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

parts of small peninsulas. So you take out your surveying equipment, 
sensing that you’re about to fall down a rabbit hole, and start measur-
ing the sizes of these peninsulas. there aren’t many of these, but they 
are much bigger than the jetties and boulders you’ve looked at already, 
and now your new average is totally different from what it was after the 
first round of measurement. And what’s more, you haven’t even taken 
into account the still-larger structures, like cornwall. or the whole 
west coast of Britain itself, since from a geological perspective it’s just 
an outcropping from mainland eurasia. And while you’re at it, you 
probably need to consider smaller structures, too. Why count boul-
ders that are several feet across, but not rocks that are just a few inches 
across?
each time you cast your net wider, the average changes dramati-
cally. You can’t seem to narrow in on a single figure. dismaying as it is 
for our Sisyphean surveyor, there’s no expected value for the average 
size of a feature on a coastline. this is a general property of fractals, 
following from their self-similarity. from one point of view, they are 
beautifully ordered and regular; from another, wildly random. And if 
fractals are everywhere, as Mandelbrot believed, the world is a place 
dominated by extremes, where our intuitive ideas about averages and 
normalcy can only lead us astray.
though he never provided details, Mandelbrot often alluded to a par-
ticularly harrowing experience toward the end of 1943, while he was 
hiding with members of the french resistance. Afterward, his protec-
tors realized that Mandelbrot couldn’t remain in tulle, and they se-
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From Coastlines to Cotton Prices 
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cured a place for him as a postgraduate student at a preparatory school 
in Lyon.
Moving Mandelbrot was a risky proposition. Lyon was one of the 
most dangerous cities in southern france for both Jews and resistance 
sympathizers; Mandelbrot was both. nikolaus Barbie, an SS officer, led 
the local Gestapo outpost from a hotel near the center of town. Known 
as the Butcher of Lyon, he was later convicted of war crimes for the de-
portation of nearly one thousand of the region’s Jews. But Mandelbrot 
was not proving to be a very persuasive rural journeyman, and the 
resistance fighters who were caring for him needed a place where he 
wouldn’t be so conspicuous. A school was a natural choice: Mandel-
brot was the right age and he carried himself like a scholar. He would 
attend under an assumed identity and live in the dormitories. Yet even 
with a good cover, Mandelbrot couldn’t risk venturing beyond school 
grounds. He was a prisoner as much as a student.
to complete the deception, Mandelbrot sat in on classes. But no one 
expected him to learn much. the school was designed to prepare the 
very brightest students for the difficult exams required for entrance 
to the grandes écoles. the atmosphere was often competitive and fast 
paced. Since Mandelbrot had not engaged in any academic work from 
the spring of 1942 to early 1944, when he enrolled at the school, he had 
once again fallen far behind his peers. It would be virtually impossible 
for him to catch up, given the caliber of his classmates and their ample 
head start.
At first, things went as expected. Mandelbrot sat quietly in the 
classes, pretending to be a student. He understood nothing. A week 
went by and then another. Mandelbrot listened as the instructor 
quizzed students on problems in abstract algebra, pushing them to 
compete to find the solutions as quickly as possible in preparation 
for the timed exams. Still, Mandelbrot understood nothing. He could 
guess at what the problems meant, but he had no clue how to solve 
them, and the discussions of various methods were lost on him. And 
then something remarkable happened. one day, after the teacher gave 
the class a problem to solve, an image appeared in Mandelbrot’s mind. 
Without thinking, he raised his hand. Surprised, the teacher called on 

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him. “Isn’t this equivalent to asking whether these two surfaces inter-
sect one another?” Mandelbrot asked, describing the two shapes he 
was picturing. the teacher agreed that the problems were equivalent 
but pointed out that the goal was to solve the problems quickly, not 
interpret them geometrically.
Mandelbrot sat back in his chair, silenced by the rebuke. But when 
the teacher read the next problem, he again tried to think of it in spa-
tial terms. He very quickly saw what the shapes in question were. Soon 
he realized he could do this reliably. He had, it turned out, a “freakish” 
(his word) gift for visualizing abstract algebraic problems. But as his 
teacher reminded him, just coming up with a geometrical interpreta-
tion of a problem wouldn’t help him on the test, and so Mandelbrot 
began thinking about how to put his talent to use. He didn’t see a way 
to solve the problems using just his geometrical intuition, at least not 
in the way the teacher wanted. But he could very quickly guess what 
the answer had to be. And he was usually right. Soon, despite his poor 
preparation and unusual status, Mandelbrot was embraced by the 
school.
Liberation came in the summer of 1944. By the end of August, the 
Mandelbrots had moved back to Paris. though he had been in Lyon 
for only six months, a single academic term, Mandelbrot’s experience 
there changed the course of his life. He learned an enormous amount 
and discovered an unusual gift for geometry, but more importantly, he 
had reclaimed his education. He decided to continue his preparations 
for the grande école examinations, and in 1944, he was admitted to one 
of the most prestigious preparatory schools in Paris. After performing 
well on the exams, he gained entrance to several grande écoles, includ-
ing the most selective of all, the École normale Supérieure.
He attended the École normale Supérieure for two days before de-
ciding that he couldn’t bear life in an ivory tower. His time away from 
the academy had made him all too conscious of real-world problems. 
Mandelbrot immediately transferred to the more practical and scien-
tifically oriented École Polytechnique. the choice augured Mandel-
brot’s path through academia: in each instance, faced with a choice 
between the pure and the applied, Mandelbrot chose the applied. In 
doing so, he brought his “freakish” geometrical gifts to bear on applied 
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