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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

Labyrinth (1986)

25:50
SARAH: faces two magical doors with strange guards (left up, left bottom, right up, right bottom)

SARAH: Somebody has been changing my markers. What a horrible place this is. It’s not fair.
LEFT (doorkeeper) BOTTOM: That’s right it’s not fair, but that’s only half of it.
SARAH: This was a dead end a minute ago.
RIGHT DOORKEEPER: No, that’s the dead end behind you.
SARAH: It keeps changing. What am I supposed to do?
LEFT BOTTOM: Well, the only way out of here is to try one of these doors.
RIGHT BOTTOM: One of them leads to the castle at the center of the labyrinth and the other one leads to certain death.
SARAH: Which one is which?
LEFT BOTTOM: We can’t tell you.
SARAH: Why not?
LEFT BOTTOM (looking at other bottom): We don’t know but they do (looking at upper parts).
SARAH: Oh, then I’ll ask them.
LEFT UP: No, you can’t ask us. You can only ask one of us. It’s in the rules. And I should warn you that one of us always tells the truth and one of us always lies. That’s a rule, too. He always lies.
LEFT UP: I do not, I tell the truth.
RIGHT UP: Oh what a lie. … (more of the same)
SARAH: All right (addresses left up). Answer, Yes or No. Would he (pointing at the other guy) tell me that this door (points to the door behind the one she asks) leads to the castle?
LEFT UP: Yes.
SARAH: Then the other door leads to the castle and this door leads to certain death.
LEFT UP: How do you know? He could be telling the truth.
Heroin: But then you wouldn’t be. So if you told me that he said Yes I know the answer is No.
LEFT UP: But I could be telling the truth.
SARASARAH:: But then he would be lying. So if you told me that he said Yes, I know the answer would still be No.
LEFT UP: Wait a minute. Is that right.
RIGHT UP: I don’t know. I’ve never understood it.
SARAH:: I know it’s right, I figured it out.

1:24:00
Scene based on Escher’s print Relativity.