Re: corrupting the youth

["John S. Denker" <jsd@MONMOUTH.COM>]

Jack Uretsky wrote:

> The Harke paper
>   http://www.harke.org/ps/intro.ps.gz
>
>  is directed to more profound
> problems than are normally faced in undergraduate mechanics,

... which is why I have repeatedly not recommended it
as a starting point.

We face a definite problem, namely the lack of
introductory pedagogical material on Clifford Algebra.
But IMHO, that is evidence of novelty not of any deep
flaw.

Perhaps the problem is that people who get good
at Clifford Algebra quickly get too good, and soon
race ahead, beyond the reach and almost beyond the
sight of the rest of the community.

I think the pedagogical agenda should be to do
a few simple things with it and stop there.  Perhaps
start with qualitative gyroscopic precession, as
illustrated by
  http://www.monmouth.com/~jsd/physics/gif48/add-bivectors.gif
and stop there.

Maybe a year later calculate areas using ||A/\B||.

Maybe a year after that get serious with rotors,
electromagnetism, and all that.

>         So,IMO, foisting this stuff on helpless undergraduates (and their
> teachers) qualifies as corruption of youth in the worst sense of ....

A) That rather depends on what one means by "this
stuff".

B) I think the real problem is not with the youth, but
with the old fogies who long ago spent a week getting
comfortable with the cross product, and who don't want
to spend a week learning something new.

The youth will have to spend a week on one thing or
the other, and it seems more-than-likely that a week
spent learning wedge products will be much more
valuable than a week spent learning cross products.  I
don't know that for sure, but I haven't seen anything
resembling evidence to the contrary.

> the positive
> subalgebra (to be defined) of the Clifford Algebra of V(4,(4)) is just the
> ordinary vector algebra that you have all used since childhood.

Practically everything you've ever heard of can be
rediscovered as some subalgebra of some Clifford
Algebra.  That means I don't need to separately learn
about vectors, spinors, complex numbers, quaternions,
pauli algebra, dirac algebra, etc. etc. etc. -- I just
learn Clifford Algebra and get all that stuff for free.

If you already know all that stuff, maybe you don't
have much to gain from Clifford Algebra ... but it
would be absurd to assume that the youth already know
all that.  And in any case it doesn't detract from the
simplicity and elegance and power of the Clifford Algebra.