The Black Swan

Stephen Kinsella∗
April 28, 2008

1 How old is the earth?

In his Histoire Naturelle 1 , J. M. de Buffon, the renowned 18th Century naturalist, produced a series of
calculations designed to determine the age of the Earth.
Whilst setting up forges for smelting iron for another purpose, de Buffon began to experiment with the
cooling of iron spheres. He theorized if the earth had originated as a ball of molten lava, he could calculate
the length of time required for sufficient cooling to form a solid surface which would support life at present
day temperatures. de Buffon made a scale model of the earth from iron, and cooled it. Using a simple ratios
argument, de Buffon’s calculations showed the Earth to be at least 75,000 years old, and probably a good
deal more ancient.
From this grossly inaccurate calculation, de Buffon created a theory of species adaptation to environments
which changed over time due to planetary cooling. His theory was a shock to the accepted view of the age
of the Earth, calculated separately by Lightfoot and Ussher, at 4004 BCE, by adding up all the ages of the
prophets in the King James Bible Dalrymple (1991); Ussher (2003/1650).
Nassim Taleb’s The Black Swan is, for me, an example of de Buffon-like tinkering with reality, fused with
de Buffon-like erudition, and de Buffon-like ambition—just inverted.
Like de Buffon, Taleb skewers the false precision pretended to by Lightfoot and Ussher, and like de Buffon,
Taleb uses his own experience as the organising principle of his book. Like de Buffon, Taleb’s scholarship is
deep, wide ranging, and thorough.
The similarities end there. de Buffon wanted to know everything with encyclopedic certainty. Taleb is
convinced we can know very, very little about anything with any certainty, and spends his readers’ time
explaining this conviction throughout the 329 pages of his book. Taleb’s central argument is concerned
with asking how human beings cope in the presence of so much uncertainty. The Black Swan is a personal
essay, a meditation on a subject, relating Taleb’s specific experiences of extreme events like war, cancer, and
stock market crashes to the more general philosophical, epistemological, and practical issues of induction
and choice under uncertainty. The book itself is an inductive leap from the specific to the general. Taleb
concludes we should be more aware of the limits of our knowledge, more skeptical regarding the empirical
data we have in our possession, and more conservative about the predictions we make based on that data.
Above all, we should simply recognise the world for what it is: a Black Swan-dominated system rather than
a Gaussian-dominated system, and adjust our behaviour accordingly.
So: how do human beings cope with these highly improbable, yet improbably important events, which
Taleb calls Black Swans?
Taleb’s answer: not very well. Human psychology is designed to ignore them, constructing the illusion
of certainty where none exists. A legion of ‘empty suit’ experts2 enshrine this ignorance as ‘fact’. For me,
Taleb echoes J.S. Mill in this regard Mill (1869, Chapter II, pgs. 6–7):
∗ Department of Economics, Kemmy Business School, University of Limerick, Ireland. Email: stephen.kinsella@ul.ie,
www.stephenkinsella.net.
1 de Buffon (1984). Fulltext available at http://faculty.njcu.edu/fmoran/buffonhome.htm
2 Neoclassical economics definitely falls under the empty suit category for Taleb.

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 There is no such thing as absolute certainty, but there is assurance sufficient for the purposes of
human life. We may, and must, assume our opinion to be true for the guidance of our own conduct:
and it is assuming no more when we forbid bad men to pervert society by the propagation of
opinions which we regard as false and pernicious. I answer, that it is assuming very much more.
There is the greatest difference between presuming an opinion to be true, because, with every
opportunity for contesting it, it has not been refuted, and assuming its truth for the purpose of
not permitting its refutation. Complete liberty of contradicting and disproving our opinion, is
the very condition which justifies us in assuming its truth for purposes of action; and on no other
terms can a being with human faculties have any rational assurance of being right.

