Re: A question about mirrors

[Abhishek Roy <fingerslip@YAHOO.COM>]

From: Jack Uretsky <jlu@HEP.ANL.GOV>
> > > > 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.
>
>         Let's go a step at a time.  We need to agree on precisely what
> you mean by "reverses".  So consider a body to be a collection of points
> in a space.  Will you agree that "reverses" means an isometric (your word)
> transformation on the collection that cannot be duplicated by a rotation
> and/or a translation?
            Agreed.
[snip]

> > > >             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?
>         This takes us back to your definition of "counterpart".
            Which is what I am trying to determine, in the first place? Just
replace 'counterpart' with enantiomorph. See the thought experiment with the
alien above.

Regards,
Abhishek




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