Incerto 4-Book Bundle: Fooled by Randomness, The Black Swan, The Bed of Procrustes, Antifragile

by Nassim Nicholas Taleb

Consider this effect. Take a random sample of any two people from the U.S. population who jointly earn $1 million per annum. What is the most likely breakdown of their respective incomes? In Mediocristan, the most likely combination is half a million each. In Extremistan, it would be $50,000 and

For any large total, the breakdown will be more and more asymmetric.

In the U.S. book business, the proportions are more like 97/20 (i.e., 97 percent of book sales are made by 20 percent of the authors); it’s even worse if you focus on literary nonfiction (twenty books

We can make good use of the Gaussian approach in variables for which there is a rational reason for the largest not to be too far away from the average.

principle: the rarer the event, the higher the error in our estimation of its probability—even when using the Gaussian. Let me show you how the Gaussian bell

The above is an application of the supreme law of Mediocristan: when you have plenty of gamblers, no single gambler will impact the total more than minutely.

or if they do exist they do not matter and do not explain much. But it gets worse. The Gaussian family (which includes various friends and relatives, such as the Poisson law) are the only class of distributions that the standard deviation (and the average) is sufficient to describe. You need nothing else. The bell

There are other notions that have little or no significance outside of the Gaussian: correlation and, worse, regression. Yet they are deeply ingrained in our methods; it is hard to have a business conversation without hearing the word correlation.

And that is the key for the Gaussian. So much in the middle washes out—and we will see that there is a lot in the middle. So, if you are playing for $1 a round, after two rounds you have a 25 percent chance of making or losing $2, but a 50 percent chance of breaking even.

This is a key attribute of the nonscalable framework to analyzing randomness: extreme deviations decrease at an increasing rate.

This property also generates the supreme law of Mediocristan: given the paucity of large deviations, their contribution to the total will be vanishingly small.

Many people accepted my Black Swan idea but could not take it to its logical conclusion, which is that you cannot use one single measure for randomness called standard deviation (and call it “risk”); you cannot expect a simple answer to characterize uncertainty.

The great book of Nature lies ever open before our eyes and the true philosophy is written in it. … But we cannot read it unless we have first learned the language and the characters in which it is written. … It is written in mathematical language and the characters are triangles, circles and other geometric figures.

The veins in leaves look like branches; branches look like trees; rocks look like small mountains. There is no qualitative change when an object changes size. If you look at the coast of Britain from an airplane, it resembles what you see when you look at it with a magnifying glass.

the fractal has numerical or statistical measures that are (somewhat) preserved across scales—the

because of the asymmetry with induction, just as it is easier to reject innocence than accept it, it is easier to reject a bell curve than accept it; conversely, it is more difficult to reject a fractal than to accept it. Why? Because a single event can destroy the argument that we face a Gaussian bell curve.

This lack of equality at all wealth levels, in a nutshell, is statistical self-similarity.

The above idea links all the parts of this book. While many study psychology, mathematics, or evolutionary theory and look for ways to take it to the bank by applying their ideas to business, I suggest the exact opposite: study the intense, uncharted, humbling uncertainty in the markets as a means to get insights about the nature of randomness that is applicable to psychology, probability, mathematics, decision theory, and even statistical physics.

thought that finance and economics were just a place where one learned from various empirical phenomena and filled up one’s bank account with f*** you cash before leaving for bigger and better things. Mandelbrot’s

The problem of the circularity of statistics (which we can also call the statistical regress argument) is as follows. Say you need past data to discover whether a probability distribution is Gaussian, fractal, or something else. You will need to establish whether you have enough data to back up your claim. How do we know if we have enough data? From the probability distribution—a distribution does tell you whether you have enough data to “build confidence” about what you are inferring. If it is a Gaussian bell curve, then a few points will suffice (the law of large numbers once again). And how do you know if the distribution is Gaussian? Well, from the data. So we need the data to tell us what the probability distribution is, and a probability distribution to tell us how much data we need. This causes a severe regress argument.

The Gaussian is used as a default distribution for that very reason. As I keep repeating, assuming its application beforehand may work with a small number of fields such as crime statistics, mortality rates, matters from Mediocristan. But not for historical data of unknown attributes and not for matters from Extremistan.

But fractal randomness does not yield precise answers. The benefits are as follows. If you know that the stock market can crash, as it did in 1987, then such an event is not a Black Swan. The crash of 1987 is not an outlier if you use a fractal with an exponent of three. If you know that biotech companies can deliver a megablockbuster drug, bigger than all we’ve had so far, then it won’t be a Black Swan, and you will not be surprised, should that drug appear.

Mandelbrot’s fractals allow us to account for a few Black Swans, but not all.

A gray swan concerns modelable extreme events, a black swan is about unknown unknowns.

You are indeed much safer if you know where the wild animals are.

We are teaching people methods from Mediocristan and turning them loose in Extremistan. It is like developing a medicine for plants and applying it to humans. It is no wonder that we run the biggest risk of all: we handle matters that belong to Extremistan, but treated as if they belonged to Mediocristan, as an “approximation.”

Look at the graph in Figure 14. In the last fifty years, the ten most extreme days in the financial markets represent half the returns. Ten days in fifty years. Meanwhile,

If the world of finance were Gaussian, an episode such as the crash (more than twenty standard deviations) would take place every several billion lifetimes of the universe (look at the height example in Chapter 15).

I will repeat the following until I am hoarse: it is contagion that determines the fate of a theory in social science, not its validity.

An ad hominem attack against an intellectual, not against an idea, is highly flattering. It indicates that the person does not have anything intelligent to say about your message.

Economists often invoke a strange argument by Milton Friedman that states that models do not have to have realistic assumptions to be acceptable—giving them license to produce severely defective mathematical representations of reality.

The entire statistical business confused absence of proof with proof of absence. Furthermore, people did not understand the elementary asymmetry involved: you need one single observation to reject the Gaussian, but millions of observations will not fully confirm the validity of its application.

want to be broadly right rather than precisely wrong. Elegance in the theories is often indicative of Platonicity

These people are professionally employed in the business of questioning what we take for granted; they are trained to argue about the existence of god(s), the definition of truth, the redness of red, the meaning of meaning, the difference between the semantic theories of truth, conceptual and nonconceptual representations … Yet they believe blindly in the stock market, and in the abilities of their pension plan manager.

my thinking is rooted in the belief that you cannot go from books to problems, but the reverse, from problems to books. This

am most often irritated by those who attack the bishop but somehow fall for the securities analyst—those who exercise their skepticism against religion but not against economists, social scientists, and phony statisticians. Using the confirmation bias, these people will tell you that religion was horrible for mankind by counting deaths from the Inquisition and various religious wars. But they will not show you how many people were killed by nationalism, social science, and political theory under Stalinism or during the Vietnam War.

Missing a train is only painful if you run after it!

Quitting a high-paying position, if it is your decision, will seem a better payoff than the utility of the money involved (this may seem crazy, but I’ve tried it and it works). This is the first step toward the stoic’s throwing a four-letter word at fate. You have far more control over your life if you decide on your criterion by yourself.

We are quick to forget that just being alive is an extraordinary piece of good luck, a remote event, a chance occurrence of monstrous proportions.

Don’t be like the ingrate who got a castle as a present and worried about the mildew in the bathroom.