Jordan Ellenberg's Blog

To The Best of our Knowledge is finished

The longtime Wisconsin Public Radio show To The Best of Our Knowledge airs its last episode this weekend. You can listen to the stream at that link or you can listen to it over the airwaves tomorrow with an FM receiver, the way God intended. Either way, there’s more than 1000 archived episodes for you to enjoy at your leisure.

I don’t know the story of why this show was cancelled, whether it had particular enemies, or whether it was the victim of budget cuts driven by hostility to public radio more generally. I’ve been on this show several times. Anne Strainchamps is one of the best interviewers I’ve ever heard. She listens, she goes wherever the thing wants to go (even when I the interviewee have no idea where it’s going to go), she’s funny in a way that works with, not in competition with, the person she’s talking to. Radio sounds old-fashioned, but it still has an sneaky, immense reach. Every time I did this show, people came up to me afterwards, people who would probably never pick up one of my books, to say, Hey, I heard you. The radio is there for everyone, everywhere, to find. It is public.

Public In the same way a public park in a small town is public, or the public schools I went to and my parents and kids went to are public, or a public highway is public. It’s not there to sell something, or to make you feel mad or angry or worried on the way to selling you something. It’s just a group of people doing some work to put something good out there for people to use. So little of our world is like this now. We should appreciate the parts that are, and mourn a little whenever one more public thing gets scraped away.

I gave a talk about machine learning and math

I, too, spoke at the CMSA Big Data conference where this cool math bio talk took place. If you’ve seen me give a talk about math and machine learning lately, you’ve seen some of the slides in this talk, but if not, here’s me talking for an hour, a bit impressionistically, about generating interesting mathematical material using machine learning. Also, you can hear Sébastien Racanière from DeepMind correct me about the difference between AlphaGo and AlphaZero in real time!

Some of the material the talk is about this paper I wrote recently with Kit Fraser-Taliente, Karan Srivastava, and Drew Sutherland. I should blog about it! Also, you should hire Karan!

Social media hiatus

I’m not sure whether readers of this blog have noticed, but I’m off social media — no Facebook, no Twitter, no Bluesky, I’ve dropped off my message boards, etc. A few thoughts on this, about a year in:

It was actually not very hard. I thought it would be a lot harder; I was a pretty heavy social media user. But this stuff is not nicotine. You stop doing it, you don’t really miss it.On the other hand, I would not say the hiatus has been dramatically life-changing. I don’t feel like I suddenly have unlimited time to accomplish my real goals. Maybe I wasn’t such a heavy social media user! Gallup says the median teen is on five hours a day. I’m pretty sure I wasn’t doing nearly that much.I won’t do this forever, because in 2027 I’ll have a new book to promote, and social media is actually useful for that. But if I didn’t have a book to sell, I think I’d stay off for good. For one thing, what would have been a tweet now becomes a blog post, and I’m happy to be back to blogging. I like blogging better. Sure, some tweets — most tweets — don’t have the substance to become blog posts. And those just stay thoughts. But that’s OK! It’s probably slightly damaging to my weak social ties; there’s some large set of acquaintances whose existence I am no longer periodically reminded of, and with whom I now have zero contact instead of commenting on a post of theirs every couple of months. Is this bad? It’s how social life worked for most of my youth, and that seemed all right. I would encourage people to try this! Even if you don’t intend to stop using social media for good, it’s useful information to know you can quit any time you want. At some point in grad school I didn’t drink coffee for a month because I was overdoing it and having some stomach problems. I think that was the last time I ever went two days in a row without drinking coffee. But I like knowing that if I ever need to decaffeinate, I can, without much suffering.

Chadeish yameinu

Shana Tova to all my fellow Jews. We are about to ask God, repeatedly, to “chadeish yameinu k’kedem” — make our days new, the way they used to be.

What does this mean? I take it to be a reminder — echoed at Kol Nidrei — that nothing is really determined and every moment is a moment where you can change paths. If you are having a day that you don’t like, or that God doesn’t like, or that neither of you likes, it isn’t determined that the next day is going to be the same, even though it might feel like tomorrow has to be like today. We are not asking God to make the year good. We’re just asking for the strength to pick what year we have. The rest is up to us.

But why k’kedem? I think the verse reminds us here that it’s not just that the future isn’t determined — it’s that the future was never determined, which means the present, the way you are, the person you are, might have been something other than what it is. That is unsettling. But prayer is supposed to be unsettling! Especially when an old year ends and a new year begins. Have a happy and unsettled 5786, everybody.

Global epistasis emerges from a generic model of a complex trait (or: random walks on a hypercube with reweighting)

I still don’t really know what global epistasis is, but I really enjoyed Gautam Reddy‘s talk about this paper at the CMSA Big Data conference two weeks ago. Here’s a simple model of evolution. There are n genes (x_1, … x_n) which can each be in one of two conditions, which we label as 1 and -1; so there are now 2^n genotypes which we have modeled as the vertices of a hypercube. You have some population of organisms and you start them off at some vertex. And then mutation happens at a constant rate, which means each organism sets off on a random walk.

But that’s not evolution yet. We need some notion of fitness, which we model as a function f on the hypercube, given by some polynomial

And organisms with higher fitness reproduce more; so you reweight at each time step, placing more probability on those walkers whose current vertex has higher fitness. And then you keep track of the mean reproduction rate as the walk progresses. It turns out that you typically get sharp improvement followed by diminishing returns, and that the shape of the curve is a good match for what’s observed in actual experiments with actual organisms. (Did you know there’s an ongoing experiment in E. coli evolution that started in 1988 and has now tracked over 80,000 generations of bacteria? Amazing.)

