Taleb Thales’ Secret, or The Intelligence of Antifragility
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Transcript of Taleb Thales’ Secret, or The Intelligence of Antifragility
A Simple Rule, Perhaps Too Simple 59
10/19/11 © Copyright 2011 by N. N. Taleb. This draft version cannot be disseminated or quoted.
Chapter 4. Thales’ Secret, or The Intelligence of Antifragility
I landed early (once) — A simple heuristic to get an inheritance — Where we discuss the idea of doing instead place of walking the Great Walk — Where the philosophers' stone was staring at us — ideas matter less than fragility
Now, the central chapter. A bit technical, but central. Or perhaps not so
technical after all, but still very central.
A SIMPLE RULE, PERHAPS TOO SIMPLE
A story, present in the rabbinical literature (Midrash Tehillim), probably
originating in Near Eastern lore, says the following. A king, angry at his son,
swore that he would crush him with a large stone. After he calmed down he
realized he was in trouble as a king who breaks his oath is unfit to rule. His
sage advisor came up with a solution. Have the stone cut into very small
pebbles, and have the mischievous son pelted with them.
This is a potent illustration of how fragility stems from nonlinear
effects. Let us leave side the idea of circumventing rules and other lessons
one might derive from it, and focus on the very simple point, in fact, that
defines fragility:
For the fragile shocks bring higher harm as their intensity increases (up to the
point of breaking).
I’ve used the intuition to show why large corporations hurt more (when
they fall) than small ones and why speed is not a good thing —whether in
traffic or in business. Your car is fragile. If you drive it into the wall at fifty
miles per hour, it would cause more damage than if you drove it into the
same wall ten times at five mph. The harm at fifty miles per hour is more
than ten times the harm at five mph.
Other examples. Drinking seven bottles of wine in one sitting, then
water for the remaining six days is more harmful than drinking one bottle of
wine a day for seven days (spread out in two glasses per meal). Every
additional glass of wine harms you more than the preceding one, hence your
system is fragile to alcoholic consumption.
Jumping from a height of thirty feet (ten meters) brings more than ten
times the harm of jumping from a height of three feet (one meter) —actually
thirty feet seems to be the cutoff point for death from freefall. Or letting a
porcelain cup drop on the floor from a height of one foot (about thirty
centimeters) is worse than twelve times the damage from a drop from a
height of one inch (2 and a half centimeters).
Figure 7- The King and His Son. The harm from the size of the stone as a function of the size of the stone (up to a point). Every additional weight of the stone harms more than the previous one. You see nonlinearity (the harm curves inwards, with a steeper and steeper vertical slope).
Let me explain the central argument —why is fragility necessarily in the
nonlinear and not in the linear? Just as with the stone hurting more than the
pebbles, if, for a human, jumping one millimeter (an impact of small force)
caused an exact linear fraction of the damage of, say, jumping to the ground
from thirty feet, then the person would be already dead from cumulative
harm. Actually a simple computation shows that he would have expired
within hours from touching objects or pacing in his living room. The fragility
A Simple Rule, Perhaps Too Simple 60
10/19/11 © Copyright 2011 by N. N. Taleb. This draft version cannot be disseminated or quoted.
that comes from linearity is immediately visible, so we rule it out because the
object would be already broken and the person already dead. This leaves us
with the following: what is fragile is something that is both unbroken and
subjected to nonlinear effects —and extreme, rare events since hits of large
size (or high speed) are rarer than ones of small size (and slow speed).
Let me rephrase it again in connection with Black Swans and extreme
events. There are a lot more ordinary events than extreme events, say, in
ordinary life, a million more hits of (to take an arbitrary measure), say, one
hundredth of a pound per square inch than hits of a hundred pounds per
square inch, or, in the financial markets, there are at least ten thousand time
more events of .1% than events of 10%. So we are necessarily immune to the
cumulative effect of small deviations, or shocks of very small magnitude,
which implies that these affect us disproportionally less (that is, nonlinearly
less) than larger ones. There are close to eight thousand micro-earthquakes
daily on planet earth, that is, those below 2 on the Richter scale —about
three million a year. That is These are totally harmless, and, with three
million per year, you would need them to be so. But shocks of 6 and higher
make the newspapers.
Let me try again and re-express my previous rule.
For the fragile, the cumulative effect of small shocks is smaller than the single effect of a large shock.
This leaves me with the definition that the fragile is hurt a lot more by
extreme events. Finito —and there is no other definition.
One more illustration. Consider that objects handled by humans, say a
coffee cup or a cell phone gets cumulative impacts equivalent to, say, tons
per square inch over the years, but break at the slightest fall.
Now let us flip the argument and consider the antifragile. Antifragility
too is grounded in nonlinearties, nonlinear responses.
For the antifragile, shocks bring more benefits (equivalently, less harm) as their intensity increases —up to a point.
A simple case —what is known heuristically by weightlifters. Lifting one
hundred pounds once brings more benefits than lifting fifty pounds twice,
and certainly a lot more than lifting one pound a hundred times. (Benefits
here mean strengthening of the body, muscle growth and beach-friendly
looks). The second fifty pounds play a larger role, hence the nonlinear (that
is, we will see, convexity) effect. Every additional pound brings more
benefits, until one gets close to the limit, what weightlifters call “failure”.
We will have more illustrations of these two simple points; they are
quite central as they allow us to immediately compare objects and classify
them in the Triad of Chapter 1.
For now, note the reach of this simple curve: if affects about anything
in sight, even medical error or size of government —anything that touches
uncertainty. And, of course, innovation.
When to Smile and When to Frown
Linearity comes into two kinds. Concave (curves inward) or its opposite
convex (curves outwards).
Figures 5 and 6 show the following simplifications of nonlinearity: the
convex and the concave.
Figure 8 The different types of nonlinearities. The convex (left) and the concave (right). The convex curves outward, the concave inward.
A Simple Rule, Perhaps Too Simple 61
10/19/11 © Copyright 2011 by N. N. Taleb. This draft version cannot be disseminated or quoted.
Figure 9 A better way to understand convexity and concavity. What curves inwards looks like a smile —and what curves outwards makes a sad face. The convex (left) is antifragile, the concave (right) is fragile (has negative convexity effects).
I use the term “convexity effect” for both, in order to simplify the
vocabulary, saying positive convexity effects and negative convexity effects
Traffic in Heathrow
Another example of the convexity effect. Traffic is highly nonlinear. When I
take the day flight from New York to London, and I leave my residence
around 5 AM (yes, I know), it takes me around 26 minutes to reach the
British Air terminal at JFK airport. At that time, New York is empty. When I
leave my place at 6 AM for the later flight, there is almost no difference in
travel time although traffic is a bit denser. You can add more and more cars
on the highway, with no or minimal impact concerning time spent in traffic.
Then, mystery, you increase the number of cars by 10% and the travel
time jumps up by 50% (I am using approximate numbers). Look at the
convexity effect at work: the average number of cars does not matter at all
for traffic speed. If you have 90,000 cars for one hour, then 110,000 cars for
another hour, traffic would be much, much slower than if you had 100,000
cars for two hours. But the hitch: travel time is a negative, so I count it as a
cost, like an expense, and a rise is a bad thing.
