Jordan Ellenberg's Blog, page 6

I dreamed I was taught a new word. The word was “frunk,” and it was a thing you said when you were grateful for something you’d been given, but you wanted to express at the same time that the thing being given to you imposed a modest burden on you. Like, somebody asks you to chair an important committee, and it’s an honor, but also a certain amount of work. “Oh, hey, I’d be glad to, frunks.”

“[T]he possibility of damnation is so immense a relief in a world of electoral reform, plebiscites, sex reform and dress reform, that damnation itself is an immediate form of salvation — of salvation from the ennui of modern life, because it at last gives some significance to living.”

What a dumb thing to say. I understand that long arguments about the details dress code, or laboring over the fine points of something like electoral reform, is boring, bureaucratic, and square. I get the appeal of saying that that sort of thing is so boring, bureaucratic, and square that even eternal torture is preferable to it. But actually, no, Tom, it is not.

And I also think “reform,” in 1930 when Eliot is writing this, is strongly associated with do-gooders, or ladies, or do-gooder men who by virtue of their do-goodery are considered by Eliot to be faintly ladylike.

Well but no. Reform is boring, bureaucratic, square, and important. It is work for both men and women to do. If you live a a safe life where the road doesn’t crack under your car and you eat lunch without shitting your guts out and you get to decide what to wear to work and you don’t have to wonder whether the bank still has your money, thank a reformer.

Whit Stillman, writer and director of my favorite movie of all time, was in Madison this week. Work commitments kept me from showing up for the screening of Metropolitan but I made it for the end of the Q&A and got to exchange a few words with him. I told him about the exchange that’s always stuck with me: one of the preppie college student protagonists asks a middle aged man in a bar (character name: Man in Bar) whether people from their background are inevitably doomed to failure, and the man says, “No, we simply fail without being doomed.”

Dream. I’m sitting around a table with a bunch of writer friends. I say

“You know what my biggest challenge as a writer is?”

But then someone else jumps in to say something slightly related and the conversation moves in a different direction and I’m feeling somewhat put out until someone says, Wait, Jordan was going to tell us about his biggest challenge as a writer.”

And I said, “The biggest challenge I have as a writer is conveying hope. Because there is hope, we know this, but at the same time there’s no argument for hope, and writing most naturally takes the form of an argument.”

I was just on campus at Caltech, where I was surprised to learn that 30% of the undergraduate student body is composed of varsity athletes. 3% are water polo players alone! Brown, where my son goes, is 13% student athletes. At UW-Madison, just 3%.

In the waning minutes before the Orioles postseason begins I ought to mark down, as is my habit, some notes on games I saw; by complete chance I was visiting Harvard CMSA (where I talked with Mike Freedman about parallel parking) the same week the Orioles were at Fenway, so I caught a couple of games. Tiny notes:

No amount of upgrades can make Fenway not feel old. The building itself, its shape and bones, makes watching a game feel like watching a game felt when I was a kid in the 80s. I guess if I ever go to Wrigley I might feel the same. But now that the Oakland Coliseum is done hosting baseball, those might be the only options.Adley Rutschman has been pressing for the whole second half; in the first game, with the bases loaded and two outs, had two great takes on close pitches to get to 3-2 and then poked an opposite field single for what turned out to be the winning margin. That’s the hitter he can be. Good to see.I got there a little late and missed a classic cheap Fenway HR by Cedric Mullins, 334 feet to the pole, but then he was kind enough to hit another one, a real one, shortly after I got there.Albert Suárez, the story of the year, journeyman plucked out of the minors turned key part of the rotation after Bradish, Means, Rodriguez all went down. He never looked dominant, a lot of guys squared up on him for loud outs, but he also induced a bunch of really ugly, lost-looking swings. I don’t know enough about the Red Sox to know whether this was Suárez or whether the Red Sox just swing like that.Went to the first game by myself; made me nostalgic for grad school, when I used to come out by myself to see the Orioles a lot. CJ came up to meet me for the second game, his first time in Fenway. Orioles looked limp the whole time but Kremer kept it close, 7 K in 7 innings, left with a 2-1 deficit which Tony Santander promptly erased with a 400-foot shot. Then Keegan Akin came in to close out a lead in the 10th and Orioles bullpen things happened.

Orioles-Royals starts in half an hour. I hope I do not have to say “Orioles bullpen things happened.” The lineup is basically back to full strength at just the right time. We only have Burnes and Kremer left out of our opening day starting rotation, but if things go well, Burnes, Kremer, Eflin and Suárez is enough starting pitching to win a playoff series.

The other morning I noticed there was a dead mouse in our yard right by the door, and I didn’t feel like dealing with it, and Dr. Mrs. Q didn’t feel like dealing with it, and that night we didn’t feel like dealing with it either, and we said, knowing we were just procrastinating, “well maybe some animal will carry it off in the night but if not we’ll deal with it in the morning.” But some animal did carry it off in the night. I was happy not to have to bag and trash a dead mouse, but also felt it was bad for my moral constitution for my procrastination to have been rewarded in this way.

