Antifragile: Things That Gain from Disorder (89 page)

 

All the terms on the left seem to be connected. We can easily explain how
rationalism, explicit,
and
literal
fit together. But the terms on the right do not appear to be logically connected. What connects
customs, bricolage, myths, knowhow,
and
figurative
? What is the connection between religious dogma and tinkering? There is
something,
but I can’t explain it in a compressed form, but there is the Wittgenstein family resemblance.

Lévi-Strauss:
Lévi-Strauss (1962) on different forms of intelligence. However, in Charbonnier (2010), in interviews in the 1980s, he seems to believe that some day in the future, science will allow us to predict with acceptable precision very soon, “once we get the theory of things.” Wilken (2010) for bio. See also Bourdieu (1972) for a similar problem seen from a sociologist.

Evolutionary heuristics:
This is central but I hide it here. To summarize the view—a merger of what it is in the literature and the ideas of this book: an evolutionary heuristic in a given activity has the following attributes: (a) you don’t know you are using it, (b) it has been done for a long time in the very same, or rather similar environment, by generations of practitioners, and reflects some evolutionary collective wisdom, (c) it is free of the agency problem and those who use it survived (this excludes medical heuristics used by doctors since the patient might not have survived, and is in favor of collective heuristics used by society), (d) it replaces complex problems that require a mathematical solution, (e) you can only learn it by practicing and watching others, (f) you can always do “better” on a computer, as these do better on a computer than in real life. For some reason, these heuristics that are second best do better than those that seem to be best, (g) the field in which it was developed allows for rapid feedback, in the sense that those who make mistakes are penalized and don’t stick around for too long. Finally, as the psychologists Kahneman and Tversky have shown, outside the domains in which they were formed, these can go awfully wrong.

Argumentation and the green lumber problem:
In Mercier and Sperber (2011). The post-Socratic idea of reasoning as an instrument for seeking the truth has been recently devalued further—though it appears that the Socratic method of discussion might be beneficial, but only in a dialogue form. Mercier and Sperber have debunked the notion that we use reasoning in order to search for the truth. They showed in a remarkable study that the purpose of arguments is not to make decisions but to convince others—since decisions we arrive at by reasoning are fraught with massive distortions. They showed it experimentally, producing evidence that individuals are better at forging arguments in a social setting (when there are others to convince) than when they are alone.

Anti-Enlightenment:
For a review, Sternhell (2010), McMahon (2001), Delon (1997). Horkheimer and Adorno provide a powerful critique of the cosmeticism and sucker-traps in the ideas of modernity. And of course the works of John Gray, particularly Gray (1998) and
Straw Dogs,
Gray (2002).

Wittgenstein and tacit knowledge:
Pears (2006).

On Joseph de Maistre:
Companion (2005).

Ecological, non-soccer-mom economics:
Smith (2008), also Nobel lecture given along with Kahneman’s. Gigerenzer further down.

Wisdom of the ages:
Oakeshott (1962, 1975, 1991). Note that Oakeshott conservatism means accepting the necessity of a certain rate of change. It seems to me that what he wanted was organic, not rationalistic change.

More formally, to complement the graphical exposition, from Taleb and Douady (2012), the
local fragility
of a random variable
X
λ depending on parameter
λ
, at stress level
K
and semi-deviation level
s
^–
(
λ
) with pdf
f
_λ
is its
K-left-tailed semi-vega sensitivity
(“vega” being sensitivity to some measure of volatility),
V
(
X
,
fλ
,
K
,
s
^–
) to
s
^–
, the mean absolute semi-deviation below Ω, here
,
. The
inherited fragility
of
Y
with respect to
X
at stress level
L
=
φ
(
K
) and left-semi-deviation level
s
^–
(
λ
) of
X
is the partial derivative
. Note that the stress level and the pdf are defined for the variable
Y,
but the parameter used for differentiation is the left-semi-absolute deviation of
X
. For antifragility, the flip above Ω, in addition to robustness below the same stress level
K
. The
transfer theorems
relate the fragility of
Y
to the second derivative
φ
(
K
) and show the effect of convex (concave or mixed nonlinear) transformations on the tails via the
transfer function
H
^K
. For the antifragile, use
s
⁺
, the integral above
K
.

Fragility is not psychological:
We start from the definition of fragility as tail vega sensitivity and end up with nonlinearity as a necessary attribute of the source of such fragility in the inherited case—a cause of the disease rather than the disease itself. However, there is a long literature by economists and decision scientists embedding risk into psychological preferences—historically, risk has been described as derived from risk aversion as a result of the structure of choices under uncertainty with a concavity of the muddled concept of “utility” of payoff; see Pratt (1964), Arrow (1965), Rothschild and Stiglitz (1970, 1971). But this “utility” business never led anywhere except the circularity, expressed by Machina and Rothschild (2008), “risk is what risk-averters hate.” Indeed limiting risk to aversion to concavity of choices is a quite unhappy result.

