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

From Coastlines to Cotton Prices 
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problems that had previously been overlooked, or that had seemed too 
difficult to crack. Like Bachelier before him, Mandelbrot asked ques-
tions that had never before occurred to anyone with his mathematical 
abilities — and he found answers that changed how scientists see the 
world.
Much later, Mandelbrot would attribute his remarkable career to two 
things. first was his unusual and oft-disrupted education. Mandel-
brot ultimately made his way to a grande école, and on to a Phd. But 
the journey wasn’t easy, and it forced him to be resourceful and inde-
pendent in ways that he wouldn’t have been, had he followed a more 
traditional path. the second was a series of serendipitous discoveries 
that introduced him to various pieces of an intellectual puzzle. Zipf’s 
formula, which he learned about when his uncle tossed a review in 
his face, was one such discovery. Another occurred several years later, 
soon after Mandelbrot finished graduate school.
At the time, he was working at IBM, another beneficiary of the in-
dustrialization of physics. though he often expressed pride at having 
completed graduate school without an advisor, this didn’t help when 
it came to seeking employment. He enjoyed a stint as a postdoctoral 
researcher at Princeton’s Institute for Advanced Study and then spent 
some time back in europe, working on thermodynamics for the french 
government’s research center, cnrS. But a full-time faculty position 
proved elusive, and Mandelbrot’s nascent disillusionment with the 
mathematical firmament deepened. When he at last received an offer 
from IBM in 1958 to work as a staff scientist for its research division, he 
jumped at the chance, even though, in his words, “there was no great 
distinction [in] getting an offer from IBM then.”
one of the goals of IBM’s research division was to find applica-
tions for its newest computers. Mandelbrot was assigned to work on 
economic data. His bosses hoped that if Mandelbrot could show how 
useful computers were for economics, banks and investment houses 
might be convinced to buy an IBM mainframe. In particular, he was 
looking at data describing income distributions throughout society. 
(Banks weren’t necessarily interested in this specific question; rather, 
the idea was to use Mandelbrot’s research as proof of concept, to dem-

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onstrate how efficient a computer could be at number-crunching fi-
nancial data.)
Income distribution had been studied before, most famously by 
a nineteenth-century Italian engineer, industrialist, and economist 
named vilfredo Pareto. A strong believer in laissez-faire economics, 
Pareto was obsessed with the workings of the free market and the ac-
cumulation of capital. He wanted to understand how people got rich, 
who controlled wealth, and how resources were doled out by market 
forces. to this end, he gathered an immense amount of data on wealth 
and income, drawing on such diverse sources as real estate transac-
tions, personal income data from across europe, and historical tax 
records. to analyze these data, Pareto would make elaborate graphs, 
with income levels and wealth on one axis, and the number of people 
who had access to that wealth on the other.
for all the diversity of his data sources, Pareto found a single pat-
tern over and over again. As he described it, 80% of the wealth in any 
country, in any era, is controlled by 20% of the population. the pat-
tern is now known as Pareto’s principle, or sometimes the 80–20 rule. 
At the time, Pareto interpreted these results much as Zipf would have, 
as evidence for a “social law” revealing that wealth is not distributed 
randomly but rather by some mysterious force that shapes markets 
and societies. once Pareto began looking, the law seemed to apply to 
everything. eighty percent of a company’s sales are usually due to just 
20% of its customers. eighty percent of crimes can be traced to just 
20% of criminals. And so on. (nowadays, Pareto’s principle is seen to 
hold approximately in many places, such as in the ratio of health-care 
costs to patients in the United States.)
the most interesting thing about Pareto’s work, at least from Man-
delbrot’s point of view, wasn’t the idea that Pareto’s data revealed some 
mathematical law of society. Instead, it was the particular relationship 
between the income distribution for a whole country and for a small 
portion of that country. Pareto showed that the 80–20 rule held, at 
least approximately, for a country as a whole. But what if you asked a 
slightly different question: How is income distributed among that 20% 
of the population that controls the overwhelming majority of wealth? 
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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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