So travel cost is fragile to the volatility of the number of cars on the
highway; it does not depend so much on their average number. Every
additional car increases travel time more than the previous one.
This is a hint to a central problem of the world today, that of the
misunderstanding of nonlinear response by those involved in creating
“efficiencies” and “optimization” of systems. For instance, European airports
and railroads are stretched, seeming overly efficient. They operate at close to
maximal capacity, with minimal redundancies and idle capacity, hence
acceptable costs; but a small additional congestion, say 5% more planes in
the sky owing to a tiny backlog can set chaos in airports and cause scenes of
unhappy travelers camping on floors, with for sole solace some bearded
fellow playing French folk songs on his guitar.
We will see applications of the point across economic domains: central
banks can print money; they print and print with no effect (and claim the
“safety” of such measure) then, "unexpectedly", the printing causes a jump in
inflation. Chapter x uses the simple idea to show how many economic results
are completely cancelled by convexity effects. The tools (and culture) of
policy makers are based on the overly linear, ignoring these hidden effects.
I have rapidly put a (very hypothetical) graph of the response in Figure
6. Note for now the curved shape of the graph. It curves inward.
Figure 10- The graph (vertical) shows how the author’s travel time (and travel costs) to JFK depend, beyond a certain point, nonlinearly on the number of cars. We show travel costs as curving inward —concave, not a good thing.
The Scaling Property
I will keep pounding the reader with illustrations and explanations from
several angles. Another intuitive way to look at convexity effects is in
considering the scaling property. If you double the exposure, do you more
A Simple Rule, Perhaps Too Simple 62
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than double the harm? If so, then this is a situation of fragility. Otherwise,
you are antifragile.
Why is the Concave Hurt by Black Swan Events?
Now the idea that has inhabited me all my life — I never realized it could
show that clearly when put in graphical form.
Figure x illustrates the effect of harm and the unexpected. The more
concave an exposure, the more harm from the unexpected, and
disproportionately so.
Figure 11- Two exposures, one linear, one nonlinear (with negative convexity). An unexpected event affects the nonlinear disproportionately more. The larger the event, the larger the difference.
How to Exit a Movie Theatre
Another example. Imagine how people exit a movie theatre. Someone shouts
“fire”, and you have a dozen persons squashed to death. So we have a
fragility of the theater to size, stemming from the fact that every additional
person exiting brings more and more trauma (a negative convexity effect). A
thousand people exiting (or trying to exit) in one minute is not the same as
the same number exiting in half an hour. Someone unfamiliar with the
business who naively optimizes the size of the place (as Heathrow airport, for
example) might miss the idea that smooth functioning at regular times is
different from the rough functioning at times of stress.
This is the problem of the “squeeze” (largely ignored): when people
have no choice but to do something, and do it right away, regardless of the
cost. They are squeezed. It so happens that modern economic optimized life
causes us to build larger and larger theaters, but with the exact same door.
They do not make this mistake too often while building cinemas and movie
theaters, but we tend to do that in other domains, with, for instance, natural
resources, or as I have just mentioned, central bank policies that ignore
nonlinear responses*.
A “Balanced Meal”
Another example of missing the hidden dimension, that is, variability. We
are currently told by the Soviet-Harvard U.S. health authorities to eat set
quantities of nutrients (total calories, protein, vitamins, etc.) every day, in
some recommended amounts (say the optimal amounts of each, the
equivalent to the optimal condition of seventy degrees in the story of the
grandmother). Aside from the lack of empirical rigor in the way these
recommendations are currently derived (as we will see in Chapter x), there is
another sloppiness in the edict: an insistence in the discourse on the
regularity. Those recommending the nutritional policies fail to understand
that “steadily” getting your calories and nutrients throughout the day, with
“balanced” composition and metronomic regularity does not necessarily
carry the same effect as having them unevenly or randomly distributed, say
by having a lot of proteins one day, fasting completely another, feasting the
third, etc.
For a long time, nobody even bothered to try to figure out whether
variability in distribution mattered just as much as long term composition. I
will go deeper into the issue in medical discussion in Part III but it turned
out that the effect of variability in food sources and the nonlinearity in the
physiological response is central to biological systems. Consuming no
* The other problem is that of the misunderstanding of the nonlinearity of natural
resources, or anything particularly scarce and vital. Economists have the so-called law
of scarcity, by which things increase in value according to their demand —but they
ignore the consequences of nonlinearities. My former thesis director Hélyette Geman
and I are currently proposing a “law of convexity” that makes commodities,
particularly vital ones, even more dear than previously thought.
When The Average is Irrelevant 63
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protein at all on Monday, and catching up on Wednesday seemingly causes a
different —better— physiological response, possibly because the deprivation,
as a stressor, activates some pathways that facilitate the subsequent
absorption of the nutrients (or something similar). And, until a few recent
(and disconnected) empirical studies, this convexity effect has been totally
missed by science —though not by religions, ancestral heuristics, and
traditions. And if scientists get some convexity effects (doctors understand
here and there nonlinearities in dose-response), the notion of convexity
effects itself, though, appears completely missed from the language and
methods, particularly biology, economics and other complex systems where
it belongs the most. No wonder there is no word for antifragility in
vocabularies.
Why Planes Don't Arrive Early
Travelers (typically) do not like uncertainty. This is a straight application of
convexity effects: fragility dislikes variability and volatility.
To see how these convexity effects play a role with any estimation and
model error, consider the following. I've taken the very same Paris-New York
flight most of my life. The flight takes about 8 hours, the equivalent of a
French novel plus a brief polite chat with a neighbor and a meal with
Bordeaux wine. I recall many instances in which I arrived early, about twenty
minutes, no more. But there have been instances in which I got there more
than 2 and 3 hours late, and, in at least one instance, it has taken me more
than two days to reach my destination.
Because travel time cannot be really negative, uncertainty tends to
cause delays, making arrival time increase, almost never decrease. Or it
makes arrival time just decrease by minutes, and increase by hours, an
obvious asymmetry. Anything unexpected, any shock, any volatility is likely
to extend the total flying time. As we will see it is very similar (though in
opposite effect) to a financial option: you cannot lose more than the
premium you spend for it and, because of that, any volatility benefits it.
This also explains the irreversibility of time, in a way, if you consider
the passage of time as an increase in disorder.
WHEN THE AVERAGE IS IRRELEVANT
We just saw with the number of cars on the highway that in the presence of
nonlinearities, the variability (or volatility) matters as much as, and
sometimes even a lot more than, the average. This is crucial, as there is a
mathematical property called “Jensen’s inequality” that shows that in
systems with positive convexity, the average underestimates the long term
benefits, and in those with negative convexity (that is, concave) ones, it
overestimates it. Let us start with the case of a grandmother’s thermal
happiness.
