Tuesday, December 14, 2004

Haircut and books

I had my hair cut this morning. I've thought for at least a month that a trim might be in order. But errands like haircuts (and grocery shopping and laundry) have seemed a good deal less interesting than other things, at least for a little while. There is at least a sense of consistency in wearing mismatched socks, piling books haphazardly on any available surface, preparing meals that are heavy on pickles and applesauce, and fighting a losing battle against my hair's creative impulses.

Winnie mentioned that I should not get my hair cut too short over the top. It makes you look even taller and thinner than you are, she said. I wasn't very clear in communicating this, though. When I say myself in the bathroom mirror later in the day, in one of those corner-of-the-eye moments that show so much more than a face-on examination, I realized that (in a hooded sweatshirt, at least), I looked like nothing so much as a stereotype of a monk. You know the image I mean: a sort of angular character, sharp around the nose, chin, eyebrows, and perhaps about ears -- the anti-Friar Tuck, if you will. I was amused by the thought; I'd be a terrible monk.

As an aside -- I'm not gaunt. I am bony around the joints -- nothing short of a sweater or thick jacket is going to make my shoulder a comfortable headrest; this has been empirically demonstrated -- but that's different.

I also did other errands, including a trip to get some books. I didn't find the biography of Euler that I wanted for myself, but I did find other books that I'd planned to get for family members. Reviews and recommendations will be forthcoming after the holidays, I'm sure.

The new SIAM Review was waiting in my mailbox when I went to the office. I'm very pleased by this issue. The Problems and Techniques suggestion includes an article on semi-separable matrices, and another on the analysis of Markov chain mixing times. The convergence of a Markov chain to it's stationary distribution is closely related to the gap between the dominant eigenvalue (one), and the second-largest eigenvalue, so building a fast-mixing Markov chains turns into a problem with a very interesting numerical linear algebra component. The authors are doing the standard Right Things with respect to the linear algebra -- including symmetry reductions -- but I'm curious whether they're doing anything that could benefit from some of my favorite algorithms.

There's also an article on the fast low-rank approximate solution of certain Lyapunov equations, too, and how the method involved (a variant of ADI, or alternating-direction-implicit methods) relates to a problem solved over a particular rational Krylov subspace. The author wrote a really cool thesis on model reduction a while ago -- it won the last Householder prize -- and the paper clarifies some connections that I didn't get when I read the thesis. And the survey article (A Survey of Public-Key Cryptosystems) also looks interesting, though I haven't yet even skimmed it. And, of course, the book reviews are always entertaining.

Anyhow, putting aside any technical jargon in the previous two paragraphs: I'm excited. The articles look cool, and I expect to learn some very useful things from them.

I've spent some of my time on leisure reading, too. I've been re-reading Ball's A Short Account of the History of Mathematics, and I've been going through another of Poincare's books. It's fascinating stuff. Ball is probably much more historically accurate than Bell, but I do sometimes find myself re-reading a section of Bell's book (Men of Mathematics) after reading a few pages of Ball's book. Bell is a lot less dry: did you know that Florence Nightingale was one of Sylvester's students; or that Poincare was notorious for his utter inability to make drawings that resembled anything in heaven and earth; or that Lobatchewsky spent a very active period as the curator of the University Museum at Kazan (in Russia), and continued to pitch in even after he became the university rector? On the other hand, Ball also mentions interesting anecdotes from time to time: I hadn't realized what a cad Cardan was, for example (a talented cad, but a cad naetheless). It's probably good for me to spend time with both books.

I wonder if there are any books out there exclusively on major mathematicians of the nineteenth and twentieth centuries? Maybe; but perhaps it's just as well they aren't in my current reading queue, or I'd spend less time on my other interesting reading on various methods for linear and nonlinear eigenvalue calculations (and applications, naturally).

  • Currently drinking: Coffee