Ranking mathematicians

I’m on the hiring committee, I chair the graduate admissions committee, and I’m doing an NSF panel, so basically I’ll be spending much of this month judging and ranking people’s mathematics.  There’s a lot I like about these jobs:  it’s a very efficient way to get a panorama of what’s going on in math and what people think about it.  The actual ranking part I don’t like that much — especially because the nature of hiring, admissions, and grant-making means you’re inevitably putting tons of very worthwhile stuff below the line.  I feel like a researcher when I read the proposals, like a bureaucrat when I put scores on them.

But of course the bureaucratic work needs to be done.  I’d go so far as to say — if mathematicians aren’t willing to rank each other, others will rank us, and that would be worse.

Tagged , , ,

Booklist 2013

This is not a typo — I was going to post about the books I read in 2015 but realized I’ve fallen out of the habit, and haven’t actually done a roundup since 2012! Here are the books of 2013:


  • 31 Dec 2013:  The Yacoubian Building, Alaa Al Aswany.
  • 17 Dec 2013: The Custom of the Country, Edith Wharton.
  • 29 Nov 2013:  Infinitesimal, Amir Alexander.
  • 19 Nov 2013:  The Simpsons and Their Mathematical Secrets, Simon Singh.
  • 2 Nov 2013:  The Panic Virus, Seth Mnookin.
  • 29 Oct 2013:  Taipei, Tao Lin.
  • 22 Oct 2013:  The Twelve, Justin Cronin.
  • 7 Oct 2013:  Fads and Fallacies in the Name of Science, Martin Gardner.
  • 15 Sep 2013:  The More You Ignore Me, Travis Nichols.
  • 11 Sep 2013:  Undiluted Hocus-Pocus:  The Autobiography of Martin Gardner.
  • 1 Sep 2013:  JoylandStephen King.
  • 27 Aug 2013:  The Ninjas, Jane Yeh.
  • 20 Aug 2013:  Time of the Great Freeze, Robert Silverberg.
  • 11 Aug 2013:  The Buddha in the Attic, Julie Otsuka.
  • 29 Jul 2013:  Lexicon, Max Barry.
  • 20 Jul 2013: Forty-One False Starts, Janet Malcolm.
  • 12 Jul 2013: Thinking in Numbers, Daniel Tammet.
  • 10 Jul 2013:  Boundaries, T.M. Wright.
  • 26 Jun 2013:  Let’s Talk About Love:  A Journey to the End of Taste, by Carl Wilson.
  • 15 Jun 2013:  Goslings, J.D. Beresford.
  • 1 Jun 2013:  You, Austin Grossman.
  • 25 May 2013:  The Night Land, William Hope Hodgson.
  • 10 May 2013:  20th Anniversary Report of the Harvard-Radcliffe Class of 1993
  • 5 May 2013:  The Vanishers, Heidi Julavits.
  • 17 Apr 2013:  Belmont, Stephen Burt.
  • 10 Apr 2013:  Among Others, Jo Walton.
  • 2 Apr 2013:  Math on Trial, by Leila Schneps and Coralie Colmez
  • 25 Mar 2013:  The Fun Parts, Sam Lipsyte.
  • 14 Mar 2013:  Mathematical Apocrypha, Steven Krantz.
  • 7 Mar 2013:  The Magic Circle, Jenny Davidson.
  • 2 Mar 2013: SnowAdam Roberts.
  • 24 Feb 2013:  A Hologram for the King, Dave Eggers.
  • 9 Feb 2013:  The Wind Through the Keyhole, Stephen King.
  • 8 Feb 2013:  The Life and Opinions of a College Class, the Harvard Class of 1926.
  • 15 Jan 2013:  When the Tripods Came, John Christopher.


34 books.  21 fiction, 11 non-fiction, 2 books of poetry (note to self:  at some point read a book of poems by a poet I don’t personally know.)  Of the novels, 8 were SF/fantasy.

Best of the year:  Impossible to choose between The Custom of the Country and Forty-One False Starts.  

Wharton often writes about the drive to acquire money and status, which she presents not as a means to meet other basic human needs (food, security, companionship) but as a basic need in itself, and pretty near the base of the pyramid.  Sometimes the particular situation is a little dated (as in the concern with divorce in Age of Innocence) but Custom of the Country, which is about a New York deformed by a sudden influx of new, uncivilized wealth absorbing everything around it, couldn’t be more topical.

Janet Malcolm is of course the best essayist alive.  Forty-One False Starts is a collection of pieces, mostly from the New Yorker I think, mostly new to me.  The title track is amazing:  just as it says, it’s 41 possible openings to an essay, each one abandoned as Malcolm tries to start again.  (Or maybe as Malcolm pretends to start again; was the collage her plan all along?  That would certainly make them “false starts” in the literal sense of the words.)  The same anecdotes appear in multiple sections, from multiple points of view, or rather, from the same point of view, Malcolm’s, which always seems to be viewing from everywhere at once.  Here’s the first paragraph from false start 3 (which is just two paragraphs long):

All during my encounter with the artist David Salle—he and I met for interviews in his studio, on White Street, over a period of two years—I was acutely conscious of his money. Even when I got to know him and like him, I couldn’t dispel the disapproving, lefty, puritanical feeling that would somehow be triggered each time we met, whether it was by the sight of the assistant sitting at a sort of hair-salon receptionist’s station outside the studio door; or by the expensive furniture of a fifties corporate style in the upstairs loft, where he lives; or by the mineral water he would bring out during our talks and pour into white paper cups, which promptly lost their takeout-counter humbleness and assumed the hauteur of the objects in the Design Collection of the Museum of Modern Art.

