Complete show on YouTube. In case you were wondering what the fuss was about.

Complete show on YouTube. In case you were wondering what the fuss was about.

One interesting feature of the heuristics of Garton, Park, Poonen, Wood, Voight, discussed here previously: they predict there are fewer elliptic curves of rank 3 than there are of rank 2. Is this what we believe? On one hand, you might believe that having three independent points should be “harder” than having only two. But there’s the parity issue. All right-thinking people believe that there are equally many rank 0 and rank 1 elliptic curves, because 100% of curves with even parity have rank 0, and 100% of curves with odd parity have rank 1. If a curve has even parity, all that has to happen to force it to have rank 2 is to have a non-torsion point. And if a curve has odd parity, all that has to happen to force it to have rank 3 is to have one more non-torsion point you don’t know about it. So in that sense, it seems “equally hard” to have rank 2 or rank 3, given that parity should be even half the time and odd half the time.

So my intuition about this question is very weak. What’s yours? Should rank 3 be less common than rank 2? The same? *More* common?

For some reason I was thinking about pieces of culture that have departed from the world but which somehow didn’t “stick” well enough to persist even in the sphere of nostalgia. Like when people think about the early 1990s, the years when I was in college, they might well say “oh yeah, grunge” or “oh yeah, wearing used gas station T-shirts with a name stitched on” or “oh yeah, *Twin Peaks*” or “oh yeah, OK Soda” or whatever.

But no one says “oh yeah, Fido Dido.” So here I am doing it.

It is inherently hard to try to list things you’ve forgotten about. My list right now consists of

- Fido Dido
- Saying “bite me”
- Smartfood
- Devil sticks (from Jason Starr)

That’s it. What have you got?

It reminds me of Martin Amis’s *The Information*, in that it is a really well-made thing, but one which I think probably *shouldn’t* have been made, and which I’m probably sorry I read, because it’s sick in its heart.

Everything else I can say is a spoiler so I’ll put it below a tab.

**Important update, 23 Jul:** I missed one very important thing about Bjorn’s talk: it was about joint work with a bunch of other people, including one of my own former Ph.D. students, whom I left out of the original post! Serious apologies. I have modified the post to include everyone and make it clear that Bjorn was talking about a multiperson project. There are also some inaccuracies in my second-hand description of the mathematics, which I will probably deal with by writing a new post later rather than fixing this one.

I was only able to get to two days of the arithmetic statistics workshop in Montreal, but it was really enjoyable! And a pleasure to see that so many strong students are interested in working on this family of problems.

I arrived to late to hear Bjorn Poonen’s talk, where he made kind of a splash talking about joint work by Derek Garton, Jennifer Park, John Voight, Melanie Matchett Wood, and himself, offering some heuristic evidence that the Mordell-Weil ranks of elliptic curves over Q are bounded above. I remember Andrew Granville suggesting eight or nine years ago that this might be the case. At the time, it was an idea so far from conventional wisdom that it came across as a bit cheeky! (Or maybe that’s just because Andrew often comes across as a bit cheeky…)

Why did we think there were elliptic curves of arbitrarily large rank over Q? I suppose because we knew of no reason there shouldn’t be. Is that a good reason? It might be instructive to compare with the question of bounds for rational points on genus 2 curves. We know by Faltings that |X(Q)| is finite for any genus 2 curve X, just as we know by Mordell-Weil that the rank of E(Q) is finite for any elliptic curve E. But is there some absolute upper bound for |X(Q)|? When I was in grad school, Lucia Caporaso, Joe Harris, and Barry Mazur proved a remarkable theorem: that if Lang’s conjecture were true, there was some constant B such that |X(Q)| was at most B for every genus 2 curve X. (And the same for any value of 2…)

Did this make people feel like |X(Q)| was uniformly bounded? No! That was considered ridiculous! The Caporaso-Harris-Mazur theorem was thought of as *evidence against Lang’s conjecture.* The three authors went around Harvard telling all the grad students about the theorem, saying — you guys are smart, go construct sequences of genus 2 curves with growing numbers of points, and boom, you’ve disproved Lang’s conjecture!

But none of us could.

They showed it during TEDxMadison. Here’s what struck me. She talked a lot about art, a lot about selflessness, a lot about performance. Many forceful moments. But there was only one point at the talk where the audience stopped her with a wave of applause, and that was when she put up a slide referring to a large sum of money.

I gave a TED talk! OK, not exactly — I gave a TEDx talk, which is the locally organized, non-branded version, but same idea. 18 minutes or less, somewhat sloganistic, a flavor of self-improvement and inspiration.

I was skeptical of the format. 18 minutes! How can you do anything? You can really just say one thing. No opportunity to digress. Since digression is my usual organizational strategy, this was a challenge.

And there’s a format. The organizers explained it to me. Not to be hewed to exactly but taken very seriously. A personal vignette, to show you’re a human. A one-sentence takeaway. General positivity. A visual prop is good. The organizers were lovely and gave me lots of good advice when I practiced the talk for them. I was very motivated to deliver it the way they wanted it.

And in the end, I found the restrictiveness of the format to be really useful. It’s like a sonnet. Sonnets are, in certain ways, all the same, by force; and yet there’s a wild diversity of sonnets. So too for TED talks. No two of the talks at TEDxMadison were really the same. And none of them was really like Steve’s TED talk (though I did read a poem like Steve) or Amanda Palmer’s TED talk or (thank goodness) like the moleeds TED talk.

No room in the talk to play the Housemartins song “Sitting on a Fence,” which plays a key role in the longer version of the argument in *How Not To Be Wrong. *So here it is now.

Review up at the Boston Globe:

If the feel of sand between your toes gets you thinking about Zeno’s Paradox or Pascal’s Wager, Ellenberg’s book is ideal beach reading. But even if your interests lie elsewhere, you may find it a challenging but welcome companion.

at NewCity Lit:

To the mathematician, math is a curious process of assumption and provocation. “How Not To Be Wrong” is part exposé—concepts most of us are never privy to are explained along with obvious surprises we just need to hear over again.

at Nature:

Ellenberg, an academic and

Slate‘s ‘Do the Math’ columnist, explains key principles with erudite gusto

and at Canada’s The Globe and Mail.

For audio fans, here’s an interview at the New Books podcast.

But actually, most of the publicity this week came from the WSJ “Hawking Index” article, which got covered all over the place. I like this Washington Post followup, which applies the methodology (such as it is!) to political memoirs. More good coverage from the National Post, featuring obligatory CanLit content. And here’s how it looks in Indonesian.

Christopher D. Long decided to see what happened if you tried to model “quotability” using a more serious dataset, scraped from Goodreads, instead of just screwing around like I did. His top 10 included some expected entries and some surprises. Any ranking where Eleanor Roosevelt and Groucho Marx place first and second is obviously doing something right.

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