## Wednesday, February 27, 2008

Plot

Sean Gullette as Maximillian Cohen, a reclusive math genius
Mark Margolis as Sol Robeson, Max's mentor, who abandoned his research into π after it nearly killed him.
Ben Shenkman as Lenny Meyer, a Hasidic Jew who introduces Max to Kabbalah.
Pamela Hart as Marcy Dawson, a representative of an investment firm that is interested in Max's research
Stephen Pearlman as Rabbi Cohen, the leader of a Jewish sect that pursues Max.
Samia Shoaib as Devi, Max's attractive and friendly neighbor.
Ajay Naidu as Farroukh, Devi's boyfriend.
Kristyn Mae-Anne Lao as Jenna, a girl who plays math games with Max. Cast
π was written and directed by Darren Aronofsky, and filmed on high-contrast black-and-white reversal film.
π had a low budget (\$60,000), but proved a financial success at the box office (\$3.2 million gross in the U.S.) despite only a limited release to theaters. It has also proven to be a steady seller on DVD.
According to the DVD's production notes, Aronofsky raised money for the project by selling \$100 shares in the film to family and friends, and was able to pay them all back with a \$50 profit per-share when the film was sold to Artisan. He paid his crew in deferred payments amounting to \$200 a day, as well as 'shares' in the film. Darren Aronofsky's next film was Requiem for a Dream (which was also sold co-packaged with π).

Production
In the film, Max periodically plays Go with his mentor. This game has historically stimulated the study of mathematics and features a simple set of rules that results in a complex game strategy. The two characters each use the game as a model for their view of the universe; Sol says that the game is a microcosm of an infinitely complex and chaotic world with Max asserting that patterns can be found in the complexity of its variations. Actors Sean Gulette and Mark Margolis both learned the game for the film from the New York City American Go Association club.

The game of Go
The film's characters make several mathematical goofs, such as
Max pursues a legitimate scientific goal, and as such, π features several references to mathematics and mathematical theories. For instance, Max finds the golden spiral occurring everywhere, including the stock market. Max's belief that diverse systems embodying highly nonlinear dynamics share a unifying pattern that bears much similarity to results in chaos theory, which provides machinery for describing certain phenomena of nonlinear systems, which might be thought of as patterns. Unlike in the film, chaos theory does not allow one to predict the exact behavior of a chaotic system like the stock market and, in fact, provides compelling evidence that such predictions are, in principle, impossible.

The film shows a drawing of the golden rectangle (with larger side length a and shorter side length b) with $frac{a}{b} = frac{a}{a+b}$. This equation has no solution for non-zero a, and the golden ratio actually refers to a ratio such that $frac{a}{b} = frac{a+b}{a}$.
The Greek letter $theta,$ (theta) is stated to be the symbol for the golden ratio. In fact, the letter used is generally $varphi$ (phi).
In the same scene as the previous goof, while discussing the links between the Fibonacci sequence and the golden ratio, Max states, "If you divide a hundred and forty-four into two hundred and thirty-three, it approaches theta." What he means is that the ratio between terms of the Fibonacci sequence and their immediate predecessors approaches the golden ratio as one looks further along the sequence. The single division 233/144 has a fixed value, so it does not approach any other value. Mathematics and π
The 216-letter name of God sought by the characters of the film is actually widely known and called the Shemhamphorash or the Divided Name. It comes from Exodus 14:19-21. Each of these three verses is composed of seventy-two letters in the original Hebrew. If one writes the three verses one above the other, the first from right to left, the second from left to right, and the third from right to left, one gets seventy-two columns of three-letter names of God. The seventy-two names are divided into four columns of eighteen names each. Each of the four columns represents one of the four letters of the Tetragrammaton.
The actual name of God, according to Jewish traditions, is the Tetragrammaton (YHWH or YHVH). This is the name that was intoned in the temple once a year during Yom Kippur, as referenced in the film. What has been lost is not the spelling of the name, as in the film, but the true pronunciation, since words written in Hebrew in the Torah do not include vowels. Furthermore, in the case of the Tetragrammaton, when vowels were used, the actual vowels were replaced with the vowels of the word Adonai to avoid pronouncing the Tetragrammaton, which is a taboo in Judaism.
In addition, it would be highly unlikely that the Hebrew Schemhamphoras would translate into 216 digits in a decimal system for several reasons:

There is no zero in Hebrew numerals.
The Hebrew number system does not work as a normal decimal system; the characters of the Hebrew Alphabet, the Aleph-Bet, correspond to the following values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, and 400. So, if the letter "A" had a value of 1, and "B" 2, and so on, you would only get up until "I" (which would have a value of 9) until you would need multiple letters to reflect numbers that are not divisible by ten and that have two or more digits (i.e., if "J" was 10, and you wanted to make the number 11, it would be "JA", or 10+1). If each single-digit number corresponded to its letter only, then you would have a 216-letter word that only uses letters A through I. Soundtrack

Pi (the mathematical constant)