MovieChat Forums > Cube 2: Hypercube (2003) Discussion > The hypercube isn't 4-dimensional

The hypercube isn't 4-dimensional

posted 18 years ago by Nonym
62 replies | jump to latest

It's actually 6-dimensional: it has 4 dimensions of space and 2 of time. But before I explain why it is 6-dimensional, I'll explain why it isn't 4-dimensional.

Most people would consider any normal old cube to be 3-dimensional, but it is in fact 4-dimensional, since it occupies the 3 dimensions of space and the one dimension of time. If it didn't occupy the 4 dimensions, the "normal" cube would literally only exist for an instant. (just as a 2-dimensional square has infinitessimal depth and only exists at a single point in the third dimension)

Now, imagine we build a perfectly normal cube with a side-length of 5m at 06:00:00 and dismantle it at 06:06:59. So, this cube has dimensions of 5mx5mx5mx419s. Now put someone in that cube. If that person exits the cube, they just exit into whatever place the cube was built in (analagous to exiting a house into your neighborhood, or exiting your car into the parking lot or driveway). If you were to attach other cubes to the sides of the first one to create a network of cubes, it would be no different from the cubes in the first movie (Note, however, that it is implied that the entire hypercube consits of only a single room at different points in time). Also, if you were to just wait until 06:06:59, when the cube is supposed to be dismantled, the cube is simply dismantled around you and you are left in whatever place the cube was built in the first place (like having your house being dismantled around you to be left in your yard, or your car dismantled around you to be left in your driveway). Obviously, such a cube is no different from the boring old cube from the first movie.

So, how many dimensions do you need to get a cube like the one in the movie? The answer is 6, and the cube isn't really a "hypercube" either... it's closer to a "hypertoroid". I'll explain why: In the movie, as I have said, it is implied that the entire cube is only one room. So, when a person leaves through a side of the cube, they simply appear on the other side (like we saw near the end of the movie, though earlier in the movie, they would actually appear back in the cube at a different point in time). Instead of starting with a cube and try to figure out how we would accomplish this, let's start out with a line. We want to deform the line so that by going in one direction, we'll eventually end up back where we started. How do we do this? By turning the line into a circle. So now we have a 2-d object, which locally appears to be 1-dimensional (since one can still only move back and forth along the "line".) Now, let's say we want to do the same thing with a square, so that if one moves off one edge, he reappears on the opposite side, or if he walks in one direction, he'll end up back where he started. We do this by mapping the square onto the 3-dimensional shape called a torus (a doughnut or bagel shape). The reason we use a torus instead of a sphere is the sphere would only truly wrap in one direction (for example, on earth, if you were to just keep going north, you wouldn't suddenly appear at the south pole after reaching the north pole, instead you start coming back down on the other side of the earth.) Also note that while the torus is 3-dimensional, it still locally appears to be 2-dimensional, since we are only walking on its surface. Now all that we do is apply the same mapping of a cube onto a 4-dimensional hypertoroid, and we get a shape which is locally 3-dimensional, but wraps in all directions - just like the hypercube in the movie.

So we now have a shape which has 4 spatial dimensions and 1 time dimension, for a total of 5 dimensions. But, with only one dimension of time, it still flows perfectly normally. This is simply solved by adding another dimension of time, but which is orthogonal to the other time dimension and the 4 spatial ones at inside of the cube, but not at the edges. (orthogonal means "at a 90 degree angle". If 2 axes or dimensions are orthogonal, then motion in one does not correspond to motion in the other, ie if I move forward, then I haven't also moved left or right. If they are not orthogonal, then motion in one *does* correspond to motion in the other.) In this way, we can have the time in one axis pass normally, while time in the other axis passes as we move through the doors in the cube. This even allows it to seem as if passing through a door moves you into a completely different room, since now you're in a different point in time in one of the axes, and your timeline doesn't intersect with the original timeline (until the cube collapses at the end, that is). Another effect of this (though it would take too long to explain why) is that people moving in the same direction through time would experience time passing at the same rate, but 2 people moving in different directions would both appear to one-another to move more slowly (seemingly [but not] paradoxically, and also contrary to the movie's portrayal of one appearing to move more slowly while the other appears to move faster. Thus, many effects in the movie can be explained by adding this second time dimension.

So, the hypercube isn't 4-dimensional: a 4-dimensional cube is nothing special. In fact, it is a 6-dimensional toroid.

[–] dsl61166 18 years ago

[spoiler]
I didn't quite understand the film until I read this post, however, I still don't quite understand how that Jerry guy gets slaughtered som many times, and how Simon suddenly is so old in the end of the movie, especially if it's all supposed to go down in 7 minutes in "the real world".
[/spoiler]

Great post though, Nonym !
Thumbs up!