How to Lose a Grandmother
You are just being informed that your grandmother will spend the next two
hours at the very desirable temperature of seventy degrees Fahrenheit
(about twenty one degrees Celsius). Excellent you should think, since seventy
degrees is the optimal temperature for grandmothers. Since you went to
Business School, you are a “big picture” type of person and are satisfied with
the summary information.
But there is a second piece of data. Your grandmother, it turns out, will
spend the first hour at zero degrees Fahrenheit (around minus eighteen
Celsius), and the second hour at one hundred and forty degrees (around 60º
C), for an average of the very desirable Mediterranean-style seventy degrees
(21º C). So it looks like you will most certainly end up with no grandmother,
a funeral and, possibly, an inheritance.
Clearly, temperature changes become more and more harmful as they
deviate from seventy degrees. As you see, the second piece of information,
the variability, turned out to be more important than the first. The notion of
average here is of no significance when one is fragile to variations —the
dispersion in possible thermal outcomes here matters much more than the
average. Your grandmother is fragile to variations of temperature, to the
volatility of the weather. Let us call that second piece of information the
second order effect, or, more precisely the convexity effect.
Here, consider that, as much as a good simplification the notion of
average can be, it can also be a Procrustean bed. The information that the
average temperature is seventy degrees Fahrenheit does not simplify the
situation for your grandmother. It is an information squeezed into a
Procrustean bed —and these are necessarily committed by scientific
When The Average is Irrelevant 64
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modelers since a model is, by its very nature, a simplification. You just don't
want the simplification to distort the situation to the point of being harmful.
Do not cross a river if it is four feet deep. We will see why numerical
summaries bring sucker problems.
Figure 4 shows the fragility of the health of the grandmother to
variations. If I plot health in the vertical axis, and temperature on the
horizontal one, I see a shape that curves inward —a “concave” shape, or
negative convexity effect.
If the grandmother’s response was “linear” (no curve, a straight line),
then the harm of temperature below seventy degrees would be offset with
benefits of temperature above it.
Figure 12 Fragility: Health as a function of temperature curves inward. A combination of 0 and 140 degrees (F) is worse for your grandmother's health than just 70 degrees. In fact almost any combination averaging 70 degrees is worse than just 70 degrees*. The graph shows concavity or negative convexity effects —curves inward.
Take this for now as we rapidly move to the more general attributes; in
the case of the grandmother’s health response to temperature:
a) there is nonlinearity (the response is not a straight line, not “linear”),
* I am simplifying a bit. There may be a few degrees variations around 70 for
which the grandmother might be better off than just 70, but I skip this nuance here. In
fact younger humans are antifragile to thermal variations, up to a point, benefiting
from some variability, then lose such antifragility with age (or disuse, as I suspect that
thermal comfort ages people and makes them fragile).
b) it curves inward, too much so.
c) the more nonlinear the response, the less relevant the average, and
the more relevant the stability around such average.
The Average is For Nerds
And, what is crucial, the absence of relevance of the average in many
domains has an epistemological dimension, linked to the idea that has
haunted me since childhood that the simplification of nerds tends to fragilize
or misses something in its reduction—which is another way to show why
fragilistas are more likely to be nerds.
The key, as we saw in Chapter x is the table of equivalence is that what
benefits from disorder benefits from the unknown.
And, a hint of what is to come in the discussion on rationalism,
remarkably, as I said earlier, those we deem intelligent, as they tend to
succeed in classes (particularly mathematics) and do well on SAT-style
exams, then make it to, say, MIT, in other words, the nerds, are even more
vulnerable to this mental distortion, and cause horrendous harm. Why?
Since the very definition of intelligence we use is grounded in their ability to
focus, hence contract and simplify, deal with, say, the average instead of a
richer set, and become blind to these small nuances. And the core of things
—of life— can reside in these nuances.
I said that reduction, compression of information in cases distorts. But
then “opinion” will also be irrelevant. Just like saying “seventy degrees” is
meaningless in the case of the grandmother, many other similar statements
such as “True/False” or “on balance” can be equally flawed. But there is
more: the convex will outperform, but we discuss a bit later with Thales’s
insight.
Walk, Don’t Run
Another illustration, this time a situation that benefits from variation—
positive convexity effects. Take two brothers, Castor and Polydeuces, who
need to travel a mile. Castor walks the mile at a leisurely pace and arrives at
destination in twenty minutes. Polydeuces spends fourteen minutes playing
with his handheld device getting updates on the gossip, then runs the same
mile in six minutes, to arrive at the same time as Castor.
Antifragility and Positive Convexity Effects 65
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So both persons have covered the exact same distance, in exactly the
same time —same average. Castor who walked all the way presumably will
not get the same health benefits and gains in strength as Polydeuces who
sprinted. Health benefits are convex to speed (up to a point, of course).
The very idea of exercise is to gain from antifragility to workout
stressors —as we saw, lifting weight, exerting exercise are just exploitations
of convexity effects.
ANTIFRAGILITY AND POSITIVE CONVEXITY EFFECTS
I am here equating and mapping everything we call fragility and antifragility
into beneficial and harmful convexity effects. It makes matters simple to
explain and tie together scientifically and provides a universal tool to detect
fragilities, a simple test, and one that will prove useful throughout the book.
The idea of nonlinear effects had been occupying my mind since the days
when I was a student, and I chose to build a professional career around it,
but I did not realize that there could be a systematic way to see clearly
through the connections, sort of a general theory until I (accidentally) coined
the term antifragility. When the universality of the application of idea
became obvious —for instance it is completely behind Black Swan events
(sensitivity to large deviations comes from harmful convexity effects)— I
wrote it down on paper in very technical language and submitted it to a
technical journal in June 2011. My idea is not just that convexity effects are
fragility (and antifragility), but that we could identify them with very simple
method that measure convexity, which makes life much, much simpler. It
means that there is a very simple mathematical property behind things,
behind the reason things survive and flourish.
So we have with convexity effects the hidden expression of antifragility
—and a way to show how things have managed to survive and flourish
against that inexorable debunker of fragility, time, time that smartest of all.
And a formal, precise, and mathematical way to express the difference
between items in the triad, the central classification we made in Table 1.
The thought of applying the exact same test as the grandmother’s
temperature to everything that matters came to me one day as I was looking
at a porcelain cup. It dawned on me —the idea I expressed at the beginning
of the chapter—that the cup was breakable because, craving a certain form of
stability, it does not like disparity of outcomes —or, in other words, as we
said, higher intensity brings more harm (up to a point). To repeat the logic,
and present another view of negative convexity effects as not liking variation
(for a given average), if I drop the cup from a height of five inches once and
one tenth of an inch ninety nine times, if will break. But the average is about
one tenth of an inch. So the cup does not depend on the average height of the
drop, but on the variation around such average. I realized that everything
fragile has to have such property, the convexity effect, and that was it.
This intuition came to me as a trader as I specialized in anything
nonlinear. I may be a little ahead here, as options are coming later, so what
is to note is that I saw that a move of twenty percent in the markets was a
hundred times better for me than a move of four percent. That was the entire
foundation of my work.
