the trap of not differentiating between the forward and the backward
2 6 8 THOSE GRAY SWANS OF E X T R E M I S T AN
processes (between the problem and the inverse problem)—to me, the
greatest scientific and epistemological sin. They are not alone; nearly
everyone who works with data but doesn't make decisions on the basis of
these data tends to be guilty of the same sin, a variation of the narrative
fallacy. In the absence of a feedback process you look at models and think
that they confirm reality. I believe in the ideas of these three books, but not
in the way they are being used—and certainly not with the precision the
authors ascribe to them. As a matter of fact, complexity theory should
make us more suspicious of scientific claims of precise models of reality. It
does not make all the swans white; that is predictable: it makes them gray,
and only gray.
As I have said earlier, the world, epistemologically, is literally a different
place to a bottom-up empiricist. We don't have the luxury of sitting
down to read the equation that governs the universe; we just observe data
and make an assumption about what the real process might be, and "calibrate"
by adjusting our equation in accordance with additional information.
As events present themselves to us, we compare what we see to what
we expected to see. It is usually a humbling process, particularly for someone
aware of the narrative fallacy, to discover that history runs forward,
not backward. As much as one thinks that businessmen have big egos,
these people are often humbled by reminders of the differences between
decision and results, between precise models and reality.
What I am talking about is opacity, incompleteness of information, the
invisibility of the generator of the world. History does not reveal its mind
to us—we need to guess what's inside of it.
From Representation to Reality
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. You will see the sneaky manifestations of the narrative fallacy, the
ludic fallacy, and the great errors of Platonicity, of going from representation
to reality.
When I first met Mandelbrot I asked him why an established scientist
THE A E S T H E T I C S OF RANDOMNESS 2 6 9
like him who should have more valuable things to do with his life would
take an interest in such a vulgar topic as finance. I 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 answer was, 11 Data, a
gold mine of data." Indeed, everyone forgets that he started in economics
before moving on to physics and the geometry of nature. Working with
such abundant data humbles us; it provides the intuition of the following
error: traveling the road between representation and reality in the wrong
direction.
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.
This regress does not occur if you assume beforehand that the distribution
is Gaussian. It happens that, for some reason, the Gaussian yields its
properties rather easily. Extremistan distributions do not do so. So selecting
the Gaussian while invoking some general law appears to be convenient.
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.
Now, why aren't statisticians who work with historical data aware of
this problem? First, they do not like to hear that their entire business has
been canceled by the problem of induction. Second, they are not confronted
with the results of their predictions in rigorous ways. As we saw
with the Makridakis competition, they are grounded in the narrative fallacy,
and they do not want to hear it.
2 7 0 THOSE GRAY SWANS OF EXTREMISTAN
ONCE AGAIN, BEWARE THE FORECASTERS
Let me take the problem one step higher up. As I mentioned earlier, plenty
of fashionable models attempt to explain the genesis of Extremistan. In
fact, they are grouped into two broad classes, but there are occasionally
more approaches. The first class includes the simple rich-get-richer (or bigget-
bigger) style model that is used to explain the lumping of people
around cities, the market domination of Microsoft and VHS (instead of
Apple and Betamax), the dynamics of academic reputations, etc. The second
class concerns what are generally called "percolation models," which
address not the behavior of the individual, but rather the terrain in which
he operates. When you pour water on a porous surface, the structure of
that surface matters more than does the liquid. When a grain of sand hits
a pile of other grains of sand, how the terrain is organized is what determines
whether there will be an avalanche.
Most models, of course, attempt to be precisely predictive, not just
descriptive; I find this infuriating. They are nice tools for illustrating the
genesis of Extremistan, but I insist that the "generator" of reality does not
appear to obey them closely enough to make them helpful in precise forecasting.
At least to judge by anything you find in the current literature on
the subject of Extremistan. Once again we face grave calibration problems,
so it would be a great idea to avoid the common mistakes made
while calibrating a nonlinear process. Recall that nonlinear processes have
greater degrees of freedom than linear ones (as we saw in Chapter 11),
with the implication that you run a great risk of using the wrong model.
Yet once in a while you run into a book or articles advocating the application
of models from statistical physics to reality. Beautiful books like Philip
Ball's illustrate and inform, but they should not lead to precise quantitative
models. Do not take them at face value.
But let us see what we can take home from these models.
Once Again, a Happy Solution
First, in assuming a scalable, I accept that an arbitrarily large number is
possible. In other words, inequalities should not stop above some known
maximum bound.
Say that the book The Da Vinci Code sold around 60 million copies.
(The Bible sold about a billion copies but let's ignore it and limit our
analysis to lay books written by individual authors.) Although we have
THE A E S T H E T I C S OF R A N D O M N E S S 2 7 1
never known a lay book to sell 200 million copies, we can consider that
the possibility is not zero. It's small, but it's not zero. For every three Da
Vinci Code-style bestsellers, there might be one superbestseller, and
though one has not happened so far, we cannot rule it out. And for every
fifteen Da Vinci Codes there will be one superbestseller selling, say, 500
million copies.