[–] timmy_501 14 years ago

Weird, how did your spoiler tag not work? I just copied and pasted it and it worked fine.

I didn't quite understand the film until I read this post, however, I still don't quite understand how that Jerry guy gets slaughtered som many times, and how Simon suddenly is so old in the end of the movie, especially if it's all supposed to go down in 7 minutes in "the real world".

The Dude abides. I don't know about you but I take comfort in that.

[–] Trigonometric 11 years ago

lol

[–] fli_wheel 17 years ago

You should try studying various theories of quantum mechanics.

Firstly, understand time is simply a perception. Try not too base too much on modern math because it is greatly flawed. Consider the creation of math - one day several million years ago, a monkey said to himself or another monkey: this is 1 and this is 2, together they equal three. Thus all variations of math are just some monkey's long stem root of agreement on variables; with such logic any solution of any agreed value at any preset terms equates any solution.

If you really want to understand a cube, much more a hypercube, you need to stripe away your preconceived perceptions.

The first things you need to do is rebuild math on solid universal level with universal values. After such time you will begin to understand the nature of the dimensions and the universe as a whole.

Personally, I don't feel like giving a whole lesson/lecture here; especially considering the immense flaws with Newtonian physics and general relativity; but I will say this: it is very possible for every moment of time to be infinite, non-existent, or both and none. This then makes it very possible for a cube or a hypercube to exists solely in three dimensions, but yet still interact with the potential of eleven or more dimensions.

Also note that you can easily end up from the north pole to the south pole.

But at the same time if your beliefs work for you, then I guess that's all that matters.

[–] StrontiumAE 17 years ago

Although I think I agree with the last poster...i dont think absolute knowledge is possible, so until newtonian physics are defunked, thats the only way we can scientifically measure the world.

**
Last 2 films watched:
Solaris 8/10
King Kong 2006: 8/10

[–] Chalcosoma 15 years ago

Ehh... Newtonian physics the only way to scientifically measure the world? I think you may have missed a couple of centuries of scientific development, mister.

By world, do you refer to the cosmos; earth; or just some dimensions, like space?

-------
All that we see or seem. Is it but a dream within a dream?

[–] blolb 17 years ago

Oh boy.

First of all, there's only one theory of quantum mechanics. And several interpretations (7 last time I checked).

Second, time is not a perception, it is a physical dimension. Check relativity theories.

Third, Although there are some philosophical discussions whether or not maths are fundamental or human creation, you should not just assert bluntly your opinion like if it were Truth. What you are asking for, with your own words: build maths on a "universal level", is already the way maths are made. Finally, no matter whether maths are fundamental or not, they're not "flawed"!

Fourth, I'd also like to know what flaws in physics you're referring to. There are many evidences that general relativity works and none that it doesn't. As for Newtonian physics, it's a subset of Relativity.

Fifth, what do you mean with "every moment of time" can be infinite?!? Non existent? How do you define that? This is neither physics nor math.

Sixth, a hypercube is, the n-dimension generalization of a cube. Saying that a hypercube can exist in 3d just means you are talking about a 3d (or less) cube.

Seventh, what do you mean "it interacts with ... eleven or more dimension"? You're using physics words that have precise meanings.

Eightth, what's this comment about poles about?!

Anyway. I'd hate to sound obnoxious, but I don't think you should give any "lesson/lecture" about this topic --especially not to the first poster who knows very well what he's talking about.

[–] elsol-3 16 years ago

Time is not a tangible dimension, used only to mark the events of the physical dimensions. The idea that time is more a perception than a dimension is essentially correct. It is for this reason that true time travel can never be achieved.

[–] sjohntucson 16 years ago

Well, if you look at the symmetry of the time/energy and space/energy equations in General Relativity, it's kinda hard to shake the conclusion that time IS a dimension, that, for some reason, humans just don't perceive in the same way as the first three. So I'd basically say, no, time is real, we just perceive it incorrectly.

[–] elsol-3 16 years ago

A distinct possibility, yes, given that all limitations of interpretation are limited to what we can perceive. Perhaps, rather tha not being able to preceive it correctly, we try to give it more tangibility than it deserves. It is a dimension only because we say it is one, but events themselves are measured in physical happenings. Without matter, there would be no time. But the question is, without time, would there still be matter?

