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

From Coastlines to Cotton Prices 
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voracious reading. Mandelbrot spent most of his time playing chess 
and studying maps.
Warsaw was hit hard by the depression — worse than western 
europe or the United States — and Mandelbrot’s father’s clothing 
business was essentially destroyed in 1931. His father then moved to 
france, hoping that the slightly better economic situation there would 
enable him to support his wife and sons from afar. With their large 
extended family in Warsaw, however, the Mandelbrots were strongly 
tied to the city. the hope was that Benoît’s father would eventually be 
able to move back to Poland and reestablish his business there. But as 
the 1930s droned on and the depression worsened, Poland became 
increasingly unsettled. ethnic and political violence grew. As Jews, the 
Mandelbrots realized that Warsaw had become dangerous for them. 
Benoît’s mother packed what belongings she could and followed her 
husband to Paris. though a difficult decision at the time, the move to 
Paris almost certainly bought the Mandelbrots their lives: of the more 
than 3 million Jews who lived in Poland before World War II, only a 
few hundred thousand survived the Holocaust.
Szolem was already in Paris when Benoît’s father arrived. He had 
moved to france in 1919, a refugee of an entirely different sort. In the 
immediate aftermath of World War I, mathematics in Poland was dom-
inated by a brilliant young mathematician named Wacław Sierpiński. 
Sierpiński worked on a topic known as set theory. He was militant 
about his preferred style of mathematics and powerful enough to dic-
tate the terms of success for any graduate student in Warsaw. Later in 
life, Szolem may have seemed unbearably rigid to the geometrically 
minded Mandelbrot, but Sierpiński was too formal even for Szolem. 
refusing to work on the topics Sierpiński required, Szolem fled to 
Paris, where the prevailing mathematical ideology was more in line 
with his own. Ironically, Sierpiński was also the discoverer of an un-
usual geometrical object known as the Sierpiński triangle — an early 
example of a fractal.
It wasn’t until Mandelbrot arrived in Paris that he had the opportu-
nity to interact with his famous mathematician uncle. Mandelbrot was 
eleven years old. though the two would later have their differences, 

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their early relationship was deeply formative. Since Mandelbrot spoke 
little french, he was placed two grades behind his age level. to keep 
him interested in his education and to encourage his talents, Szolem 
fed him bits of mathematics. It was largely Szolem’s influence during 
this period that pushed Mandelbrot toward mathematics. despite the 
difficult economic and political situation, under Szolem’s tutelage Ben-
oît found a way to thrive in his new home.
Unfortunately, it would not last. In 1940, Germany invaded france. 
And once again, the Mandelbrots were forced to flee.
How long is Britain’s coastline? this might seem like a simple ques-
tion — one that could be easily settled, say, by a team of competent 
surveyors. As it turns out, however, the question is more complicated 
than it appears. there’s a deep puzzle built into it, sometimes known as 
the coastline paradox. to figure out the length of a coastline, you need 
to take some measurements, presumably with some sort of ruler. the 
puzzle concerns how long your ruler needs to be. Suppose you started 
with a single enormous ruler that stretched from cape Wrath, at the 
northernmost tip of Scotland, all the way down to Penzance, at the 
southwestern tip of cornwall. this would give you an estimate of the 
length of the coastline.
But not a very good one. A coastline is hardly a straight line. the 
coast of Britain dips in at the Bristol channel and the Irish Sea, jutting 
out again near Wales, so taking one very long ruler isn’t going to give 
an accurate measurement. to get a better measurement, you would 
want to use a somewhat smaller ruler — one that could easily accom-
modate the additional length that the various peninsulas and bays add 
to the coast. You might try adding up the distances from, say, Penzance 
to Bristol, and then from Bristol to St. david’s in Wales, and then from 
St. david’s to carmel Head at the northwestern tip of Wales, and so on 
all the way up the coast. this total distance would be a lot longer than 
the first distance you calculated, but it would be more accurate.
now, though, a pattern begins to emerge. this smaller ruler, it turns 
out, underestimates the length in the same way the original long ruler 
did. Using the smaller ruler, you miss cardigan Bay altogether, not to 
mention the dozens of smaller harbors and inlets along the cornish 
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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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