Re: A question about mirrors

[Abhishek Roy <fingerslip@YAHOO.COM>]

From: Jack Uretsky <jlu@HEP.ANL.GOV>
Sent: Saturday, August 05, 2000 2:32 AM
> 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!
            ?! How does this have to do with anything? Please explain.
> > 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.
           If you mean by this that a Moebius strip and its mirror image may
be super-imposed, then this is simply incorrect- they are enantiomorphs. If
you mean something else by orientation then please explain.

> >             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.
            Replied to by John Denker. By the alien analogy, I meant to ask
how intelligent beings would - on first chancing upon an asymetrical object
reason that it has a (only one) counterpart. Of course if they were familiar
with a standard mirrors, or atleast the mathematical transformation, they
might explain it way. But without the above, it seems to me that they would
first - by pure cerebration - discover the property of 'handedness' (in the
general case- not just for that object or a class of objects). And my
original question was - how?



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