The consequences of ignoring the existence of Black Swans–—any high impact, low probability event—–
can be disastrous. 9/11 was a Black Swan, the success of the Harry Potter series was a Black Swan, a taxi
driver receiving a 100 dollar tip on a five dollar fare is a Black Swan. These events are rare enough to be
highly improbable, but, coming from a power-law infested world as we do, the events are more common than
the ‘empty suits’ suppose in their Gaussian-driven models. Taleb avers the course of history itself is driven
and directed by Black Swans, and, thanks to globalisation, mass communication, and sheer chance, their
impacts are driving history forward at an unprecedented rate.
In the spirit of announcing the limits to our knowledge, this review is not without its problems. The
Black Swan deliberately defies compression or truncated description, and the ideas lodged within its covers
are deep, and quite scary. Taleb himself is disquieted by them. He writes on page 215:

I have spent my entire life studying randomness, practicing randomness, hating randomness. The
more that time passes, the worse things seem to me, the more scared I get, the more disgusted I
am with Mother Nature.

Therefore any review of this book (and there have been many) will be partial, less a guide or a summary,
and more a smattering of impressions, thoughts, and questions on certain aspects of the book. To the reader
I apologise.
The book begins with Taleb’s story, coming from the Levant, living through a war, cancer, and stock
market crashes. We, the readers, are then given an overview of Taleb’s arguments about scaling and non
scaling distributions, as well as an introduction to the problem of induction, of which a Black Swan is a
symptom. We are told to consider the fate of the turkey. Three days before he is to die, the turkey has
no inkling of his fate, and assumes his fattening will go on forever. To the turkey, his death is a Black
Swan event, given the way he has been treated up to the moment of his death. Taleb urges us not to be
turkeys, and shows us why we continue to behave like them in our daily lives. First, humans are blessed
and cursed with biases which mask the presence of Black Swans. We seek evidence to confirm our opinions,
and once we find that evidence regardless of whether it happens to be the truth, we cling to that evidence
as ‘fact’. We seek simple, linear stories to fit the complex chain of events which has just occurred. We
ignore silent evidence, and choose to believe we live in a nice, safe world—Gaussian-dominated—rather than
the power-law dominated world we actually see. Taleb writes on page xix,“[i]t is easy to see that life is the
cumulative effect of a handful of significant shocks”. There are no outliers—just observations we don’t have
explanations for. The result of these blind spots is a failure to predict with any accuracy over long time
horizons. The ‘expert’, then, becomes just another shaman dancing in the dust, because his science cannot
do much better than prayer in predicting what will happen in complex environments like the macroeconomy.
We are given a snapshot of what to do when we cannot predict, of which more below, and the book closes
with an exhortation not to be a sucker by simply acknowledging the presence of Black Swans, and acting
accordingly. It is your actions which should change in the light of this new knowledge, not your thinking.

2 Who are your heroes?

Your heroes define you, in a certain sense. Their stories, behaviours, and achievements constitute a theoretical
upper bound to one’s own activities, especially in the professional realm.

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 If I were smarter, luckier, or more hard-working, I would be more like Richard Feynman, or Alan Turing,
or Adam Smith. My heroes tell you something about me. Among Nassim Taleb’s heroes are Karl Popper,
G.L.S. Shackle, and Sextus Empiricus. Each hero resonates with a different part of Taleb’s argument.
Karl Popper exposed the crucial problem of induction in a world where the transition from specific
evidence to general claim through a simple causal story is fundamentally flawed. Taleb sums the position
up nicely on page 55: “Alas, with tools and fools, anything can be easy to find. You can take past instances
that corroborate your theories and you treat them as evidence”.
George Lennox Sherman Shackle focused on the role of uncertainty and expectations in economic pro-
cesses, identifying, in some sense, the role of un-knowledge in economics Shackle (1990 [1949], 1972); Koppl
(2001). Shackle’s lesson to Taleb is to ditch the search for general theories of economic behaviour (Taleb,
2007, pg. 185), in favour of some measure of ‘un-knowledge’. Taleb offers us the vision of Paul Samuelson as
knowing only a little mathematics, and this little knowledge, applied in an overly didactic and confident way,
can sway a discipline if the expositor is in the right place (a reputed wunderkind, at MIT, leading textbook
writer, etc, etc).
Sextus Empiricus belonged to a school of thinkers who trained themselves to doubt everything “and thus
attain a level of serenity”(Taleb, 2007, pg. 46). The school believed that any dogma was incorrect, because
any dogma requires belief in a stable system. From Sextus Empiricus, Taleb takes the lesson of relentless
trial and error in the face of unquantifiable uncertainty.
Taleb cites the work of other scholars as well. Taleb dedicates the book to Benoit Mandelbrot, the father
of fractal geometry, and lionises Algazel, Bastiat, Bayle, and to a lesser extent, Hume ((Taleb, 2007, pgs.
43-50)). So Taleb is in good company for his exploration of effects of uncertainty on normal life.