What’s more, there is lots of interesting math that goes into understanding what we can learn about the function f (which can’t be directly observed) from the changes in reproduction rate (which can.) In particular — though this is the part I’m not sure I totally followed — I think they were saying that experimental results aren’t really compatible with f having no cross-terms; in other words, one can see that there have to be a lot of terms like x_1 x_2, where the sign of the effect of changing x_1 depends on the value of x_2, and vice versa. I think this is what “epistasis” means.

Reddy’s co-author Michael Desai (who has his own myriad-generational population of yeast bubbling away in his lab) is teaching a really interesting multi-disciplinary double-counted undergraduate course for Harvard students interested in the modern life sciences.

The course uses examples from biology as an integrating theme, principles from physics and mathematics to reduce complex problems to simpler forms, and computer simulation to allow students to develop their intuition about the behavior of the dynamical systems that control the physical and biological universe. The course includes bootcamps to introduce students to biological experiments and the computer language, Python. Each semester will include a project lab, in which students will work in small teams to do original research on unsolved biological problems.

Sounds fun!

Pre-covers

Listening to the songs on the Vinyl Vault 30-minute Peloton ride in the hotel gym at the conference I just came back from (about which more later?) I had two thoughts about old songs that sound like newer songs.

The Hollies, “The Air That I Breathe” is basically Radiohead’s “Creep”, 20 years earlier:

And the final “na na na” part of “Hey Jude,” but not the “na na na,” the way the guitar and drums and horns sound, well, I feel like all of British acid house was basically a cover of it — see e.g. “Loaded,” seven minutes of heaven of which I will never tire.

OK, wait, having already written this post, I have just been informed by Wikipedia that the similarity between “Creep” and the “The Air that I Breathe” is not just my imagination, but indeed was the basis of legal action that ended with the writers of the latter awarded co-writing credit on the former.

Mura Yakerson interviewed me

And we talked about math, writing, standup comedy, the art of interviewing (meta!)

Mura’s whole channel is great. Bisi Agboola! Helene Esnault! Steve Strogatz! Mura’s mom! Check it out.

Klartag improves the sphere-packing constant

Hey! It escaped my notice until this week that Boaz Klartag has recently shown the existence of lattice sphere packings in dimension d of density at least c d^2 2^-d. This lower bound was stuck at d 2^-d for a long time, and was only recently improved by a factor of log d, which I learned about from Marcus Michelen‘s job talk (unfortunately for us, as the link will show you, he chose to go to Northwestern!) So it’s very cool that Klartag jumps this up a whole power of d, and by an entirely new method. As in Michelen’s work, though, the approach is probabilistic.

Here’s the idea in a nutshell. Showing the existence of a lattice packing with large density is equivalent to showing the existence of a large ellipsoid which contains no nontrivial point of the standard lattice. (Just take a linear transformation which sends the big ellipsoid to a unit sphere, and which thus has small determinant; apply it to the lattice too, and you have a dense lattice which misses the unit sphere, and Bob’s your uncle.) It turns out you can get such an ellipsoid by almost-aimless wandering! More precisely: start with some ellipsoid whose disjoint from the (nonzero elements of the) lattice, and then carry out some form of Brownian motion in the space of all ellipsoids, subject to one very important rule: every time your ellipse hits a lattice point x, you “freeze” that intersection point, and from now on the ellipsoid wanders in the one-dimension-smaller space of ellipsoids which pass through x. The process thus stops when you’ve hit about (1/2)n^2 points, because that uses up all your degrees of freedom. The game, then, is to show that there’s a slight constant drift towards increasing volume, so that in the length cn^2 lifetime of your process, the ellipsoid acquires c n^2 volume, and that’s exactly where the n^2 in the theorem comes from.

Very cool that such a charming idea actually works!

Bertrand Russell on rationality and math

“Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was one which does not now seem very impressive; it was, that some people can do sums.”

Russell was one quotable individual.

Yu Darvish has beaten 29 out of the 30 MLB teams

But not the Orioles, against whom he is now 0-3. He got beat by Dylan Bundy in the 2016 game, then by Grayson Rodriguez (remember Grayson Rodriguez?) in 2023, and by Tyler Wells this week. That’s only the regular season, though. The game I really remember is the 2012 AL wild card game, the first playoff game for the Orioles in more than a decade. Darvish, then an MLB rookie, started for the Rangers. And we beat him then, too. I just claimed to really remember that game, but if you asked me who won it for the Orioles? You could give me fifty guesses and I wouldn’t have come up with Joe Saunders.

I would have thought it was hard to beat every team, but in the balanced schedule / interleague schedule it’s gotten a lot easier. Of course Wikipedia has a page of everybody who’s done it. Our old friend Kevin Gausman has managed to beat all 30 teams despite having only 110 wins. Maybe even more impressive is Jameson Taillon (who I saw beat the Brewers a couple of weeks ago in my first-ever trip to Wrigley Field, a game I never got around to blogging about), who is 0-1 against the Dodgers in 4 tries, but who has beaten all 29 other teams with only 80 career wins!

Wikipedia is really an incredible triumph of human cooperation. Why does it work so well? How is it so unpolluted? How is it that when some very weird niche question like “which pitchers have beaten all 30 teams,” comes to my mind, some human being has already compiled this and put it there? I don’t know. But I’m glad it exists.

I don’t know why there are so many baseball posts right now. They’re faster to write than math posts. More math posts to come, I promise! (But there’s also one more Orioles post I want to write…)