BLACK SWANS 42

This essay is based on the 2007 book The Black Swan: The Impact of the Highly Improbable by Nassim Nicholas Taleb (1960 - ). It is hardly an obscure tome, having been on the New York Times bestseller list for several weeks. Before I get to the essence of this essay I believe explaining what the term “Black Swan” means and saying a few words about the author would be in order.

It was once thought in the Old World that only white swans existed. Then from Australia came the realization that there were black swans. And no, they were not white swans made black by bootblack or any other artificial coloring medium. After millennia of observations in the West of millions of white swans, the sighting of one black swan was enough to invalidate this long and firmly held belief. In a broader sense then A Black Swan is a sudden, monumental, and completely unexpected event. WWI, WWII, and 9/11 were Black Swans. If one were to win a multi-million dollars lottery that would be a personal Black Swan (Black Swans are not all negative, although given the troubles experienced by some of these huge lottery winners, this might also be negative).

But a Black Swan is more than this – it goes to the heart of and challenges the putative acceptance of Gaussian probabilities. Least you think Gaussian or bell shaped probability functions are theoretical only and not important in real life, then consider that not only mathematics, but engineering, medicine, social sciences, economomics, the insurance industry, Wall Street, and other fields of science and the arts use Gaussian probabilities in their calculations and predictions. I will get much deeper into this later in the essay.

Nassim Nicholas Taleb is an odd name to the Western ear. In fact he grew up in a family from the Greco-Syrian community from what was the last Byzantine outpost in northern Syria and which was incorporated into the country of Lebanon after the fall of the Ottoman Empire. This part of the Middle East was relatively stable until the last quarter of the 20th century. The mosaic of cultures and religions in this region consisted of Christians of all varieties – Maronites (The father of the reputed richest man in the world, Mexican Carlos Slim Helú, was a Maronite Christian who emigrated from Lebanon to Mexico), Armenians, Greco-Syrian Byzantine Orthodox, Byzantine Catholics, in addition to a few Roman Catholics left over from the Crusades; Muslims (Shiites and Sunnis); Druzes; and a few Jews. The Taleb family had been successful for generations. On his mother’s side both his grandfather and great-grandfather were deputy prime ministers of Lebanon and on his father’s side (his father was an oncologist) his grandfather was a Supreme Court Justice. In 1861 his four times great grandfather was a governor of the Ottoman semi-autonomous province of Mount Lebanon.

The Civil War between Christians and Muslims which began in 1975 came completely out of the blue and, although Taleb did not realize it at the time, would later contribute to his philosophy of the Black Swan. At that time people would say with seeming confidence that the war would last at most just a few weeks. It went on for 15 years.

Taleb holds an MBA from the Wharton School at the University of Pennsylvania and a Ph.D in management science from the University of Paris.

It is difficult to define the métier of Taleb. Clearly he is a polymath. He has worked as a securities analysis on Wall Street, a Visiting Professor of Marketing at the London Business School, the Dean’s Professor in the Sciences of Uncertainty at the Isenberg School of Management at the University of Massachusetts Amherst, Adjunct Professor of Mathematics at the Courant Institute of New York University, and affiliated faculty member at the Wharton Business School Financial Institutions Center. He previously authored a best selling book titled Fooled by Randomness which has been published in 20 languages.

Predicting the future based upon the past is universally done, yet there are pitfalls in this. Consider the turkey which has been fed for 1000 consecutive days. This avian creature has no logical reason to believe this pattern will not continue indefinitely. Think of the surprise awaiting the hapless bird when on Wednesday, day 1001, the process starts for making the turkey the center of attraction for the feast the next day. Sacre blu!

Explaining historical events in hindsight is facile and far from convincing since, for the most part, nobody could or does predict what eventually unfolds beforehand. In a very general way there may be some basis for assigning cause and effect to certain events. One may reasonably hold that the Franco-Prussian War of 1870 contributed to WWI which in turn led to WWII. The Prussians won that 1870 war, temporarily occupied Paris, extracted a billion dollars in reparations, and expropriated previously held French territory. After being on the winning side of WWI, the French imposed onerous conditions on the Germans at least partially because of what happened to them in 1870. In WWII the Germans reacted to what had happened to them after WWI with a fury that was unjustified, to say the least, yet without the dour economic conditions which occurred in Germany after WWI, WWII may not have happened.

Even so, after the Napoleonic conflicts, except for the 1870 Franco-Prussian casus belli, the European continent experienced a period of peace that would belie any anticipation of the carnage that would result in WWI, The Great War of 1914-19, that would be the deadliest conflict, until then, in the history of mankind.

In the summer of 1982 large American banks lost many billions of dollars as countries in South and Central America defaulted at the same time on loans made by these banks. The early 1990’s brought the now defunct savings and loan industry meltdown which required a taxpayer funded bailout of close to half a trillion dollars. Now in 2007 it is the turn of the home mortgage lenders and lendees in what is called the “sub-prime” market, to require many billions of dollars in another bailout. There are obviously serious problems with standard Gaussian risk assessment tools employed by the people in these industries.

