What’s new with me?

Mathematics:

I’ve been doing special relativity, controls in Carstens, and I just started geometric topology in Bloch. In addition, I’m still playing with normal operators in linear algebra.

Oh, and at bedtime i’m rereading Leon Lederman’s “The God Particle.” I needed to look up a quotation from it, and decided it was worth rereading for the fun of it.

Geometric topology? I’m finally picking up the book I meant to start with after Weeks’ “the shape of space”, vis. Bloch’s “first course in geometric topology and differential geometry”. Truth to tell, Weeks’ 2D projections of 3D manifolds don’t work for me, but I’ll keep it handy while I’m doing Bloch.

Controls? I do control theory for fun. We have engineers at work who it for serious. I’m not an engineer and I don’t do controls professionally.

Right now I’m working through Carstens’ “automatic control theory and components”. To be specific, I’ve just worked through a control system design for steering a robotic cart. To be very specific, he has just used root-locus and bode plots to select the servomotor, gear train, rate generator, and overall gain for the system. I’ve got a lot of theory rattling around in my head; this is the first time I’ve worked a problem that included spec sheets for electromechanical devices.

I wouldn’t enjoy that as a steady diet, but I felt a serious need to get down and dirty for a while.

Special relativity? Sure, I’ve had general relativity, but I don’t do special relativity very often, and when I do it’s not pretty. A friend and I, however, are trying to get our feet under us so we can tackle Zwiebach’s “first course in string theory”. To do that, we’re working thru Griffiths’ “introduction to elementary particles”. And that has us smashing things together at relativistic speeds. I’m trying to construct a compact summary and a collection of typical problems.

For the blog:

As you see, I’m almost exclusively doing PCA / FA. Most of that has already been done, as mathematics: I’ve worked the appropriate chapters in Harman, Jolliffe, Davis, Malinowski, and Bartholomew et al., from each of which I expect to draw an example. i’ve also worked through the appropriate chapters of Brereton, Lindeman et al., Christensen, and at least one book i haven’t listed yet; I seem to recall that there’s an example I need to mention in one of them.

I’ve done that math; I “just” need to select examples to illustrate my conclusions, write everything up more carefully than I have, and publish.

Meanwhile, I expect that by the time I finish putting all the PCA / FA out here, I will have assembled a whole lot more mathematics for which I will do the same thing.

It’s nice that I don’t need to work new mathematics for tonight’s blog entry; I just need to make some of my old mathematics presentable. I’m not under the gun.

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