Today, I meant to write a page or two of my dissertation. This particular bit is somewhat hard going; it's the literature review section, in which I discuss the previous work on the problem that I'm proposing a solution to, and describing why that previous work doesn't sufficiently solve the problem. A bit over seven years ago (now there's a scary number!), when I was starting on this project, I did a draft of almost exactly this, to learn how other people were approaching the problem. I hoped that I'd be able to use that as the basis for this chapter in my dissertation, with a little work to bring it up to date, but it turns out that it's not going to be that easy.

The difficulty isn't that the field has advanced enough in seven years to make it obsolete -- it certainly hasn't -- but that the question I'm looking at has shifted just enough that the focus is all wrong. The flows that I'm simulating (things like water droplets in air) involve three complicating factors that need to be dealt with -- there's the fact that the simulation has to keep track of the location of the surface, there's the surface tension force, and there's the fact that the density and viscosity are very different in the two fluids. The initial review writeup I did centered around the methods for tracking the surface, because that's the obvious first problem to solve, and it gets the most attention. However, it turns out that the work that I did pretty much ignores that problem and is instead all about the other two. So, even though it's mostly the same papers that go into the review (or updated papers from the same people), they need to be reorganized into completely different categories.

And there are also things I come across, like a set of papers by someone about my age (I think, based on when she got her degrees) from Sweden, which have a fairly deep mathematical analysis of the accuracy of some of the existing methods. This is really a nice thing to have -- the first papers to mention this trick that I've seen were in 1992, and it's based on something from 1977, but this paper from 2003 is the first that I've seen that actually does a rigorous analysis of how good it is. And it's a nice thing to have for my dissertation, too; I can cite it and say that this method has errors that are proportional to the curvature of the surface and don't work at all when the curvature is too small, and so forth, rather than having to handwave and say "it's crummy" and have to come up with my own explanation of why. But getting there means that I have to read through the paper, and distill the rather detailed results into a few particular numbers for the relevant cases, which takes a while.

So, anyhow, I haven't been making all that much progress on this, particularly today.

What I ended up doing, mostly, was straightening my desk. It's been accumulating piles of cruft, and I suppose they've been getting to me, because today I've been noticing things and doing something about them, and I'm now to a point where my desk is really pretty close to being clean. It's not actually clean, by any stretch, but about half of it is clear, and the piles of mail that needed to be dealt with (nothing urgent) have been dealt with and sorted into the to-file stack, and the broken reindeer has been glued together and is sitting Elsewhere with a clamped foot for the glue to dry, and I'm finding that I'm feeling a fair bit calmer about things. Though, arguably, that may just be that it's late at night, and the desk-cleaning has been an advanced case of cat vacuuming.

In any case, where I was going with this was that just a bit ago I went and polished my shoes. I haven't done this in probably a year, and it was showing; they've been getting quite scuffed. (Judging from the soles, I should probably think about getting a new pair. Some time ago, I got a pair of Clarks that I really quite liked. After three years or so of daily wear, they'd pretty much worn out, so I went to a Clarks store, took them off, and said, "I'd like another pair, please". Three years later, and I repeated the process. And I think it's been another three years since then.) It's a fairly gratifying process, polishing shoes. It's not really a lot of work, aside from remembering to do it and gathering the stuff, and my shoes are no longer scuffed and battered and worn-looking; they're shiny and look well-cared-for. And I can look at them, and say, I did something today, and something that was in disrepair is now put right.

These things are important, even when they are only small things, put right with no more than a little shoe polish and a buffing cloth.