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Re: A question about mirrors



A simple geometric construction, which allows construction of a pair
of objects of opposite handedness and which only requires knowing what
"perpendicular" means, might be:

Select a pair of perpendicular directions (call them A and B). Now,
there are only two choices for a third perpendicular direction (call
them C and D). The triplet of directions, ABC, has opposite
handedness to ABD; and reflection in a mirror can transform ABC into
ABD and vice versa.

Note that this construction doesn't tell you which triplet is
right-handed and which is left-handed; only that they have opposite
handedness. For us and other intelligent beings to "correctly" assign
the handedness, we all would have to have access to an object on which
we all agree has a given handedness.

Though it seems obvious that there must only be these two, I don't
have a rigorous proof why there are only two. Perhaps, appealing to
the uniqueness of the perpendicular to a plane through a point in the
plane.

Glenn A. Carlson, P.E.
St. Charles County Community College
St. Peters, MO
gcarlson@mail.win.org


Subject: A question about mirrors
From: Abhishek Roy <fingerslip@YAHOO.COM>

[snip]
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.
[snip]
Abhishek Roy

________