quivering through sun-drunken delight: February 2006

Hi, everyone. Long time no see. Qu'est-ce qui se passe?

The big news at the beginning of the semester is and must be the new classes, but we're still easing into that (one hasn't yet begun, even), so I'll hold off for the moment. Suffice to say that this year's crop looks to surpass that from the fall, with two number theory classes, including one taught by Andrew Wiles (which hasn't begun, so who can say if it will be beyond the horizon), and a geometry-flavoured class. Indeed, all would be perfect except for a foul scheduling accident that I had to watch happen, in person, with all the dread of watching two trains ram, from a distance, slow-motion-like. The other number theory class was originally at 1630-1830 Monday evening, so it was no surprise to me when the first order of business there yesterday was to negotiate a new time. Alas! Miserere, misero me, the time picked was 1400 Tuesday, consuming, like Jormungandr, the likewise-located discrete math class of Paul Seymour that I had so anticipated. An embarrassment of riches, verily. If this is the mightiest problem we encounter --

-- but it is not; finding the damn'd local chess club is far thornier. It is far more difficult than checking their website. However, I heard today that Ed Witten (yes, that Ed Witten) plays chess at such-and-such a location Fridays at nine o'clock in the evening or so. Needless to say I was struck profoundly by this remarkable confluence, and will have to investigate this rumour.

I should say where I heard it: over dinner. The dean of the graduate school, Bill Russell, hosts monthly gatherings for a small number of random invitees. Tonight my ticket came up. Despite having several days to think about it, though, I didn't manage to ask for a suggestion on dress. This kills me every time. I end up coming with the most mongrel compromises. Today I interpolated my blue sweater between the lavender shirt (and tie) and my suit jacket, with the light pants (and the good shoes, needless to say). I think this worked quite well; in fact the assistant dean had a red sweater-vest type under his suit jacket, and I managed not to be better dressed than the host, which would presumably be unforgiveable. (That was my fear, anyway; you can set me straight on protocol, a subject which didn't quite come up in the past.)

Anyway, dinner was quite the usual story: I managed to definitely not impress before and during dinner but relaxed into the setting afterward. I had a lovely chat with variously an historian, an architect, an economist, and a neural microbiologist. I asked our economist whether he feels (as I had read in a paper recently) that his field has gotten out of touch with the real world, and he told me that he likes the elegance of his theories. I suggested he move to Fine Hall. Architects, it turns out, have a huge breadth of knowledge that they draw on professionally, and we found a mutual interest in Greek philosophy and Bach, inter alia. Finally our historian friend won my heart by enthusiastic interest in my mathematical anecdotes and asking to keep my demonstration napkin.

I'll spare us all the meditations on the nature of happiness and our relationship to the Platonic Realm and instead present a preliminary trifecta of anecdotes.

Birthday Surprise. This is a fun trick to warm up with that consistently astonishes people who've never heard it. It has a good moral, too, that statistics does not come intuitively to people in general. The question is: how many people do you need in a room before it's more likely than not that two of them share a birthday? I observe, trying out some showmanship, that of course you'd need 367 to be certain of it. Now no one ever ventures a guess about number, but on first impression 23, the correct answer, is rather small!
Bottle Imp Paradox. This is one of my favourite problems, but you might want to replace it with something else, because I've never yet met someone who thought the same way. The set-up is this. You are offered a chance to purchase, for any price you care to name, a bottle imp. This bottle imp grants an unlimited number of wishes for you, with the sole condition that you must in turn sell (not discard or gift) the bottle imp to someone else after some finite time span, say twenty years. The condition of sale is that you must sell the imp for a strictly smaller amount of money. (Now, this is a game theory problem, not a gedankenexperiment in the value of a thing, so what this means is that if I pay one hundred cents then I sell it for at most ninety-nine cents. There is no such thing as a half-cent or a peso or inflation or whatever.) Failure to sell (by you, or by the next person, who inherits all the conditions) results in a terrifically gruesome, unspecified penalty exacted by Mephistopheles, from whom you cannot hide. (Or maybe Samiel, the Dark Huntsman.) The question: Do you buy the bottle imp? And if so, for how much? The rational answer is that you do not buy it, for any price: for clearly you would not buy it at one cent, for then no one would be able to buy it; but then not at two cents, for then no one would be willing to buy it; or if not n cents, then also not n+1. But, and I think I'm not alone here, I definitely would buy the damn thing, for as much as I had in my piggy bank. (The bottle imp can make currency, so it's all funny-money anyway.) I'm not saying the bottle imp's wishes would make me happy, technically speaking, but it's got to be worth it; and after all if I'm being irrational in buying it, I can bet there's an irrational person to sell it to....
Angle trisection. Save the best for last, assuming they're still paying attention. Many people (most, frankly, considering the audience you've got to have even to consider telling these stories) have heard that it's impossible to trisect an (arbitrary) angle using straight-edge and compass, or at least can think back to their high-school geometry and what it means. (Bonus points for me: mention that one uses Galois theory to show this, giving a beautiful application of the theory which I tell everyone I study when they ask.) Regular listeners will of course recollect that this can be done by origami, and the construction is wonderfully simple and easy to demonstrate with a pen that writes well on napkins.

So, a very pleasant evening. Moving on, more miscellany. Of course the Olympics have started. I hoped to catch highlights on cbc.ca, as they stream their daily newsprograms -- but the perverse Olympic broadcast regulations force them exactly not to stream their shows for the duration. So I'm completely blanked out, with the sole consolation that the curling scores are updated more-or-less in real time. It would have been nice to see the figure skating program (heck, to watch the curling!) although it seems my favourite guy, Alexei Yagudin, has bowed out (he was having knee problems last I heard, which was years ago... it's been a while without television, really).

Also: you may have heard there was a lot of snow here recently. We're relatively south and still got quite a bit. I'm told it's expected to warm up very shortly, and then it will all be gone. Already much of it seems to have melted. This meant only that I had to act fast, of course. So I took a quick jaunt to get the shot I needed, and picked up a few incidental ones along the way. My batteries, let it be known, did not fail me.

The view almost immediately outside my room. Continue past an archway hidden by the tree:

For those worrried I would catch my death of chill going to eat breakfast and dinner, the far building opens into the dining hall, so splice this one with the last and you'll see about how far I walk. Speaking of which, time for a little indulgence in an old passtime.