Re: another way of corrupting the youth

[Ken Caviness <caviness@SOUTHERN.EDU>]

"John S. Denker" wrote:

> As the saying goes, learning proceeds from the
> known to the unknown.
>
> So I wrote up a discussion of complex numbers in
> one column, compared to Clifford Algebra in the
> other column.
>
> I'm imagining a sequence where people learn in
> the following sequence:
>  -- plain old real numbers
>  -- vectors
>  -- complex numbers
>  -- Clifford Algebra.
> or perhaps
>  -- plain old real numbers
>  -- complex numbers
>  -- vectors
>  -- Clifford Algebra.
>
> The point being that most of the ideas in
> Clifford Algebra can be seen as non-shocking
> generalizations of ideas that are already
> known from complex numbers, with a little
> bit of vector technology thrown in.
>
> http://www.monmouth.com/~jsd/physics/complex-clifford.htm


Very useful comparisons!  This makes the multivectors of Clifford Algebra as
generalizations of complex numbers and vectors.  I've been saving messages in
this thread to spend some time on when I come up for air.  This hasn't
happened yet, so I probably shouldn't comment yet, but I will anyway.  ;-)

Any ideas of how these multivectors relate or compare to tensors?  Tensors are
(in a sense) generalizations of scalars & vectors (scalar = zero-order tensor,
vector = first-order contravariant tensor), so my first guess was that
multivectors might be tensors, but examples we've seen seem to rule that out.

Having fun,

Ken Caviness