I have a question regarding the actual relation between an
(asymetrical) object and its mirror image. They are said to be enantiomorphs
or of opposite handedness. But I still cannot see how (as a thought
experiment) an intelligent being who had never seen a mirror could explain
the difference (or similarity?) between say, a right hand and a left hand.
Along the same line, how do you show that apart from L and R forms there is
not a third - X form of the hand which is 'opposite' to both the others. Of
course, if you try making a model it inevitably collapses into one of the
others, but how do you prove that there are only two.
I'd really be glad if someone could help or refer to me to an online
source, as I am at a complete loss. A remark in Martin Gardner's 'The New
Ambidextrous Universe' about the difference between topological and metrical
chirality, led me to think that, perhaps there was a deep mathematical basis
for this depending on the kind of geometry, but the book did not elaborate
at all, which was quite frustrating.
Thanks,
Abhishek Roy