We said that if the porcelain cup was linearly harmed, it would be
affected every time you put your finger on it. But there is a difference
between the mechanical and the organic. A cup may be harmed by long term
use, owing to what is called “material fatigue”, and never strengthens
organically from use, but humans and other biological entities not only do
not suffer material fatigue but , actually, as we saw in Chapter 1, age faster
when they are not used.*
The Effect on the Unseen
Let me stop and summarize the point of this (very central) l chapter. Behind
fragility and antifragility there is nonlinearity (convexity or concavity). The
method of ferreting out hidden convexity effects can be generalized; it is not
much more complicated than that but obvious points tend to disappear from
learned minds.
A more important discussion in this chapter is the extension to the
problems of knowledge: since the convexity effect is unseen, not visible, it
carries epistemological considerations. Those who do not see it or take it into
account will have a sucker problem. And boy, quite a sucker problem.
Further, convexity is a replacement for intelligence.
* The type of accumulated harm called “material fatigue” causing sudden
(discontinuous) break is different from progressive disintegration as they play a
different role in overall breakage.
Thales of Miletus 66
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Let us now forget about the grandmother, traffic, etc. for a few pages,
and go to the source of this convexity effect: both the notion of optionality
and the very beginning of the idea of philosophy.
The Secret Language of Convexity
This second order effect, the source of both fragility and antifragility, is the
secret of life, behind evolution, almost everything —though hidden in the
background. It is a dimension that few manage to see consciously, let alone
notice; as we saw in Chapter 1, this is similar to cultural without biological
colorblindness, causing us to be less aware of it culturally than practically.
Imagine the following Procrustean bed situation: living in a world in
three dimensions (our world, in 3-D), but seeing things in only two
dimensions (2-D). The missing dimension (variability) will be a problem,
but (I assume) not too big a deal if you are an ant and live in a perfectly flat
surface with no consequential indentations. If you happen to be a bird,
however, three dimensions would matter a lot more for you. In the case of
the grandmother, the missing dimension is linked to the variability around
the average. The first dimension is the desired average temperature (you are
interested in seventy degrees); the second one is the effect of the variability
of the temperature on her health.
Where is this second order effect ignored? The rest of the book will
present longer discussions; let me say for now that it is ignored almost
everywhere where it matters: medicine, business, economics, government
policies, risk studies, Harvard-Soviet inspired policies, computation of
governmental deficits, projection of cash flows by firms, etc. Anything
modern and man-made will be affected. The convexity effect is sometimes
identified and studied locally for a special situation, but never systematically
or globally. Scholars who get it in one domain over a problem miss it in
another.
And remarkably, this effect seems to provide a secret language of
antifragility, the language of nature, as nature is master at these convexity
effects.
THALES OF MILETUS
An anecdote appears in Aristotle's Politics concerning the pre-Socratic
philosopher and mathematician Thales of Miletusxxx. This story, barely
covering half a page, is at the center of both this entire idea of antifragility
and its denigration. And the remarkable aspect of this story is that Aristotle,
arguably the most influential thinker of all times, got the central point of his
own anecdote exactly backwards. So did his followers, particularly after the
enlightenment and the scientific revolution. I am not saying that to denigrate
Aristotle, but to assert the main idea of this book: intelligence makes you
discount antifragility and ignore convexity effects.
Thales was a Greek-speaking Ionian of Phoenician stock philosopher
from the coastal town of Miletus in Asia Minor, and like some philosophers,
enjoyed what he was doing. Miletus was a trading post and had the
mercantile spirit usually attributed to Phoenician settlements. But Thales, as
a philosopher, was characteristically poor. So he got tired of his buddies with
more transactional lives telling him that "those who can, do, and others
philosophize". He set to prove that he could both “do” and philosophize, and
that he chose to philosophize out of love and respect for the occupation, not
because he had no other option. So he performed the following prowess: he
put a down payment on the seasonal use of every olive press in the vicinity of
Miletus and Chios which he got at low rent. The harvest turned out to be
extremely bountiful and there was demand for olive presses, so he let the
owners of olive presses on his own terms, realizing large sums of money.
What he collected was large, perhaps not enough to become massively
wealthy, but enough to make the point that he could talk the talk and was
truly above, not below, wealth. This in my vernacular I've called "f*** you
money" —a monetary sum large enough to get most of the advantages of
wealth (the most important one being independence and the ability to
occupy your mind with matters that interest you) but not its side effects of
filth, conversations with the name-dropping class, chronic stresses
associated with a large estate and the multiplicity of servants, and hidden
punishment from material benefits. Worse, imagine the greatest punishment
for a philosopher: having to attend a black-tie charity event and being forced
to listen to polite exposition of the details of the marble-rich house
renovation —beyond a certain level of wealth and independence, people tend
to be less and less personable and their conversation less and less
interesting.
Strong and Weak Antifragility 67
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The story has many morals, all of which permeate this book. But the
central one is related to the following account by Aristotlexxxi: "But from his knowledge of astronomy he had observed while it was still winter that there was going to be a large crop of olives..." So for Aristotle, clearly, the
stated reason was Thales' superior knowledge. Knowledge.
If we look at it with the eyes of antifragility, the story is altogether
different. It is, rather, the skilled expression and exploitation of ignorance,
not knowledge. Thales put himself in a position to take advantage of his lack
of knowledge —and the secret property of convexity effects. The key to the
message of this book is that he did not need to understand too much the
messages from the stars.
Simply, he had, an option, “the right but not the obligation”, which he
bought cheap: there was no need to be right on average —so long as you pay
a low price that allows you to have greater upside than downside. His payoff
was so large that it could have afforded him to be wrong very, very often and
still make a bundle in the long run. Explained in another way: he had a
positive exposure to Black Swans, convex and antifragile to variations —
recall graph 3 on page x.
This is the center of my ideas about knowledge, as we shall see in
chapter x as Fat Tony rules —and my association of antifragility in exposure
and the problems of knowledge. We just don't need to know what's going on
when we buy cheaply —when we have positive convexity effects. But this
property goes beyond buying cheaply: we do not need to understand things
when we have some edge. And, I repeat, the edge is in the larger payoff when
you are right
How is there convexity when one has limited downside? Look at Figure
x. The vertical axis has the profits, the horizontal axis the rent. I use in this
example, for currency of Asia Minor, the stater, a variant of the Phoenician
Thekel, sometimes spelled Shekel, which means “weight” in Semitic
languages. Figure x [7] the asymmetry as in this situation, the payoff is larger
one way (if you are right, you “earn big time”) than another (if you are
wrong, you “lose small”).
Figure 13- Thales' antifragility- He pays little to get a huge potential. We can see positive convexity effects in his payoff as his payoff curves outward (think “smile” as in Figure x), particularly on the left side of the graph. Note that trial-and-error tends to have the same payoff of limited downside.
All the reader needs to note from the picture is the asymmetry I
mentioned earlier. It is convex, owing to its shape that curves outward. The
opposite to the health of the grandmother in Figure x. And the exact same
shape (though in reverse) as what we saw in the graph of traffic to JFK in
Figure x.
STRONG AND WEAK ANTIFRAGILITY
Economics is a number... the sky is the limit. When we work with an
unbounded variable...
