The markov diffusion process has an induced metric, and (Darling, 1998a) gives a connector; and Metric + Connection = GEOMETRY!!! Finally figured out what the hell he was talking about. This is a Good Thing™.
It may not actually make a lot of sense put that way though, I suppose 😀
Basicly, RWR Darling wrote a few papers on a kind of filter called the Geometrically Intrinsic Nonlinear Recursive Filter in 1998 and for my PhD thesis I’m applying it to a specific area of robotics; but I’ve been having some problems with decyphering the maths (it’s somewhat past where engineering maths left off). And every so often, the four tons of math I’ve been chewing on in my head crystalises a little more and I get a better picture of what he’s talking about; and that happened tonight in the middle of writing a position paper for ICINCO’09. So yay!
Actually, today was the first day in a long while that I got to spend entirely on academic work. And I’d forgotten how good that felt; too many years of learning not to care about the work because the customer might change their mind tomorrow and cancel the project. But academic stuff, you decide to chase after the stuff that interests you, anything you produce and write up lives in the store of human knowlege forever (barring catastrophe, that is!), and if you’re very very good and a bit lucky, you might actually discover or develop something that lots of people benefit from.
I wish more jobs could be like that…