Re: A question about mirrors

[Abhishek Roy <fingerslip@YAHOO.COM>]

From: Jack Uretsky <jlu@HEP.ANL.GOV>

>         I'm still not clear on what you are asking, so let's see if we
> can rephrase the question:
>         You are asking about the possible transformations of an object
> (rotations, translations, etc.).  But I'm not clear on what it is that
> you are willing to keep constant.  If it is the size and shape of the
> object, then the answer to your guestion is (to indulge in name-dropping)
> the group of orthogonal transformations - these are the transformations
> that, when infinitesimal, preserve something called the "metric".
            I am asking specifically about the transformation that reverses
handedness (or orientation). 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. Actually my primary
query was regarding a definition of 'handedness' independent of both
specific examples and mirrors. The fact there are only two objects of
opposite handedness and that a single reflection may turn one into the
other, would then follow immediately from this.

> Re my last message: are you asking how to communicate "handedness" to
> beings on another planet?
            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. 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).

Regards,
Abhishek





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