With the following example many people would get it wrong: A town has one large hospital and one small one. On a given day in one of the hospitals 60% of the births were boys. Which one was it likely to be? The correct answer is that the smaller hospital would more likely have the bigger difference in parity of births because the sampling would more likely be smaller and therefore more prone to deviate from the average.

An acronym used in medical literature is NED (No Evidence of Disease). There is no such thing as END (Evidence of No Disease), yet Taleb related that during a routine cancer examination he was told by the doctor that “There is evidence of no cancer.” When Taleb asked him how he knew he said, “The scan is negative.” I have never heard a scientist or even a medical doctor make a claim that observational absence of something was evidence that it did not exist, yet who am I to say that Taleb remembered incorrectly?

We see the obvious and visible consequences of certain actions, not invisible and less obvious ones. When Islamic terrorists flew two airplanes into the Twin Towers of the World Trade Center, flew an airplane into the Pentagon, and caused an airplane to crashed in Pennsylvania, approximately 3000 people died. In the final three months or so of that year an estimated 1000 people also died as a result of the terrorist attack. How so? These were the people who, out of fear of flying, chose to drive on the country’s highways and because of the much higher mortality rate versus flying became additional casualties.

There are drugs which can prolong people’s lives, yet occasionally someone will have a fatal reaction to that drug. When this risk is known will doctors still prescribe this drug to their patients? Many will not because of the threat of lawsuits by the few thereby claiming invisible victims for the many.

A coin which we are told is “fair”, that is to say, it has an equal probability of either being heads or tails, is flipped and comes up heads 99 times in a row. What is the probability of it being heads on the 100th flip? Theoretically the odds would be 50%, but what would the practical answer be? Given that the coin has come up the same 99 times in a row it would be far more likely that the given initial conditions are wrong, i.e. the coin is not “fair” and therefore the probability of it being heads again is far more likely.

Three relatively recent technologies that have had the most impact on the world today are the computer, the internet, and the laser. They were all unpredicted, unplanned, and unappreciated – they were all Black Swans. In fact, in terms of their anticipation and utility, almost all of the great discoveries in the world were Black Swans. Occasionally there is a discovery which was predicted, although its use not even close to being fully realized. After the invention of the wireless (radio), in 1908 someone predicted that people would be able to carry around a device, a portable telephone, to communicate with each other over wide ranges of distances. That was remarkable insight given that earth satellites and microwave towers were not even dreamed of. It was the rare exception. It was what might be called a White Swan.

In 1928 Alexander Fleming noticed that one of his bacteria plates which had been contaminated with a mold had the odd effect of clearing a zone around itself in which the bacteria did not grow. He assigned so little importance to it that he turned to the then popular investigation of sulfa as an anti-bacterial drug. It wasn’t until years later that Fleming got interested in the strange properties of the mold. He received the Nobel Prize for medicine in 1945 for his contribution in the discovery of penicillin.

One of philospher Karl Popper’s central insights is that in order to predict historical events you need to anticipate technological innovation which is fundamentally unpredictable.

Henri Poincaré was one of the first mathematicians/philosphers to formulate the limits unlinearities put on forecasting.

Predicting the first impact of billiard balls on a table is not difficult given the initial state of the billiard balls, the table, and the impact of the cue. In predicting the 56th impact every single elementary particle in the universe needs to be accounted for in the calculations.

In the 1960’s an MIT meteorologist produced a computer model of weather dymanics that ran a simulation projecting a weather system a fews days in advance. Later he tried to repeat the same simulation with the same model and what he thought were the same input data. He got wildly different results. He initially thought he had a computer bug or a calculation error. Subsequently he realized the different results were caused by small roundings in the input parameters. This became known as the “butterfly effect” since a butterfly moving its wings in India could cause a hurricane in New York two years later.

In 1931 Belgian Roman Catholic priest/cosmologist, Georges Lemaître, postulated that the universe started as a primeval atom. Astronomer George Gamow expanded upon this idea and predicted in 1948 there should be background radiation left over from the Big Bang (The term was coined sardonically by Fred Hoyle who believed in the steady-state theory of the universe). In 1965 Arno Penzias and Robert Woodrow of Bell Telephone Laboratories were working on a radiometer to be used in radio astronomy and satellite communications. They kept getting an anomalous background noise which was of the same intensity wherever it was pointed in the sky. It turned out they had inadvertantly discovered the background radiation from the Big Bang. It was a Black Swan. In 1978 they received the Nobel Prize in physics.

Our intuition about nonlinear multiplicative effects is rather weak. According to the story (possibly apocryphal), the inventor of the chessboard requested the following compensation for his invention: one grain of rice for the first square, two for the second, four for the third, eight for the fourth, and so on. The king granted his request thinking he was asking for a mere pittance. The king was outsmarted because the total amount of rice was more than all of the possible rice reserves in the world (2 to the 63rd power = 9.2234….times 10 to the 18 power + 2 to the 62nd power = 4.6117….times 10 to the 18th power, etc.)!

