It feels like this weekend has been mostly blog technical matters, a lot more PCA / FA stuff than is ready to go out, and Bloch’s geometric topology book. In addition, the latest “happenings” posts were filling in details from two weekends ago, and last weekend had some control theory and relativity.
I was determined to make some progress in Bloch’s Geometric Topology, so I’ve been doing one section first thing each morning. For the record, I’ve read through the book twice. The first time, I made a note of anything at all that looked… well… noteworthy.
The second time through, I had a printout of the first set of notes (so I didn’t duplicate anything), but I was looking specifically for exceptions, limitations, and counterexamples.
Now, I’m working through the sections.
This is the first time I’ve completed that kind of overview; I usually bog down after a while. For one thing, it’s usually very difficult to see noteworthy things late in a book: after a while, there’s just so much that’s unknown that I lose the ability to assess what I’m looking at. Bloch describes in words what he’s doing, in addition to writing out theorems and definitions, so it’s easy to understand what and why he’s doing something 200–300 pages into the book, even though the statement of the theorem is couched in terminology I don’t know yet.
But I’ve decided that, henceforth, I will try to read through an entire book before I sit down to work through it. I’ll let you know how that goes. Hmm. There are a few books I’m already working through for which I have not done that. Should I stop working through them and try taking notes cover to cover? But… I’d have to stop working.
There’s a strong reason for trying to do it. A few times in my life someone has asked me, “what do you think of the great theorem (or amazing equation) in the book?”
I hate having to say I missed it, that the great theorem or the amazing equation never registered. In most cases, they were toward the end of the book. One of them, however, was in the second chapter of the book, but I had skipped what I viewed as introductory material and dove into the early middle of the book.
Schur’s Theorem in Halmos (math, linear algebra) was one of those. I’ll tell you about a couple more, down the road.
Anyway, I’m actually working through Bloch. In special relativity, I think I’m ready to assemble a list of standard problems to work through.
In controls, I’m more at the stage of saying, “if a transfer functions falls out of the sky into my hands, or I find one on a snipe hunt, or I modify one, what all can I say about it?” at one point I wrote, “I’m almost afraid to try a serious example, in case it fails.” well, it slows down, but it works: I did a 3rd order process with a PID controller, with all 3 control parameters unknown; and I plotted both the system output and the control effort (the output from the controller). So, two graphs and three parameters. The display doesn’t change instantaneously; “hesitant” would be a fair description, “slow” would be an exaggeration. I’m thrilled that it works.
In quantum mechanics, I’ve found another really cool calculation. I know how to rotate the measuring apparatus. I don’t know why, yet, but I have at least 3 books that seem to describe this in the detail I need.
I’ve put a lot of work into PCA / FA, answering the questions I posed on March 31. One such post is out.
Oh, finished rereading Lederman’s “The God Particle”. It’s a fun book. And one quotation is appropriate for the next topic.
“Although French, English, Italian and German were common, the official language of CERN was broken Fortran.”
I’ve been mucking about with the underpinnings of the blog. “test input for biblio” describes some of what I’ve learned. Most important was discovering that I could include some HTML in my raw source file without having to write all the required HTML. (By contrast, as soon as I told wordpress that I wanted “recent posts” over on the right, I had to tell it everything I wanted on over on the right.)
It is so nice to be able to format the bibliography page, and other pages, completely in a source file, without putting bold, italic, and underscore on as afterthoughts in the wordpress editor. Now the only required afterthought is inserting images.
Almost as important was the discovery of a Mathematica® command that would give me TeX output for one object, e.g. a matrix. The Davis review (2) post was done without a TeX file, composed straight from the Mathematica® notebook. This meant that when I found a mistake, all I had to rewrite and rerun was two commands in the notebook; I didn’t have to recreate a full TeX file.
That my text editor can sort lines has let me reconstruct a raw form of the bibliography – one line per entry – and automate the insertion of new entries in the right place. Then formatting it just a matter of … let me count … 4 “replace all” commands. (If I couldn’t specify bold titles in that raw file, I wouldn’t be willing to re-sort and re-edit it.)
I fixed the bibliography page, adding those 5 new books from “test input for biblio”; I created a new page for the “here be dragons” post, calling it something a bit more suggestive… like, “Suggestions”.
Still, these changes mean that I’m writing TeX and HTML in addition to English.