It’s been an interesting week… although nothing unusual has happened.
Regression. I’m working on all of the examples I expect to put out in the next few posts. If anything, my version of stepwise regression works even better than I thought. But we’ll see what happens after I’ve checked all my work… again. (It’s not that I haven’t run a lot of stepwise regressions, I have… what I have not run much of is all possible subsets.)
Incidentally, I went looking for the latest editions of the econometrics books by Johnston and Ramanathan… I can’t seem to find them new, and there seems to be some variety among used copies of the latest editions… international editions versus US editions. And I’m not sure I trust the bookstores to have associated the correct ISBN with the book they are selling. Let me think about this.
The magic omega formula (infinitesimal rotations). What a mess! My aircraft books use this magic equation in order to derive something else. I can almost derive the something else without the magic equation — but I’m off by a negative sign. That is, I seem to have dropped a negative sign early on in the work… and so I got the right answers… but when I look back at the work, I can’t imagine why I dropped that negative sign. Maybe I had a good reason….
On the other hand, I am absolutely certain of how to derive the magic omega formula itself — but the algebra doesn’t work out at all! Talk about frustrating!
Other than that, I’ve been trying to figure out what spinors are. I’ve just about decided to go back to the masters: Elie Cartan and Paul Dirac. I think Cartan gets them as representations of Lie groups; Dirac got them as the wave functions of electrons.
I think I know what the answers are in general terms… the wave functions which describe electrons (fermions in general) are undeniably spinors… and they do not transform the way tensors do… but they do transform “nicely” under Lorentz transformations… and that means they must be a different representation of the Lorentz group. (In fact, I note that they show up as representations of other groups, too.)
And yet, the simple unadorned fact is that I wouldn’t recognize a spinor if it bit me on the ass.
I am reminded of a simple tale. Acquaintances sometimes ask me to tutor them in elementary mathematics, by which I mean middle school and high school and community college mathematics. I generally aim them at a middle school mathematics teacher I know.
After one of the times I did that, it seemed to be working out very well for the tutor and his student. Over cards one night, they joked that it really helped that they were both able to swear at the mathematics. (This was community college algebra.)
The middle school teacher, of course, is not allowed to swear at mathematics in his own classroom… he found it a pleasant release… and so did the college student he was working with. Not only was the student able to express how he felt… but he also found it encouraging that the teacher sometimes felt the same way.
So I’m going to leave that simple unadorned fact just the way I described it. This isn’t a middle school classroom.
Now, back to magic omega? Or to regressions?
Lunch. I’ll think about them.