4D moibus strip *spelling error*

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4D moibus strip *spelling error*

Postby papernuke » Wed Nov 28, 2007 6:12 am

If a 3D moibus strip can be a 2D dimension, with 2D beings living on it, could a 4D moibus strip harbor 3D life/objects on it? what would it be like? what would it be like to us if we were on the 4D moibus strip?
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Postby Keiji » Wed Nov 28, 2007 8:09 am

*Möbius, and what you mean is a Klein bottle, which is the 4D analog of the strip.

It's nonorientable, so we'd constantly be flipping left-handed and right-handed chiral molecules... life as we know it couldn't possibly exist in a realm that was a Klein bottle.
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Postby papernuke » Thu Nov 29, 2007 3:03 am

so we'd constantly be flipping left-handed and right-handed chiral molecules

What does that mean?
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Postby papernuke » Thu Nov 29, 2007 3:06 am

But i searched an image of a klein bottle (i dont know how to post it here), but it has a hole at the top that we can enter/leave from the third dimension. or are all those pictures just what the bottle would seem to us when a 4D being sticks it into our universe?
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Postby Keiji » Thu Nov 29, 2007 5:44 am

The Möbius strip also has a hole in it, if you think about it.
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Postby papernuke » Fri Nov 30, 2007 12:34 am

Do you mean the 2D people/things on the strip could just go up and get off/out of the strip? the equivalent of the hole in the klein bottle?
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Postby Keiji » Fri Nov 30, 2007 11:28 am

Uhm...

A Klein bottle is a 2D manifold, not a 3D one. Sorry about that.

So 2D beings would live in a Klein bottle in that situation, and 3D beings would live in one of five possible 3D manifolds.
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Postby papernuke » Sat Dec 01, 2007 4:18 am

Hayate wrote:A Klein bottle is a 2D manifold, not a 3D one. Sorry about that.

How is a Klein bottle a 2D manifold? isnt it a 3D object?

Hayate wrote:So 2D beings would live in a Klein bottle in that situation, and 3D beings would live in one of five possible 3D manifolds.

What are the five 3D manifolds?
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Postby zero » Sat Dec 01, 2007 6:20 am

The Klein bottle is just a möbius strip with no edge. So yes, it is a two-dimensional manifold.

You cannot embed it in three dimensions without the manifold intersecting itself, but it can avoid self-intersection if embedded in four-dimensional space.
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Postby Keiji » Sun Dec 02, 2007 8:53 am

papernuke wrote:
Hayate wrote:A Klein bottle is a 2D manifold, not a 3D one. Sorry about that.

How is a Klein bottle a 2D manifold? isnt it a 3D object?

Hayate wrote:So 2D beings would live in a Klein bottle in that situation, and 3D beings would live in one of five possible 3D manifolds.

What are the five 3D manifolds?


I can't really say, because they don't have names (or I don't know what the names are), and I don't know of any notation for describing manifolds in general...
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Postby papernuke » Sun Dec 02, 2007 8:08 pm

Can you describe the manifolds?
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Re: 4D moibus strip *spelling error*

Postby The Keeper of Secrets » Tue Apr 08, 2008 8:02 pm

Surely...

In order for a mobius strip to exist it has to be in the 3rd dimension or it has no directon in which to twist. Therefore a 3d equivilent bist twist into the fourth direction, for it to exist. Therefore it muse exist in the fourth dimension, thus we cannot have it exist here and cannot visualise it.
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Re: 4D moibus strip *spelling error*

Postby Keiji » Tue Apr 08, 2008 9:59 pm

http://teamikaria.com/wiki/Net_space

When we say "the Mobius strip is 2D", the 2D refers to its net space, i.e. how many dimensions you need to reference a point in it. Yes, a Mobius strip can only be embedded in 3D or higher, but it encloses a 2D hypervolume.
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Re: 4D moibus strip *spelling error*

Postby The Keeper of Secrets » Sun Apr 13, 2008 7:44 am

Fair enough, I still frown on the idea of a 3d version existing in 3d space, but understand how you could plot any point on in with 3 dimension vectors.
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