I have been interested in Usenet again. It is funny to read ones post after a long time. For example this one, where my mild dislexya putted me to invoked the use of the sguare root three times in a road.
Sci.math is still there and I feel that Lounesto would have a lot to say today. There were interesting discussions on quaternions back in 2000, which is precisely when I started to get interested in them although for more modest reasons than Geometric Quantization, in my case exotic spheres. Baez intuition is good, as seen by these posts here. He was close:
Somewhere else I read a nice
definition of analytic functions from the quaternions to the quaternions
that went like this: take your function f: H -> H, think of it as
a function f: R^4 -> R^4, and think of *that* as a 1-form A on R^4 with
its usual Euclidean metric. (We use the metric to pull this stunt,
of course.) Now form F = dA and write down the equations F = *F.
These equations supposedly are analogous to the Cauchy-Riemann equations.
They're obviously nice from a physics viewpoint: they're the self-dual
Maxwell equations on Euclidean spacetime! But how are they related to
the above stuff? I don't know yet. I need to calculate....
I wonder what he calculated...anyway, coming back to present days, perhaps a more modern (read categorical) treatment might be tested. In particular I wonder on what extent it is possible to extract geometric insight from the quiral ring in a methodical way. I can wait until they
find a definition for weak n-cathegory. One problem, is that I don't grasp categories, but that should be solvable.
