Category Archives: offhand


I was just at a conference where someone asked me if I had coined any mathematical terms. Well, sort of! I was the one who decided on the name “FI-modules” for the abelian category Tom Church, Benson Farb and I wrote about in this paper. More informally, I’m pretty sure I’m the originator of using “Bhargavology” to mean “the program of counting arithmetic things by putting them in bijection with orbits of the integral points of a group acting on the integral points of a space.” At least, I can find this usage in emails I wrote in 2003, after Manjul’s thesis but before any of the papers came out. And that still seems to be something people say.

My coinages have not always been successful. Nobody ever again mentioned the “esperantist graphs” from my paper with Hall and Kowalski. (They were named so in honor of Harald Helfgott, who speaks Esperanto, and because in some sense they are typically graphs we hope are expanders.) Nor did “superduperstrong approximation” catch on.

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Lecture and egotism

I was doing guest lecture / Q&A in a science communication course at Cornell, where I was a professor at large last week. A friend of mine was in the back of the room, and later told me: “A bunch of students were on their laptops, but only about half of them were looking at Instagram and the other half were looking at information about you and your books!”

He meant this to be a compliment but my initial reaction was — what? Students were looking at their laptops while we were talking? I had no idea. In my mental construction of the event, both while it was happening and afterwards, every eye in the room was on me.

And this made me reflect — when I am giving a talk, or even a classroom lecture, I’m inclined to always think I’m being listened to. But of course that’s not true! It couldn’t be true!

There are limits, of course. If I’m lecturing and I’ve lost the whole room, I see their eyes die and I notice it. I stop and regroup and change course. But if half the kids are tuned out? I’m just gonna be honest, I probably don’t notice that.

Now you can read this as saying I’m a huge egotist who relies on unrealistic assessments of how interesting I’m being, and thanks to this reliance am failing to engage the class. Or you could say it’s very, very hard to teach class in such a way that there’s not some notable proportion of students tuned out at any given moment, and that it would be even harder to teach class well if you were constantly aware of which students those were. And as a counterpoint to that sympathetic assessment, you could say it’s not a random and constantly shifting sample of students who are tuned out; there might be a notable proportion who are almost tuned out and who I’m allowing myself to fail, or rather to not even try, to reach.

I don’t really know!

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I’d like to make a request, II

In re my last post about WIBA Madison’s Classic Rock; a couple of days later I was listening again and once again the DJ was taking listener calls, but this time it was because he was angry that McDonald’s was using Cardi B as a spokeswoman; he wanted the listener’s opinion on whether Cardi B indeed represented, as McDonald’s put it, “the center of American culture” and if so what could be done about it. Nothing, the listeners agreed, could be done about this sad, the listeners agreed, state of affairs. It has probably been 20 years since I heard the phrase “rap music” uttered, certainly that long since I heard it uttered so many times in a row and with such nonplus.

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I’d like to make a request

I was listening to WIBA 101.5 Madison’s Classic Rock in the car while driving home from an east side errand and heard something that startled me — the DJ taking requests from listeners calling in! Now that startled me — why wait on hold on the phone to talk to a DJ when in 2023 you can hear any song you want at any time, instantly?

And then I thought about it a little more, and realized, it’s not about hearing the song, it’s about getting other people to hear the song. Like me, in the car. 2023 is a golden age of listening to whatever you want but is an absolute wasteland for playing music for other people because everybody is able to listen to whatever they want! So there’s much less picking music for the whole room or picking music for the whole city. But at WIBA they still do it! And so listeners got to play me, in my car, this song

and this song

neither of which was really my cup of tea, but that’s the point, radio offers us the rare opportunity to listen to not whatever we want.

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“The pandemic made things worse.”

The Hill reports on a Pew Research study showing high proportions of Americans without romantic partners:

Recent years have seen a historic rise in “unpartnered” Americans, particularly among the young. The pandemic made things worse.

Here’s the Pew report the Hill piece draws on, which says:

Roughly six-in-ten young men report being single. Overall, three-in-ten U.S. adults are single, meaning they are not married, living with a partner or in a committed romantic relationship. This share has not changed since the Center asked this question in 2019.

Always click the links to see what the study really says!

As for me, I’d estimate I was single somewhere between 50-60% of the time between the ages of 18 and 29.

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Uncontested touchdown

The Chiefs beat the Eagles in the Super Bowl and even people who liked the outcome didn’t like the ending. With a little under two minutes left, the score tied, and the Eagles out of time outs, running back Jerick McKinnon broke free and headed for the end zone; but he stopped at the 2 yard line and took a knee, setting up the opportunity for the Chiefs to run down the clock to nothing and then kick a chip-shot game-winning field goal. Had McKinnon scored a touchdown, the Eagles would have been 7 points down, but Jalen Hurts would have had the chance to try to make it back up the field, with no time outs left, and even the score.

