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Re: corrupting the youth



paul o johnson wrote:

If Clifford Algebra is the mother's milk you say it is, why don't they teach
it in high school and college? I never heard of it until this thread
started.

0) I never heard of it either. Basically I have no idea
why it hasn't gotten more notice.

1) Leigh Palmer actually mentioned it in this forum six
years ago (September 1996).

2) David Hestenes has some remarks on the history (including
a fancy diagram) at
http://modelingnts.la.asu.edu/html/Evolution.html
but doesn't explain why it hibernated for decades before
the 1960s.

3) Some useful links and remarks can be found at
http://www.helsinki.fi/~lounesto/

4) Timothy Havel has a few interesting things to say about
the history and the math:
http://mrix4.mit.edu/iap00_index.html
http://mrix4.mit.edu/IAP-00/lect0.pdf

5) There's always google:

http://www.google.com/search?q=clifford-algebra+OR+geometric-algebra+history

=====================

BTW ... I made web pages out of the recent notes on scientific methods
and on area of parallelograms / volume of parallelepipeds.
http://www.monmouth.com/~jsd/physics/scientific-methods.htm
http://www.monmouth.com/~jsd/physics/area-volume.htm

==================

Jack Uretsky wrote:

A/\B and AxB are one and the same animal.

No, they are not. They are closely related, but as I
pointed out before, it would be unwise to replace the
triple scalar product AxB.C with A/\B.C ... the proper
scalar volume is ||A/\B/\C||.

possibility.... that the Clifford algebra approach
offers no new insights.

I guarantee that those who don't bother to understand it
won't get any new insights from it.

As for me, I have already achieved one new insight, namely
that the Maxwell equations work just fine in two spatial
dimensions (plus time) ... provided they are properly
written, without nasty cross products. This insight came
to me unbidden -- it was the answer to a question that I
hadn't ever asked. But there it was: a solution not
involving the 3rd spatial dimension, just sitting there
staring up at me. This insight won't go down in history
alongside the invention of indoor plumbing, but it is
more than sufficient to disprove the hypothesis that no
new insights are offered.