# Message #3841

From: Marc Ringuette <ringuette@solarmirror.com>

Subject: Re: [MC4D] Chirality, orientation (~= handedness, inside-outness)

Date: Fri, 24 Nov 2017 13:05:11 -0800

Hi, Joel,

Thanks, yeah, trying to equate orientation and inside-outness was a poor

idea on my part. I’m trying to properly define the inside-out

operation. How about this instead:

1. I will define a mirror operation to be any linear transformation

that flips the sign of the orientation.

2. If even one mirror operation is permitted, then even asymmetric

objects become achiral.

- An n-1 dimensional shell around an n dimensional object can be

mirrored by puncturing or slicing it and turning it inside-out (if the

inside and outside colors are the same at every point).

4. The inside-out operation results in a mirror operation (a linear

tranformation that flips orientation), but cannot be broken down into a

sequence of infinitesimal linear transformations. We could stretch the

object and squeeze it through the puncture nonlinearly (think rubber

balloon). Or, if the object is composed of n-1 dimensional flat faces,

we may cut a number of n-2 dimensional seams along the face

intersections, allowing some previously adjacent points to become

non-adjacent for the duration of the inside-out operation, and then

perform a distinct series of infinitesimal linear transformations for

each face (think cardboard box).

Does that hold together better?

Cheers

Marc