Re: GA in high schools?

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

Arnulfo Castellanos-Moreno wrote, apparently (?) in reply
to a message of mine:
> When you study complex number ...
> you are combining a "real number" plus an "imaginary number".
> This mean two "different things".

Agreed.  As I point out at
  http://www.monmouth.com/~jsd/physics/complex-clifford.htm
it's like adding apples and oranges.  People do
that all the time.  You cannot easily !!compare!! apples
and oranges, but that's a different matter entirely.

> Thus
>
>      AB := A.B + A/\B
>
> are another pair of different things.

I have no problem with that. I have no problem writing
the non-definitional equation
      AB = A.B + A/\B
whenever it is true (which includes all of D=2 and D=3).

The problem is, it isn't always true in D=4 and higher.
It's bad luck to take a non-true equation as the definition
of anything.

> Certainly, you can start with the geometric product to separate in a
> symmetric plus
> antisymmetric part. But it is just another approach.

Not "just".  It is IMHO an approach with fewer opportunities
for misunderstanding.

We know what  AB  means in D=4.
We know what  A.B + A/\B  means in D=4.
They do !!not!! mean the same thing.
Beware: many people misunderstand this.

That was the point of my previous message.

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

In general:  please, folks, make sure your reply includes the relevant
context.

This posting is the position of the writer, not that of Saint Achilleus,
Saint Agatha, or Saint Agnes.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.