Figure 14- Strong Antifragility (Extremistan)
Options 68
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Figure 15 – Weak Antifragility (Mediocristan), with bounded maximum
Other Morals
There are other morals related to the theme of this book, antifragility, and
the ethical considerations developed in Chapter x. Financial independence
makes you robust; it allows you to make the right choices without
modernity’s middle class disease of fitting ethics to profession. And a thinker
who does not have a patron does not have the fragilities, the fear of offending
the hand that feeds him. Further, it allows freedom from the university
system and avoids the prostitution of academia (academia is to knowledge
what prostitute is to love).
But there is the notion of internal motivations: plenty of people are
poor against their initial wish and only become robust by spinning a story
that makes them lose their fragility to income and develop the illusion of
being poor by choice, as if they had the option. But they don’t really have the
option —they constructed it. The essayist Michel de Montaigne sees the
Thales episode as a story of avoidance of sour grapes: you need to know
whether you do not like the pursuit of money and wealth because you
genuinely do not like it, or because you are rationalizing your inability to be
successful at it with the argument that the grapes you cannot reach are sour.
Are you fooling yourself? So the episode enlightened Thales about his own
choices in life –how genuine his pursuit of philosophy was. He had other options. And, it is worth repeating, options, any options, by allowing you
more upside than downside, have positive convexity effects, hence harbor
antifragility*.
*I suppose that the main benefit of being rich (over being just independent) is to
be able to despise rich people (a good concentration of whom you find in glitzy ski
resorts) without any "sour grapes" (i.e., when someone convinces himself that he is not
A second moral is that there are two varieties of people: those who
write books or those who write checks for other people to write books,
create, innovate, or pursue knowledge and claim some credit for having
facilitated it. Rich people can enhance their obituary or buy some form of
minor immortality by having a building, a hallway or, perhaps, a small
staircase named after them. They can also buy some derivative social
prominence in ceremonies for patrons of the arts. The recipients would look
at them with a mixture of scorn or resentment, sometimes with a modicum
of gratitude (the snobbish conductor von Karajan called the Carnegie Hall
philanthropists the “fur coat set” buying their way into creativity). Thales,
however, by funding his own philosophy, became his own Maecenas, perhaps
the highest rank one can attain: that of being both independent and
intellectually productive. He now had even more options.
OPTIONS
We can formulate this rule about asymmetry: If you make more when you are right than you are hurt when you are equally wrong then you have positive convexity effects and you will benefit, in the long run, from volatility (and the reverse). This asymmetry equates to my rule of
accelerated benefits.
An option (as opposed to an obligation) has an asymmetry: because you
have the upside (you have the option of taking the good and neglecting the
bad), with little downside (no obligations). You will be antifragile when you
have it unless, of course, you pay too much for it. The next few examples will
attempt to makes matters clearer. The next few vignettes will present the
notion of options situations similar to those of Thales.
Saturday Evening In London
A first example of what an option is. It is Saturday afternoon in London. I am
coping with a major source of stress: where to go tonight. I am fond of the
brand of the unexpected one finds in parties (going to parties, we will see, is
an option, perhaps the best advice for someone who wants to benefit from
uncertainty with low downside). My fear of eating alone in a restaurant while
interested wealth in order to feel good for being wealthy). It is even sweeter when they
don't know that you are richer than they are.
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re-reading the same chapter of Seneca's Letters that I have been carrying for
a decade to read whenever I am eating alone; my fear was alleviated by a
telephone call. Someone, not a close friend, upon hearing that I was in town,
invited me to a dinner gathering in Kensington, but somehow did not ask
me to commit, with the "drop by if you want". Going to the party is better
than eating alone with Seneca's Letters, but these are not very interesting
people (many are involved in the City and people employed in financial
institutions are rarely interesting and even more rarely likeable) and I know
I can do better, but I am not certain to be able to do so. So I can call around:
if I can do better than the Kensington party, with, say, a dinner that groups
any of my friends J.G, B.A, and W.G., or similarly charming and erudite
people with, I would go there. Otherwise I would take a black taxi to
Kensington. I have an option, not an obligation. It came at no cost since I did
not even solicit it. So I have a small, nay nonexistent downside, a big upside.
Your Rent
Second example: consider living arrangements. Assume I am the official
tenant of a rent-controlled apartment in New York City. I have the option of
staying in it as long as I wish, and no obligation to do so. Should I decide to
move to Ulan Bator, Mongolia, and start a new life there, I can simply notify
the landlord a certain number of days in advance, and thank you good bye.
Otherwise, the landlord is obligated to let me live there somewhat
permanently, at a predictable rent. Should rents in town increase
enormously, and real estate experience a bubble-like explosion, I am largely
protected. On the other hand, should rents collapse, I can easily switch
apartments and reduce my monthly payments --or even buy a new
apartment and get a mortgage with lower monthly payments.
So consider the asymmetry. I benefit from lower rents, but am not hurt
from higher ones. How? Because here again, I have an option, not an
obligation. In a way uncertainty increases the worth of such privilege. Should
I have a high uncertainty about future outcomes, with possible huge
decreases in real estate value, or huge possible increases in them, my option
would become more valuable. The more uncertainty, the more valuable the
option.
Books, Again
Let us assume that there is for your reputation the equivalent to an Amazon
review (ranking between one and five stars, one star meaning horrible and
five stars meaning, literally, stellar), freely posted in the public domain by
people you may or may not know. You are fragile —in reputation— if you
prefer to have 100 pct four stars rather than 80% five stars and 20% one-
star. Just like the grandmother, you do not want dispersion as you feel severe
harm from the one-star comments. On the other hand you are robust, or
antifragile when you do not care about the bad reviews and, like an option,
focus on the good ones hence love dispersion.
Let me repeat: you care more about the average than about the
volatility (or dispersion) around the average. Fragile is when you don’t like
dispersion, antifragile when you prefer it.
Further, when it comes to real books or ideas, the convexity effects is
much more accentuated. As I wrote in the last chapter, an author or artist or
even a philosopher is much better off when a very small segment of the
readers people like his work, mildly, on average, rather than have a very
small number of fanatics and a large majority of indifferent or haters. This
should be clear now in light of optionality —this we call a remote option.
Because, as in Thales’ option, all that matters is the upside, and the most
fanatic fans and supporters is what counts. The more uncertainty, the more
upside. Those who do not buy your book or your work do not have a negative
contribution beyond not buying your book. Further, it helps when the
supporters are both enthusiastic and influential. Wittgenstein, for instance,
was largely considered as a lunatic (he almost had no publications to his
name), but had very few main fans creating a cult, and some, like Bertrand
Russell and J.M. Keynes, were massively influential.
THE THALESIAN AND THE ARISTOTELIAN
The Thalesian focuses on the payoff, the consequence of the actions (hence
includes convexity effects). The Aristotelian focuses on being right and
wrong—raw logic. They intersect less often than you think.
For Fat Tony, the distinction maps into sucker-nonsucker. Things are
always simpler with Fat Tony.
