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Re: A question about mirrors



On Fri, 4 Aug 2000, Abhishek Roy wrote:

I am asking specifically about the transformation
that reverses
handedness (or orientation).
I will add "and nothing else". Your use of the word
"reverses" implies the answer -> the reverse of a reverse is
the identity, so there is only 1 reversal possible.
Next question: Can I have n-different "hands",
corresponding to the n'th roots of unity for some n?

Answer: Not in classical physics, where representations of
real objects must be real numbers. The only real n'th
roots of unity are +-1.

So an answer to your question is that there are
only two "hands" because there are only two real roots of unity!


It may be isometric, but I read in one of
Martin Gardner's books that it is impossible to transform
a Moebius strip
into its mirror image by any continuous deformation.

I don't think that this fact is relevant to your
question because a Moebius strip has no orientation.

No. I actually asked, how aliens who had never seen a mirror
would explain both the difference and similarity between say, a right and
left helix.
Send the chemical formula for a substance with 2 isomers;
then keep sending your agreed symbol for the number "2".

Or (assuming they are super-intelligent) how would they, on
seeing an asymetrical object for the first time, would deduce that it had
one and only one counterpart (again lacking a mirror).

Since most objects are asymetrical, I don't understand
your question. There can only be one inversion in 3-space
because two co-ordinates determine a plane and the "handednedness"
of the co-ordinate system is determined by the orientation of
the 3rd co-ordinate.
Regards,
Jack