Нассим Талеб - The Black Swan. The Impact of the Highly Improbable

* It is indeed the absence of higher order representation—the inability to accept statements like “Is my method for assessing what is right or wrong right or wrong?”—that, we will see in the next section, is central when we deal with probability, that causes Dr. Johns to be suckers for measures and believe in them without doubting their beliefs. They fail to understand the metaprobability, the higher order probability—that is, the probability that the probability they are using may not be True.

† The nontechnical reader should skip the rest of this section.

V

(PERHAPS) THE MOST USEFUL PROBLEM IN THE HISTORY OF MODERN PHILOSOPHY

Small may not be the idea, after all—Where to find the powder room—Predict and perish—On school buses and intelligent textbooks

I am going to be blunt. Before The Black Swan (and associated papers) most of epistemology and decision theory was, to an actor in the real world, just sterile mind games and foreplay. Almost all the history of thought is about what we know, or think we know. The Black Swan is the very first attempt (that I know of) in the history of thought to provide a map of where we get hurt by what we don’t know, to set systematic limits to the fragility of knowledge—and to provide exact locations where these maps no longer work.

To answer the most common “criticism” by economists and (now bankrupt) bankers I mentioned in Section III, I am not saying “S**t happens,” I am saying “S**t happens in the Fourth Quadrant,” which is as different as mistaking prudence and caution for paranoia.

Furthermore, to be more aggressive, while limits like those attributed to Gödel bear massive philosophical consequences, but we can’t do much about them, I believe that the limits to empirical and statistical knowledge I have shown have sensible (if not vital) importance and we can do a lot with them in terms of solutions, by categorizing decisions based on the severity of the potential estimation error of the pair probability times consequence. For instance, we can use it to build a safer society—to robustify what lies in the Fourth Quadrant.

LIVING IN TWO DIMENSIONS

A vexing problem in the history of human thought is finding one’s position on the boundary between skepticism and gullibility, or how to believe and how to not believe. And how to make decisions based on these beliefs, since beliefs without decisions are just sterile. So this is not an epistemological problem (i.e., focusing on what is true or false); it is one of decision, action, and commitment.

Clearly, you cannot doubt everything and function; you cannot believe everything and survive. Yet the philosophical treatment of the problem has been highly incomplete, and, worse, has not improved much over the centuries, if it has improved at all. One class of thinkers, say the Cartesians, or the academic skeptics some eighteen centuries before them, in their own way, started with the rejection of everything upfront, with some even more radical, such as the Pyrrhonians, rejecting so much that they even reject skepticism as too dogmatic. The other class, say the medieval Scholastics or the modern-day pragmatists, starts with the fixation of beliefs, or some beliefs. While the medieval thinkers stop there, in an Aristotelian way, the early pragmatists, with the great thinker Charles Sanders Peirce, provided a ray of hope. They proposed to update and correct beliefs as a continuous work in progress (albeit under a known structure of probability, as Peirce believed in the existence and attainability of an ergodic, long-run, reachable state of convergence to truth). That brand of pragmatism (initially called pragmaticism) viewed knowledge as a rigorous interplay between anti-skepticism and fallibilism, i.e., between the two categories of what to doubt and what to accept. The application to my field, probability, and perhaps the most sophisticated version of the program, lies in the dense, difficult, deep, and brilliant forays of Isaac Levi into decision theory with the notion of corpus of belief, doxastic commitment, distance from expectation, and credal probabilities.

A ray of hope, perhaps, but still not even close. Not even remotely close to anything useful.

Think of living in a three-dimensional space while under the illusion of being in two dimensions. It may work well if you are a worm, certainly not if you happen to be a bird. Of course, you will not be aware of the truncation—and will be confronted with many mysteries, mysteries that you cannot possibly clear up without adding a dimension, no matter how sophisticated you may get. And, of course, you will feel helpless at times. Such was the fate of knowledge all these centuries, when it was locked in two dimensions too simplistic to be of any use outside of classrooms. Since Plato only philosophers have spent time discussing what Truth was, and for a reason: it is unusable in practice. By focusing on the True/False distinction, epistemology remained, with very few exceptions, prisoner of an inconsequential, and highly incomplete, 2-D framework. The third missing dimension is, of course, the consequence of the True, and the severity of the False, the expectation. In other words, the payoff from decisions , the impact and magnitude of the result of such a decision. Sometimes one may be wrong and the mistake may turn out to be inconsequential. Or one may be right, say, on such a subject as the sex of angels, and it may turn out to be of no use beyond intellectual stamp collecting.

The simplified, philistinified, academified, and glorified notion of “evidence” becomes useless. With respect to Black Swans, you act to protect yourself from negative ones (or expose yourself to positive ones) even though you may have no evidence that they can take place, just as we check people for weapons before they board a plane even though we have no evidence that they are terrorists. This focus on off-the-shelf commoditized notions such as “evidence,” is a problem with people who claim to use “rigor” yet go bust on occasion.

A probabilistic world has trouble with “proof” as it is, but in a Black Swan world things are a lot worse.

Indeed, I know of almost no decision that is based on notions of True/False.

Once you start examining the payoff, the result of decisions, you will see clearly that the consequences of some errors may be benign, those of others may be severe. And you pretty much know which is which beforehand. You know which errors are consequential and which ones are not so much.

But first let us look at a severe problem in the derivation of knowledge about probabilities.

THE DEPENDENCE ON THEORY FOR RARE EVENTS

During my deserto period, when I was getting severe but entertaining insults, I found myself debating a gentleman then employed by a firm called Lehman Brothers. That gentleman had made a statement in The Wall Street Journal saying that events we saw in August 2007 should have happened once every ten thousand years. Sure enough, we had three such events three days in a row. The Wall Street Journal ran his picture and if you look at it, you can safely say, “He does not look ten thousand years old.” So where is he getting his “once in ten thousand years” probability? Certainly not from personal experience; certainly not from the records of Lehman Brothers—his firm had not been around for ten thousand years, and of course it didn’t stay around for another ten thousand years, as it went under right after our debate. So, you know that he’s getting his small probabilities from a theory. The more remote the event, the less we can get empirical data (assuming generously that the future will resemble the past) and the more we need to rely on theory .