In real life, exposure is more important than knowledge; decision-
effects supersede logic. Textbook “knowledge” misses a dimension, the
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hidden convexity effect —just like the notion of average. The need to focus on
the payoff from your actions rather than the structure of the world (or
understanding the “True” and the “False”) has been largely missed in
intellectual history. Horribly missed. The payoff, what happens to you (benefits or harm from it), is always the most important thing, not the event itself. In other words, let me repeat it, that we need to be smarter in doing than knowing, better in acting, than understanding —wiser, less error
prone, and, of course, better for long term survival of our species. But the
giant of rationalism, the Medieval philosopher Averroes (Ibn Rushd)
considered Aristotle the supreme expression of human intellect — precisely
because the latter represented “rationalism”, the pure reliance on reasoning,
that thing we call reasoning, in comprehending things. And visibly this is
the very reason Aristotle missed the point, because he overestimated the
reach of human reasoning. Thales' success was automatically imparted to
knowledge about the stars, or about the future coming from the stars, not
from the nature of the bet.xxxii
So Aristotle overvalued knowledge and discounted the action, or
decision, taken off that knowledge.
My point is that True and False (hence what we call “belief”) play a
poor, secondary, role in human decisions; it is the payoff from the True and
the False that dominates —and it is almost always asymmetric, with one
consequence much bigger than the other, i.e. harboring positive and negative
convexity effects. Let me explain. We check people for weapons before they
board the plane. Do we believe that they are terrorists, True or False? False,
as they are not likely to be terrorists (a small probability). But we check them
nevertheless because we are interested in the payoff, and the consequence, or
payoff of the True (that they turn out to be terrorists) is too large and the
costs of checking are too low. Do you think the nuclear reactor is likely to
explode in the next year? False. Yet you want to behave as if it were True and
spend millions on additional safety. A third example: Do you think that this
random medicine will harm you? False. Do you ingest these pills? No, no,
no.*
* Philosophers are split into two categories, those who believe in absolute truth
and falsehoods, usually analytical tradition, and those who believe in the relativity of
truth and falsehood, found in many traditions including the school called the
pragmatists (as well as those called continental and postmodern philosophers). My
message is entirely within the analytical tradition (if not even more extreme); it is not
If you sat with a pencil and jotted down all the decisions you’ve taken in
the past week, or, if you can, over your lifetime, you will realize that almost
all of them have asymmetric payoff, with one side carrying a larger
consequence than the other. There is a positive or negative convexity effect
somewhere since what has big downside, small upside is concave and the
reverse.
So we go by the True- False distinction only in situations of symmetry,
say flipping a coin, where the gains of one outcome are equal to the loss of
the other, and these seem to only exist in logical textbooks. Now I am not
getting into post-modern denial of True or False, to the contrary; I am just
saying that it is insufficient a representation, like using a two dimensional
drawing for something in three dimensions.
That payoffs are more important than events is intuitively grasped in
some applications. But all of the examples above (terrorist, nuclear plant,
medication), representing a small probability of a very large adverse
outcome, are easy to understand as we humans are well wired for risk
aversion (when I talk about Black Swans most people tend to immediately
imagine negative things). These examples correspond to situations of
fragility, the ones I showed in column one of Table 1 and in Figure 2. And we
still have enough instinct (unless we studied economics) to understand that
mitigating fragility is more important than knowledge. Now, the Thales
story represents the exact mirror image of these unlikely favorable outcomes,
of a small probability of a large and unbounded favorable outcome (to
Thales). It is antifragility, and this has not penetrated our philosophical
consciousness†.
Confidence levels. Let me rephrase the idea of the irrelevance of
True/False in decision-making in the real world, particularly when
probabilities are involved. Scientists have something called “confidence
level”; a result obtained with a 95% confidence level means that there is no
more than 5% probability of the result being wrong. The idea of course is
inapplicable for the same reason of size of effects, and extreme events. If I
tell you that some result is true with 95% confidence level, you would be
that True and False are irrelevant, but rather that the distinction is insufficient for
decision-making.
† Thales’ bet is not at all similar to a lottery ticket (which is a human artificial
contraption), mostly because the outcome is both unknown and unbounded, i.e., we do
not know the upper limit.
Bachelier, Jensen and Friends 71
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quite satisfied. But what if I told you that the plane was safe with 95%
confidence level? Even 99% confidence level would not do, as a 1%
probability of a crash would be quite a bit alarming (today commercial
planes operate with less than 1 in 100,000 probabilities of crashing and the
ratio is improving). So the probability (hence True/False) does not work in
the real world; it is the payoff that matters.
How to be Stupid
Accordingly, you don't have a need for much of what is commonly called
intelligence, knowledge, insights, skills, and these complicated things that
take place in the brain cells. For you don't have to be right that often. All you
need is wisdom to not do foolish things to hurt yourself (some acts of
omission) and know if an outcome if fine (after its occurrence), not before.
Otherwise, if convexity effects work against you, sorry, but you are doomed,
no matter how intelligent you are and how many PhDs from Harvard are on
your staff—for there may be a small thing that will escape you and hurt you
very badly. The hair holding the sword of Damocles will eventually break, in
time, with certainty.
I learned about convexity effects in class at the Wharton School, in the
lecture on financial options that determined my career, and immediately
realized that the professor did not understand it himself —he understood it
in spots, but not everywhere. It hides where we don't want it to hide. I will
repeat that options benefit from variability and convexity effects.
BACHELIER, JENSEN AND FRIENDS
The discovery of convexity effects (though not the connection to fragility)
was made by several men, one of whom got a bit of mishandling by history*.
On March 29, 1900, a student at the Sorbonne who worked as a
stockbroker in order to support himself, Louis Bachelier, defended a doctoral
thesis in mathematics. The idea was about how to value financial options,
these asymmetric contracts that give the right but not the obligation to buy a
stock at a specified price (also called contingent claims). Now finance being
* A technical point. The following researchers discovered first order convexity
effects; fragility and antifragility are second (and higher) order convexity effects. See
Appendix X.
an uninteresting (and largely despicable) subject, there is no need to focus
on the subject and figure out what a financial option is beyond that it is “a
right not an obligation” (as with the dinner in London), that one can buy for
small and that can carry an occasional (and rare) payoff, large upside and no
or small downside (for the owner). In short, the option has convexity effects†.
Bachelier’s doctoral thesis was poorly received by the head of the
committee, no less a person than the great mathematician and scientific big-
picture thinker Henri Poincaré. So Bachelier received the grade
euphemistically called "honorable", not the "très honorable" that was
necessary to get a real academic position. His work was said to lack in rigor but there was also this unattractiveness of the financial topic for the
committee: finance was never seen in France as particularly respectable
intellectually. Bachelier never managed to have a decent academic career as
he was plagued with the stigma, along with an additional black ball when, in
his fifties, he was about to get his first real position of professor. Many
people later rediscovered his results in the pricing of derivatives, and
something I find scandalous, two men, Robert Merton and Myron
Scholesxxxiii, received the Bank of Sweden Prize in Economic Sciences (called
the "Nobel" in economics) as the Swedish academy, rather poor in
knowledge of the history of ideas, had the illusion that they discovered his
equation. Furthermore, Robert C. Merton, while trying to pass for “option
guru” had spent his career developing models in finance that increase risks
precisely that they missed convexity effects.
