Hmm, I seem not to have posted anything in here for months. I'm not quite sure whether my life has been more boring recently, or whether it's just that my interestingness threshold for bothering to post in this diary has gone up.
I've had a new silly project preoccupying me since I last posted, which is to arrange a means of computer-typesetting music that doesn't irritate me. Until now I've been using a program I wrote myself when I was 15 and have stuck with on the grounds that I already knew how to use it and it's just about good enough, but it shows definite signs of having been written by a 15-year-old, and in particular the copyright status on its font of musical symbols was uncertain so I couldn't distribute it. Every alternative I've looked at since then has irritated me for at least one reason, and in particular I haven't found any replacement set of symbols that were both to my taste and copyright-unproblematic. So in the last couple of months I decided enough was enough and drew a new set from scratch, and then dropped that into the least irritating of the existing typesetting software. As of the weekend just past, the result is passing its stress test collection and I think I prefer its output to everything else I've seen including my own program. I can witter on about this at much greater length if anyone is interested and hasn't already been subjected to two months of said witter in the pub :-)
Last week I finally got round to dealing with the fact that nobody is currently selling acceptably nice gluten-free pizza bases, by experimenting with my breadmaker's pizza dough setting. This was successful after a couple of attempts (and even the first attempt wasn't too bad), so I now have a sudden urge to feed pizza to everyone I know.
Other unexpected things that have happened to me in the last couple of months include unexpectedly being called on to help catch a young woman jumping off a roof (she'd apparently climbed up there for a laugh and then found getting down was harder than getting up; I was walking past at the time), accidentally re-proving a theorem of Erdős in conjunction with ![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
drswirly (it struck me as an interesting question and we managed to prove the answer before finding out who'd already done it), accidentally finding the inverse cosine of 0.9 (a number I picked completely at random was so close to it that it completely confused a test program I was running) and having a cold while on holiday (bah).
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First one is standard Lilypond; second one is mine. Things I specifically disliked about LP and prefer about mine include the treble clef (LP's is absurdly tall by the standards of most others, the curved line down the middle makes it look as if it's leaning backwards, and a couple of parts are rather unevenly curved); the trill (LP's is unpleasantly ornate, mine is more in the style I was used to from music I actually played); the time signature digits (IMO much more readable if they're small enough not to collide with the outer stave lines, though actually making them miss at both ends turned out to take some cheating!); the sharp (LP's is too wide and also too slanted for my taste); the fermata (mine looks like an arc of a circle whereas LP's non-vertical ends make it look oddly parabolic); the quaver tails (some differences between the down and up tails are a good thing, but I think LP takes it a bit far). And if you look very closely, LP's minim head has a knobbly outline, but it isn't really clear at this resolution.
Most importantly, I find I can read my version without the notation jumping out at me: I find it does a better job of fading into the background. Standard LP looks like strangely stylised music, whereas mine just looks (to me) like music.
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What was the theorem, and how hard was it to prove?
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The theorem: given a positive integer n, how many integers do you need in order to guarantee that n of them sum to a multiple of n? (answer and five different proofs) I think it took us about an afternoon or so of serious thought between us to find a proof, once we'd decided what we thought the right answer was to start with (for which I cheated by computer search). Of the five proofs given there, ours was pretty similar to the first one (though Erdős's version, as one might expect, was more elegant and included a more neatly reusable lemma).
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