Wednesday, February 19, 2014

Order Out of Chaos in Pi (1998)

NB: The following does not contain a spoiler but it does refer to one of the fundamental concepts of the movie Pi (1998)..

There is a sequence in the movie Pi which I am very fond of and which I wish to bring to your attention.  The purpose of the sequence is, imho, to explain to the audience what is meant by the idea of nature exhibiting mathematical principles.  This is a rather abstract concept for our filmgoers who are used to a steady diet of giant robots and teenage lust dilemmas.

The heart of the movie Pi (1998) by Darren Aronofsky is the search by a mathematician for a number, a number which describes the underlying structure of reality. In a sense this missing number would be to chaos theory what 3.14159 is to geometry but even more profound, it would be the single number that is the key to understanding the chaos that is our universe. Finding such a number would bring meaning to randomness, and order out of chaos. It would change everything: one could predict the weather or know which way Wall Street was going to go, and this very same number may even contain the secret name of God, according to some orthodox Jewish mystics.

Of course no such single number exists, that we know of, but its still an amusing premise and Aronofsky extracts some entertaining plot points from the idea.

The filmmaking problem becomes how do you explain to a general audience what it means to say that there is mathematics underlying the structure of reality. The audience for Pi will be a bright independent film going crowd, but likely math is not their strong subject. Probably most of the audience gets no closer to number theory than figuring out how to calculate the mortgage on their house or the interest on their student loan. So how do you explain this to them?

Well, one way to do this, and the way I think would also be entertaining, would be to stop the movie, bring up a white board, and have a famous mathematician give a short lecture on the origins and meaning of chaos theory. But there is this age old bias against this sort of thing in the conventional and anti-intellectual motion picture business, so giving a lecture in the middle of the film is out.

How else would one present the idea that that there is math everywhere in nature?

I put the 2:28 minute sequence up on Youtube and the right thing to do is to watch it before I say anything more. The mathematician is the guy sitting at the counter reading the paper.

The sequence is at



So Max, our mathematician, is at the counter in a coffee shop trying to get some work done when someone he has recently met, but doesn't really know, comes in. Its Lenny, the orthodox student of Jewish mysticism who proceeds to explain the number theory of the Gematria (1) to Max. The idea is that Hebrew is all numbers and the Torah is a long series of cyphers and crossword puzzles. As Lenny starts to add up the "garden of Eden" and the "Tree of Knowledge", while Max looks on, he comes up with two numbers in the Fibonacci sequence. Max hijacks this discussion of numerology in the Torah and moves it to more standard high school math.   The Fibonacci sequence is one of those concepts that keep mathematicians happy because there are so many uses and weird coincidences, but the only one that Max/Aronofsky goes for here is that you can use the Fibonacci sequence to calculate Theta which is a number that describes a kind of spiral.   So we go effortlessly from Torah numerology to Fibonacci numbers to spirals and boom we are home.   All that is left to do is smoke your cigarette or pour cream in your coffee and the point is made.

"You see", says Lenny, "there is math everywhere".

I still think having a mathematician give a lecture would have worked, but this is probably more concise and any excuse to discuss numerology is OK by me.

For an introduction to Fibonacci numbers see

An introduction to Numerology in general

A reasonable introduction to Gematria and Jewish Mysticism in general

A Gematria Calculator

Pi (1998) on IMDB



1. Actually he fails to explain the Gematria to Max, getting a variety of things wrong but hey its good enough to get the point across.

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