Category Archives: movies

Therein lies madness

This got me a bit puzzled: why would a comment on this post link to a BBC documentary on Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing?

Given that I don’t know as much about the history of mathematics as I probably should, and that I was too tired late last night to do anything more intellectually challenging, I ended up clicking through and watching all 10 parts of the documentary.

The mathematics involved – Cantor’s hierarchy of different-sized infinities, Boltzmann’s statistical mechanics and entropy, Gödel’s incompleteness theorem – is described remarkably well. An expert might quibble about how some of the explanations are ambiguous and imprecise, especially where it concerns Gödel’s work, but that’s a relatively small price to pay for being able to communicate the excitement, audacity and impact of mathematical ideas to a lay audience. The images and animations are, for the most part, well done and helpful. Several mathematicians and scientists (including Roger Penrose) were interviewed for the documentary, and I am guessing that experts were consulted quite extensively about the mathematical content.

That’s only one part of it, though. The movie chooses to focus on Cantor, Boltzmann, Gödel and Turing not only for their groundbreaking contributions to mathematics, but also for the mental anguish and personal tragedy in their lives. Boltzmann and Turing committed suicide, Cantor and Gödel suffered from mental illness and were hospitalized for it, and Gödel ended up starving himself to death. Now, I understand that these are undisputed historical facts. I also understand that troubled characters make for a more interesting movie. But I’m tired of watching the media portray mathematicians as socially challenged and mentally unstable, not to mention poorly dressed. You’d never know that it is quite possible for a great mathematician to be a well adjusted and fully functional human being, to have a long, happy and accomplished life, or to face and overcome adversity without developing a mental illness.
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The movie, set in a not necessarily very distant future, starts with a voice-over monologue, advertisement style. You see, back in the old days we used to rely on fossil fuels for our energy. That caused smog and pollution, affecting our health and that of the planet. (We get some impressive shots of smog in Los Angeles.) Thankfully, those times are long gone. Our skies are clear, our water is fresh, and we have enough clean energy to convert deserts into farmlands. You may ask yourself, how did we get there? Part of it, the voice-over informs us, has to do with the mining of something called Helium 3 on the far side of the moon and using it as fusion fuel. The rest of the answer will be forthcoming shortly. You might not like it.

With the opening credits still running, we meet Sam Bell (Sam Rockwell), the sole operator of one such Helium 3 mining station on the moon. He’s almost at the end of a 3-year contract, the true nature of which will be revealed gradually over the course of the movie. He is not doing well. He looks pale and disheveled, he has been talking to himself, and his mental state is so fragile that he starts to experience hallucinations. Or does he see dead people?
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The Monty Hall problem

On a plane flight back from a recent trip, I watched the movie 21. The plot, advertised as “based on a true story”, is roughly as follows. (In case you have not seen the movie and would like to, I will try to avoid major spoilers.)

Ben Campbell, an idealistic and somewhat naive MIT student, impresses a math professor (Kevin Spacey) by answering correctly a couple of tricky questions in class. Soon afterwards, the professor asks Ben to join his card-counting blackjack team in return for a share of the profits. The team travels to Las Vegas on weekends, plays blackjack at major casinos, and wins millions of dollars by placing themselves strategically at the right tables and employing the card-counting techniques taught by the professor. Ben refuses at first (“and if you tell anybody, I’ll make sure that you won’t graduate”), but there’s no other way that he can pay for his dream med school, and he’s attracted to a female student on the team, and besides, if he didn’t join the team, there would be no movie, so guess what happens.

That’s about the first quarter of the movie, and I’ll leave it there, because this is already enough to raise serious questions about just how close to a “true story” we are here.

My first question was, has there really been an MIT math professor who made a fortune off a team of student card players? Wouldn’t that be serious professional misconduct, and would an MIT professor (not a bad job) really take this sort of risk? As it turns out, the movie is somewhat loosely based on the adventures of a real-life MIT card counting team (one of several that MIT has had over the years). However, the teams were all entirely composed of, and run by, the students. There were no professors involved, and the Spacey character is completely fictional.

Which also preempted my follow-up question. There’s a classroom scene where the Spacey character asks his students what applications of Newton’s method they know. A student suggests, “Nonlinear equations?…” Spacey responds along the lines of “Yeah, that’s very clever, because this course is called Nonlinear Equations. Why don’t you tell me something I don’t already know.” My impression was that Spacey’s demeanor, and this exchange in particular, was a little bit too snarky. A professor is not supposed to do that if he (or, especially, she) wants to get good student evaluations.

The user comments on IMDB include several reviews by authors who appear to be well familiar with casinos, blackjack and card counting, and are not entirely happy with the treatment of the subject. I’ve never played blackjack, or been to a casino, but their criticism makes sense to me.

But here’s the reason why I’m writing this post. How exactly does Ben manage to impress Spacey’s character? Spacey asks him the following question:

You’re on a game show. The host asks you to choose one of three doors. Behind one of them there’s a car, behind each of the other two there’s a goat. You pick one door, say Door 1. The host, who knows where the car is and is not allowed to reveal that information, opens Door 3, behind which there is a goat. He then asks you if you want to choose Door 2 instead of 1. Is it to your advantage to switch?

In case you’d like to think about it, the rest of post is behind the cut.

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Where’s Scarlett Johansson when you need her?

Just came back from a screening of There Will Be Blood. Daniel Day Lewis’s acting is extraordinary, and the church scenes are priceless… but… the ending is ridiculous, and the movie is too long and too relentlessly grim. Compare it for instance to The Prestige, one of my favourite movies of 2006. Many of the themes are the same: ambition, competition, obsession, selling your soul to the devil in the name of professional one-upmanship. But where There Will Be Blood never lightens up, The Prestige is flamboyant, entertaining, and, yes, there’s Scarlett Johansson. Her character was criticized at the time for being underdeveloped and unnecessary. Without her, though, The Prestige would have been a lot more like Blood. And that would be a pity.

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