Apply the same logic to wealth. Say the richest person on earth is
worth $50 billion. There is a nonnegligible probability that next year
someone with $100 billion or more will pop out of nowhere. For every
three people with more than $50 billion, there could be one with $100 billion
or more. There is a much smaller probability of there being someone
with more than $200 billion—one third of the previous probability, but
nevertheless not zero. There is even a minute, but not zero probability of
there being someone worth more than $500 billion.
This tells me the following: I can make inferences about things that I
do not see in my data, but these things should still belong to the realm of
possibilities. There is an invisible bestseller out there, one that is absent
from the past data but that you need to account for. Recall my point in
Chapter 13: it makes investment in a book or a drug better than statistics
on past data might suggest. But it can make stock market losses worse
than what the past shows.
Wars are fractal in nature. A war that kills more people than the devastating
Second World War is possible—not likely, but not a zero probability,
although such a war has never happened in the past.
Second, I will introduce an illustration from nature that will help to
make the point about precision. A mountain is somewhat similar to a
stone: it has an affinity with a stone, a family resemblance, but it is not
identical. The word to describe such resemblances is self-affine, not the
precise self-similar, but Mandelbrot had trouble communicating the notion
of affinity, and the term self-similar spread with its connotation of
precise resemblance rather than family resemblance. As with the mountain
and the stone, the distribution of wealth above $1 billion is not exactly the
same as that below $1 billion, but the two distributions have "affinity."
Third, I said earlier that there have been plenty of papers in the world
of econophysics (the application of statistical physics to social and economic
phenomena) aiming at such calibration, at pulling numbers from
the world of phenomena. Many try to be predictive. Alas, we are not able
to predict "transitions" into crises or contagions. My friend Didier Sornette
attempts to build predictive models, which I love, except that I can2
7 2 THOSE GRAY SWANS OF EXTREMISTAN
not use them to make predictions—but please don't tell him; he might stop
building them. That I can't use them as he intends does not invalidate his
work, it just makes the interpretations require broad-minded thinking, unlike
models in conventional economics that are fundamentally flawed. We
may be able to do well with some of Sornette's phenomena, but not all.
WHERE IS THE GRAY SWAN?
I have written this entire book about the Black Swan. This is not because
I am in love with the Black Swan; as a humanist, I hate it. I hate most of
the unfairness and damage it causes. Thus I would like to eliminate many
Black Swans, or at least to mitigate their effects and be protected from
them. Fractal randomness is a way to reduce these surprises, to make some
of the swans appear possible, so to speak, to make us aware of their consequences,
to make them gray. 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.
Thus Mandelbrot's fractals allow us to account for a few Black Swans,
but not all. I said earlier that some Black Swans arise because we ignore
sources of randomness. Others arise when we overestimate the fractal exponent.
A gray swan concerns modelable extreme events, a black swan is
about unknown unknowns.
I sat down and discussed this with the great man, and it became, as
usual, a linguistic game. In Chapter 9 I presented the distinction economists
make between Knightian uncertainty (incomputable) and Knightian
risk (computable); this distinction cannot be so original an idea to be absent
in our vocabulary, and so we looked for it in French. Mandelbrot
mentioned one of his friends and prototypical heroes, the aristocratic
mathematician Marcel-Paul Schiitzenberger, a fine erudite who (like this
author) was easily bored and could not work on problems beyond their
point of diminishing returns. Schiitzenberger insisted on the clear-cut distinction
in the French language between hasard and fortuit. Hasard, from
the Arabic az-zahr, implies, like alea, dice—tractable randomness; fortuit
is my Black Swan—the purely accidental and unforeseen. We went to the
Petit Robert dictionary; the distinction effectively exists there. Fortuit
THE A E S T H E T I C S OF RANDOMNESS 2 7 3
seems to correspond to my epistemic opacity, l'imprévu et non quantifiable;
hasard to the more ludic type of uncertainty that was proposed by
the Chevalier de Méré in the early gambling literature. Remarkably, the
Arabs may have introduced another word to the business of uncertainty:
rizk, meaning property.
I repeat: Mandelbrot deals with gray swans; I deal with the Black
Swan. So Mandelbrot domesticated many of my Black Swans, but not all
of them, not completely. But he shows us a glimmer of hope with his
method, a way to start thinking about the problems of uncertainty. You
are indeed much safer if you know where the wild animals are.
Chapter Seventeen
LOCKE'S MADMEN, OR BELL CURVES
IN THE WRONG PLACES*
What?—Anyone can become president—Alfred Nobel's legacy—Those
medieval days
I have in my house two studies: one real, with interesting books and literary
material; the other nonliterary, where I do not enjoy working, where I
relegate matters prosaic and narrowly focused. In the nonliterary study