3 Statistics of the Black Swan

Taleb’s central argument is that in a world dominated by extreme events, uncertainty does not diminish
under averaging as the sample size increases, as it does in a Gaussian world. Taleb’s world is a power-law
dominated world, where the chances of a truly extreme event are much greater. The real world, when
sampled, can be made to look like a Gaussian world, but the relation is specious, because over time large
deviations become more and more likely, suggesting an extreme distribution fits the data better, as DeVany
and Walls (1996) have found in the movie industry.
The generating (or probability mass) function for the series of discrete observations we can record in the
real world (if there is such a thing) is what we as social scientists would like to find. Scientists would like to
have the explanation of where these fluctuations come from to be able to predict, and therefore hedge away,
the effects of these fluctuations. But Taleb’s argument (flowing from his heroes Shackle, Sextus Empiricus,
and Popper) skewers the scientists’ hope of finding that function. In a world of unmeasurable un-knowledge,
there is no chance, in finite time, of discovering the One True Theory. The quest for the general theory
must be abandoned, and the search for the predictive engine called off. We cannot predict anything with
certainty—-doing so under false assumptions only makes things worse when people over commit to the idea
of a stable, predictable future that can’t exist, and get caught out when their stable future refuses to emerge.
That is the real tragedy of living in a Black Swan world.
Mill’s quote above highlights the central human dilemma Taleb’s book explores. Sensible people must
predict, they must look forward by looking backward, and they must make decisions based on partial
information in the presence of un-knowledge. People in the real world cannot grasp this fact, Taleb argues,
because of epistemic arrogance about the quality of their knowledge, predictive tools based on incorrect
Gaussian assumptions, and inbuilt psychological biases working against the would-be predictor, blinding
them to the presence of uncertainty lying just outside the artificial intellectual categories they create to
house their concepts. What then, to do? The key to living sensibly in a Black Swan world, according to
Taleb, is to practice for uncertain events by exposing oneself to them through trial and error, thus allowing a
greater role for blind luck to play its part. Seize any opportunity, or anything that looks like an opportunity,
because one of them will pay off (Taleb, 2007, pages 205–207)—-this is Taleb’s Barbell strategy. Accept that
no one knows anything for certain over large timescales, especially experts, and beware of long term precise

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plans by large organisations like governments—they can only be incorrect.
One issue Taleb does not explore is what would happen if everyone took his advice. In a world of Talebs,
all aware on a genetic level of the fact that absence of evidence is not evidence of absence, conscious of their
ignorance and open to any opportunity, the effects of Black Swans would likely be increased rather than
decreased on society.
Consider the following simple model of income determination with uncertainty built into it, and the role
of the Black-Swan aware population becomes clear. The Black Swan economy, let us call it, is created from
a randomly generated population of agents indexed by i = 1, . . . , n. Each of these agents is endowed with a
normally distributed level of resources, RES, opportunities, OPP, and abilities, ABIL, creating a human capital
index of the population of agents in the first period of the model as follows:
n
!
Hit = (Oppit + RESit + ABILit ). (1)
i=1

The initial distribution of the level of human capital in the system looks Gaussian, as figure 1 shows.

Figure 1: Initial overall wealth in the toy economy.