[–] imtheknife 15 years ago

elsol-3: thank you for setting that straight, i was gonna do it myself.

i will offer my (similar) version of an explanation/response:

the way i see it, time is considered a 'dimension' for two main reasons.
first, mathematically speaking, time can usually 'easily' be dealt with mathematically in the same ways as spacial dimensions (the math works, we just can't draw or graph it accurately, since we can only perceive 3 spacial dimensions), and, second, because it's the easiest, most intuitive way to treat time based on the way we understand the universe so far.

time can be calculated, it can be regarded equally (in most cases) amongst the 3 primary spacial dimensions, it just can't be represented visually unless it is used to replace one of the primary 3.

[–] imtheknife 15 years ago

first, there is A theory of quantum mechanics. i dunno where you get the number 7 in this context, but i won't say there aren't variations. there are variations to every theory. sounds to me like you're probably thinking of string theory, which has 5 versions, all of which combine to form m-theory. check it out.

second, relativity THEORIES, right? that's what you said? if so, then lose the sentence before it.

third, take your own advice.

fourth, newtonian physics is not a subset of relativity. relativity is a set of concepts that describe certain things in nature, usually in the context of newtonian physics, but they are by no means mutually inclusive. and there's definately some evidence that general relativity may not be complete/correct/'works', as there is with newtonian, quantum theory, etc. as for the flaws in physics, how about the fact that relativity and quantum theory are, last i checked, incompatible. they don't both produce the same predictions when applied to the same phenomenon. hence the growing popularity of string theory, which attempts to reconcile this, as well as pretty much every other inconsistency in modern physics..

fifth, okay, you can have that one.

sixth, who taught you to talk like that? no physics professor.

seventh, the other poster was referring (i believe) to the 11 dimensions that m-theory requires.

eighth, you can have this one too.

and i DO know quite a bit about a lot of this stuff, for the record.

[–] Tales-from-the-Goondocks 12 years ago

Yeah, well, care to explain WHY/HOW you know "quite a bit about a lot of this stuff"? If you are going to express that you have your credentials, you might aswell explain what credentials are those.

[–] x10n 17 years ago

Please tell me why do you think the "counting monkey" way of getting into math was the wrong idea. I don't understand your point. Do you know the saying "All roads lead to Rome"? I mean, PI will ever be irrational and j always be imaginary no matter what perceptions you are applying to it. So why do you have to "stripe away conceived conceptions" about "1+1=2" to understand a hypercube? What is a universal value? It sounds esoteric to me. Isn't it just fine watching it's projection into lesser dimensions? It not very difficult to do that with "counting monkey"-math. ;)

[–] dwarrior2002 17 years ago

I thought 1+1=2 was proven. Sorry, I'm just trying to get at least a piece of our maths back.

[–] orritomasson 14 years ago

no 1+1=2 is not something that has been proven. 2 is simply defined as 1+1. :)

[–] wel_da_war 12 years ago

Some people here are just being semantical pricks. We could refer to the concept of "one" as "bork" and the concept of "two" as "baaven" and the math is still the same.

bork(1) + bork(1) = baaven(2)

We peoples of the English speaking nations assign the labels of "one" and "two" to the mathematical concepts of "one" and "two", but you can call them whatever you like and the math is still the same.

The world is yours & everything in it. Its out there; get on your grind & get it.

[–] sjohntucson 16 years ago

Do you do an incredible amount of speed, or something? Because your assertions really only make sense if you pervert the meanings of your words to mean things that people generally don't agree on them meaning. This is a common mental defect among people in amphetamine psychosis, and has something to do with making crappy analogies that don't hold up in any system of logic.

Math is indeed a universal system of fact-finding, although it is true that there are several different types of tools in the system. The trick is often finding the tools that correctly explain the physical behaviors you are investigating. So, Newtonian physics is explained very well using tools of Euclidean geometry, algebra, and the calculus. But it is only explanatory in the realms in which Newtonian physics approximates real-life, which is to say, at sizes much greater than quarks and at speeds much slower than light.

When you're investigating behaviors closer to the speed of light, you have to dig out the non-Euclidean geometries. When you're investigating quantum behaviors, you have to dig out different non-Euclidean geometries. Does this mean that Euclidean geometry is somehow flawed? Only if you're a meth-head. It has its uses, and in fact describes, within a ridiculously precise degree of error, pretty much everything a human, which is much bigger than a quark and much slower than the speed of light, is going to encounter.

Basically, you're just spouting an amazing amount of s**t. The reason that you don't feel like giving a lesson is that you couldn't follow your explanation to any logical conclusion if there was a pound of pure waiting for you at the end.

(sorry folks, but babbling speed freaks really get my back up. The psychologically-minded among you will have no trouble figuring out why)

[–] rbergen-4 16 years ago

Hear, hear!

