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?
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