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

Primordial Seeds 
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at least from de Méré’s perspective. But what do these numbers really 
mean? Most people have a good intuitive idea of what it means for 
an event to have a given probability, but there’s actually a deep philo-
sophical question at stake. Suppose I say that the odds of getting heads 
when I flip a coin are 50%. roughly, this means that if I flip a coin over 
and over again, I will get heads about half the time. But it doesn’t mean 
I am guaranteed to get heads exactly half the time. If I flip a coin 100 
times, I might get heads 51 times, or 75 times, or all 100 times. Any 
number of heads is possible. So why should de Méré have paid any at-
tention to Pascal and fermat’s calculations? they didn’t guarantee that 
even his first strategy would be successful; de Méré could go the rest 
of his life betting that a 6 would show up every time someone rolled 
a die four times in a row and never win again, despite the probability 
calculation. this might sound outlandish, but nothing in the theory of 
probability (or physics) rules it out.
So what do probabilities tell us, if they don’t guarantee anything 
about how often something is going to happen? If de Méré had thought 
to ask this question, he would have had to wait a long time for an an-
swer. Half a century, in fact. the first person who figured out how to 
think about the relationship between probabilities and the frequency 
of events was a Swiss mathematician named Jacob Bernoulli, shortly 
before his death in 1705. What Bernoulli showed was that if the prob-
ability of getting heads is 50%, then the probability that the percentage 
of heads you actually got would differ from 50% by any given amount 
got smaller and smaller the more times you flipped the coin. You were 
more likely to get 50% heads if you flipped the coin 100 times than if 
you flipped it just twice. there’s something fishy about this answer, 
though, since it uses ideas from probability to say what probabilities 
mean. If this seems confusing, it turns out you can do a little better. 
Bernoulli didn’t realize this (in fact, it wasn’t fully worked out until the 
twentieth century), but it is possible to prove that if the chance of get-
ting heads when you flip a coin is 50%, and you flip a coin an infinite 
number of times, then it is (essentially) certain that half of the times 
will be heads. or, for de Méré’s strategy, if he played his dice game 
an infinite number of times, betting on 6 in every game, he would 
be essentially guaranteed to win 51.7477% of the games. this result 

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is known as the law of large numbers. It underwrites one of the most 
important interpretations of probability.
Pascal was never much of a gambler himself, and so it is ironic that 
one of his principal mathematical contributions was in this arena. 
More ironic still is that one of the things he’s most famous for is a 
bet that bears his name. At the end of 1654, Pascal had a mystical ex-
perience that changed his life. He stopped working on mathematics 
and devoted himself entirely to Jansenism, a controversial christian 
movement prominent in france in the seventeenth century. He began 
to write extensively on theological matters. Pascal’s Wager, as it is now 
called, first appeared in a note among his religious writings. He argued 
that you could think of the choice of whether to believe in God as a 
kind of gamble: either the christian God exists or he doesn’t, and a 
person’s beliefs amount to a bet one way or the other. But before tak-
ing any bet, you want to know what the odds are and what happens if 
you win versus what happens if you lose. As Pascal reasoned, if you 
bet that God exists and you live your life accordingly, and you’re right, 
you spend eternity in paradise. If you’re wrong, you just die and noth-
ing happens. So, too, if you bet against God and you win. But if you 
bet against God and you lose, you are damned to perdition. When he 
thought about it this way, Pascal decided the decision was an easy one. 
the downside of atheism was just too scary.
despite his fascination with chance, Louis Bachelier never had much 
luck in life. His work included seminal contributions to physics, fi-
nance, and mathematics, and yet he never made it past the fringes of 
academic respectability. every time a bit of good fortune came his way 
it would slip from his fingers at the last moment. Born in 1870 in Le 
Havre, a bustling port town in the northwest of france, young Louis 
was a promising student. He excelled at mathematics in lycée (basi-
cally, high school) and then earned his baccalauréat ès sciences — the 
equivalent of A-levels in Britain or a modern-day AP curriculum in the 
United States — in october 1888. He had a strong enough record that 
he could likely have attended one of france’s selective grandes écoles, 
the french Ivy League, elite universities that served as prerequisites for 
life as a civil servant or intellectual. He came from a middle-class mer-
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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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