Why so bad? The team ERA has dropped almost half a run since I wrote that post, from 6.15 to 5.75. Their RS and RA for June were about the same as they were for May, but they went 6-20 instead of 8-19.
I can’t believe I’m saying this, but — maybe the Orioles aren’t really that bad? Their Pythagorean record is 28-59, which is terrible, but not even worst in MLB right now. (That honor belongs to the Tigers.) John Means continues to be great and Andrew Cashner and Dylan Bundy have now been pretty consistently turning in utterly acceptable starts.
The thing about baseball is, things happen suddenly. On Tuesday, September 5, 2017, less than two years ago, Manny Machado hit a 2-run homer in the bottom of the 9th to give the Orioles a 7-6 win against the Yankees. The Orioles were 71-68.
The next game after that, they lost 9-1. And then went 4-18 the rest of the way. They haven’t had a full month since then with a record better than .360. The Orioles became terrible in an instant. I don’t see why it can’t go the other way.
Back from nearly two weeks at the Institut Henri Poincare, where we were reinventing rational points, though they actually seem pretty much as they have always been. But lots of new ideas floating around and in particular lots of problems I see as potentially rich ones for students.
Last week featured the hottest temperatures ever recorded in France, reminding one that when you move the mean of a distribution even a little, the frequency of formerly rare events might jump quite a lot. Paris was spared the worst of the heat; after initial predictions of temperatures going over 100F, the hottest day of the conference was 97 and the rest of the week was in the mid-90s, regular old East Coast US summer weather. But of course France doesn’t have regular old East Coast US summer air-conditioning. Faiblement climatisé is the order of the day. The word for heatwave in French is “canicule,” which comes from the Italian word for Sirius, thought to be a bringer of hot weather.
It’s also the Women’s World Cup. Tickets for the US-France quarterfinal, held the night before I left, were going at 350 euros for the very cheapest, but I don’t think I’d have wanted to go, anyway. The Orioles are the only team I love enough to really enjoy rooting for them as the visiting team. Instead I went to Scotland-Argentina, which looked like a laugher 70 minutes in with Scotland up 3-0, but ended in a controversial tie after Scotland’s apparent save of a last-minute penalty kick was called back when VAR showed the goalie jumping off the line a moment before the ball was kicked. The ref called end of time directly after the second kick went in to tie the game, to the confusion and dismay of the players on the field; both teams needed a win to have a real chance of advancing past the group stage, and the tie left them both out. Scottish forward Erin Cuthbert pulled something out of her sock and kissed it after her goal; later I found out it was a picture of herself as a baby. I like her style!
I ate well. I ate whelks. They’re OK. I ate thiebou djienne at this place near IHP which was much better than OK. I ate a watermelon-chevre salad that was so good I went to a spice store and bought the pepper they used, piment d’espelette, and now I have a spice Penzey’s doesn’t sell. Favorite new cheese I ate on this trip was Soumaintrain.
I went to the museum of Jewish history where I saw this campaign poster:
And I saw the computer teen Blaise Pascal built for his dad in 1642, which is at the Musée des arts et métiers, along with a revolutionary 10-hour clock:
And right there at the museum, later that night, just by my good luck, there was a free Divine Comedy concert as part of the Fête de la Musique. It was sold out but, my good luck part deux, someone’s friend didn’t show up and in I went. Great set. Sort of a beautifully multinational moment to watch an Irish guy play a They Might Be Giants song in Paris in front of a cast of the Statue of Liberty:
I also learned on this trip that when French kids play Capture the Flag they use an actual French flag:
I gave a talk at Williams College last year and took a little while to visit one of my favorite museums, Mass MoCA. There’s a new installation there, by Taryn Simon, called Assembled Audience. You walk in through a curtained opening and you’re in a pitch-black space. It’s very quiet. And then, slowly, applause starts to build. Bigger and bigger. About a minute of swell until the invisible crowd out there in the dark is going absolutely fucking nuts.
And I have to be honest, whatever this may say about me: I felt an incredible warmth and safety and satisfaction, standing there, being clapped for and adored by a recording of a crowd. Reader, I stayed for a second cycle.
As an eternal 1990s indie-pop nerd I could not but be thrilled this week when I realized I was going to Bristol
on the National Express.
