The Black Swan: The Impact of the Highly Improbable

This brings us to Sir Doktor Professor Karl Raimund Popper’s attack on historicism. As I said in Chapter 5, this was his most significant insight, but it remains his least known. People who do not really know his work tend to focus on Popperian falsification, which addresses the verification or nonverification of claims. This focus obscures his central idea: he made skepticism a method, he made of a skeptic someone constructive.

Just as Karl Marx wrote, in great irritation, a diatribe called The Misery of Philosophy in response to Proudhon’s The Philosophy of Misery, Popper, irritated by some of the philosophers of his time who believed in the scientific understanding of history, wrote, as a pun, The Misery of Historicism (which has been translated as The Poverty of Historicism).[34]

Popper’s insight concerns the limitations in forecasting historical events and the need to downgrade “soft” areas such as history and social science to a level slightly above aesthetics and entertainment, like butterfly or coin collecting. (Popper, having received a classical Viennese education, didn’t go quite that far; I do. I am from Amioun.) What we call here soft historical sciences are narrative dependent studies.

Popper’s central argument is that in order to predict historical events you need to predict technological innovation, itself fundamentally unpredictable.

“Fundamentally” unpredictable? I will explain what he means using a modern framework. Consider the following property of knowledge: If you expect that you will know tomorrow with certainty that your boyfriend has been cheating on you all this time, then you know today with certainty that your boyfriend is cheating on you and will take action today, say, by grabbing a pair of scissors and angrily cutting all his Ferragamo ties in half. You won’t tell yourself, This is what I will figure out tomorrow, but today is different so I will ignore the information and have a pleasant dinner. This point can be generalized to all forms of knowledge. There is actually a law in statistics called the law of iterated expectations, which I outline here in its strong form: if I expect to expect something at some date in the future, then I already expect that something at present.

Consider the wheel again. If you are a Stone Age historical thinker called on to predict the future in a comprehensive report for your chief tribal planner, you must project the invention of the wheel or you will miss pretty much all of the action. Now, if you can prophesy the invention of the wheel, you already know what a wheel looks like, and thus you already know how to build a wheel, so you are already on your way. The Black Swan needs to be predicted!

But there is a weaker form of this law of iterated knowledge. It can be phrased as follows: to understand the future to the point of being able to predict it, you need to incorporate elements from this future itself. If you know about the discovery you are about to make in the future, then you have almost made it. Assume that you are a special scholar in Medieval University’s Forecasting Department specializing in the projection of future history (for our purposes, the remote twentieth century). You would need to hit upon the inventions of the steam machine, electricity, the atomic bomb, and the Internet, as well as the institution of the airplane onboard massage and that strange activity called the business meeting, in which well-fed, but sedentary, men voluntarily restrict their blood circulation with an expensive device called a necktie.

This incapacity is not trivial. The mere knowledge that something has been invented often leads to a series of inventions of a similar nature, even though not a single detail of this invention has been disseminated – there is no need to find the spies and hang them publicly. In mathematics, once a proof of an arcane theorem has been announced, we frequently witness the proliferation of similar proofs coming out of nowhere, with occasional accusations of leakage and plagiarism. There may be no plagiarism: the information that the solution exists is itself a big piece of the solution.

By the same logic, we are not easily able to conceive of future inventions (if we were, they would have already been invented). On the day when we are able to foresee inventions we will be living in a state where everything conceivable has been invented. Our own condition brings to mind the apocryphal story from 1899 when the head of the U.S. patent of flee resigned because he deemed that there was nothing left to discover – except that on that day the resignation would be justified.[35]

Popper was not the first to go after the limits to our knowledge. In Germany, in the late nineteenth century, Emil du Bois-Reymond claimed that ignoramus et ignorabimus – we are ignorant and will remain so. Somehow his ideas went into oblivion. But not before causing a reaction: the mathematician David Hilbert set to defy him by drawing a list of problems that mathematicians would need to solve over the next century.

Even du Bois-Reymond was wrong. We are not even good at understanding the unknowable. Consider the statements we make about things that we will never come to know – we confidently underestimate what knowledge we may acquire in the future. Auguste Comte, the founder of the school of positivism, which is (unfairly) accused of aiming at the scientization of everything in sight, declared that mankind would forever remain ignorant of the chemical composition of the fixed stars. But, as Charles Sanders Peirce reported, “The ink was scarcely dry upon the printed page before the spectroscope was discovered and that which he had deemed absolutely unknowable was well on the way of getting ascertained”. Ironically, Comte’s other projections, concerning what we would come to learn about the workings of society, were grossly – and dangerously – overstated. He assumed that society was like a clock that would yield its secrets to us.

I’ll summarize my argument here: Prediction requires knowing about technologies that will be discovered in the future. But that very knowledge would almost automatically allow us to start developing those technologies right away. Ergo, we do not know what we will know.

Some might say that the argument, as phrased, seems obvious, that we always think that we have reached definitive knowledge but don’t notice that those past societies we laugh at also thought the same way. My argument is trivial, so why don’t we take it into account? The answer lies in a pathology of human nature. Remember the psychological discussions on asymmetries in the perception of skills in the previous chapter? We see flaws in others and not in ourselves. Once again we seem to be wonderful at self-deceit machines.

THE NTH BILLIARD BALL

Henri Poincare, in spite of his fame, is regularly considered to be an undervalued scientific thinker, given that it took close to a century for some of his ideas to be appreciated. He was perhaps the last great thinking mathematician (or possibly the reverse, a mathematical thinker). Every time I see a T-shirt bearing the picture of the modern icon Albert Einstein, I cannot help thinking of Poincare – Einstein is worthy of our reverence, but he has displaced many others. There is so little room in our consciousness; it is winner-take-all up there.

Third Republic-Style Decorum

Again, Poincare is in a class by himself. I recall my father recommending Poincare’s essays, not just for their scientific content, but for the quality of his French prose. The grand master wrote these wonders as serialized articles and composed them like extemporaneous speeches. As in every masterpiece, you see a mixture of repetitions, digressions, everything a “me too” editor with a prepackaged mind would condemn – but these make his text even more readable owing to an iron consistency of thought.

Poincare became a prolific essayist in his thirties. He seemed in a hurry and died prematurely, at fifty-eight; he was in such a rush that he did not bother correcting typos and grammatical errors in his text, even after spotting them, since he found doing so a gross misuse of his time. They no longer make geniuses like that – or they no longer let them write in their own way.

Poincare’s reputation as a thinker waned rapidly after his death. His idea that concerns us took almost a century to resurface, but in another form. It was indeed a great mistake that I did not carefully read his essays as a child, for in his magisterial La scienceet l’hypothese, I discovered later, he angrily disparages the use of the bell curve.

I will repeat that Poincare was the true kind of philosopher of science: his philosophizing came from his