Jordan Ellenberg's Blog

That is a truly world-class roster of municipal nicknames.

Tomorrow is Memorial Day.

William James, in 1897, dedicating the monument to Col. Robert Gould Shaw and the 54th regiment, a monument which still stands in Boston Common today:

“And when South Carolina took the final step in battering down Fort Sumter, it was the fanatics of slavery themselves who called upon their idolized institution ruin swift and complete. What law and reason were unable to accomplish, had now to be done by that uncertain and dreadful dispenser of God’s judgments, War – War, with its abominably casual, inaccurate methods, destroying good and bad together, but at last able to hew a way out.”

More James:

“What country under heaven has not thousands of such youths to rejoice in, youths on whom the safety of the human race depends? Whether or not they leave memorials behind them, whether their names are writ in water or in marble, depends mostly on the opportunities which the accidents of history throw into their path”

The monument, and James, and the 54th regiment, and the atom bomb, are all in Robert Lowell’s poem “For the Union Dead”:

“He is out of bounds now. He rejoices in man’s lovely,
peculiar power to choose life and die—
when he leads his black soldiers to death,
he cannot bend his back.”

Shaw died in the assault on Fort Wagner too. William James’s younger brother was a volunteer in the 54th, and was gravely wounded; his presence there goes unmentioned in James’s speech.

James concludes by emphasizing that military valor is not the only kind of valor, not even the only kind that Col. Shaw himself displayed and was cast in bronze for.

“What we really need the poet’s and orator’s help to keep alive in us is not, then, the common and gregarious courage which Robert Shaw showed when he marched with you, men of the Seventh Regiment. It is that more lonely courage which he showed when he dropped his warm commission in the glorious Second to head your dubious fortunes, negroes of the Fifty-fourth. That lonely kind of courage (civic courage as we call it in times of peace) is the kind of valor to which the monuments of nations should most of all be reared, for the survival of the fittest has not bred it into the bone of human beings as it has bred military valor; and of five hundred of us who could storm a battery side by side with others, perhaps not one would be found ready to risk his wordly fortunes all alone in resisting an enthroned abuse. The deadliest enemies of nations are not their foreign foes; they always dwell within their borders. And from these internal enemies civilization is always in need of being saved. The nation blest above all nations is she in whom the civic genius of the people does the saving day by day, by acts without external picturesqueness; by speaking, writing, voting reasonably; by smiting corruption swiftly; by good temper between parties; by the people knowing true men when they see them, and preferring them as leaders to rabid partisans or empty quacks. Such nations have no need of wars to save them.”

I was thinking the other day about this old question, a favorite of mine.

Here’s another version of it — if anything along the lines of Belyi’s proof of Belyi’s theorem works, one might expect this to be true.

Question: Suppose given five points p_1, .. p_5 in P^1(Q(t)). Is there a map F from P^1 to P^1 such that the the critical values of F and F(p_1), … F(p_5) are all contained in a set of size four?

This would be “Belyi for M_{0,5},” I suppose. I have to admit, I feel like the answer is probably no.

Why it seems hard: every set of p_1, .. p_5 obtainable is obtained from some family of covers of P^1 branched at four points — in other words, it’s the image in M_{0,5} of some 1-dimensional Hurwitz space. So you have some countable union of curves in M_{0,5}. Now all you have to do is write down a curve in M_{0,5} which is not one of these. But… how do you know you can do this? If you were allowed to work over C, it’s easy! But there are only countably many curves in M_{0,5} defined over Q, or for that matter over Qbar. Maybe the Hurwitz curves use them all up! I doubt it. But I don’t see how to rule it out. Stranger, or at least equally strange things have happened; I am thinking, of course, of Belyi’s theorem itself, which one simply can’t believe until one sees the proof, and even then, only just.

It’s not obivous to me that this is hard. There might be a quick way to write down a p_1, .. p_5 for which there’s no such F. Good problem to chew on with the help your favorite example-generating large language model! (So far I couldn’t get Claude Opus 4.7 to have any luck with it, but your mileage may vary.)

Last night: my second visit to Wrigley Field, once again to see the Brewers. Did I blog the last one? Doesn’t seem I did. I went with CJ and a bunch of his friends (whence the aphorism.) Brief description, because it’s late.

At least three Baltimore chops in this game.

Lines for food at Wrigley are at least an inning long. Shouldn’t this be a solved problem?