The porcelain cup and its concavity:
Clearly, a coffee cup, a house, or a bridge doesn’t have psychological preferences, subjective utility, etc. Yet each is concave in its reaction to harm: simply, taking
z
as a stress level and Π(
z
) the harm function, it suffices to see that, with
n
>1, Π(
n z
) <
n
Π(
z
) for all 0
< n z, where
Z*
is the level (not necessarily specified) at which the item is broken. Such inequality leads to Π(
z
) having a negative second derivative at the initial value
z
. So if a coffee cup is less harmed by
n
times a stressor of intensity
Z
than once a stressor of
n Z,
then harm (as a negative function) needs to be concave to stressors up to the point of breaking; such stricture is imposed by the structure of survival probabilities and the distribution of harmful events, nothing to do with subjective utility or some other figments.

Scaling in a positive way, convexity of cities:
Bettencourt and West (2010, 2011), West (2011). Cities are 3-D items like animals, and these beneficial nonlinearities correspond to efficiencies. But consider traffic!

“More Is Different”:
Anderson (1972).

Comparative fragility of animals:
Diamond (1988).

Flyvbjerg and colleagues on delays:
Flyvbjerg (2009), Flyvbjerg and Buzier (2011).

Small Is Beautiful, the romantic views:
Dahl and Tufte (1973), Schumacher (1973) for the soundbite. Kohr (1957) for the first manifesto against the size of the governing unit.

Size of government:
I can’t find people thinking in terms of convexity effects, not even libertarians—take Kahn (2011).

Small states do better:
A long research tradition on governance of city-states. It looks like what we interpret as political systems might come from size. Evidence in Easterly and Kraay (2000).

The age of increasing fragility:
Zajdenwebber, see the discussion in
The Black Swan
. Numbers redone recently in
The Economist,
“Counting the Cost of Calamities,” Jan. 14, 2012.

Convexity effect on mean:
Jensen (1906), Van Zwet (1966). While Jensen deals with monotone functions, Van Zwet deals with concave-convex and other mixtures—but these remain simple nonlinearities. Taleb and Douady (2012) applies it to all forms of local nonlinearities.

Empirical record of bigger:
Mergers and hubris hypothesis: in Roll (1986); since then Cartwright and Schoenberg (2006).

Debt in ancient history:
Babylonian jubilees, Hudson et al. (2002). Athens, Harrison (1998), Finley (1953). History of debt, Barty-King (1997), Muldrew (1993), Glaeser (2001). The latter has an anarchist view. He actually believes that debt precedes barter exchange.

Food networks:
Dunne et al. (2002), Perchey and Dunne (2012), Valdovinos and Ramos-Jiliberto (2010). Fragility and resources, Nasr (2008, 2009).

Fannie Mae:
They were concave across all meaningful variables. Some probability-and-nonlinearity-challenged fellow in the Obama commission investigating the cause of the crisis spread the rumor that I only detected interest rate risk of Fannie Mae: not true.

Costs of execution:
“Price impact,” that is, execution costs, increase with size; they tend to follow the square root—meaning the total price is convex and grows at exponent 3/2 (meaning costs are concave). But the problem is that for large deviations, such as the Société Générale case, it is a lot worse; transaction costs accelerate, in a less and less precise manner—all these papers on price impact by the new research tradition are meaningless when you need them. Remarkably, Bent Flyvbjerg found a similar effect, but slightly less concave in total, for bridges and tunnels with proportional costs growing at 10 Log[
x
] of size.

Small Is Beautiful, a technical approach:
To explain how city-states, small firms, etc. are more robust to harmful events, take
X,
a random variable for the “unintended exposure,” the source of uncertainty (for Soc Gen it was the position that it did not see, for a corporation it might be an emergency need to some inventory, etc.). Assume the size of this unintended harm is proportional to the size of the unit—for smaller entities engage in smaller transactions than larger ones. We use for probability distribution the variable of all unintended exposures ∑
X
_i
where
X
_i
are independent random variables, simply scaled as
X
_i
= X/N
. With
k
the tail amplitude and
α
the tail exponent, π(
k
,
α
,
X
) =
α k
^α
x
^-1-
α
. The
N
-convoluted Pareto distribution for the unintended total position
N
∑
X
_i
: π(
k/N
,
α
,
X
)
_N
where
N
is the number of convolutions for the distribution. The mean of the distribution, invariant with respect to
N
, is
α k
/α−
1
).

Losses from squeezes and overruns:
for the loss function, take
C
[
X
]= -
b X
^β
, where costs of harm is a concave function of
X
. Note that for small deviations, β = 3/2 in the microstructure and execution literature.

Resulting probability distribution of harm:
As we are interested in the distribution of
y,
we make a transformation of stochastic variable. The harm
y=C
[
X
] has for distribution: π[
C
^-1
[
x
]]/
C
’[
C
^-1
[
x
]]. Consider that it follows a Pareto distribution with tail amplitude
k
^β
and tail exponent
α
/β,
which has for mean
. Now the sum: for the convoluted sum of
N
entities, the asymptotic distribution becomes:
with mean (owing to additivity) as a function of the variables which include
N:
. If we check the ratio of expected
losses in the tails for
N
=1 to
N
=10 at different values of the ratio of β over
α
, the ratio of the expectation for 1 unit over 10 units
reveals the “small is beautiful” effect across different levels of concavity.