In addition, in that very same doctoral thesis, Louis Bachelier observed
properties of randomness that were rediscovered (and publicized) by
Einstein five years later. More depressingly the man who disparaged him,
quite unfairly, Henri Poincaré, has been my intellectual hero most of my
conscious life and that of most people who like the notions complexity.
Another giant who missed the point of antifragility –there will be many
more.
Note that Bachelier was an option trader (who disliked his career) —
and this book, which has almost nothing to do with finance, will be driven by
similar intuitions by yours truly, a former option trader (who disliked his
career). Now that I got the sad story of Bachelier off my chest, let's forget
about economics for a few chapters.
† Further, my experience shows that the only interesting options are the “hidden”
ones, those that are not recognized as financial options.
Why Some Errors Go One Direction 72
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Bachelier was using a result he took for granted, but that was
formalized (in much simpler form) five years later, completely
independently. The more formal presentation of that result took place as
follows, five years later. On 17 January 1905, one Johann Ludwig Jensen, an
obscure mathematician, by day Danish employee of a telephone company,
exposed in a presentation some derivation showing the convexity effect on
the long term average, showing in the grandmother’s story that the average
health of the grandmother across temperatures is worse, “unequal” to her
health for a single average temperature.xxxiv Jensen, in fact, was generalizing
an earlier, almost a century old result by the French mathematician
Augustin-Louis Cauchy. Neither he nor the audience realized how
fundamental this result was for about everything —no more than the
audience in the thesis committee of Monsieur Bachelier, knew the import of
that poor man's work. The paper by the Dane was published the following
year in French in the Swedish mathematical journal Acta Mathematica with
the eloquent title “On convex funtions and their inequality for average
values” ("sur les fonctions convexes et les inégalités entre les valeurs
moyennes") —and went unnoticed for a long time, a very long time, as, 105
years later I hardly found anyone who took its consequences to their
conclusion. I built on his result to extend it from the effect of convexity on
the “average” to “dispersion”, hence fragility and antifragility.
The plot is even thicker. It was recently discovered that a French
intellectual and stockbroker Jules Regnault in Calcul des chances et philosophie de la bourse , published in 1863, also discovered a milder form
of these effects —but unlike Bachelier he used his knowledge to make f***
you money over a few years and become catalogued a rentier.
WHY SOME ERRORS GO ONE DIRECTION
We saw that errors and uncertainty tend to make planes land later, not
earlier. Same with traffic, disturbances tend to increase travel time from
Kensington to Picadilly circus, never shorten it.
The errors are one-sided: that’s a negative convexity effect (the
opposite of, say, a Thales bet or an option-style position in which errors tend
to be positive). So this typically causing both underestimation of randomness
and underestimation of harm owing to the fact that one is more exposed to
harm than benefits; as we call it he is “short an option”.
Example of such situations: Predictions of projects, wars, deficits...
{discussion on the graphs}
Projects and prediction
Just as when you add uncertainty to a flight, the planes tend to land later,
not earlier, projects tend to cost more (and take longer). This applies to
many, in fact, almost all projects. In The Black Swan I showed that the
underestimation of the random structure of the world (Mediocristan as
opposed to Extemistan) caused such problems —these unexpected Black
Swan events tend to hit by lengthening, not shortening project time. Black
Swan blindness was the source.
The puzzle was of course that many large-scale projects one and a half
centuries ago were completed on time; many of the tall buildings and
monuments we see today were completed within, and often ahead of
schedule. These include not just the Empire State Building (still standing in
New York), but such items such as the Crystal Palace erected during the
Great Exhibition of 1851, the hallmark of Victorian reign, based on the
inventive ideas of a gardener. The Palace, which housed the exhibition, went
from its organization to the grand opening in just nine months. The building
took the form of a massive glass house, 1848 feet long by 454 feet wide and
was constructed from cast iron-frame components and glass made almost
exclusively in Birmingham and Smethwick.
The obvious is usually missed here: the Crystal Palace project did not
use computers, and the parts were built not far away from the source, with a
small number of entities as part of the food chain. Further, there were,
thankfully, no business schools at the time to teach something called “project
management” and increase overconfidence. And there were no consulting
firms and the agency problem was weak. In other words, it was a much more
linear economy —less complex— than today.
I had been telling anyone who would listen to me that Black Swan
effects had to be increasing, necessarily as a result of complexity,
interdependence between parts, globalization, and the beastly thing called
“efficiency” that make people now sail too close to the wind. Add to that
consultants and business schools. One problem somewhere can halt the
entire project —so the projects tend to get as weak as their weakest link in
the chain (an acute negative convexity effect). The world is getting less and
Why is The Large Fragile? 73
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less predictable, and we rely more and more on technologies that have errors
and interactions that are harder to estimate, let alone predict.
And the information economy is the culprit. My colleague Bent
Flyvbjerg showed that the problem of cost overruns and delays is much more
acute in the presence of Information Technologies (IT), as computer projects
cause a large share of these costs overruns and it is better to focus on these
principally (Black Swan Risks are often solved with small rules, not
complicated ones)xxxv. But even outside of these IT-heavy projects, we tend to
have very severe delays. And, of course there is the fallacy of prediction:
these are underestimated, and chronically so.
But the logic is simple: negative convexity effects are the cause. There is
an asymmetry in the way errors hit you. Decision scientists and business
psychologists have theorized something called the “planning fallacy”, in
which they try to explain the fact that projects take longer rarely shorter with
recourse to psychological factors, which play a role but less than Black Swan
effects. Decision scientists ground it in human errors, not in exposure to
Extremistan, with in this case exposure to negative Black Swans rather than
positive Black Swans. But no psychologist realized that, at the core, it is not
the psychological problem, but part of the nonlinear structure of the project.
Just as time cannot be negative, a three month project cannot be completed
in zero or negative time. So errors add to the right end, not the left end of it.
If uncertainty were linear we would observe some projects completed early
(just as we would arrive sometimes early, sometimes late). But this is not the
case.
Wars, Deficits, and Bonds
The second war was estimated to last only a few month; by the time it was
over it got France and Britain heavily in debt, at least ten times what they
thought their financial costs would be, aside from all the destruction. The
same of course for the second war caused the U.K. to become heavily
indebted, mostly to the United States.
In the United States the prime example remains the Iraq war, expected
by George W. Bush and his friends to cost thirty to sixty billions, and so far
can be at more than two trillion. Complexity, once again.
But wars are only illustrative of the way governments underestimate
convexity effects and why they should not be trusted with finances.
Governments do not need wars to run deficits: the underestimation is
chronic for the very same reason ninety-eight percent of modern projects
have overruns.
WHY IS THE LARGE FRAGILE?
We can apply the idea of convexity effects here —in fat the exact same graph
as the one about travel time — on the idea of size. When one is large, one
becomes vulnerable to these errors going in one direction.
