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Re: corrupting the youth



"RAUBER, JOEL" wrote:

a) minor precursor point, I gather from what you say that it is vitally
*important* to distinguish circulation from chirality;

Yes, there's good physics in the distinction
(although it isn't quite a "life-and-death" issue :-)

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.

I'll bet that's the right analysis.

Note that students take quite a while to get up-to-speed
with the right-hand rule. We professionals take it for
granted only after long experience with it.

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.

100% agreement so far.

E.g.
In application of Gauss' Law we choose to have it pointing "outward", only
works if the surface is closed.

Lost me there. Bad example, I think.

The concept of "outward" is non-chiral. Idealize the earth
as a spinning sphere. The "circulation + outward vector"
is a right-handed system in the northern hemisphere, but
a left-handed system in the southern hemisphere.

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.

Yes, assuming the cardboard also has a sense of circulation
marked on it, perhaps by considering it a bivector and
ordering the edges (first this edge, then this other edge).

Or for contour integrals around the perimeter of the area and use of Stokes
law one typically uses a right hand rule. etc etc.

Yes.

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.

Yes.