# Message #3832

From: Marc Ringuette <ringuette@solarmirror.com>

Subject: Yes, there is handedness in 4D, 5D, etc

Date: Tue, 21 Nov 2017 10:04:59 -0800

(I’m re-sending this after 24 hours of not seeing it show up on the list)

Don’t believe everything you read in a book.

I spent a long time yesterday trying to figure out how to reconcile the

claim that Ed quoted, that "handedness has no meaning in spaces with 4

dimensions or more", with the fact that I observe a handedness in MC4D

(we cannot create the left-right mirror image of the solved position via

any sequence of rotations; nor could I conceive of any non-stretching

rotations that MC4D could be lacking).

The resolution is simple: the quote is WRONG, completely wrong. There

is handedness in n-space for every n, called "orientation".

https://en.wikipedia.org/wiki/Orientation_(vector_space)

There are always two orientations, corresponding to a positive and

negative determinant of the unique linear transformation between a pair

of ordered bases. In every dimension n, if we put distinct colors on

all 2n sides of an n-dimensional hypercube, the object can never be

rotated into its mirror image.

Now I will try to expunge that wrong idea from my head.

Hmph.

Marc