Re: corrupting the youth

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

John D.

I read what you wrote regarding the magnetic compass needle and chirality
and was having some trouble with it.    The passage at the end which I quote
below has helped me the most, but I want to paraphrase it in a different
language and see if you think the paraphrasing is pertinent or at least
related.

> -----Original Message-----

. . .
> You need both the circulation (to create a bivector)
> _and_ the red paint (to indicate which side of the
> bivector is called "north") before you have something
> that is chiral.
>
> ==========

a) minor precursor point, I gather from what you say that it is vitally
*important* to distinguish circulation from chirality; I know I have
difficulty distinguishing them, but I think it is simply because I am
mentally automatically using the right hand rule to convert the circulation
into a "chiral" vector (the end of the compass needle that is painted N);
and then find it hard to see the difference.



b)  "Paraphrasing" (much of which you have stated already in varying
contexts)

I imagine this is all geometrically equilavent to using a normal vector to
represent a patch of area versus using a bi-vector to represent the same
patch of area.

If we choose to use a normal vector, the magnitude of the vector is the area
of the patch and the direction is perpendicular (normal).

However, there is an ambiguity as to how to orient the normal vector.  One
has two choices.  And you must contrive an arbitrary rule to decide.  E.g.
In application of Gauss' Law we choose to have it pointing "outward", only
works if the surface is closed.  Or if its a piece of opaque cardboard, you
can paint a dot on one side and say the normal vector must point that way.
Or for contour integrals around the perimeter of the area and use of Stokes
law one typically uses a right hand rule.  etc etc.

The use of the bi-vector omits this need to distinguish one side of the
patch from the other when representing the area.  Which seems more natural
to me.

All comments are appreciated.

Joel Rauber