Artiste and vectors

I just read Henning Dekant's blog post contemplating an alternative history with William K. Clifford enjoying a longer life and more influence on physics. It introduces us to 'geometric algebra' with the central idea to define the non-commutative product of two vectors as
AB = A*B + A/\B
where * is the usual scalar product and /\ the anti-commutative wedge product.

In a conventional textbook this is a big no-no, because it adds a scalar to a vector, but it nicely relates to complex numbers in 2D and quaternions in 3D and it supposedly simplifies everything in 2D and a lot in 3D.
I added this to my to-do list of things I need to understand better, which already contains an entry about algebraic topology and another about non-commutative geometry (more about that perhaps later).

Btw it seems that Henning Dekant and Robert R. Tucci have (re)created Artiste as a company to develop software and software patents for quantum computers. Of course, the necessary hardware does not really exist yet, but perhaps it is not such a bad idea to try this time to think about software before quantum computers become available. (Is 'hardware' really a good term for a quantum computer?)
How would classical computers look like if e.g. Python would have been developed already in the 1940s? Or in a less distant alternative universe - how would computers look like if a Lisp interpreter had been implemented before the first Fortran compiler?


Anonymous said...

In three dimensions, Clifford's products look a lot like Hamilton's quaternions. A minor Victorian intellectual war was conducted over whether vectors or quaternions would rule E&M and physics.

wolfgang said...

>> minor Victorian intellectual war

Perhaps somewhere in the multiverse the
Quaternion Society won this struggle ... would physicists there try to quantize GTG instead of GR?

rrtucci said...

Wolfgang, I just came across this post. Better late than never, right Thanks for mentioning us. If the new and improved Artiste takes off, we want you to be our Bahamas representative. Our Man In Bahamas.

wolfgang said...

Thanks, I'm honored and I know at least one hedge fund here which would be interested in a working quantum computer.