Message #36

From: Jay Carlton <oscar@its.caltech.edu>
Subject: Re: [MC4D] Orientations of the centre cubes
Date: Mon, 08 Sep 2003 15:30:04 -0700

mahdeltaphi wrote:

>(I used to mark the centre square of each 3x3 face to indicate in
>which direction it should be pointing, and doing so reduced the
>number of possible solutions down to 1 from a total of (4^6)/2).
>
By making that change, you’re causing a fundamental change in the
underlying rules of the puzzle, perhaps almost as radical as extending
from 3 to 4 dimensions. The fact that a center face on the original
cube can be rotated is a necessary flaw, but one that I believe the
state counting already takes into account. As the system configurations
are defined traditionally, there is still only one solution. It’s a
similar problem to the one that comes up in inverse trigonometry all the
time (e.g. arcsin(1) = pi/2 + k*pi, for any integer k. Although the k=0
solution is more pleasing, it’s no more valid than any of the others.)
So I guess my point is that if you want to differentiate the
orientations of the "fixed" faces, you’re altering, not merely
clarifying, the rules. In the original cube, the correct orientation of
any piece is defined by its neighbors, not by the configuration it comes
from in the factory.

Also, from an aesthetics standpoint, one of the most pleasing aspects a
solved 3x3x3 cube is the fact that each face is a solid color, with 9
identical squares. I think the elegance would suffer if you mark the
center square.

Lastly, the center cubes in the 4D system are fairly difficult to see as
it is, and if they were marked with seven different colors each, it
would just be painful.

So I guess my vote is that if this feature is included, it should be
optional and non-default.

-Jay