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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross


The Bank (2001)

Paul Jackson (David Wenham) is a math genius who’s father is driven to commit suicide by CantaBank one of Australia’s largest bank. To revenge his father’s death, Paul takes on the name Jim Doyle and gets a PhD in mathematics specializing in modelling the stock exchange. Now he is ready to confront CentaBand and it’s evil CEO, Simon O’Reilly (Anthony LaPaglia). Opening titles: Class reciting seven times one is one, seven times two is fourteen, seven times three is twenty one, …. seven times twelve Simon O’Reileigh

BANK REP: If you just save 50 cents a week at the bank doubling your investment every three years, then 25 years from now each of you would have 727000 dollars of your own.
JIM (as a school kid): That is impossible. There is only 52 weeks in a year.
BANK REP: Yes, yes, that‘s right (writes 52 X 25 on the blackboard) you’ll only have 1300 weeks.
JIM: That’s right.
BANK REP: Let me show you how it works. Compound interest, you get interest on your interest. Do you understand?
JIM: Yes, I do. (writes down the formula)

Title sequence features the Mandelbrot set

Jim scribbling math on a piece of paper.

He switches to working on a computer.

JIM: Ok, that should correct the climate variation. Can’t quite get it to predict the weather yet.

Jim’s program is called B.T.S.E. Jim and his friend are faxing the results to a bank to attract their attention.

Simon receives message
SIMON: So what is it?
VINCENT: It’s fractal theory. He is using it to try and predict the stock market correction.
SIMON: And can he?
Stipid: Not yet, but if these figures are accurate, he is getting very close.
SIMON: I have seen this kind of thing before. A black box ???? 12 months before collapsing and taking a half a billion with it.
VINCENT: This is much more advanced than that. He is smarter.
SIMON: Yes, well they are all smarter, until they are not.

VINCENT: It’s a chaos-based technique. It attempts to find order in the madness of the trading floor by…
SIMON: Really, can he take into account a trader with a bottle of red under his belt who decides to long on the yen because his wife is having an affair with a Japanese sushi chef. You see that’s the one thing, Vincent, that these things never take into account. The human factor.
VINCENT: Maybe they can. He is building a program that can evolve that can learn from its experience in the market.

Jim explaining tho the bankers why his system is better than all the other systems that have been used for predicting the stock market.
JIM: They all missed one fundamental principle. See, tying to predict what one person will do, it’s almost impossible. To try to predict what a hundred people will do is much much easier. So, with that in mind I began delving into the nether regions of mathematics, fuzzy logic, nonlinear dynamic, chaos theory. Of particularly intest to me was the work of Madelbrot?? and his breakthrough with fractal geometry. (faces show that nobody understands anything) Excuse me, can I borrow your pen for a minute?
Opens pen and splashes some drops of ink on the table cloth. Ok, we (???) think a bit like this. Any simple inciting (??) event has significant and complex results that brings about things that we could never imagine being able to predict, things like weather patterns, cloud formations, right down to the very point, the very millimetre where this ink will fall, until now. This mathematics allows us to predict almost anything. If we can predict this
(draws an infinity sign), then predicting the stock market is easy.

Running a test of the program

Check for formula in prediction
His new girlfriend Michelle tries to find out what he does.
JIM: I’m a genius, maths … Oh, and in bed of course.

Simon describing what trading stocks is like.
SIMON: Jim, you’d love it. You have numbers flying through your mind and you bounce them back at each other at all different angles to see which ones come out you can hurl back into the world.

Michelle giving it another go.
JIM: It’s actually my first job since I completed my PhD. I guess they lured me in.
MICHELLE To make your fortune.
JIM: Mhm, so to speak.
MICHELLE: So, what do you do?
JIM: I am not allowed to tell you.
MICHELLE: Come on, just a hint. Something abstract.
JIM: Well, I design mathematical systems to predict things. Yeah well, today I learned to actually make money, very effectively make money, nothing more exciting than that.
MICHELLE: Like a system to beat lotto.
JIM: To beat the stock market.
MICHELLE: Every loser has a system whether it is buying shares or playing blackjack.
JIM: It’s a little bit more complicated than that. It’s ahm … that’s all I can tell you.