My first time seeing Les Miz pitch. Maybe my last, as I have to believe that a guy can’t throw this fast this consistently without his arm flying off his body sometime very early in his career. Prior to this game, Misiorowsky had thrown 233 pitches at 100+mph. All other MLB starters combined: 149.

Brewers cruise most of the game, Cubs getting 3-hit, they rally in the eighth against unusually shaky Aaron Ashby, loading the bases and scoring a run on what should have been an inning-ending grounder when Luis Rengifo in a very ex-Angel fashion fumbled the pickup. But Chad Patrick got Michael Conforto to ground out to end the threat.

Impressive organ work at Wrigley. Runner dives back to first to avoid the pickoff: “Get Back,” by the Beatles. Batter fouls one off high above his head: “Straight Up,” by Paula Abdul. Best of all was the organist’s welcome for Garrett Mitchell: the theme song from “The Facts of Life.” How many people at Wrigley Field last night got that reference? Well, I got it, Wrigley Field organist, and I appreciated it.

If something is the case, it is low-key the case.

In the fall of 1992, my senior year of college, I took a seminar on Social Psychology of Language with Roger Brown. (Roger Brown the psychologist, not Roger Brown the painter, one of my very favorites since I saw this exhibition in 1987) — how have I never blogged about him?)

This was the class where we learned about universals of politeness, the way a direct demand (“Pass the salt”) is always impolite, and is euphemized into a nominally factual question about the possibility of the demand being granted (“Could you pass the salt? Is there salt?”) We developed a habit of asking “Does salt exist?”

Brown seemed incredibly old to me at the time. In fact, he was only 68, but in poor health. (He would die in 1997 — Stephen Pinker’s obituary for him is rich in incident.) About two-thirds of the way through the class, he had some kind of medical event and his grad student had to take over the rest of the term.

But back in October, I turned in a short paper about singular “they,” which I was very optimistic about. I compared it with “Ms.,” writing:

“It is interesting in this context to note the example of “Ms.,” discussed in Graham’s article. In 1973 the new word was seen as an orthographic invention; its “correct” pronunciation was a matter of controversy. Of course the version that won out was “miz,” the pronunciation that sounds like the blurred phoneme produced by a speaker unsure which of “Miss” or “Mrs.” is appropriate. Had the pronunciation “Emm Ess” been chosen, I am confident, the term would not have gained the acceptance that it has.”

Brown wrote in the margins:

“I never did hear Ms. said ver often and I and others no longer write it. The point was that Ms. should be used for all women married or single, like Mr., but married women don’t want to be called Ms. Marriage is status-relevant.”

Brown was undoubtedly one of the giants of linguistics, but he was wrong about this!

“I had been for the past year an editor of a new encyclopedia, and a hack who had been fired, after turning in several poor and inaccurate articles (he cribbed from older encyclopedias, and even his cribbing was mixed up, inaccurate, and disjointed) thought that I was the person who had been the cause of his losing his job. So he had called me at three o’clock in the morning, and attempted to hold a genial and intimate conversation, and when I told him I was trying to sleep, he asked if I had a woman with me! I hung up in anger, and he kept calling, night after night, until at last I told him how unkind he was to wake me up at that hour, and he replied, “My hatred of you has turned to pity,” but he had continued to call and then hang up without speaking.” –Delmore Schwartz, “The Track Meet,” 1959.

Of the writers I truly admire, Schwartz might be the one whose power is most mysterious to me. There were moments when I felt I had successfully imitated him a little bit but never figured out how to do it reliably. This passage is in some ways like the Richard Brautigan sentence (rather, non-sentence) I praised here, 15 years ago. 15 years ago! I’ve been blogging a long time. The constant return to the past (or the constant intrusion of the past on us, unasked for but not wholly unexpected, like a phone call deep in the night) is also Delmore Schwartz-like, as in, of course “In Dreams Begin Responsibilities,” which Schwartz wrote in a single weekend when he was 21 — 21! — if you haven’t read it, please, with what authority I have or can pretend to have over you I urge you, do.

“Like a snail I have lived in a small shell, which I found snug and comfortable, yet longed to desert often to inhale outside atmosphere. Each time I thrust my tentacle out, I felt it touching something unfriendly and drew it back to the old hole. Thus I have led a blank life and seem to be destined to it. Archery and Chinese penmanship take most of my time, though I am not good at them.” –Yutaka Maeshima, 15th anniversary report of the Harvard class of 1923

A photo to go with this old paper.

It’s weird that the plural of Alex and the plural of Alice are both “Alices.” Sort of a base/basis problem.