# Message #40

From: ojcit <oscar@its.caltech.edu>

Subject: Re: Orientations of the centre cubes

Date: Tue, 09 Sep 2003 09:54:34 -0000

> This change is not fundamental at all.

"Fundamental" isn’t the best word for what I think I was trying to

get at. I shouldn’t have reacted without reading the whole thread.

All I was trying to say was that assigning a stringent orientation

requirement is a change to the goal of the game, whereas extending

the cube to four dimensions is a generalization of the same game.

I’m 0-1 with math analogies so far, but I’m feeling lucky so here’s

another one: If I’m defining an algebra that works on, say,

matrices, I have to define, among other things, a notion of

equality. I can define the equality test for any nxn matrix

system. If I am accustomed to using matrices in R3x3, and I switch

to R4x4, I expect my equality concept to survive the migration.

What I meant when I said that the orientation stipulation was

a "fundamental" change was that it would be like redefining the

concept of equality for my matrix system, and that change requires a

whole different algebra.

> Jay’s attempted analogy is just a particular case

> of the very common situation (like x**2 = 1) in which

> an equation admits multiple solutions. So what?

What I was trying to illustrate was a simple example of the same

solution state being described in multiple ways, leading to an

invertibility problem. It really doesn’t have much relevance, but

the fact that it’s a common problem doesn’t make it an trivial one

to deal with. That said, everyone here seems more than equipped to

deal with it, but I find it fascinating. It’s the first time I’ve

gotten to think about complex analysis and stuff in a while, so I

got kinda excited. I wonder if the center sticker is a branch

point…

> >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.

>

> Huh?

By neighbor, I meant adjacent sticker, but now that I think about

it, I’m wrong. For the center and edge cubies of each face,

matching colors on only two adjacent stickers is sufficient to

ensure that the cubie is in the proper orientation, but for the

corners, you have to look at the diagonal neighbors. Since

neighborhoods don’t stay put, I’ll refrain from using them as a

state descriptor in the future.

Also, you’re very right about the need for orientation of the center

cubie if you’re going to map a surface on to the faces, but, like

you said, it’s a different puzzle.