I met Mike Freedman last week at CMSA and I learned a great metaphor about an old favorite subject of mine, random walks on groups.

The Heisenberg group is the group of upper triangular matrices with 1’s on the diagonal:

You can take a walk on the integral or Z/pZ points of the Heisenberg group using the standard generators

and their inverses. How do you get a central element

with these generators? The way that presents itself most immediately is that the commutator [x,y] is the central element with 1 in the upper right-hand corner. So the matrix above is [x,y]^c, a word of length 4c. But you can do better! If m is an integer of size about , then [x^m, y^m] is central with an m^2 in the upper right-hand corner; then you can multiply by another or so copies of [x,y] to get the desired element in about steps.

Mike F. likes to think of the continuous version of this walk. This is a funny process; the Heisenberg group over R is a 3-manifold, but you only have two infinitesimal directions in which you’re allowed to move. The cost of moving infinitesimally in the c-direction above is infinite! (One way of thinking of this: by the above argument, it costs to travel in that direction, but when is close to 0, the cost per unit of distance goes to infinity!

This is what’s called a subriemannian structure. It’s like a Riemannian metric, but in each tangent space there’s a proper subspace in which you’re allowed to move at nonzero speed. But the brackets between things are substantial enough that you can still get anywhere on the manifold, you just have to shimmy a bit.

That was not a very clean definition, and I’m not going to give you one, but I will give you a very useful metaphor Mike explained to me. It’s like parallel parking! The state of your car is described by a point on a three-manifold R^2 x S^1, where the first two coordinates govern the car’s position on the street and the last the direction of the wheels. (OK this is probably an interval in S^1, not the whole S^1, unless you have a very cool car, but set that aside.) And at any point you have the ability to turn the wheels sideways, or you can inch forward or backwards, but you can’t hop the car to the side! So there’s a two-dimensional subspace of the tangent space in which you can move at finite costs. But if you need to move your car two feet in a direction orthogonal to the direction you’re facing — that is, if you need to parallel park — you can do it. You just have to shimmy a bit, where “shimmy” is the parallel parking term for “commutator” — this is really the same thing as [x,y] giving you a positive amount of motion in the infinite-cost direction.

During the summer I gave a talk at PROMYS and afterwards had dinner with a bunch of the undergraduate teaching assistants. At one point I said, “The wonderful thing about math is that while of course we’re proud of what we do, we also know that everything we make and understand would be made and understood by someone else, in time, if we hadn’t done it. So it’s not really about our own personal glory, it’s about contributing to the communal enterprise.” The woman next to me looked very stricken. I said, “That was supposed to be inspiring, not depressing.” She said, “No, it’s depressing.”

I can understand her reaction in the abstract! The feeling of wanting to be unique and indispensable, to know that the world would be quite different without your mark on it. And I do believe that as human beings, each of us is unique and indispensable. But as mathematicians, no. I don’t think we are and I don’t feel it as a loss not to be. Nor do I think our dispensability is cause to feel an ounce less pride in the things we build.

I found out today that the UW-Madison library has digitized copies of old Wright Directories of Madison. A Wright Directory is kind of like the white pages, but it also has a section where people are listed in order of their address, and it lists peoples’ occuptations as well as their phone numbers. I’d never heard of this book until earlier this week when AB and I ran across the 1975 edition in Paul’s Book Store.

I had thought our house was built in 1920, but the fact that our address (like most of the addresses on our block) appears in the 1917 Wright Directory but not in the 1916 edition makes me think 1916 or 1917 is actually the year. And in 1917 a man named Henry J. Hunt lived there, with occupation given as “engineer with Mead and Seastone.” Mead was an engineer at UW-Madison and an expert on hydroelectric power. I don’t know what happened to Seastone, but that company is now called Mead and Hunt! Our co-resident became a partner in 1946. Here he is, presumably around that time:

The directories show Hunt living on N. Blair St. until our house is built in 1917. At that point he lives with his wife, Sadie. But by 1921, he’s living there with “Mrs. Sarah McGann, nurse.” What happened? Maybe his wife died? But who’s McGann? She’s married, but not to Hunt, so — maybe a widowed sister who moved in with Hunt after his wife was gone? I wasn’t able to figure this out.

Hunt appears in one more notable way: he was the defendant in the case State ex Rel. Morehouse v. Hunt, decided by the Wisconsin Supreme Court on May 7, 1940. Hunt was on the zoning board of Madison, and in this capacity ruled that a man who owned a house which had been used as a fraternity house, but for one year moved his family in to live in part of the house, did not thereby revert the house to single-family zoning, and still maintained his right to the “non-conforming use” of renting to future frats. The neighbors didn’t like it and went to court. Almost a hundred years later Madison is still wrestling with how rigidly we’re going to enforce that the residents of houses are one or two parents and some subset of their children!