Re: A question about mirrors

["Glenn A. Carlson" <gcarlson@MAIL.WIN.ORG>]

> Subject: Re: A question about mirrors
> Date: Thu, 3 Aug 2000 12:35:25 +0530
> From: Abhishek Roy <fingerslip@YAHOO.COM>
>
> > 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.
>
>   This occurred to me I started thinking about this problem (since the two
> co-ordinate systems are referred to as left and right handed). But I believe
> that here we are using a specific geometrical object and its mirror image.
> We could just as well use the L-shaped solid  fromed by nailing two 1x1x2
> blocks at right angles one on top of the other. With a little manipulation,
> I could easily convince myself there were only 2 forms which could not be
> super-imposed. But this doesn't me closer to a definition for a similae
> demonstration for *any* object.

I think it does get you closer since the triplets have the necessary
AND sufficient properties to demonstrate opposite handedness.  That
handedness of any other object can be compared to the triplets.

For example in the CHFClBr molecule, let C-H-F define a plane, and
choose two perpendicular directions in that plane, one generally in
the direction of H, the H direction, and the other generally in the
direction of F, the F direction.  Now there are only two choices for a
third perpendicular direction, in the direction of Cl, the C
direction, and in the direction of Br, the B direction.  Thus, we
demonstrate that CHClBr has the necessary and sufficient properties to
demonstrate that there are two and only two forms of the molecule with
opposite handedness, the HFC form and the HFB form.

I assert the same argument can be made for *any* object.  We use the
coordinate system analogy not just because it is simple, but because
it contains the necessary and sufficient conditions needed to
demonstrate the property of handedness.

> > 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.
>
>    We can, I think, conduct an experiment involving radioactive decay.

We still have to agree on which situation we call right-handed and
which we call left-handed.  There is handedness (opposite handedness)
to beta decay, but there is no rightness or leftness until we agree on
which is right and left.  We could just have easily agreed to call
right left and left right, but the physics would remain unchanged.

Consider your two hands.  The only reason we call the right hand the
right hand is because we all agree that such hands are right hands.

Try to construct a general definition which distinguishes your right
hand from your left hand without using the terms right or left.  Even
the dictionary definition that the right side is the side opposite the
heart appeals to a standard object, the human body, which has a
specific handedness.