Let’s endow the agents with power-law like reserves of some value-holding good we’ll call capital, so some
are very rich, and some are very poor. The distribution of capital, K, in the economy initially looks like
figure 2 below.
Now let’s allow the agents to take advantage of their luck in a labour market, where they contract for
services next period with a firm who hires them with reservation wage ri , where for each agent i, ri ≥ Hit .
If they make a deal with the firm to their advantage, households save the difference, and this adds to their
wealth. If they don’t make a deal, agents receive a ‘dole’ of 0.1 × (ri ).
If we iterate this simple model over 100 periods, a log normal distribution of wealth emerges with exponent
α = 0.8 3 , as we can see below from figure 3, and our simulation can start. This simple model is set up,
deriving much inspiration from Champernowne (1998).
Let’s allow our agents now to experience Black Swans. Let them set their expectations on income in
the next period based on their incomes received in the past, so Hi,t+1 = Hi,t , though they may be way off,
especially if their reservation wage is much greater than the dole they receive while unemployed. Households
3 Mathematica code for this simulation is available from the author at stephen.kinsella@ul.ie.

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 K

3.5
3
2.5
2
1.5
1

Households
20 40 60 80 100

Figure 2: Initial distribution of capital, K.

% Wealth

0.3

0.25

0.2

0.15

# Households
20 40 60 80 100
Figure 3: Evolution of wealth distribution after 100 periods.

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can save what they have earned, hedging away against uncertainty, or not. Those that save a lot, because they
know the world is uncertain, I’ll call Black Swan households. Other households we can call ’Turkeys’. Now
firms can begin making erratic, essentially random, wage decisions, from period to period, creating ‘turkey’
households. The households in the system must now deal with the consequences of misplaced expectations,
in periods going forward. Some households are turkeys, others are not. The dispersion of income increases
by a factor of nine in my little simulation. So, even though some households do better (they happen to be
driving the cab Nassim Taleb is sitting in, and receive the 100 dollar tip), most do not, whether they are
aware of the presence of uncertainty or not.
This is why we have the institution of insurance and reinsurance, because, as (Shaw, 1956, pg. 1527) put
it “A bookmaker who gambles will ruin himself as certainly as a [bartender] who drinks”.

3.1 Building bridges

What to do when faced with limited knowledge? Once one has found the limits of one’s knowledge, one
can hedge against it. Take the case of John A. Roebling, the engineer behind the Brooklyn Bridge. Before
1960, most bridges were susceptible to aerodynamic lift phenomena, arising from wind sheer. The collapse
of ‘Galloping Gertie’, the Tacoma Narrows Bridge which tore itself apart in a windstorm in 1940 was an
example of this. Suspension bridges had been prone to ripping themselves apart for at least eighty years
before Galloping Gertie. In performing the correct engineering calculation of the forces acting on the bridge,
which involve nonlinearities, model the eddy spectrum. Nobody knew how to model the eddy spectrum
correctly in detail until the 1950’s. So, why hasn’t the Brooklyn Bridge torn itself apart, like Galloping
Gertie?
One reason may be because John Roebling had sense enough to know what he didn’t know. His notes
and letters on the design of the Brooklyn Bridge still exist, and they are a shining example of a good engineer
recognizing the limits of his knowledge (McCullough, 1982, pg. 83.). He knew about aerodynamic lift on
suspension bridges; he had watched it happen on earlier constructions like the Waco Suspension Bridge,
completed in 1869. Roebling knew he didn’t know enough to model the forces acting on the Brooklyn
Bridge. So, he designed the stiffness of the trusses on the Brooklyn Bridge roadway to be six times what
a normal calculation, based on known static and dynamic loads, would have called for. And he specified a
network of diagonal stays running down to the roadway, to further stiffen the entire bridge structure, for
good measure.
Thus Roebling built a good bridge which still stands, by employing a huge safety factor to compensate
for his ignorance. In a Black Swan world, when you’re in a domain where long term plans are useless (Taleb
chooses the macroeconomy as an example), you should start planning for events you can’t control. This is
hard and very counter intuitive. But of course, we want the bridge to stay up and the financial system to
be secure. So seemingly exceptional prudence might be called for in important circumstances.