Bristol, besides having lots of great mathematicians to talk to, is much lovelier than I knew. There’s lots of terrain! It seems every time you turn a corner there’s another fine vista of pastel-painted row houses and the green English hills far away. There’s a famous bridge. I walked across it, then sat on a bench at the other side doing some math, in the hopes I’d think of something really good, because I’ve always wanted to scratch some math on a British bridge, William Rowan Hamilton-style. Didn’t happen. There was a bus strike in Bristol for civil rights because the bus companies didn’t allow black or Indian drivers; the bus lines gave in to the strikers and integrated on the same day Martin Luther King, Jr. was saying “I have a dream” in Washington, DC. There’s a chain of tea shops in Bristol called Boston Tea Party. I think it’s slightly weird to have a commercial operation named after an anti-colonial uprising against your own country, but my colleagues said no one there really thinks of it that way. The University of Bristol, by the way, is sort of the Duke of the UK, in that it was founded by a limitless bequest from the biggest tobacco family in the country, the Willses. Bristol also has this clock:
What’s the chance that a random curve has ordinary Jacobian? You might instinctively say “It must be probability 1” because the non-ordinary locus is a proper closed subvariety of M_g. (This is not obvious by pure thought, at least to me, and I don’t know who first proved it! I imagine you can check it by explicitly exhibiting a curve of each genus with ordinary Jacobian, but I’m not sure this is the best way.)
Anyway, the point is, this instinctive response is wrong! At least it’s wrong if you interpret the question the way I have in mind, which is to ask: given a random curve X of genus g over F_q, with g growing as q stays fixed, is there a limiting probability that X has ordinary Jacobian? And this might not be 1, in the same way that the probability that a random polynomial over F_q is squarefree is not 1, but 1-1/q.
Bryden Cais, David Zureick-Brown and I worked out some heuristic guesses for this problem several years ago, based on the idea that the Dieudonne module for a random curve might be a random Dieudonne module, and then working out in some detail what in the Sam Hill one might mean by “random Dieudonne module.” Then we did some numerical experiments which showed that our heuristic looked basically OK for plane curves of high degree, but pretty badly wrong for hyperelliptic curves of high genus. But there was no family of curves for which one could prove either that our heuristic was right or that it was wrong.
Now there is, thanks to my Ph.D. student Soumya Sankar. Unfortunately, there are still no families of curves for which our heuristics are provably right. But there are now several for which it is provably wrong!
15.7% of Artin-Schreier curves over F_2 (that is: Z/2Z-covers of P^1/F_2) are ordinary. (The heuristic proportion given in my paper with Cais and DZB is about 42%, which matches data drawn from plane curves reasonably well.) The reason Sankar can prove this is because, for Artin-Schreier curves, you can test ordinarity (or, more generally, compute the a-number) in terms of the numerical invariants of the ramification points; the a-number doesn’t care where the ramification points are, which would be a more difficult question.
On the other hand, 0% of Artin-Schreier curves over F are ordinary for any finite field of odd characteristic! What’s going on? It turns out that it’s only in characteristic 2 that the Artin-Schreier locus is irreducible; in larger characteristics, it turns out that the locus has irreducible components whose number grows with genus, and the ordinary curves live on only one of these components. This “explains” the rarity of ordinarity (though this fact alone doesn’t prove that the proportion of ordinarity goes to 0; Sankar does that another way.) Natural question: if you just look at the ordinary component, does the proportion of ordinary curves approach a limit? Sankar shows this proportion is bounded away from 0 in characteristic 3, but in larger characteristics the combinatorics get complicated! (All this stuff, you won’t be surprised to hear, relies on Rachel Pries’s work on the interaction of special loci in M_g with the Newton stratification.)
Sankar also treats the case of superelliptic curves y^n = f(x) in characteristic 2, which turns out to be like that of Artin-Schreier in odd characteristics; a lot of components, only one with ordinary points, probability of ordinarity going to zero.
Really nice paper which raises lots of questions! What about more refined invariants, like the shape of the Newton polygon? What about other families of curves? I’d be particularly interested to know what happens with trigonal curves which (at least in characteristic not 2 or 3, and maybe even then) feel more “generic” to me than curves with extra endomorphisms. Is there any hope for our poor suffering heuristics in a family like that?
I’ve said all along it was wrong to imagine the Orioles being as bad as they were last year. And so far my optimism has been borne out. Don’t get me wrong; they’re bad. But they’re not excruciatingly, world-historically bad. The Orioles, on April 24, are 10-16; last year it took them until May 10 to win their 10th game, at which point they were 10-27. Chris Davis, after starting 0-for-everything, has hit .360 and slugged .720 since the middle of April. Nothing makes me happier than to see this poor guy hit after his long winter, even if it’s only for awhile. And Trey Mancini, who’s just about the right age to have a sudden career renaissance if he’s going to have one, is maybe… having one?
The pitching is terrible. 6.15 ERA in the early going, a half-run worse than anyone else in the league; flashes of goodness from Hess, Cashner, and Means, all of whom could be OK, but there’s no real reason for confidence any of them will be. And of course the team could make the choice, as they did last year, to flip Mancini, Means, and anybody else who’s producing for prospects at midsummer and lose their last 70 games; who knows? But for now; why not?
Instructive anecdote. I needed a somewhat expensive book and the UW library didn’t have it. So I decided to buy it. Had the Amazon order queued up and ready to go, $45 with free shipping, then had a pang of guilt about the destruction of the publishing industry and decided it was worth paying a little extra to order it directly from the publisher (Routledge.)