To see how size becomes a handicap, consider the reasons one should
not own an elephant as a pet, regardless of what emotional attachment you
may have with an animal of such size. Say you can afford an elephant as part
of your household budget and have one delivered to your backyard. Should
there be a water shortage, you would have to pay a higher and higher price
for each additional gallon of water. That’s fragility, right there, a negative
convexity effect coming from getting too big. The unexpected cost, in
percentage of the total, would be monstrous. Owning, say, a cat or a dog
would not bring about such high unexpected additional costs over the
regular at times of squeeze —adjusting of for the size of each animal.
In spite of what is studied in Business School, size hurts you at times of
stress; it is not good for fragility.
Some economists have been wondering why mergers of corporations do
not appear to play out. The combined unit is now much larger, hence more
powerful and more “efficient”. But numbers show no gain, at best —that was
already true in 1978, as people then voiced the “hubris hypothesis” finding it
irrational for companies to engage in mergers given the poor record of the
idea. And recent data, more than three decades later, confirm the behavior.
There appear to be something with size that is harmful to corporations.
Well, like the elephant as pet, squeezes are much, much more
expensive (relative to size) for large corporations. The gains from size are
visible but the risks are hidden, and some concealed risks seems to bring
frailties into the companies —hence the system.
Let us look at a case study. On January 21, 2008, the Parisian bank
Société Generale rushed to sell in the market close to seventy billion dollars
of stocks, a very large amount for any single “fire sale”. Markets were not
very active (called “thin”) as it was Martin Luther King day in the United
States and markets worldwide dropped precipitously, close to ten percent,
costing the company close to six billion dollars in losses from their fire sale.
74
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For they had, over the weekend, uncovered a fraud. Jerome Kerviel, a rogue
back office employee, was playing with humongous sums in the market and
hiding these exposure from the main computer system. They were squeezed
and had no choice but to sell, immediately sell these stocks they didn’t know
they owned.
Now to see the effect of fragility from size, look at Figure x showing
losses as a function of quantity sold. A fire sale of 70 billion leads to a loss of
6 billion. But a fire sale of 5 or 10 billion has no loss at all, as markets would
absorb the quantities without panic. So this tells us that if, instead of having
one very large bank, with Monsieur Kerviel as a rogue trader, we had ten
smaller banks, each with a proportional Monsieur Mini-Kerviel, and each
had his rogue trading independently and at random times, the total losses for
the ten banks would be nothing.
Figure 16
We will use the argument again when discussing corporate size during
my apology of artisanal economies.
WHY IS THE “EFFICIENT” NOT EFFICIENT?
HORMESIS
Figure 17- Hormesis for an organism: we can see a stage of benefits as the dose increase (initially convex) slowing down into a phase of harm as we increase the dose (initially concave), then things flattening out at the level of maximum harm (beyond a certain point, the organism is dead so there is such a thing as a bounded and known worst case scenario in biology) – Note that (medical papers and textbooks make the mistake of having concave curve at the early stages, which would be mathematically impossible).
A Second Graphical Interlude 75
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Figure 18- Wrong graph showing initial convexity
A SECOND GRAPHICAL INTERLUDE*
Let us look at the point graphically†, but in a different manner, this time
looking at probabilities.
The Horizontal line presents outcomes, the vertical one their
probability (i.e., their frequency). This is a different representation —this
time, probabilistic — of the outcomes. Before that we saw functions and
variable, with nonlinear responses between one and the other. And before
that we saw what is called the time series: what happens over a certain
period, with the passage of time
Absence of convexity effects are shown to the first graph, Figure x —the
symmetric case, as the potential gain is somewhat equal to potential harm.
Figure 19- Case 1, the Symmetric. Injecting uncertainty in the system makes us move from one bell-shape —the first, with narrow possible spate of outcomes—to the second, a lower peak but more spread out. So it causes an
* The intelligent reader innocent of social science and economics can most
certainly skip these graphs as there is nothing for him to unlearn.
† Technical note: when a payoff has negative skewness, increases in dispersion (or
variance, volatility) lead to a degradation of the expectation, making it more negative.
Hence underestimation of uncertainty implies underestimation of the expected
variable. I show in the appendix (as well as in Taleb, 2011) how a concave payoff from
a symmetric random variable is itself a payoff with negative skewness and the
consequences for fragility, underestimation of the mean, and increases in risk.
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increase of both positive and negative surprises, both positive and negative Black Swans*.
Negative convexity effects lead to Figure x; there is a possibility of a
severe unfavorable outcome (left), much more than a hugely favorable one,
as the left side is thicker than the right one.
Figure 20- Case 2, Negative Convexity Effects, Limited gains, larger losses. Fragile, prone to negative asymmetries, negative convexity effects (for example, projects). Increasing uncertainty in the system causes an augmentation of mostly (sometimes only) negative outcomes, just negative Black Swans.
* Technical Comment: Note that I am not using in these example the classical bell-
shaped Gaussian, rather, distributions with power-law “fat tails”.
Figure 21- Case 3, Positive Convexity Effects, with Limited losses, unlimited benefits. Antifragile, prone to positive asymmetries, positive convexity effects. Increasing randomness and uncertainty in the system raise the probability of very favorable outcomes, and accordingly expands the expected payoff. Note that it is the EXACT opposite of figure x {previous}, which means that discovery is, mathematically, exactly like an anti-airplane delay.
Let us apply this analysis to how planners make the mistakes we discussed
earlier, and why deficits tend to do worse than planned:
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Figure 22- The Gap between predictions and reality: probability distribution of outcomes from costs of projects in the minds of planners (above) and in reality (below). In the top graph they assume that the costs will be both low and quite certain. The lower graph show outcomes to be both worse and more spread out, particularly with higher possibility of unfavorable outcomes. These undesirable events are on the left and we can see a left “tail” forming). This misunderstanding of the effect of uncertainty applies to government deficits, plans that have IT component, travel time (to a lesser degree) and many more.
The greater dispersion shows underestimation of uncertainty. The
worse average outcome shows underestimation of the expected outcome.
Innovation, on the other hand, have exact opposite properties of the
graph in Figure x: errors tend to cause more benefits than harm. When you
inject more uncertainty in the system, it improves.
Next: Discovery as an Anti-deficit
This chapter got deeper into the plumbing behind antifragility, evolution,
and survivorship. We used the grandmother story to present convexity
effects —sort of, the grammar of antifragility —and the story of Thales to
present this notion of “convexity”, “optionality”, something that tends to
benefit from variation and lessens our dependence on knowledge; how
convexity can supersede understanding and how Aristotle —and about most
of traditional Greek and Levantine philosophy missed the point. The
opposite situation is that of the grandmother suffering from thermal
variations.
Next, let us discuss discovery —and how it is grounded in antifragility,
hardly anything else. Just think of an airplane ride, or the costs and duration
of a project, as represented in Figure x: almost every bit of uncertainty tends
to increase your flying time, your project costs, and worsen your situation.
With discovery (and antifragile situations) the reverse holds as about every
bit of uncertainty improves your situation. Let us see how.