That’s football! That’s what people want to see! Instead, we got the Chiefs taking a knee.

What if McKinnon weren’t allowed to do what he did? That is — what if a touchdown play that the defense chose not to contest simply counted as a touchdown? Or, more simply — what if the defense, at any time, were allowed to concede a touchdown as “uncontested,” give up 6 points and the conversion, and force a kickoff?

It would be kind of like the intentional walk of football. Or even more specifically the intentional bases-loaded walk, where you give up points on purpose to achieve a larger strategic goal. But the uncontested touchdown rule, instead of avoiding a thrilling faceoff between the tiring pitcher and the fiercest slugger, would avoid… the weak fart of an ending we just saw.

I think teams would hardly ever do this. In fact, I can’t really think of any situation where a team would do this other than the exact situation that came to pass in this Super Bowl. And I think the Super Bowl would have been better football if the rules had given Philadelphia this option.

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Little did I know (real analysis edition)

I just finished teaching Math 521, undergraduate real analysis. I first took on this course as an emergency pandemic replacement, and boy did I not know how much I would like teaching it! You get a variety of students — our second and third year math majors, econ majors aiming for top Ph.D. programs, financial math people, CS people — students learning analysis for all kinds of reasons.

A fun thing about teaching outside my research area is encountering weird little facts I don’t know at all — facts which, were they of equal importance and obscurity and size and about algebra, I imagine I would just know. For instance, I was talking about the strategy of the Riemann integral, before launching into the formal definition, as “you are trying to find a sequence of step functions which are getting closer and closer to f, because step functions are the ones you a priori know how to integrate.” But do Riemann-integrable functions actually have sequences of step functions converging to them uniformly? No! It turns out the class of functions which are uniform limits of step functions is called the regulated functions and an equivalent characterization of regulated functions is that the right and left limits f(x+) and f(x-) exist for any x.

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Mask-wearing as vegetarianism

We might find out that COVID-19 infection carries with it a parcel of unwanted downstream effects. Say, a modestly increased risk of heart attack, of stroke, of early dementia. And maybe that those risks go up with repeated infection. It’s in no way certain any of this is the case. I’m not even sure it’s likely! But the probability seems high enough that it’s worth thinking about what the consequences of that would be.

My instinct is that the practice of wearing masks in crowded indoor settings would end up looking like the practice of vegetarianism does now. In other words, it would be something which:

  • clearly has individual health benefits although the magnitude is arguable;
  • clearly has public-good benefits although the magnitude is arguable;
  • most people don’t do;
  • some people feel they ought to do but don’t, or don’t fully;
  • changes over time from seeming “weird” to being well within the range of normal things people do, though there remain aggrieved antis who can’t shut up about how irrational and self-righteous the practitioners are;
  • is politically impossible to imagine being imposed by government

Would I be one of the people who kept up mask-wearing in crowded public places? I mean, I’ve been doing it so far, though certainly not with 100% adherence.

I do still eat meat, even though the environmental case for vegetarianism is clear-cut, and there’s a reasonably compelling argument that eating meat is bad for my own health. But giving up meat forever would be a lot harder on me than wearing a mask to the grocery store forever.

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Robin Laid a Gun Redux

A while back I blogged about the variation of “Jingle Bells” my daughter brought home, in which “Batman Smells” is followed by the strange line “Robin Laid a Gun.” I just noticed that YouTuber Tom Scott has posted a video with a definitive account of the popularity and geographic/demographic variation of many, many versions of “Jingle Bells, Batman smells,” including “Robin laid a gun”:

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I was driving home from picking up sushi the other night, and another car was tailgating me. I was really annoyed. I was on a curvy road, it was icy out, and I was going the speed limit, 25 – and this guy was riding my bumper, with those new really bright halogen headlights shining right into my rear-view mirror. I was not going to speed up to satisfy him, and anyway I was just going a couple more blocks. But when I turned onto my block, the tailgater turned with me, and when I pulled into my driveway, he parked next to my house. Now I was kind of freaked out. Was the guy going to get out of his car and scream at me for slowing him down? He did get out of his car. No chance of avoiding a conversation. He came up to me and asked where a certain address on my street was. He was a DoorDash delivery guy. Tailgating me because his ability to make enough money to live on depends on getting a certain number of deliveries done per hour, and that means that it’s an economic necessity for him to drive too fast on icy roads.

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