Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

Infinity (1996)

A movie about Richard FEYNMAN (Matthew Broderick) the famous physicist and his wife ARLINE Greenbaum (Patricia Arquette).

Opening titles: Infinity sign.

10:25
Feynman makes a Moebius strip and shows it to ARLINE.
FEYNMAN: This is a Moebius strip. One surface, one side. Here try it. Make a line on it.
ARLINE: This is wonderful, this is a Moebius strip?

13:25
FEYNMAN challenges an abacus expert.
FEYNMAN: I challenge you.
ABACUS EXPERT: Challenge?
FEYNMAN: Yeah, I’d like to. Yeah, I bet I can calculate faster with my head than you can with this abacus. Suppose you write down two less than identical numbers and then hand them to us at the same time.
ABACUS EXPERT: Ok.
FEYNMAN: Wait, let me get a pad.
Second multiplication: equally fast 500,046.
Third cube root of 1729.03
Feynman gets integer part 12 first. When his competitor catches up, he then asks for more digits. When he says this he already puts down 12.002. Competitor still gets the first 0 after the decimal point, but by that time Feynman is already up to 12.002384.

Outside the shop…
FEYNMAN: That was nice.
ARLINE: Wasn’t it. So, how’d you do it?
FEYNMAN: Ah, you don’t want to know how I did it. He doesn’t know anything about numbers, just beads. …
In a coffee shop
With an abacus you don’t have to know anything about arithmetic, you just buzz those beads around. He doesn’t know numbers. I don’t know beads, but I know arithmetic. So, the harder the problem gets the better off I am, and the worse off he is … How are you supposed to approximate half a bead. Also, I got lucky. The number the guy picked was 1729.03
ARLINE: Was it?
FEYNMAN: Yeah. I happened to know that a cubic foot contains 1728 cubic inches. So, the answer is just a tiny bit more than 12.
ARLINE: Well, where does 12 come in?
FEYNMAN: ‘cause there is 12 inches in a foot.
ARLINE: Ok, well I didn’t notice that.
FEYNMAN: So, the excess, the difference between the guy’s number and the number of inches in a cubic foot is 1.03 and that’s only one part in nearly 2000 and I know that in calculus that for small fractions the cube root’s excess is one third of the number’s excess, so all I had to do was find the fraction 1/1728 multiplied by four, divided by 3 and multiplied by 12. So, I was able to pull out a whole bunch of extra digits that way. Cubic roots, that much be his top notch exercise in Abacusland.

29:10
Feynman to Arline.
FEYNMAN: Mathematics is a language. It’s very difficult, it’s subtle. You couldn’t say those things any other way. Then I could talk to dead people with it, I talk to Copernicus every day.

43:11
blackboard

1:06:25
blackboard

1:47:23
Feynman talking to a kid.
FEYNMAN: Hey Henry. Did you know that there are twice as many numbers as numbers?
HENRY: Oh, come on, Dick!
FEYNMAN: There are. Let me show you. Name a number.
HENRY: One million.
FEYNMAN: Two million.
HENRY: Twenty-seven.
FEYNMAN: Fifty-four. Now you try it. Six.
HENRY: Twelve!
FEYNMAN: Six million.
HENRY: Twelve million!
FEYNMAN: Light beginning to dawn?
HENRY: So, there are three times as many numbers as there are numbers.
FEYNMAN: Hmm, prove it.
HENRY: You know, three times anything. You say five, I say fifteen. I say five billion four hundred seventy three..
FEYNMAN: Three times that.
HENRY: So, is there a biggest number?
FEYNMAN: Well, how can there be? So that idea, the idea that there is no end how big a number can be, that’s called infinity.