Mind you: I'm not a master of physics, so in no way an expert, but the various lines of physics have always interested me and I've read a number of fairly detailed scientific texts because of that. And to put it shortly: Nonym's post makes perfect sense to me, and fli_wheel's none at all.

Generally speaking, if you choose to dismiss the current scientific views on time, all mathematics, Newtonian physics and general relativity (all of which were put together by guys who were like... pretty smart, you know) in one breath then you SHOULD explain the grounds on which you do that.
Otherwise, chances are that you come across as someone with atypical brain chemistry and a grudge against anyone who actually knows what he's talking about.

Oh, and I perfectly understand why they called it "hypercube" instead of "hypertoroid". I think most viewers would otherwise say something along the lines of "but it looks like a cube, and what the *beep* is a toroid anyway?".

[–] jeffpk 14 years ago

fli_wheel:

+1 for impressive sounding psuedo-mystical techno-babble

-32 for actually knowing anything about what you are trying to talk about.

"it is a tale
Told by an idiot, full of sound and fury,
Signifying nothing."

Shakespeare

[–] jeffpk 14 years ago

So, I figured you were just a 13 yr old used to faking it around people dumber then you are, fli.

But a friend of mine suggested that maybe I'm not giving you enough credit. And that maybe THIS explains your post...

http://www.youtube.com/watch?v=WeYsTmIzjkw

[–] NaomiWattsFan1 13 years ago

>Try not too base too much on modern math because it is greatly flawed.

Stopped right there. Please do not listen to this pseudo-intellectual. He has absolutely not a single clue what he is talking about.

This is coming from a math major.

[–] jamals 10 years ago

You should try studying various theories of quantum mechanics.

Firstly, understand time is simply a perception. Try not too base too much on modern math because it is greatly flawed. Consider the creation of math - one day several million years ago, a monkey said to himself or another monkey: this is 1 and this is 2, together they equal three. Thus all variations of math are just some monkey's long stem root of agreement on variables; with such logic any solution of any agreed value at any preset terms equates any solution.

If you really want to understand a cube, much more a hypercube, you need to stripe away your preconceived perceptions.

The first things you need to do is rebuild math on solid universal level with universal values. After such time you will begin to understand the nature of the dimensions and the universe as a whole.

Personally, I don't feel like giving a whole lesson/lecture here; especially considering the immense flaws with Newtonian physics and general relativity; but I will say this: it is very possible for every moment of time to be infinite, non-existent, or both and none. This then makes it very possible for a cube or a hypercube to exists solely in three dimensions, but yet still interact with the potential of eleven or more dimensions.

Also note that you can easily end up from the north pole to the south pole.

But at the same time if your beliefs work for you, then I guess that's all that matters.

The 'immense' flaw of Newtonian physics is simply that it is based on Galilean relativity, and not the Lorentz transformations. Classical mechanics is nevertheless a good approximation, certainly not a bad theory.

Secondly, general relativity is not immensely flawed either, it's predictions agree with experiments. It does have a limited scope like most theories however, it fails when one applies it to phenomena at or below the Planck scale. Once again, I fail to see why this is an immense flaw, general relativity has offered us many insights.

Could you also elaborate on how you think 'modern mathematics' is greatly flawed? The point of mathematics is to only accept a new knowledge claim as being true if it is rigorously proved, mathematically. These proofs are irrefutable, providing that the axioms they are based on, if any, are true.

Furthermore, why recommend to 'study various theories of quantum mechanics'? It is not relevant in the forum's discussion of hyperspace, extra dimensions, etc. Also, there is only one formulation of quantum mechanics that is considered valid by the majority of the scientific community. (Perhaps you were referring to the different pictures of QM, the interaction picture, Heisenberg picture and Schrodinger picture? These aren't separate theories, but are part of the same one.)

My advise to those that encounter this user's post: do not take it to be credible, the writer is probably one of those maniacs that sends wild theories and claims to professors at universities, claiming other well-known ACCEPTED theories are 'wrong.'

[–] DurakSuka 7 years ago

You're an imbecile.

Hama cheez ba-Beer behtar meshawad!

[–] Doots 17 years ago

did you seriously write all of that

[–] fredluna-1 17 years ago

Sorry, i didnt have the patience to read all that u guys wrote! haha

[–] 17 years ago

[deleted]

[–] greg_studer 17 years ago

I think U should have wrote this movie. ;-)

[–] 17 years ago

[deleted]

[–] tuffasnails17 17 years ago

Oh man. That's the most attractive thing I've probably ever heard. No one has ever been able to sucessfully explain anything advanced math related to me; and with such insight! I think I'll go flaunt my new-found knowledge in front of my friends now. You're wonderful, thank you so much for sharing.