The Physics of Wall Street: a brief History of Predicting the Unpredictable

Tyranny of the Dragon King 
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king because, if you try to match plots like Pareto’s law—the fat-tailed 
distribution governing income disparity that Mandelbrot studied at 
IBM — to countries that have a monarchy, you find that kings don’t fit 
with the 80–20 rule. Kings control far more wealth than they ought to, 
even by the standards of fat tails. they are true outliers. And they, not 
the extremely wealthy just below them, are the ones who really exert 
control. the word dragon, meanwhile, is supposed to capture the fact 
that these kinds of events don’t have a natural place in the normal bes-
tiary. they’re unlike anything else. Many large earthquakes are little 
ones that, for whatever reason, didn’t stop. these are not predictable 
using Sornette’s methods. But dragon-king earthquakes, the critical 
events, seem to require more. Like ruptures, they happen only if all 
sorts of things fall into place in just the right way. A good example of 
a dragon king is the city of Paris. france’s cities follow Zipf’s law re-
markably well. the distribution of cities in france is fat-tailed, in that 
the very biggest cities are much bigger than the next biggest cities. But 
if you plot the size of french cities by their population size, as Zipf’s 
law would have you do, Paris is still much too big. It breaks the mold.
taleb’s argument trades on the fact that black swans can have enor-
mous consequences. dragon kings are similar in their influence. they 
are tyrannical when they appear. But unlike black swans, you can hear 
them coming. Sornette does not argue that all black swans are really 
dragon kings in disguise, or even that all market crashes are predict-
able. But he does argue that many things that might seem like black 
swans really do issue warnings. In many cases, these warnings take 
the form of log-periodic precursors, oscillations in some form of data 
that occur only when the system is in the special state where a mas-
sive catastrophe can occur. these precursors arise only when the right 
combination of positive feedback and amplifying processes is in place, 
along with the self-organization necessary to make a bang, and not a 
whimper.
the Prediction company, on the one hand, and Sornette, on the 
other, offer two ways in which one might fill in the gaps in the now-
standard Black-Scholes-style reasoning. the Prediction company’s 
methods might be thought of as local, in the sense that their strat-
egy involved probing the fine-grained financial data produced every 

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instant by the world’s markets for patterns that had some temporary 
predictive power. these patterns allowed them to build models that 
could be used over a short window of time to make profitable trades, 
even though the patterns were often fleeting. Along with these meth-
ods, they developed the tools necessary to evaluate the effectiveness 
of the patterns they were finding, and to tell when they had passed 
their prime. In a way, the Prediction company’s approach is modest 
and conservative. It is easy to see why it should work, as a part of what 
makes markets more efficient.
Sornette, conversely, has taken a more global approach, looking for 
regularities that are associated with the biggest events, the most dam-
aging catastrophes, and trying to use those regularities to make pre-
dictions. His starting point is Mandelbrot’s observation that extreme 
events occur more often than a normal random walk would predict; 
Sornette believes that catastrophic crashes happen even more than 
Mandelbrot proposed. In other words, even after you accept fat-tailed 
distributions, you still see extreme events unusually often. Sornette’s 
intuition, on seeing these apparent outliers, is that there must be some 
mechanism that, at least sometimes, amplifies the largest catastrophes. 
this is a riskier hypothesis — but it is one that can be tested, and so far, 
it seems to have passed.
If you think of Mandelbrot’s work as a revision to the early accounts 
of random markets, pointing out why they fail and how, then Sornette’s 
proposal is a second revision. It is a way of saying that, even if markets 
are wildly random and extreme events occur all the time, at least some 
extreme events can be anticipated if you know what to look for. these 
dragon kings can upend the entire world economy — and yet they can 
be studied and understood. they are the stuff of myths, but not of 
mystery.
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t h e p h y s i c s o f wa l l s t r e e t

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A
nother debate. Pia Malaney put her arms on the table 
and leaned in to listen to her fiancé, eric Weinstein. Wein-
stein was a postdoctoral researcher at MIt who had recently 
finished a Phd in mathematics at Harvard. they were sitting in a bar 
in cambridge, Massachusetts, where Weinstein was holding forth on 
how the ideas used in his dissertation could be applied to hers. the 
trouble was that his work had been on an application of abstract geom-
etry to mathematical physics. Her work, meanwhile, was in econom-
ics. the two projects seemed as different as could be. She sighed as she 
recalled, with a sense of the irony, how much easier these discussions 
had been before she had won him over to her side.
Malaney had met Weinstein in 1988, while he was a graduate stu-
dent and she was an undergraduate economics major at Wellesley, the 
women’s college located just outside of Boston. Back then, Weinstein 
had a dim view of economics — a view shared by many of his mathe-
matician colleagues. He thought it consisted of mathematically simple 
theories that couldn’t hope to capture the full complexity of human 
behavior. Weinstein would get a rise out of friends in the economics 
department by calling their field “cocktail party conversation”: unsub-
A New Manhattan Project
c H A P t e r 8

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stantial, trivial. He would happily have admitted that he didn’t know 
much about economics, because, after all, there wasn’t much to know.
Malaney was not fond of the view frequently espoused by her fi-
ancé. for years, she steadfastly defended her colleagues’ work against 
Weinstein’s attacks.
And then one day, she found she had convinced him. All of a sud-
den, he went from trying to tell her that economics was worthless to 
declaring that they should collaborate. All Weinstein could talk about 
was how, with his training in mathematics and physics and her training 
in economics, they could tackle all sorts of problems that had stumped 
economists in the past. the point had long been to get her boyfriend 
to read enough economics to understand that there was substance be-
hind it. now, though, Malaney found herself wading into the world of 
mathematical physics. It was not what she had bargained for.
Still, she couldn’t deny that their collaboration was already proving 
fruitful. they had begun to focus on something called the index num-
ber problem. the problem concerns how to take complex information 
about the world, such as information about the cost and quality of 
various goods, and turn it into a single number that can be used to 
compare, say, a country’s economic health and status at one time to its 
economic status at another time. Some familiar examples are market 
indices like the dow Jones Industrial Average or the S&P 500. these 
are numbers that are supposed to encode all of the complicated infor-
mation about the state of the U.S. stock market. Another index that 
one often hears about is the consumer Price Index (cPI), which is 
supposed to be a number that captures information about the cost of 
the ordinary things that a person living in a U.S. city buys, such as food 
and housing. Index numbers are crucially important for economic 
policy because they provide a standard to compare economic indi-
cators over time, and from place to place. (the Economist magazine 
has proposed a particularly straightforward index, called the Big Mac 
Index. the idea is that the value of a Big Mac hamburger from Mc-
donald’s is a reliable constant that can be used to compare the value of 
money in different countries and at different times.)
together, Malaney and Weinstein developed an entirely novel way 
of solving the index number problem by adapting a tool from math-
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