# Message #547

From: spel_werdz_rite <spel_werdz_rite@yahoo.com>

Subject: Re: Something interesting and strange about permutations

Date: Sun, 10 Aug 2008 22:08:00 -0000

Well, there’s a simple way to think of this that I believe I brought

up to Roice about a few months ago. The axis of rotation of an a

figure in N-space will always be composed of a segment of N - 2

dimensions. To put this in visual terms, look at a cube (or any 3D

solid) and rotate it. You can imagine a line about which the figure

rotates. When you rotate a piece on MC4D, you will always see 3

stickers that stay in place (maybe not orientation) through which a

line could pass. The same holds true for any 2D solid. Rotate a dollar

bill, or a face on a Rubik’s cube. There exists a unique point, as

there did a unique line in 3D through which any part of matter in it

stays stationary. Anybody familiar with vectors can imply this as curl

F = 0. Even if you look at a face on MC5D, you will see

a 3x3 array of stickers that do not move. A 4D face’s movement has a

2D plane of rotation. But in the case of rotating a line, this would

imply -1D axis, which, of course, does not exist! You may think of

twisting it through 2-Space as done in MC2D, but this is analogous to

turning a shirt inside out. This process is not allowed in out concept

of "twisty puzzles." Thus, MC2D is really a non-existent puzzle, even

a misnomer! Magic Cube 2D!

-Nelson G.