Re: Chuck's Knotty Problem

Charles Biehl (cbiehl@UDel.Edu)
Tue, 10 Dec 1996 05:44:19 -0500 (EST)

The only problem I have with this explanation is that the folks in
flatland could never have put that twist in the string, since it would
require twisting in a direction they don't have. This is the problem I'm
having with the whole situation. Pat's explanation requires the Flatland
knot to be tied in the third dimension, quite unlike a normal 3D knot. I
understand how to untie the 4D knot now, but am still stuck on the 4D
roation of a 3D knot.

On Tue, 10 Dec 1996, Patrick Carney wrote:

> This might not be the most profound way to look at it but it might help.
> Consider a loop that you have twisted into a figure 8 floating about a foot
> above your desk (ain't math wonderful -- no limitations on the mind like with
> physical ones). You can plainly see that at the point of intersection, one
> strand is on top of the other. But the people in Flatland (i.e., on your
> desk) who see only the shadow, see a figure that they could not make into one
> loop without cutting. But you can with a simple twist get the loop back. Thus
> I would imagine that the seemingly untieable know that I see in 3-D is but a
> shadow of a much less complicated item in 4-D. Just as the Flatlanders cannot
> untie that figure 8 in their world, but it is a simple twist in another
> dimension, so it would be for us if only we had that other dimension.
> Well, I hope tat helps. I know it may not be a profound proof, but it is the
> way I try to see into such things.
> As ever,
> Bro. Pat Carney