In a restaurant calculating on a table cloth.

Simon has a look at the table cloth

getting closer

MICHELLE: What’s the celebration?
SIMON: The Yarra, 38 kilometres of prime crown waterfront real estate. As of 6 p.m. today, it’s ours.
JIM: I’m sorry.
SIMON: Split it into 4 acre lots, you do the maths Jim, how much do we make.

Jim tells Simon that he has made his breakthrough.
JIM: Have you thought of the consequences?
SIMON: Of course I have.
JIM: I have spent years of research, 10 years of postgraduate study for this.

SIMON: You will insult every single one of these people, if you turn your back on this opportunity.
JIM: An opportunity to achieve what?
SIMON: An opportunity to join your peers like Mandelbrot, to take your place in history with the great mathematicians and scientists, like Pythagoras, Foucoult ??, Newton, Einstein, Oppenheimer.
JIM: They used Oppenheimer’s work to make the atom bomb.
SIMON: The bomb ended the war.

Vincent and Jim talking about life.
JIM: Did you think you’d end up here, Vincent?
JIM: No, when you were a kid, when you knew that mathematics was what made you tick.
VINCENT: I don’t know. My guess it that it has just been one foot after the other for me. Top of the class at school, university. First job out---Centre Bank.
JIM: Yeah, but there must have been a time when you loved it, where you dream where it could take you.
VINCENT: Mathematics, permutations, logic, strategy, maybe chess, I used to play a lot of chess, I learned it when I was about 4 or 5. I played a grand master once at Westfield shopping centre, he was playing 20 people at once and I came so close to winning. It’s a brilliant game. I haven’t played it for years.
JIM: We should have a game one day.

JIM: Well, I cracked the mathematics of it. It was just a matter of speed.

SIMON: There are huge risks.
JIM: No, there is no risk.
SIMON: Yes, there are always risks.
JIM: No, not this time, it’s mathematically proven.

JIM: Something you want to say, Vincent?
VINCENT: Yes, I’ve worked for this bank for 10 years and I have never been ashamed, until today. We didn’t use to be like this. I know we do some shitty things sometimes, but..
JIM: You were the one who told me about turning a blind eye.
VINCENT: Yeah, well maybe I did. But I just wished I hadn’t been there and I hadn’t lie and fuck that family’s case out of existence. I respect your mind, Jim, I envy it. You know I wished I could comprehend even just a fraction of what you can. Most days I look across the lab at you and I wish it was me, I wish I was the one who could come up with this formula, but I know this much. I could never do what you did today and if that’s what it takes, then good fucking luck to you, Jim.

The Bank is going down

The bank just ceased to exist. Jim’s signature, the infinity sign appears on the screen. The infinity sign shows up on both table cloths that Jim writes on earlier on in the movie.

Vincent studies the table cloth and realizes that the equations on it are false.

Director’s commentary
All these equations here are derived from chaos theory. Although we have taken some creative licence with it.

The fractal graphics throughout the film as seen in the opening titles and sporadically throughout the film actually gave us an opportunity to make the mathematics much more interesting to look at. We realized early on that graphs and equations weren’t going to be enough to keep people interested. And thankfully chaos theory and fractal geometry is very much related to the area of mathematics that the character of Jim Doyle is working in. It may just be pretty pictures but it certainly mathematically is quite accurate.

Sheldon Gardner at MCM Interactive designed the fractal sequences

In this sequence here on the walls of Jim’s apartment are all these artworks by Melbourne based artist Jeff Knees. You know choosing artworks to just hang in the backgrounds in a flat is something that could be treated very superficially, but if you look at the artworks they are actually concentric circles very mathematically created from cardboard.

Major graphics scene in the film, grand decent into the fractal like into a black hole.

Infinity sign as Jim’s signature.