Not a lot happened last weekend, at least nothing new really happened.
Yes, I managed to prepare and put out two posts. I feel good about that. I made a little progress on wavelets, and a little progress on category theory. That’s good too, even though I had no breakthrough in wavelets. I may, just may, have been hasty when I said the really marvelous computation – which I don’t understand – is only in one of my wavelet books; it might, just might, be related to something in two of my other books. I expect I’ll be spending time in them this afternoon.
Research is what I’m doing when I don’t know what I’m doing.
Wernher von Braun
(I have seen that attributed to several people. And, truth to tell, I have not verified that the attribution to Von Braun is correct. But it’s a great line. Oh, I checked the spelling of his name on a little book by him, “The Mars Project”, University of Illinois, 1962; it’s some early calculations for getting a rocket to Mars!)
Along the way, I replied to two newsgroup posts, one on sci.math and one on comp.soft-sys.matlab. I didn’t get any responses, but that’s okay. I got something out of the posts.
The post to the mathematics newsgroup (Eigenvalues/vectors of Weingarten/Shape Operators, Sunday Mar 8th) was about differential geometry, explaining the relationship between the geometric definition of principal curvatures and the modern definition which says that the principal curvatures are the eigenvalues of the shape operator.
The post to the matlab newsgroup (Principal Component Analysis (PCA), Sunday March 8th) was about PCA, explaining that Malinowski and Brereton did something similar to what the questioner wanted to do; I aimed him here, after telling him what Matlab command Brereton recommended.
My first reaction to the mathematics post was that I didn’t have time to answer it; my kid took care of that: he wanted to do it, he got to do it.
My last reaction to the Matlab post was that my collection of 50 blog posts on PCA was going to be rather overwhelming. I need to work on my summary of PCA, and it should include a guide to the posts themselves.
I just went out to newsgroups to see if there were any responses since I last looked, yesterday. I think I should step into a FORTRAN newsgroup (comp.lang.fortran) post that mentioned “generalized eigenvectors” and got them wrong. But probably not today.
Briefly then: I am still getting my kid free rein when I first start doing mathematics for myself in the morning; I’m still distinguishing between my mathematics and my blog posts; I’m still keeping my eye on the big three (differential geometry, timeseries, and control theory).