Re: magnetic field of a long straight wire

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        Oh, come on!  "Can be visualized" does not, IMO, qualify as a
definition.  I comes across as an analogy.
                                        Regards,
                                                Jack
On Fri, 6 Sep 2002, John S. Denker wrote:

> Bob LaMontagne wrote:
>
> > (I guess
> > I'm looking for a good clear definition of the wedge product).
>
> Given vectors A, and B, the wedge product A /\ B can
> be visualized as the parallelogram having A on one
> edge and B on the other edge, with the sense of
> circulation given by "A, then B".
>
> > Perhaps if we had concrete examples of wedge products between a variety
> > of 3 dimensional vectors we could see why there is no handedness
>
> Given that definition you should be able to construct
> all the concrete examples you want.  A card with
> circulation marked on it is chiral if and ONLY if
> one face is distinguishable from the other face.  If
> the card is "transparent" so that markings on one face
> show up on the other face, the card is not chiral.  For
> details see
>   http://www.monmouth.com/~jsd/physics/pierre-puzzle.htm
>
>
> > Cross products and wedge products both give the correct results, but
> > neither gives insight into the actual physics.
>
> Neither?
>
> Does that mean that equations never give insight into
> the physics of electromagnetism?
>
> If cross products are no good and wedge products are
> no good, do you have anything better to offer?  Or
> should we all just give up and go home?

--
        "What did Barrow's lectures contain?  Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
drawings.  (Concerning Bourbaki's books it can be said that in a thousand
pages there is not one drawing, and it is not at all clear which is
worse.)"
                                        V. I. Arnol'd in
                                Huygens & Barrow, Newton & Hooke