|squish7 /CUBE THE MATH OF CUBE (this room makes me feel retarded).|
|Warning: SPOILER Page
Page is a bit out of date; don't bother correcting me on things I have wrong, I probably know about them.
In Cube (see Wikipedia for a detailed plot summary) A handful of people wake up in a cubical structure of 26 by 26 by 26 cubical rooms, or 17,576 (a cube of 26-cubed cubes), which are shifting around, plus a "bridge" that moves through the maze. It is easy to fathom them moving if you assume there is the technology of anti-gravity, but otherwise engineering to do it is incredibly difficult to fathom (Even anti-gravity is considered by Wikipedia to be improbable to even be possible within the grounds of our current sciences). It is also possible for them to move within the cube, moving close together to accumulate the small spaces inbetween each cube into enough space to move around, and this is how they say the structure works. It's somewhat similar to the old Mac tile game where you have to re-arrange a scrambled picture of tiles with only one tile missing. However, we never see a gap between the cubes in the movie, probably due to the low budget and understandable lack of obsession with getting all the physics perfect.
The group combine their skills except for a cop who just yells at people and eventually kills three of his new buddies, to navigate the death-trapped rooms and find an exit, while people die and so forth. Each room is labeled on all sides with nine digits, 3 three-digit numbers, which tell us quite a bit, but not enough for them to navigate the Cube. Leaven finds that the original coordinates of the rooms are obtained by adding the digits together so "123 456 789" is located at 1+2+3, 4+5+6, 7+8+9, or [6, 15, 24], which is possible because the minimum and maximum coordinates are 0+0+0=0 and 9+9+9=27. However, this is not enough to navigate because she has no idea where the origin is which could be any of the eight corners (the origin would be 1,1,1; it could not be 0,0,0 because the maximum coordinate is 26. It would be 25 if it were 0,0,0, becase this would count as a room), and even if she knew it still could not navigate to begin with because they had no idea the rooms were shifting around at the beginning (or if she did, how fast they were).
She later deduces this is revealed by "subtracting the digits from one another" instead of adding then using permutations (the number of permutations of 4 things are 4*4*4*4) and combinations (4*3*2*1). It seems more likely that the rooms would move in permutations, I can't see how combinations might be involved). We're not given any hint as to what kind of system she is using (for instance, in what way the digits are subtracted; "123" could be subtracted 1 - 2 - 3, or 3 - 2 - 1), but whatever her theory, I believe the numbers would not be enough to tell her how the rooms are moving around.
I had previously theorized that the number of these possible systems would be infintie, because whatever system we establish, there could be a system that works in reverse order, or one where every third number is shifted around. In fact, these systems become infinite using combination and separation themselves. But then I realized that the same would apply to the addition, and yet with the addition, her system makes sense, the simplest one: the three numbers are x,y,z co-ordinates, if we otherwise disregard the fact of not knowing the origin. We can't really fathom Leaven saying "I got it, the numbers shift around five billion ways before giving us the proper coordinates." And so if such a simple system is possible, perhaps the claim that there is a single obvious way for the subtractions to give the re-arranging patterns is correct, but I'm too damn lazy to go figure this out. In any case, I'd guess that such a system would simlarly lack some information like the origin for the additions.
They theorize the trapped rooms are marked if any of the three numbers are prime, but later theorize the trapped rooms are marked if any of the number of prime factors of any of the marked numbers is not a power of a prime.* (Leaven says the trapped rooms are identified by prime powers, not marked by prime powers, which could mean identified somehow in some way using prime powers. When they begin using prime factors to determine the trapped rooms when we've been told nothing about how the prime factors factor in, the simplest conclusion is that the three number of factors of the three numbers (i.e. the numbers Kazaan is throwing around: 2, 3, 2.... 4, 2, 3...) are the numbers that identify whether the room is trapped or not).
If we follow them through the movie, this theory holds true. For instance, the first trapped room they come to after theorizing this has a number of prime factors of one, which is not a prime power, and, incidentally, any number with only one prime factor is a prime number itself. This explains how the system could have worked for them up to a certain point: A room is trapped if it has a prime number! But it is not the only thing which identifies the traps, there are plenty of other numbers that are not a power of a prime than one.
*A prime power is a positive integer power of a prime number, including all primes (5^1 = 5). Others are 7 (7^1), 27 (3^3), and so on. This is possible and also disallows them to just sit and calculate which rooms are trapped because there are multiple numbers that yield the same coordinates (i.e. 123 and 321), although they still could not navigate without knowing the origin.
At last they reach the extra room, the bridge which leads Kazaan into a gumdrop labyrinth in which there is such an abundance of gumdrops that he decides to ask for rubix cubes in reward for his help instead.
A few extra minor nitpicks:
a. There are white lights coming from all the rooms when looked at externally, not colored as they should be.
b. Even with anti-gravity, I can't fathom the physics of how the rooms connect enough for the door on both sides to open/close from opening/closing just one side, though maybe this is just me.
c. They seem to have trouble navigating, but do not even consider the possibility of reaching the top or bottom in order to walk around the whole thing making it much easier to navigate around trapped rooms.
d. Leaven cannot write on the walls/floor. If you look close there is a sharp pin on the button, which nobody could have had.
e. Quentin could not have torn off the bar, sharpened it (was it sharp?), or either way thrust it through Leaven's body, and I doubt had the strength to lift up a body with one arm, even more so with no sleep, and lastly could not have snuck in the room anyway (there was no noise) or if he did, creep up right behind them without any of the three noticing.
f. For Leaven to figure out all the math, she would half to be
a complete genius, as it baffles almost anyone watching the movie, even
an ex-college-student like me who baffingly reached Calc3 who's been
trying to understand Leaven's math for years.
She says she has an astounding facility for remember numbers, so
this makes sense, but my nitpick is that Leaven would have known she
was a supergenius, when she says initially that she's nobody, she's
You can finally, finally sleep at night. You're welcome. Just don't snore too loud or the impossibly high-technology spikes will activate and poke you to bits.