understates prevention.
An accident that follows from the structure of a complex, tightly coupled system rather than from any single error. Adding safety devices can add coupling and make it likelier.
The point at which a long period of stability, having encouraged ever more debt, turns into a sudden collapse of asset prices. Named by Paul McCulley for the Russian crisis of 1998; the theory is Hyman Minsky's.
Antifragile: gaining from disorder, the opposite of fragile rather than merely robust. Barbell: most of one's exposure in the very safe, a little in the very bold, nothing in the middle.
An operation carried out so that it appears to come from another party; from ships sailing under another nation's colours. Mukden, Gleiwitz and the second Tonkin incident are the documented cases; the term is also applied, without evidence, to almost every shock since.