Happenings – 18 Sept

I may very well start putting posts out here real soon now, but I might as well warm up by talking about where the hell I disappeared to.

Nowhere.

And everything is just fine.

All that happened was that I got distracted by other things. There are always potential distractions, but I don’t let too many of them grab me unless I’ve lost my way in the mathematics. Some things ganged up on me, and some things I welcomed.

First off, work got a little busier than usual; I am still a working stiff. Then there was a birthday and some socializing. There was the US Open (tennis). There were some interesting DVD courses from The Teaching Company (and I haven’t finished the third one yet). And then I just said, “Enough!” and curled up to read or reread a few fantasy books. And a biography of the geometer Coxeter.

And the mathematics?

For PCA / FA, I saw something unexpected in the latest (next, and possibly the last) example; as usual, it’s just as well I didn’t try to force the issue, because I finally realized I was mixing up two ideas, and then all was clear. I know how to discuss the next example. In addition, it looks like I may have to break down and actually summarize the “scores” and “loadings” terminology (which is not something I want to do).

For Bloch (topological geometry), I was all set to post a simple generalization of the Euler characteristic. Well, it looked simple enough, until I remembered that topological, piecewise linear, and differential structures do not coincide above dimension 3… and just exactly how do they not coincide, and by the way, exactly what has piecewise linear to do with simplicial? And who invited CW-complexes to this picnic? I’ve been looking thru a lot of books without getting much to talk about, but I think I’ll put something out here to show just how complicated it can be. (And I’ve ordered another 10 books from the bibliographies in Bloch and Thurston.)

For rotations, I’m as sure as I can be that there’s a closed form solution for the axis of rotation of a 3×3 rotation matrix, but the algebra to prove it is killing me. (I just ask Mathematica for eigenvectors and I’m done, but there is another way to get it.) And I still have to work on a magic formula for the axis of rotation in terms of Euler angles (before I can get back to control theory for airplanes).

For myself, I started to chase down finite fields, but I’ve gotten distracted by non-UFDs (unique factorization domains), and by a nice abstract algebra package for Mathematica. Of course, all that took some reading and playing that didn’t culminate in anything I could post.

I’m doing some solar energy calculations for a friend, but I want to present them in a plausible way: too many equations, too easy to get so lost in numbers that we can’t actually trust them.

And I’ve been playing with color models.

In other words, I’m still here, mostly reading and thinking instead of doing and writing.

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