The empirical methods of the Greeks of two millennia ago are being revived. Before the role of bacteria in disease was known, doctors distained hand washing because it made no sense to them despite the evidence of a meaningful decrease in hospital deaths when hygienic methods were used. Similarly it may not “make sense” that acupuncture works, but if pushing a needle into someone’s toe systematically produce relief from pain then it could be there are functions too complicated for us to understand, so why not do it while we keep an open mind on the subject.

The notion of asymmetric outcomes is central to the alternative of Gaussian probability. The unknown will always be by definition unknown. However one can guess how it might affect them and therefore base one’s decisions on that.

The mathematician and philospher Blasé Pascal proposed the following: I do not whether God exists, but I have nothing to gain by being an atheist if God does not exist, whereas I have a great deal to lose if He does exist. Hence this justifies my belief in God. Theologically this makes no sense because God would surely know if someone’s belief in Him were so contrived and self-serving. Outside of theology it makes a great deal of sense. It eliminates the need to understand the probabilities of a rare event; rather we can concentrate on the payoffs and benefits of an event if it takes place. The probabilities of very rare events are not computable; the effects of an event on us are considerably easier for us to ascertain. We can have a clear idea of the consequences of an event, even if we do not know how likely it is to occur. We don’t know the odds of an earthquake, but we can imagine the effects it would have on San Francisco.


Before the currency was replaced by the euro, the German 10 deutschmark bill contained a portrait of Carl Friedrich Gauss and a representation of his Gaussian bell shaped curve. There is irony here because the reichmark, as it was then called, went from four per dollar to four trillion per dollar in just a few years in the 1920’s. In the random fluctuations of currencies there is no possible accounting for such a colossal deviation from the norm with Gaussian probability distributions.

Casino owners understand the principle of not relying on Gaussian probability distributions by limiting the size of the bets for each gambler. They will take limited bets from many individuals while rejecting very large bets from a few. No casino is going to lose a billion dollars on a single bet.

Sir Francis Galton, Charles Darwin’s first cousin and Erasmus Darwin’s grandson, was blessed with no mathematical baggage, but he had a rare obsession with measurement. Galton applied the bell curve to areas like genetics and heredity, in which its use was justified. But his enthusiasm helped thrust nascent statistical methods into social issues.

Galileo Galilei said that the Great Book of Nature is written in mathematical language and the characters are triangles, circles, and other geometric figures. Taleb asks: “Was Galileo legally blind? Mountains are not triangles or pyramids; trees are not circles; straight lines are almost never seen anywhere.” I ask, how could such a normally perceptive and original thinker as Galileo be so self-deluded?

The problem of the circularity of statistics is as follows: How can we tell if we have enough data to put forth a hypothesis? From the probability distribution. If it is a Gaussian bell curve then a few points will suffice. And how do we know the distribution is Gaussian? Well, from the data. So we need the data to tell us what the probability distribution is, and a probability distribution to tell us how many data we need.

As measured by the S&P 500, by removing the 10 biggest one-day moves in the stock market in the last 50 years there is a huge difference in returns – and yet conventional financial analysis interprets these one-day jumps as mere anomalies. Similarly if the top 40 best single market days were missed in the last 10 years one’s market returns would be greatly reduced even though 21 of those days came during the brutal 2000-2002 bear market. The equities market is too dominated by Black Swans to allow successful market timing.

The entire statistical business confuses absence of proof with proof of absence. You need only one single observation to reject the Gaussian, but millions of observations will not fully confirm the validity of a Gaussian distribution. Why? Because the Gaussian bell curve disallows large deviations, but non-Gaussian distributions, the alternative, do not disallow long quiet periods.

“Forget everything you have ever heard in college statistics or probability theory. If you never took such a class, even better. Let us start from the very beginning.”

“If you ever took a (dull) statistics class in college, did not understand much of what the professor was excited about, and wondered what “standard deviation” meant, there is nothing to worry about. The notion of standard deviation is meaningless…..”

“Standard deviations do not exist outside the Guassian, or if they do exist they do not matter and do not explain much. But it gets worse. The Guassian family (which includes various friends and relatives, such as the Poisson Law) are the only class of distributions that the standard deviation (and average) is sufficient to describe. You need nothing else. The bell curve satisfies the reductionism of the deluded.”

“This monstrosity called the Gaussian bell curve is not Gauss’s doing. Although he worked on it, he was a mathematician dealing with a theoretical point, not making claims about the structure of reality like statistical-minded scientists. The bell curve was mainly the concoction of a gambler, Abraham de Moivre (1667-1754), a French Calvinist refugee who spent much of his life in London, though speaking heavily accented English.”

These are the words of Taleb. He has a point, but in my opinion he goes a bit too far in rejecting Gaussian probability functions. Where there are extreme deviations from the normal as in the examples of currency inflation or in single day stock market moves clearly Gaussian distributions are useless, but if, for example, one would measure the length of squirrel tails, there would be a standard bell shaped Gaussian curve. Nature does not always reject Gaussian distributions. However, Taleb is certainly correct in aserting that overwhelmingly most monumental events are Black Swans.