Probability on a Thermometer

Probability on a Thermometer

This distinction, misused in practice, resembles another deficient separation discussed earlier, between what economists call Knightian risk (computable) and Knightian uncertainty (uncomputable). This assumes that something is computable, when really everything is more or less incomputable (and rare events more so). One has to have a mental problem to think that probabilities of future events are “measurable” in the same sense that the temperature is measurable by a thermometer. We will see in the following section that small probabilities are less computable, and that this matters when the associated payoffs are consequential.

Another deficiency I need to point out concerns a strangely unrealistic and unrigorous research tradition in social science, “rational expectations,” in which observers are shown to rationally converge on the same inference when supplied with the same data, even if their initial hypotheses were markedly different (by a mechanism of updating called Bayesian inference). Why unrigorous? Because one needs a very quick check to see that people do not converge to the same opinions in reality. This is partly, as we saw in Chapter 6, because of psychological distortions such as the confirmation bias, which cause divergent interpretation of the data. But there is a mathematical reason why people do not converge to the same opinion: if you are using a probability distribution from Extremistan, and I am using a distribution from Mediocristan (or a different one from Extremistan), then we will never converge, simply because if you suppose Extremistan you do not update (or change your mind) that quickly. For instance, if you assume Mediocristan and do not witness Black Swans, you may eventually rule them out. Not if you assume we are in Extremistan.

To conclude, assuming that “randomness” is not epistemic and subjective, or making a big deal about the distinction between “ontological randomness” and “epistemic randomness,” implies some scientific autism, that desire to systematize, and a fundamental lack of understanding of randomness itself. It assumes that an observer can reach omniscience and can compute odds with perfect realism and without violating consistency rules. What is left becomes “randomness,” or something by another name that arises from aleatory forces that cannot be reduced by knowledge and analysis.

There is an angle worth exploring: why on earth do adults accept these Soviet-Harvard-style top-down methods without laughing, and actually go to build policies in Washington based on them, against the record, except perhaps to make readers of history laugh at them and diagnose new psychiatric conditions? And, likewise, why do we default to the assumption that events are experienced by people in the same manner? Why did we ever take notions of “objective” probability seriously?

After this foray into the psychology of the perception of the dynamics of time and events, let us move to our central point, the very core of our program, into what I have aggressively called the most useful problem in philosophy. The most useful, sadly.

Robert Merton, the villain of Chapter 17, a person said to be of a highly mechanistic mind (down to his interest in machinery and his use of mechanical metaphors to represent uncertainty), seems to have been created for the sole purpose of providing an illustration of dangerous Black Swan foolishness. After the crisis of 2008, he defended the risk taking caused by economists, giving the argument that “it was a Black Swan” simply because he did not see it coming, therefore, he said, the theories were fine. He did not make the leap that, since we do not see these events coming, we need to be robust to them. Normally, such people exit the gene pool; academic tenure holds them a bit longer.

Robert Rubin had pocketed more than $100 million from Citigroup’s earning of profits from hidden risks that blow up only occasionally. After he blew up, he had an excuse—“It never happened before.” He kept his money; we, the taxpayers, who include schoolteachers and hairdressers, had to bail the company out and pay for the losses. This I call the moral hazard element in paying bonuses to people who are not robust to Black Swans, and who we knew beforehand were not robust to the Black Swan. This beforehand is what makes me angry.

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.

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 “St happens,” I am saying “St 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.