OK......my brain

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OK......my brain

Postby Tetroace » Tue Dec 11, 2007 5:07 pm

ve just finished reading Brief history of time(outdated as it is but interesting as it is).Ive spent all day on youtube(and various other sites)looking up string theory(amongst other things)and now I found this.This is insanely interesting stuff.4 dimensions......

So in a 4D world a cube could just pass through say another cube,because it has no standard physical 3D "boundaries" as such Right?Or am I totally wrong.
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Postby Keiji » Tue Dec 11, 2007 10:46 pm

no

4D is just like any other dimension, it just has four axes. Stuff can't pass through other stuff just cause it's 4D.

It may look like cubes were passing through each other in a projection to 3D, but in 4D they are simply moving past each other like two cars on opposite sides of a road.
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Postby Tetroace » Tue Dec 11, 2007 11:51 pm

So the lines perpendicular to the 3d cubes points make up this extra dimension called trength.Which in 3d is not visible.So in 3d it would appear that 2 cubes are passing through each other but,what is actually happening is they are entering the area given to them by trength.

Like a folded out 3D cube it essentially looks like a 2d cross.A folded out 4D cube would look like 2 3D crosses fused together in their centres(making it look like a + from above) am I right?
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Postby Keiji » Wed Dec 12, 2007 4:03 pm

Tetroace wrote:So the lines perpendicular to the 3d cubes points make up this extra dimension called trength.Which in 3d is not visible.So in 3d it would appear that 2 cubes are passing through each other but,what is actually happening is they are entering the area given to them by trength.


Not really. That's only if you happen to use a perspective projection (one cube will appear smaller than and inside the other) or eliminate one axis (two cubes will appear as one cube).

Like a folded out 3D cube it essentially looks like a 2d cross.A folded out 4D cube would look like 2 3D crosses fused together in their centres(making it look like a + from above) am I right?


This is also wrong - a tesseract ("4D cube") has a net of... oh, just look at the wiki page: http://fusion-global.org/wiki/Tesseract .

That page also has several projections by the way, and lots of info on trying to visualize it if that's what the problem is.
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Postby zero » Thu Dec 13, 2007 4:50 am

Tetroace wrote:A folded out 4D cube would look like 2 3D crosses fused together in their centres (making it look like a + from above) am I right?

Yes, if I understand you correctly, that would be a fair description of one of the several ways you might conceptualize "unfolding" the eight cubical sides of a tesseract.

As for the idea of cubes "passing through" each other in four dimensions, I think that terminology is rather misleading. Taking it down a dimension where you imagine a square lifted out of the plane into three dimensional space, it would simply pass around ("over" or "under," you might say) any squares that remain in the original reference plane. Likewise, if you imagine a cube being lifted out of its original space into a four dimensional hyperspace, that cube would pass around other cubes left behind in the space, without passing "through" them in any way.

Here's another way to look at it. Imagine a smaller square enclosed in a larger one. So long as both shapes are restricted to the same 2-D manifold, they are locked together. By introducing a third degree of freedom, however, the smaller square could be lifted "out" of the plane and then placed back "into" it some distance away without ever intersecting the larger square. That should be relatively easy to conceptualize.

Now move up a dimension. You have a smaller cube enclosed in a larger cube. So long as both shapes are restricted to the same 3-D manifold, they are locked together. Now introducing a fourth degree of freedom allows the smaller cube to be lifted "out" of the space and then placed back into it some distance away without intersecting the larger cube. Congratulations! With an extra dimension at your disposal, safe-cracking is now child's play.
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Postby Apeironian » Sun Dec 16, 2007 6:42 pm

Image
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Postby Keiji » Mon Dec 17, 2007 9:37 am

The wiki wrote:Image


Isn't that good enough?
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Postby zero » Tue Dec 18, 2007 5:27 am

The second one is harder to make out than the first. For me, at least.
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