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Mathematics Goes to the Movies
by Burkard Polster and Marty Ross
All about using prime numbers to avoid being sliced and diced. Too much stuff. There is a whole chapter in the book dedicated to this movie.Here are just some snippets of dialogue.
QUENTIN: Leaven, what do you read in school? Math?
HOLLOWAY: What can they mean?
Leaven puts on her glasses and begins to study the numbers.
Leaven opens a new door. The numbers we see are 645 372 (and later) 649.
LEAVEN: Prime numbers. I can't believe I didn't see it before.
QUENTIN: See what?
LEAVEN: It seems like if any of these numbers of prime, then the room is trapped. Ok, 645... 645, that's not prime. 372... no. 649... Wait, 11 x 59, its not prime either. So that room is safe.
QUENTIN: Wait, wait, wait. How can you make that assumption based on one prime number trap?
LEAVEN: I'm not. The incinerator thing was prime: 083. The molecular-chemical thingy had 137, the acid room had 149.
HOLLOWAY: You remembered all that in your head?
LEAVEN: I have a facility for it.
After Quentin almost got killed in a room although its numbers were not prime.
LEAVEN: I guess the numbers are more complicated than I thought.
WORTH: Maybe they mean nothing at all.
LEAVEN: No, it means they're more involved, they worked for us up to now have just been bad, I just need more time with them.
After Worth has confessed that he designed the outer shell of the labyrinth and that its overall shape is that of a cube.
LEAVEN: What are the dimensions of the outer shell?
WORTH: 434 feet square.
What he probably means by this is that the length of an edge of the inner shell is 434 feet.
Leaven starts to take steps inside the room to figure out its dimensions.
LEAVEN: 14 by 14 by 14.
WORTH: The inner cube cannot be flushed by the shell. There is a space.
LEAVEN: One cube?
WORTH: I don't know. It makes sense.
LEAVEN: Well, the biggest the cube then can be is... 26 rooms heigh, 26 rooms across, so... 17.576 rooms.
Dividing 434 by 14 gives 31. This would suggest that 31x31x31 rooms fit into the outer shell and therefore 29x29x29 into the inner shell. However, this does not take into account the thickness of the walls. Working backwards, we divide 434 feet by 28 to arrive at 15.5 feet, which suggests that the walls are about (15.5-14)/2 feet=1.5 feet thick, which sounds about right.
HOLLOWAY: 17.576 rooms? Oh, God that makes me queasy.
Leaven opens a new door and puts on her glasses.
LEAVEN: Leaven, you are a genius!
We see three numbers: 517 478 565
LEAVEN: Cartesian co-ordinates, of course, coded Cartesian coordinates. They are uses in geometry to plot points on a three-dimensional graph.
QUENTIN: In English. Slower.
LEAVEN: Bonjour, these numbers are markers, a grid-reference, like altitude and longitude on a map. The numbers tell us where we are inside the cube.
QUENTIN: Then where are we?
LEAVEN: It works! Ok, all I have to do now is add the numbers together. The x-coordinate is 19
Here she scribbles 928 on a piece of metal and therefore 9+2+8=19. This also means that she is not talking about the number triple 517 478 565 that we just came across
Y is . . . Here she scribbles 856 giving 8+5+6=19 … 26 rooms. So that places us... seven rooms from the edge. (because 26-19=7)
QUENTIN: What's the matter?
LEAVEN: These co-ordinates: (14,27,14).
QUENTIN: What about them?
LEAVEN: Well, they don't make sense. Assuming the cube is 26 rooms across, there can't be a co-ordinate larger than 26. If this were right, then we would be outside the cube.