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

From Coastlines to Cotton Prices 
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example of the law in action: Zipf had gone through and counted how 
often various words appeared in various texts. He then showed that if 
you ordered the words by how often they appeared in a piece of writ-
ing, you usually found that the most common word appeared about 
twice as often as the second most common word, three times as often 
as the third most common word, and so on for all of the words in the 
document.
Szolem was right that Zipf’s work was just the kind of thing his 
nephew would be interested in. But he was wrong that it was trash
— or at least that it was all trash. Zipf’s law is a peculiar combination 
of estimation and numerology and Zipf was a crank. But there was a 
gem hidden in his book: Zipf had worked out a formula that could 
be used to calculate how often a particular word would appear in a 
book, given its rank on the list and the total number of different words 
appearing in the text. Mandelbrot quickly realized that the formula 
could be improved upon, and moreover that it had some unexpected 
and interesting mathematical properties. despite the resistance of the 
brightest lights in the mathematical establishment, his uncle included, 
Mandelbrot wrote a dissertation on Zipf’s law and its applications. He 
did so without an advisor and received his degree only by pushing his 
thesis through the university’s bureaucratic channels himself. It was 
highly irregular.
Indeed, Mandelbrot made a career out of the highly irregular, both 
in his impetuous rejection of the mathematical community and in his 
topics of study. Whereas the vast majority of mathematicians focus 
on shapes that are “smooth,” the kinds of shapes you can make out 
of Play-doh, Mandelbrot’s most famous discovery, which he named 
“fractal geometry,” arose out of the study of jagged and fractured 
shapes, like the surface of a mountain or a shard of broken glass. this 
work on fractal shapes made Mandelbrot realize that there are variet-
ies of randomness in nature that are far more extreme than the kind 
of randomness you get by flipping a coin over and over again — with 
consequences for virtually all mathematical science, including finance.
Mandelbrot was a revolutionary. even today, decades after his most 
important papers, his ideas remain radical, with mainstream scientists 
in many fields still debating them. the situation is particularly striking 

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in economics, where Mandelbrot’s central ideas have gone down like 
a bitter pill. If they are correct, almost everything traditional econ-
omists believe about markets is fundamentally flawed. It didn’t help 
that Mandelbrot was uncompromising, both as a person and as a sci-
entist, never bending to academic pressures. He often found himself 
at the fringes of respectability: esteemed, though never as highly as 
he deserved; criticized and dismissed as much for his style as for the 
unconventionality of his work. Yet over the past four decades, as Wall 
Street and the scientific community have encountered new, seemingly 
insurmountable challenges, Mandelbrot’s insights into randomness 
have seemed ever more prescient — and more essential to understand.
Benoît Mandelbrot was born in 1924, to Lithuanian parents living in 
Warsaw, Poland. Although his father was a businessman, two of his 
uncles (including Szolem) were scholars. Many of his father’s other rel-
atives were, in Mandelbrot’s words, “wise men” with no particular em-
ployment, but with a group of followers in the community who would 
trade money or goods in exchange for advice or learning. His mother, 
meanwhile, was also well educated, trained as a physician. As a boy, 
Mandelbrot often felt that he was expected to pursue an academic life 
of one sort or another, though his father urged him to choose a practi-
cal form of scholarship, such as engineering or applied science.
despite the family’s focus on learning, however, the young Mandel-
brot had a very unusual education. His parents’ first child, a daughter, 
died very young when an epidemic ripped through Warsaw. Benoît’s 
mother developed a deep fear of childhood illnesses and sought to pro-
tect her two young sons from her daughter’s fate. So rather than send 
Benoît to school, she hired one of his uncles to tutor him. this uncle, 
though related by marriage, was cast firmly in the mold of Mandel-
brot’s father’s family: well educated and unemployed, with esoteric in-
terests. He despised rote learning, so didn’t bother to teach Benoît such 
mundane topics as arithmetic or the alphabet (indeed, in a speech he 
gave after receiving the Wolf Prize for physics, Mandelbrot admitted 
that he still had trouble multiplying, as he had never learned his mul-
tiplication tables). Instead, the uncle encouraged creative thought and 
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