4 Perspective matters
Say you own a car. You wish to drive the car down a road through a ‘T’ junction like the one shown in
figure 4 below. The problem is to drive out onto the road without being hit by an oncoming car. The cars
drive on the right. For the most part, you can see the road to the left and right. This is a winding road
however, and there can be a car in the knees of the curves either side at any moment. So, while most cars
coming towards the driver are observable, some are not.
There is a probability distribution around the numbers of cars the driver sat at the T junction might
see, were they to sit there for a few days, stopping traffic behind them. From the perspective of an overhead
helicopter with all day to wait, the solution is simple. But our driver cannot wait, and cannot see, and is their
problem. The problem is a simple stochastic one, unless one is the unfortunate driver there and then on the
road. The driver must drive out now, and in doing so, they take the chance of being hit while invalidating the
probabilistic argument for staying put. Taleb and Mandebrot call this the problem preasymptotic4 —because
4 See http://www.fooledbyrandomness.com/preasymptotics.htm.

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 Figure 4: Faced with oncoming traffic he can’t see from the left, what is our driver to do?

we live now, not in the limit, many of the central predictions of modern statistics fail us, as (Shackle, 1990
[1949], pg. 7) would attest. So as far as repeated trials of a fixed system go, probability theory is mostly
useless to the driver—conditions are changing, and they do not have repeated chances to turn right, they
must turn right now. Taleb’s argument in the Black Swan is to be aware of the knee in the bend and, as
much as possible, make sure to try and avoid being hit by someone traveling at speed through that bend
at the moment the driver turns right. The driver following this advice would therefore edge very slowly
forward, trying to see whether a car is coming. This shows they recognise the danger of their situation.
But, as Mill shows us, we must act, and so, in spurting forward, our driver takes their life into their hands,
and all the awareness in the world means nothing for them beyond this point. But, by taking the time to
look both ways and edge out slowly—avoiding unnecessary reliance on long range predictions (for example,
“there’s never anybody on that road after 7pm”)—the driver might be made a little safer. They might still
get squashed.
The regulation school solution to this problem is traffic lights at the intersection but, when those do not
exist, or work incorrectly, the problem of getting squashed remains.
Taleb’s arguments (given on pages 201–208) are more varied than this caricature might lead the reader
to believe, however, the book does not address the central issue of what to do when we cannot predict with
any accuracy. Be human; be humble regarding the quality of your knowledge; be open to every opportunity.
These recommendations might help us stop the Brooklyn Bridge from wobbling, but I doubt they will stop
the financial system from collapsing again in five years’ time, or stop ‘experts’ from attempting to predict
the future.

5 The Black Swan is a starting point

Taleb shows us there is a problem, and proceeds to shows us glimpses of possible solutions. A manifesto for
change this is not. Rather, it is a wake up call for those who heed the word of experts and act on those
words.
Taleb is, I think, not against experts. He is one himself. I’m sure he takes the economist’s viewpoint
of their activities: experts seek to maximise their own gains subject to whatever constraints they fight

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against. A story must be told, so they tell it. If every expert came with a warning sign strapped around
his or her waist like cigarette packets, Taleb would not be happy. Their arrogance, he claims, leads them
to oversell the linear story, and damn the future by leaving it more and more at the mercy of Black Swans.
For economists, where we study a domain where long term plans are useless (like the macroeconomy), we
should start planning for events we can’t control. Such planning is hard, and very counter intuitive. Taleb,
as a story teller, cannot be against that. What he is against is practioners taking the words of the experts
as gospel, and harming themselves and society as a consequence.
The Black Swan is a starting point toward a more general understanding of the role of uncertainty in
human affairs which, while imperfect, has created a debate around the nature of forecasting in unpredictable
environments like the macroeconomy and the stock market, and for that Nassim Taleb is to be thanked.

References
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D. McCullough. The Great Bridge. Simon and Schuster, New York, 1982.
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2007.
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