Re: mirrors: two or more?

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:17 AM 8/4/00 -0500, Glenn A. Carlson wrote:

> Suppose an object had two possible mirror images.  Which image would
> you see if you placed the object in front of a mirror?

That argument is ingenious, but it does not really answer the questions
Abhishek Roy has been asking.

The argument is somewhat circular because it assumes there is only one kind
of mirror.  This is not a safe assumption, for the following reasons:

1) Suppose we had two kinds of mirrors;  let's call them V and W
respectively.  We could then have the following properties:
        two V-reflections makes a W-reflection  (V^2 = W)
        two W-reflections makes a V-reflection  (W^2 = V)
        V^3 = W^3 = VW = WV = I

How do you KNOW that no such thing exists?

2) Suppose we have two kinds of mirrors;  this time let's call them V and C
respectively.  We could have
        V^2 = C^2 = I
        VC = CV
        VC != I

How do you KNOW that no such things exist?