Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance. Outside of textbooks and casinos, probability almost never presents itself as a mathematical problem or a brain teaser. Mother nature does not tell you how many holes there are on the roulette table, nor does she deliver problems in a textbook way (in the real world one has to guess the problem more than the solution). In this book, considering that alternative outcomes could have taken place, that the world could have been different, is the core of probabilistic thinking.
Before the “enlightenment” and the age of rationality, there was in the culture a collection of tricks to deal with our fallibility and reversals of fortunes. The elders can still help us with some of their ruses.
I start with the platitude that one cannot judge a performance in any given field (war, politics, medicine, investments) by the results, but by the costs of the alternative (i.e., if history played out in a different way). Such substitute courses of events are called alternative histories. Clearly, the quality of a decision cannot be solely judged based on its outcome, but such a point seems to be voiced only by people who fail (those who succeed attribute their success to the quality of their decision).
…epic poet did not judge his heroes by the result: Heroes won and lost battles in a manner that was totally independent of their own valor; their fate depended upon totally external forces, generally the explicit agency of the scheming gods (not devoid of nepotism). Heroes are heroes because they are heroic in behavior, not because they won or lost. Patrocles does not strike us as a hero because of his accomplishments (he was rapidly killed) but because he preferred to die than see Achilles sulking into inaction. Clearly, the epic poets understood invisible histories. Also later thinkers and poets had more elaborate methods for dealing with randomness, as we will see with stoicism.
This is one of the many reasons that journalism may be the greatest plague we face today – as the world becomes more and more complicated and our minds are trained for more and more simplification.
A mistake is not something to be determined after the fact, but in the light of the information until that point.
Mathematicians of probability give that a fancy name: ergodicity. It means, roughly, that (under certain conditions) very long sample paths would end up resembling each other.
Accordingly, it is not how likely an event is to happen that matters, it is how much is made when it happens that should be the consideration. How frequent the profit is irrelevant; it is the magnitude of the outcome that counts. It is a pure accounting fact that, aside from the commentators, very few people take home a check linked to how often they are right or wrong. What they get is a profit or loss.
But there is a more severe aspect of naive empiricism. I can use data to disprove a proposition, never to prove one. I can use history to refute a conjecture, never to affirm it.
Accordingly, I will use statistics and inductive methods to make aggressive bets, but I will not use them to manage my risks and exposure. Surprisingly, all the surviving traders I know seem to have done the same. They trade on ideas based on some observation (that includes past history) but, like the Popperian scientists, they make sure that the costs of being wrong are limited (and their probability is not derived from past data).
I am now thinking of the next step: to recreate a low-information, more deterministic ancient time, say in the nineteenth century, all the while benefiting from some of the technical gains (such as the Monte Carlo engine), all of the medical breakthroughs, and all the gains of social justice of our age. I would then have the best of everything. This is called evolution.
It is worth stopping, at this juncture, and discussing the distinction between normative and positive sciences. A normative science (clearly a self-contradictory concept) offers prescriptive teachings; it studies how things should be. Some economists, for example those of the efficient-market religion, believe that our studies should be based on the hypothesis that humans are rational and act rationally because it is the best thing for them to do (it is mathematically “optimal”). The opposite is a positive science, which is based on how people actually are observed to behave. In spite of economists’ envy of physicists, physics is an inherently positive science while economics, particularly microeconomics and financial economics, is predominantly a normative one. Normative economics is like religion without the aesthetics.
Ask your local mathematician to define probability; he would most probably show you how to compute it. As we saw in Chapter 3 on probabilistic introspection, probability is not about the odds, but about the belief in the existence of an alternative outcome, cause, or motive. Recall that mathematics is a tool to meditate, not compute.