The Black Swan: The Impact of the Highly Improbable

Pranks can be compassionate. I remember in my early trading days, at age twenty-five or so, when money was starting to become easy. I would take taxis, and if the driver spoke skeletal English and looked particularly depressed, I’d give him a $100 bill as a tip, just to give him a little jolt and get a kick out of his surprise. I’d watch him unfold the bill and look at it with some degree of consternation ($1 million certainly would have been better but it was not within my means). It was also a simple hedonic experiment: it felt elevating to make someone’s day with the trifle of $100. I eventually stopped; we all become stingy and calculating when our wealth grows and we start taking money seriously.

I don’t need much help from fate to get larger-scale entertainment: reality provides such forced revisions of beliefs at quite a high frequency. Many are quite spectacular. In fact, the entire knowledge-seeking enterprise is based on taking conventional wisdom and accepted scientific beliefs and shattering them into pieces with new counterintuitive evidence, whether at a micro scale (every scientific discovery is an attempt to produce a micro-Black Swan) or at a larger one (as with Poincaré’s and Einstein’s relativity). Scientists may be in the business of laughing at their predecessors, but owing to an array of human mental dispositions, few realize that someone will laugh at their beliefs in the (disappointingly near) future. In this case, my readers and I are laughing at the present state of social knowledge. These big guns do not see the inevitable overhaul of their work coming, which means that you can usually count on them to be in for a surprise.

HOW TO LEARN FROM THE TURKEY

The überphilosopher Bertrand Russell presents a particularly toxic variant of my surprise jolt in his illustration of what people in his line of business call the Problem of Induction or Problem of Inductive Knowledge (capitalized for its seriousness)—certainly the mother of all problems in life. How can we logically go from specific instances to reach general conclusions? How do we know what we know? How do we know that what we have observed from given objects and events suffices to enable us to figure out their other properties? There are traps built into any kind of knowledge gained from observation.

Consider a turkey that is fed every day. Every single feeding will firm up the bird’s belief that it is the general rule of life to be fed every day by friendly members of the human race “looking out for its best interests,” as a politician would say. On the afternoon of the Wednesday before Thanksgiving, something unexpected will happen to the turkey. It will incur a revision of belief.[16]

The rest of this chapter will outline the Black Swan problem in its original form: How can we know the future, given knowledge of the past; or, more generally, how can we figure out properties of the (infinite) unknown based on the (finite) known? Think of the feeding again: What can a turkey learn about what is in store for it tomorrow from the events of yesterday? A lot, perhaps, but certainly a little less than it thinks, and it is just that “little less” that may make all the difference.

The turkey problem can be generalized to any situation where the same hand that feeds you can be the one that wrings your neck. Consider the case of the increasingly integrated German Jews in the 1930s—or my description in Chapter 1 of how the population of Lebanon got lulled into a false sense of security by the appearance of mutual friendliness and tolerance.

Let us go one step further and consider induction’s most worrisome aspect: learning backward. Consider that the turkey’s experience may have, rather than no value, a negative value. It learned from observation, as we are all advised to do (hey, after all, this is what is believed to be the scientific method). Its confidence increased as the number of friendly feedings grew, and it felt increasingly safe even though the slaughter was more and more imminent. Consider that the feeling of safety reached its maximum when the risk was at the highest! But the problem is even more general than that; it strikes at the nature of empirical knowledge itself. Something has worked in the past, until—well, it unexpectedly no longer does, and what we have learned from the past turns out to be at best irrelevant or false, at worst viciously misleading.

FIGURE 1: ONE THOUSAND AND ONE DAYS OF HISTORY