thegreatbeyond

nt

Hypercube! Hah! What's nt?

nt = no text

Bah. You make fun because you know not what a hypercube is.

By the way, to all those who weren't there, I was talking to a friend on the way back from T3 about a conversation I had with another friend involving fourth dimensional statistics. The instant I said hypercube, Pez, Chewi, and RosCoe burst out into laughter. Go figure.

Blame me! Wait?

What's a hypercube?

A hypercube is basically a fourth-dimensional equivalent of a cube. When I say fourth-dimensional, I mean four dimensions of space, not three of space and one of time. There's no real way for us to picture a hypercube in our minds, since we can't think in four dimensions, but there's a way of representing it on your screen. At http://dogfeathers.com/java/hyprcube.html, you can see a hypercube rotating around, as represented in two dimensions. If you click on the "stereo" button twice, you should get to a mode where you can cross your eyes and see a hypercube as represented in three-dimensions.

Now, for a technical explanation: a zero dimensional "cube" is just a point, as it has no dimensions. A one dimensional "cube" is a line, which is a single point moved back and forth in the first dimension. A two dimensional "cube" is a square, which is a line moved back and forth in the second dimension. A three dimensional cube is just a square moved back and forth in the third dimension. As you've probably guessed, a hypercube is just a cube moved back and forth in the fourth dimension. As we can't think in four dimensions, this is impossibe to visualize. but it's a cool concept.

I'm learning in the summer. How about that.

Wait, that's not funny..

I've always wondered about dimensions and stuffs. The only question I had is, wouldn't anything lower then three dimensions not exist? I mean, even a dot has length and width, and even a line has width. If someone has no width, it couldn't be seen, right? Eh, I'm just waiting to be proved wrong somehow, but that question was bugging me for a while.

Also, learning in the summer sucks.

I don't know how to prove people wrong. But I'm REAL good at proving myself wrong ^_^

Actually, Molvaki, you're right, in a sense. In our third-dimensional world (no comments about Einstien's extra dimension of time), there cannot be anything that is not 3 dimensional. So, a point in our world has some length, some width, and some height, no matter how insignificant.

The only place I know of where other dimensional objects can exist is within my mind, and others have also found this out. You can easily imagine a two-dimensional world, something like an old Mario game, except that nothing can overlap, like Mario's arms over his body, or Mario over the backgroud. In this imaginary world, the world itself is a plane, with some length, some width, but absolutely no height. In fact, height doesn't even exist in this world, so it doesn't matter how high you choose to imagine it. It could be so thin that looking at it from the side causes it to disappear, or it could be so think that it is your entire field of vision. It all depends on how you choose to view it.

Personally, I see the zeroth-dimension as a dimensionless point, with no width, no length, and no height. The first dimension is an infinitely long line, with infinite length, no width, and no height. The second dimension is as I described it earlier. This is how I see it all, but your experience may vary.

There is a story about lower dimensional worlds called Flatland. It describes a strange two dimensional world called Flatland, and also goes into some stuff about extra dimensions (the main character, a square, is shown the three dimensional world by a sphere, and also encounters 1 and 0 dimensional worlds).

Here's a link to a plaintext transcription of the second edition of the book: ftp://sailor.gutenberg.org/pub/gutenber ... lat10a.txt

It was published in 1884 so the copyright has expired and this free copy can be found online. Project Gutenberg throws in a few pages of headers and stuff before the story, so just scroll down until you get to the ascii art title page thing where the book actually begins.

I'm confused..

Well, perhaps you should follow the link that Vorpy gave and read Flatland. It's a wonderful book which introduces people into the theory behind multiple dimensions of space.