I know, of course, that my posts have been few and far between recently. What’s going on?
Nothing complicated. I’m working on 6 things, and none of them is ready to post. Once upon a time I saw a statement by Isaac Newton that the secret of his success was that he worked on any given problem until he had solved it. I’m sure there was more to his success than that. In any case, I tend to walk away from problems, let them stew while I do something else, and hope for new insight when next I pick them up. I remembered his comment precisely because it’s what I don’t do.
For PCA / FA, I was hoping to find a good example in Malinowski to show just what he does with target testing. I found the example, way back on page 6, with further details around page 20. It’s more than good; it’s a great example. Not that it made any sense to me before I had worked through chapter 5. There’s just one thing I don’t quite know how to explain.
For the Blakelock book on control of aircraft, I got completely sidetracked by a really neat equation for angular velocity. That led to the posts about rotating coordinate systems, but I’m still struggling with the really neat equation. I have the feeling that I know all the pieces, and that the derivation is right on the tip of my pen – but I haven’t actually been able to put it all together. So far, every attempt has bogged down and seemingly gotten nowhere.
For Bloch, specifically for simplicial surfaces, I’m bouncing between simplicial complexes and polygonal disks. Andrew Wiles’ comment comes to mind: I’m walking around a dark room banging my shins on the furniture.
In addition, I still want to address Jim’s comment about gluing a sheet of paper into a torus, but it’s hard to write about. Jim and I talked about it over lunch, and all it took was a couple of minutes of hand waving – literally waving my hands – but that doesn’t translate well into cold pure text.
Special relativity has fallen by the wayside; my physicist friend has been too busy, and without his interest, mine flags. I might be getting interested in the classical theory of fields, in the old sense. A modern book on the classical theory of fields is electromagnetism & gravity. An old book on the classical theory of fields is really about continua: the smooth approximation of huge numbers of molecules. Somewhere in between, the theory of continua fragmented into fluids, elasticity, electromagnetism, gravity. I have, of course, a couple of books about continua. I probably have more than I realize: I’m not sure how many of my books about elasticity begin with general treatments…. ok, having searched the appropriate shelf, I know which two books I’ll start with, if I start this.
I’m still working through Cox-Little-O’Shea Varieties, slowly, and I’m in the middle of “monomial ideals”. I think they’re not difficult, in fact they almost look easy, but right now they’re mostly strange. I never got comfortable with ideals in general. Hell, I never got comfortable with abstract algebra once we moved beyond group theory.
Finally, I picked up color theory again. Hey, I’ve always been intrigued by the quantification of color, and by color combinations. If I start looking at a book of color combinations, I end up trying to quantify the choices. I should put out an introductory post.