View previous topic :: View next topic � |
Author |
Message |
Chewi Pez-Eater
Joined: 12 Jun 2003 Posts: 151
|
Posted: Sun Jul 06, 2003 2:41 am�� �Post subject: HyperCube! |
|
|
nt _________________ "If at first you don't succeed, skydiving is not for you." |
|
Back to top |
|
|
Pez-Man Pez-Man
Joined: 18 May 2002 Posts: 3443
|
Posted: Sun Jul 06, 2003 2:42 am�� �Post subject: |
|
|
Hypercube! Hah! What's nt? |
|
Back to top |
|
|
Chewi Pez-Eater
Joined: 12 Jun 2003 Posts: 151
|
Posted: Sun Jul 06, 2003 2:43 am�� �Post subject: |
|
|
nt = no text _________________ "If at first you don't succeed, skydiving is not for you." |
|
Back to top |
|
|
chromus Pez-Ruler
Joined: 13 Aug 2002 Posts: 1703
|
Posted: Sun Jul 06, 2003 2:51 am�� �Post subject: |
|
|
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. |
|
Back to top |
|
|
Pez-Man Pez-Man
Joined: 18 May 2002 Posts: 3443
|
Posted: Sun Jul 06, 2003 2:54 am�� �Post subject: |
|
|
Blame me! Wait? |
|
Back to top |
|
|
ayana Kawaii akujin
Joined: 28 Feb 2003 Posts: 917 Location: Mount Allison
|
Posted: Sun Jul 06, 2003 2:51 pm�� �Post subject: |
|
|
What's a hypercube? _________________ Ayana @ TGB.net |
|
Back to top |
|
|
chromus Pez-Ruler
Joined: 13 Aug 2002 Posts: 1703
|
Posted: Mon Jul 07, 2003 1:14 am�� �Post subject: |
|
|
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. |
|
Back to top |
|
|
ayana Kawaii akujin
Joined: 28 Feb 2003 Posts: 917 Location: Mount Allison
|
Posted: Mon Jul 07, 2003 5:31 pm�� �Post subject: |
|
|
I'm learning in the summer. How about that. _________________ Ayana @ TGB.net |
|
Back to top |
|
|
ayana Kawaii akujin
Joined: 28 Feb 2003 Posts: 917 Location: Mount Allison
|
Posted: Mon Jul 07, 2003 7:53 pm�� �Post subject: |
|
|
Wait, that's not funny.. _________________ Ayana @ TGB.net |
|
Back to top |
|
|
Molvaki Pez-Eater
Joined: 20 May 2002 Posts: 219 Location: Missing
|
Posted: Sat Jul 12, 2003 9:17 pm�� �Post subject: Wierd. |
|
|
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. _________________ Too much of a good thing is an awesome thing. But too much of an awesome thing is... uhh... really, really dumb... and bad.
I am a man of few words. My favorite ones being, "Aardvark" and "Spatula". |
|
Back to top |
|
|
ayana Kawaii akujin
Joined: 28 Feb 2003 Posts: 917 Location: Mount Allison
|
Posted: Sun Jul 13, 2003 4:11 pm�� �Post subject: |
|
|
I don't know how to prove people wrong. But I'm REAL good at proving myself wrong ^_^ _________________ Ayana @ TGB.net |
|
Back to top |
|
|
chromus Pez-Ruler
Joined: 13 Aug 2002 Posts: 1703
|
Posted: Sun Jul 13, 2003 11:31 pm�� �Post subject: |
|
|
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. |
|
Back to top |
|
|
Vorpy What's a Pez?
Joined: 22 Feb 2003 Posts: 17
|
Posted: Wed Jul 16, 2003 3:34 pm�� �Post subject: |
|
|
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/gutenberg/etext95/flat10a.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. |
|
Back to top |
|
|
ayana Kawaii akujin
Joined: 28 Feb 2003 Posts: 917 Location: Mount Allison
|
Posted: Sat Jul 19, 2003 8:26 pm�� �Post subject: |
|
|
I'm confused.. _________________ Ayana @ TGB.net |
|
Back to top |
|
|
chromus Pez-Ruler
Joined: 13 Aug 2002 Posts: 1703
|
Posted: Mon Jul 21, 2003 1:01 am�� �Post subject: |
|
|
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. |
|
Back to top |
|
|
|