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

From Coastlines to Cotton Prices 
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and Welsh coasts. to account for these features, which turn out to add 
rather a lot of distance, you need a smaller ruler still. But again, the 
same problem arises. In fact, no matter what size ruler you pick, the 
answer you get by measuring the coastline with that ruler is always too 
small. In other words, you can always get a larger answer to the ques-
tion by picking a smaller ruler.
this is where the paradox arises. It is often the case that choosing 
more precise instruments gives you a better measurement of some-
thing. You can get a sense of how hot a pot of water is by sticking your 
finger in it. An alcohol thermometer would do the job even better, and 
a high-tech digital thermometer would bring the accuracy to within a 
fraction of a degree. there is a sense in which the imprecise tools are 
adding measurement error, and as you devise better and better instru-
ments, you home in on the real temperature. But with a coastline, no 
matter how precise your measuring device — that is, no matter how 
small your ruler — your measurement is always much too small. In 
some sense, a coastline doesn’t have a length, or at least not in the way 
that simple shapes like a line or a circle do.
Mandelbrot addressed the coastline paradox in a groundbreaking 
paper in 1967. It was one of his first attempts to describe a fractal shape
— as, indeed, a coastline turns out to be, though Mandelbrot didn’t 
coin the term until 1975. coastlines (and other fractals) are remark-
able from a mathematical point of view because they have a property 
called self-similarity. to say that something is self-similar is to say that 
it is composed of pieces that look just like the whole; these pieces in 
turn are composed of still smaller pieces that also look like the whole, 
and so on ad infinitum. If you begin with the whole west coast of Brit-
ain and carve it up into several pieces, you will notice that each of 
these also looks like a coastline; just like the full coastline, the smaller 
stretches of coast have their own little inlets and peninsulas. And if 
you break up one of these smaller bits of coast further, the still-smaller 
pieces exhibit all the same features of the larger structures.
once you start looking for self-similarity, you quickly realize it’s a 
ubiquitous feature of nature. A mountaintop looks much like a whole 
mountain in miniature; a tree branch looks like a little tree, with 
smaller branches of its own; river systems are built out of smaller rivers 

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and estuaries. the principle even seems to extend to the social world. 
As Mandelbrot later pointed out, a battle is made up of smaller skir-
mishes, and a war is composed of battles, each a microcosm of the war 
as a whole.
When World War II broke out, the Mandelbrots fled Paris, where they 
expected the fighting to be quite intense, and settled in a town called 
tulle, in the region of france known as corrèze. once again, the Man-
delbrots showed great foresight, not to mention luck: they left Paris in 
late 1939, mere months before the nazi invasion of france. tulle turned 
out to be an extremely fortuitous choice. It was far enough south that it 
would soon become part of unoccupied (vichy) france.
the vichy government cooperated with the Germans, but anti-
Semitism in the south was less virulent than in the German-occupied 
territories. for a few years, at least, Mandelbrot was able to attend high 
school in tulle. He was now fluent in french and he quickly moved 
through school, catching up to his peers by the time the Germans took 
control in 1942. Still, the Mandelbrots lived in constant fear of depor-
tation. In 1940, the vichy government had begun to review the status 
of all immigrants naturalized after 1927. they stripped about fifteen 
thousand (mostly Jews) of their citizenship, as a precursor to sending 
them to German concentration camps. though the Mandelbrots man-
aged to escape notice in little tulle, the threat was ever present.
Matters became worse in 1942. on november 8, the British and 
American armies invaded french north Africa. In response, the Ger-
mans occupied southern france, anticipating an assault on continen-
tal europe. With the German army came the Gestapo, and as southern 
france became a staging ground for defensive Panzer divisions, even 
tulle became a minor battleground. though it was home to only a few 
thousand people, tulle was the traditional capital of the region. As the 
German presence in southern france increased, tulle became a place 
of strategic interest to both the vestiges of the vichy government and 
the leaders of the resistance. the Mandelbrots could no longer rely on 
the obscurity of their little town for safety.
In his autobiographical writings and interviews, Mandelbrot often 
spoke of the war’s impact on his education. After finishing second-
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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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