The Unapologetic Mathematician

Mathematics for the interested outsider

First Day in Faro: Random Thoughts

Well, it was an adventure getting from my flight arriving in Lisbon through customs (even with nothing to declare and no checked baggage) and on to my next flight. On the way, Scott Morrison got to see me grumbling (I partly chalk that up to such a long time without indulging my addiction) and as I got to the connection I ran into Peter Ozsvath, which was a nice little surprise.

He and I ran into each other again a little while ago while wandering around. I was killing time until I could check in to my hotel and he was just trying to stay awake. So we had lunch. It was good, a little more than I’d have liked to pay, but there’s time to find the little holes-in-the-walls later. I’m also hoping his general reactions were due to being tired rather than me being insanely boring. It’s probably a little of both.

Anyhow, I’ve started to bump into a few more people, and we’re starting to clump a bit. I like to think I’m rather cosmopolitan, but culture shock is still a real thing. And it’s easier to manage in a small group, ’cause someone won’t be a complete idiot in a given situation. On the other hand, before running into Oszvath (the second time) I negotiated my way around a bit. The lemon gelado here is good for cutting through the heat, and it scours your palate with a refreshing sourness that lingers on.

Another random thought: in the Philadelphia airport I randomly ran into a guy who’d just graduated high school and is on his way to Cornell. I mention this because while he was still undecided last fall he sat in on my Calculus 3 class on a campus visit. One hour he saw me — almost a full year ago, no less — and he still recgonized me and wanted to say hi and that he’d liked that one lecture. Of course, since it’s a compliment I said thianks (I’ve manged to learn to do that much at least), wished him good luck, and told him to watch out for that high suicide rate in Ithaca. Yeah, I’m a bad person.

More on the mathematical front, I bought Douglas Hofstadter’s I Am a Strange Loop for this trip. It’s a good read so far, but that’s to be expected from him by now. Particularly nice is the way he approaches (reapproaches) epiphenomena, and specifically how we talk about them. He notes that at a certain point it’s not only unhelpful to describe a macroscopic system explicitly in terms of its microscopic pieces, but it’s flat-out harmful.

Sure, an engineer could write down untold numbers of equations describing the position and momentum of every single molecule of gasoline and air in a car’s cylinder, but “pressure” isn’t about this molecule or that one. It’s an epiphenomenon that a very large number of different microstates give rise to. If we talk about statistical mechanics instead of thermodynamics we’re missing the forest and the trees alike for the leaves

I’ve been saying much the same thing. In particular, with regard to the natural numbers: we don’t care how we build them, we just want them to satisfy the universal (epiphenomenal) property and we use that property to prove everything else without caring about the petty details of how our model satisfies the condition.

But this all then raises a natural question: we’re looking at microstates (statistical mechanics) and declare examples of them to be “the same” if their macrostates are the same. But we don’t like “the same” — we like “isomorphic. So, is the passage from statistical mechanics to thermodymanics a decategorification?

Anyhow, I’m going to also push through until the local sleep time. In a bout an hour I’m meeting up with someone and we’ll try to figure out how to get from here to the university. This ought to be fun.

July 4, 2007 Posted by | Uncategorized | 3 Comments