From the publisher it was $41, with free shipping.
I think it really did used to be true that the Amazon price was basically certain to be the best price. Not anymore. Shop around!
David Brooks writes in the New York Times that we should figure out how to bottle the civic health southwest Nebraska enjoys:
Everybody says rural America is collapsing. But I keep going to places with more moral coherence and social commitment than we have in booming urban areas. These visits prompt the same question: How can we spread the civic mind-set they have in abundance?
For example, I spent this week in Nebraska, in towns like McCook and Grand Island. These places are not rich. At many of the schools, 50 percent of the students receive free or reduced-cost lunch. But they don’t have the pathologies we associate with poverty.
Crime is low. Many people leave their homes and cars unlocked.
Is it? And do they? I didn’t immediately find city-level crime data that looked rock solid to me, but if you trust city-data.com, crime in Grand Island roughly tracks national levels while crime in McCook is a little lower. And long-time Grand Island resident Gary Christensen has a different take than Brooks does:
Gary Christensen, a Grand Island resident for over 68 years says times are changing. “It was a community that you could leave you doors open leave the keys in your car and that kind of thing, and nobody ever bothered it. But those days are long gone,” said Gary Christensen, resident.
One way you can respond to this is to say I’m missing the point of Brooks’s article. Isn’t he just saying civic involvement is important and it’s healthy when people feel a sense of community with their neighbors? Are the statistics really that important?
Yes. They’re important. Because what Brooks is really doing here is inviting us to lower ourselves into a warm comfortable stereotype; that where the civic virtues are to be found in full bloom, where people are “just folks,” are in the rural parts of Nebraska, not in New Orleans, or Seattle, or Laredo, or Madison, and most definitely not in Brooklyn or Brookline or Bethesda. But he can’t just say “you know how those people are.” There needs to be some vaguely evidentiary throat-clearing before you launch into what you were going to say anyway.
Which is that Nebraska people are simple dewy real Americans, not like you, urbanized coastal reader of the New York Times. I don’t buy it. McCook, Nebraska sounds nice; but it sounds nice in the same way that urbanized coastal communities are nice. You go someplace and talk to a guy who’s on the city council, you’re gonna be talking to a guy who cares about his community and thinks a lot about how to improve it. Even in Bethesda.
Constantly they are thinking: Does this help my town or hurt it? And when you tell them that this pervasive civic mind-set is an unusual way to be, they look at you blankly because they can’t fathom any other.
There’s Brooks in a nutshell. The only good people are the people who don’t know any better than to be good. By saying so, he condescends to his subjects, his readers, and himself all at once. I don’t buy it. I’ll bet people in southwest Nebraska can fathom a lot more than Brooks thinks they can. I think they probably fathom David Brooks better than he fathoms them.
Madison had a primary election last night for mayor and for several seats on the City Council and School Board. Turnout was high, as it seems to always be in Dane County lately. The Dane County Clerk has all the results in handy csv form, so you can just download things and start having some fun! There were four major candidates for mayor, so each ward in the city can be mapped to a point in R^4 by the vote share it gave to each of those; except of course this is really R^3 because the vote shares sum to 1. It’s easier to see R^2 than R^3 so you can use PCA to project yourself down to a nice map of wards:
This works pretty well! The main axis of variation (horizontal here) is Soglin vote, which is higher on the left and lower on the right; this vector is negatively weighted on Rhodes-Conway and Shukla but doesn’t pay much attention to Cheeks. The vertical axis mostly ignores Shukla and represents Cheeks taking votes from Rhodes-Conway at the top, and losing votes to Rhodes-Conway at the bottom. You can see a nice cluster of Isthmus and Near West wards in the lower right; Rhodes-Conway did really well there. 57 and 48 are off by themselves in the upper right corner; those are student wards, distinguished in the vote count by Grumpy Old Incumbent Paul Soglin getting next to no votes. And I mean “next to no” in the literal sense; he got one vote in each of those wards!
You can also do some off-the-shelf k-means clustering of those vectors in R^4 and you get meaningful results there. Essentially arbitrarily I broke the wards into 5 clusters and got:
Now what would be interesting is to go back and compare this with the ward-by-ward results of the gubernatorial primary last August! But I have other stuff to do today. Here’s some code so I remember it; this stuff is all simple and I have made no attempt to make the analysis robust.
Update: I did the comparison with the August primary; interestingly, I didn’t see very many strong relationships. Soglin-for-mayor wards were typically also Soglin-for-governor wards. Wards that were strong for Kelda Helen Roys were also strong for Raj Shukla and weak for Soglin, but there wasn’t a strong relationship between Roys vote and Rhodes-Conway vote. On the other hand, Rhodes-Conway’s good wards also tended to be good ones for… Mike McCabe??