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Dear David,

came across your post.I s a bit like a fiber bundle but the `fiber' is not a usual space as its coordinates are non-commutative, the quaternion algebra. You could say algebra bundle. But the new bit is that Connes shows that the Geometry in the nc fiber direction, i.e. the Dirac operator, encodes the
two dozen undetermined constants in the standard model and imposes constraints between some of them (mass relations). You can see his chapter of `On Space and Time' where he explains why this is fundamentally different from usual fibre bundles. The treatment if SU_3 is a bit by hand and might be improved one day. Whats mainly missing is no explanation of why there are duplicated families of particles in this theory any more than in the standard model. But for each family its a good fit with explanatory power. I agree would be cool to try octonions instead of quaternions. You'd need nonassociative geometry and I may talk about that in a later post.
Shahn Majid