Extra action in 4D

[Myriaract]

You know that things can't fold or knot in 1D, knot in 2D ,but what can 4D people do that we can't?

[Myriaract]

e.g.
2D can fold 1D,
3D can fold 2D and knot 1D,
4D can fold 3D, knot 2D, and do something to 1D.
What can they do?

[papernuke]

Since they're so boring to the 4D beings, they can just throw the infinatesimally small dot into the trash (and let it cut a hole through everything).

[Keiji]

...what?

[papernuke]

if you're talking to me.. then ignore what i said ..

[Myriaract]

no... we can knot a line , 2D can fold a line, so 4D can do SOMETHING to a 4D "line".

[papernuke]

a 4D line is a 2D plane.. or it should be..

[zero]

To paraphrase horribly, "A line is a line is a line."

It's always one dimensional, though approximate representations of it will of necessity be three dimensional when we make them, because the physical objects we use are three dimensional. If there were such a thing as a two-dimensional physical reality, then representations of a line would be two dimensional approximations within it, and likewise for any other physical n-space.

[Keiji]

Back to the original topic... what could tetronians do with a line that we can't?

[wendy]

Tetronians(4d beings), can do less to a line than we can do, but they can do more to a hedrix (2-cloth), than we can. For example, they can make a non-crossing klein bottle.

In essence, the magic of what you can do to a thing of n dimensions, ends at 2n+2. In n+2 to 2n+1, one can knot a cloth, the crossing having of dimension, w-n-2 (where w is the world-dimension).

For 1-cloth, a knot is possible in 3d to 3d, the crossing becomes 3-1-2 = 0d (ie a point).

For 2-cloth (hedrix), a knot is possible in 4d, 5d, the knot crosses at 1d, 0d respectively.

For 3-cloth, a knot is possible in 5d, 6d, 7d, with a crossing of 2d, 1d, 0d respectively.

etc

For any dimension higher than the maximal self-knot, one can only do topological things to the surface itself. (ie a klein bottle is still possible in 6d, but you can't turn it into a knotted surface).

[kingmaz]

For example, they can make a non-crossing klein bottle.

I was not aware of that.

[Keiji]

You could also consider folding as the trivial case of knotting. So 2D beings could "knot" a line with a 1D "crossing", 3D beings could "knot" a plane with a 2D "crossing", and so on.