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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

Ma Nuit Chez Maud (1969)

From the Video cover: The second of Rohmer’s “contes moraux” is constructed around Pascal’s famous wager: the proposition that it is worth gambling on God’s existence, because if he exists you gain eternity, and if you lose, you lose nothing.

9:23
JEAN-LOUIS studies some mathematics. Details not visible on video.

12:35
JEAN-LOUIS looks at some textbooks of probability in a bookshop. The one on the left seems to be the same as the one on the right.

13:08
Has a look at one of Pascal’s books.

15:50
Runs into VIDAL, a friend who he has not seen for years.
JEAN-LOUIS: Do you often come here?
VIDAL: Almost never. And you?
JEAN-LOUIS: I’ve never set foot here before.
VIDAL: And yet our paths cross right here. How strange.
JEAN-LOUIS: Not at all. Our ordinary paths never cross, therefore the point of intersection is in the extraordinary. I’ve been dabbling in mathematics lately. I’d like to work out the odds against our meeting since last October (this is when he moved to this city).
VIDAL: Is it possible?
JEAN-LOUIS: It’s a matter of classifying data, provided they exist. Obviously, if I don’t know where a person lives or works the possibilities cannot be calculated. Are you interested in maths?
VIDAL: Maths is increasingly important for a philosopher. For example, in linguistics, or even in simpler things, Pascal’s artithmetical triangle is linked with his ‘wager’. That is why Pascal is so amazingly modern. Mathematician and metaphysician are one.
JEAN-LOUIS: Pascal …. Funny you mention him, I am just re-reading him.
VIDAL: And?
JEAN-LOUIS: I am disappointed.
VIDAL: Really, why is that?
JEAN-LOUIS: Oh, I don’t know. I feel I almost know him by heart, yet he tells me nothing. He seems so empty. I’m a Catholic, or at least try to be, but he doesn’t fit in with my Catholicism. It’s because I am a Christian I resent his severity. If Pascal represents Christianity, then I am an atheist. Are you still a Marxist?
VIDAL: To a communist Pascal’s wager is very real. Basically, I very much doubt that history has any meaning, but I stake my bet that it has, so I am in a Pascalian situation. Hypothesis A: Society and politics are meaningless. Hypothesis B: History has a meaning. I’m not certain B is more likely to be true than A. Rather the reverse. Suppose the odds are ten to one in favour of A being true. Nevertheless, I wouldn’t hesitate, I’d have to bet on B, I’d bet history has a meaning because it’s the only hypothesis to justify my life. Suppose I bet on A and B was true, against all the odds I’d have thrown away my life. So, I must choose B to justify my life and deeds. The odds are ten to one against me, but that doesn’t matter.
JEAN-LOUIS: Mathematical expectation, gain divided by probability (the product of gain and probability?). With your hypothesis B the probability is finite but the gain would be infinite. For you a meaning to life, for Pascal, eternal salvation.
VIDAL: Gorki, Lenin or maybe Mayakovsky talking about the Russian revolution said that circumstances forced them to take the chance in a thousand because it was infinitely better to take that chance, than no chance at all.
At Maud’s house
VIDAL: There must be a Pascal here in a Freemason’s house…. What did I tell you. Isn’t there a specific reference to mathematics in the “wager’? (quoting) If there are not infinite chances of loosing, against that of winning, do not hesitate, stake all. You are obliged to play, so renounce reason if you value your life.
JEAN-LOUIS: That’s mathematical expectation. It’s always infinite with Pascal. Unless his life probability is nil –infinity times zero equals zero. A worthless argument for non-believers.
VIDAL: But with one grain of belief it becomes infinite again.
JEAN-LOUIS: Then you must bet. If I think there is a probability and the gain is infinite.
VIDAL: You believe that? Yet you stake nothing. You give up nothing.
JEAN-LOUIS: I give up some things.
VIDAL: Not Chanturgue (some kind of wine).
JEAN-LOUIS: It’s not a stake. Why should I give it up? What I don’t like about Pascal’s “wager” is the lottery aspect. Giving something in exchange. Call it choice, rather, between finite and infinite. If I choose Chanturgue, I’m not rejecting God. That’s not the choice.

40:24
JEAN-LOUIS: Now, I may shock you once again, but pursuing girls does not estrange one from God any more than mathematics, for example. To return to Pascal, not only did he condemn good food but, at the end of his life, he even condemned mathematics.
VIDAL: But really I am more …. No, you are more Pascalian than I
JEAN-LOUIS: Maybe. Mathematics distracts from God. A useless intellectual diversion, worse than other diversions.
VIDAL: Why worse?
JEAN-LOUIS: Because it is completely abstract and thus inhuman