What literally is the Fourth Dimension?

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What literally is the Fourth Dimension?

Postby Blue_X » Fri Jun 30, 2006 2:17 am

Now I'm new and I've done a little wandering on this forum, now what is the literal fourth dimension?

The First is left/right or bredth (represented as the X axis)
The Second is up/down or height (represented as the Y axis)
The Third is forward/backward or depth (represented as the Z axis)
Now all I really know about the fourth dimension is that it's represented as the W axis and you cannot point in the direction of it

Now please give me some true information because sometimes the internet isn't reliable.
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Postby PWrong » Fri Jun 30, 2006 4:33 am

When we talk about the fourth dimension, we're usually talking about a hypothetical universe that has four spatial dimensions. Some call it ana/kata or trength. It doesn't really matter, because the four dimensions are all the same.

Most of the stuff on Alkaline's website is reliable. http://www.tetraspace.alkaline.org
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Postby moonlord » Fri Jun 30, 2006 5:45 pm

...and all the other is unreliable because we haven't sorted it out... This includes some threads on the forum and, in part, the wiki. Welcome, anyway!
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"Not only does God play dice, but... he sometimes throws them where we cannot see them." -- Stephen Hawking, late 1900's.
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Postby Blue_X » Fri Jun 30, 2006 9:00 pm

Actually I have another question...
How can you tell if a shape is fourth dimensional? I mean to me a hypercube looks third dimensional? I mean the only difference is that 3D objects are made of faces, edges, and vertices. While 4D figures are made of cells, ridges, edges and vertices.

I'm sorry for my obvious stupidity toward the Fourth Dimension, but I thought I'd just put that question in here before I make another useless thread, and thanks again for answering my questions. :)
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Postby Nick » Fri Jun 30, 2006 9:49 pm

You're not being stupid... no question is ever stupid. Unless you ask why no question is ever stupid. Then you're a moron (jk).

The hypercube you see is a 3d representation of the four dimensional object. See the lines connecting the two cubes? Those are actually moving along the fourth axis, but since we can only allow for three in our world, we draw it moving diagonal. The inner cube and the outer cube on on different "cells". For example, think of a 3d cube. The square on top is on a different plane then the square on the bottom.

If we draw a 2d representation of a cube, we would get a square within a square, with the vertices connected. The inner square would be on the bottom of the cube, whereas the outer square would be on top. In reality, however, both squares are equal size.

That's probably confusing. I'll post some pics in a minute.

Update:
Image
This picture is a cube, when viewed top-down. It's the 2 dimensional picture of a cube, with one of the sides shaded purple. Notice that the side is a trapezoid, when in reality it is a perfect square. Notice that the face farthest away from you is smaller than the one closest to you. These are distortions you get when you flatten an object. The hypercube you see with a cube within a cube is a hypercube flattened, so there will be distortions; the inner cube is smaller, when in reality it is the same size, and lies in a cell farther away from you four-dimensionally. You also get the "trapezoids" (except their actually prisms now, with one of the bases smaller than the other), that are actually supposed to be perfect cubes, but once again, their distorted as well.

Update #2:
Image
Here's a picture of a hypercube, jacked from this site, except I added the purple fill-in, to highlight one of the "trapezoid" prisms, for clarity.
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Postby Blue_X » Thu Jul 06, 2006 3:05 am

Thanks, I think I'm starting to understand it. I've been looking online, and made a few sketches, the one thing I still can't understand, is that how is a hypercube bound by eight cubes??? And how is that possible?
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Postby Hugh » Thu Jul 06, 2006 3:14 am

Blue_X wrote:Thanks, I think I'm starting to understand it. I've been looking online, and made a few sketches, the one thing I still can't understand, is that how is a hypercube bound by eight cubes??? And how is that possible?

How is a 2d square bound by 4 lines, or a 3d cube bound by 6 squares? They just are, same as a tetracube is bound by 8 cubes. There is a lot of extra room in 4d. :)
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Postby Nick » Thu Jul 06, 2006 11:21 am

See how the top down view of the square in my previous post has two squares and four trapezoids? Those are the 6 sides binding the cube. But where is the space? Because we are putting a 3d object on a 2d surface, we eliminate all 3d space, so all you have is some 2d squares and trapezoids stuck together.

Look back at my hypercube. Remember the purple prism? That's one of the 8 cubes surrounding the hypercube (See if you can find the other 5 trapezoid-like prisms). We eliminate 4d space, and in the end, all we have is two cubes and eight prisms stuck together.

Hope this helps :)
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Postby Hugh » Thu Jul 06, 2006 9:29 pm

irockyou wrote:in the end, all we have is two cubes and eight prisms stuck together.

In actual 4d space though, remember that all the 8 boundary cubes of the tetracube are not distorted but perfect cubes, just as the 6 boundary squares of a 3d cube are not distorted in actual 3d space.

In trying to visualize 4d, I've often found a 2d diagram consisting of a "+" over an "X" helpful. The "+" represents the right/left and up/down axes, and the "X" represents the forward/backward and wint/zant axes. Try to see the x, y, and z axes in 3d perspective first, then try to visualize putting that 4th (w) axis in place in perspective, so that it's at 90 degrees to the first three axes. You might catch a glimpse of full 4d. :)
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