“assumed the hauteur”  I love.  The capitals of Design Collection and Museum of Modern Art I love.  And there’s the presence of money in New York and the anxiety it stirs into the world of for-lack-of-a-better-word “culture”, just as in Wharton.  And Wharton is in Forty-One False Starts, too, in Malcolm’s essay “The Woman Who Hated Women”.  In fact, I’m pretty sure it was that essay that spurred me to start reading Wharton again, which I’ve been doing on and off ever since.  Malcolm writes:

There are no bad men in Wharton’s fiction. There are weak men and there are foolish men and there are vulgar New Rich men, but no man ever deliberately causes harm to another person; that role is exclusively reserved for women.

As for The Custom of the Country:

With Undine Spragg, the antiheroine of ”The Custom of the Country” (1913), Wharton takes her cold dislike of women to a height of venomousness previously unknown in American letters, and probably never surpassed. Undine’s face is lovely, but her soul is as dingy as Gerty Farish’s flat. Ralph Marvell, one of her unfortunate husbands, reflects on “the bareness of the small half-lit place in which his wife’s spirit fluttered.”

I hate to disagree with Janet Malcolm.  But I disagree!  Back in 2013 I had a very well-worked out theory of this book, in which Undine Spragg was not particularly a villain, but rather the character who was best able to adapt to the new customs and the new country.  The men are weak, as Malcolm says, but indulgence of weakness can be a way of deliberately causing harm.  For every one of Undine’s “can’t believe she did/said that” moments in the book, there’s an analogous crime committed by one of the other characters, but expressed with more gentility.  Anyway, I’ve forgotten all my examples.  But it was a good theory, I promise!  I will admit that, having now read Ethan Frome, I can’t deny that there’s some extent to which Wharton experiences femaleness as a kind of horror.  But I don’t think that’s what’s going on with Undine Spragg.  (I also disagree with Roxane Gay about May Welland, who I totally think is meant by Wharton to be sympathizable-with but not likable compared with Countess Oleska, whose side I think Age of Innocence 100% takes, if it takes anyone’s.  Maybe more on this in the 2015 post.)

Others I should have blogged about:  I read Taipei because I was curious about Tao Lin, who some people think is a prankster masquerading as a fiction writer and other people think is really a fiction writer.  It’s the latter.  I mean, look at this map:


He’s clearly somebody who sees himself in the tradition of experimental English-language fiction (Grace Paley!  Barthelme!  Stephen Dixon!  James freaking Purdy!) and I thought Taipei reflected that.  It was way more Barthelme than it was weird Twitter.  I had a good worked-out theory for this one, too, which I also forgot to blog.  Negative space:  it was a novel about a poet who is never seen writing or reading or performing poetry; i.e. a novel which places the experience of not-producing-poetry at the center of the poetic project.  Also there was something about the emphasis on Apple products and the relationship with China, where they’re produced — i.e. the novel is intently focused on use of Apple products while hiding the production of Apple projects, just as it’s intently focused on poetry while hiding the production of poetry.  But I was more into this interpretation before the novel actually goes to Taipei.  (And yes I know Taipei is not in the PRC; I felt willing to fudge the geography.)

Fads and Fallacies in the Name of Science:  from 1956, but, like Custom of the Country, almost painfully topical.  People don’t believe in orgone therapy anymore but the anti-scientific style in American culture is as healthy as ever.  Let’s Talk About Love:  the best book in existence about the problem of the “guilty pleasure,” or of art being “so bad it’s good,” or the basic difficulty of criticism of living culture:  is the critic’s job to tell you what to like and why to like it, or to understand why the people who like it like it?   (“Neither” is an OK answer here but let’s face it, these are the two leading candidates, unless “dispassionately analyze the class position of the work and the material circumstances of its production” still counts.)

Kou Shui Ji at ZenZen Taste

New, very good Chinese place out by West Towne:  ZenZen Taste, featuring what Steph Tai calls “contemporary Chinese” food, neither traditional nor Americanized.

I have had Szechuan peppercorn before but never so much Szechuan peppercorn as in their kou shui ji (literally “saliva chicken,” here rendered “mouth-watering chicken.”)  It is hard to describe in words what this actually does to your mouth.  To an extent you feel you have chewed a lemon.  At the same time your lips buzz as if you’ve eaten something spicy-hot and salty.  When you drink water, the water tastes sour and fizzy.  How much kou shui ji did I eat?  I ate two bites of kou shui ji.  I was defeated by the kou shui ji.

Tagged , , , ,

My Erdos-Bacon-Sabbath number is 11

I am pleased to report that I have an Erdös-Bacon-Sabbath number.

My Erdös number is 3; has been for a while, probably always will be.  I wrote a paper with Mike Bennett and Nathan Ng about solutions to A^4 + B^2 = C^p; Mike wrote with Florian Luca; Luca wrote with Erdös.

A while back, I shot a scene for the movie Gifted.  I’m not on the IMDB page yet, but I play against type as “Professor.”  Also in this movie is Octavia Spencer, who was in Beauty Shop (2005) with Kevin Bacon.  So my Bacon number is 2.

That gives me an Erdös-Bacon number of 5; already pretty high on the leaderboard!

Of course it then fell to me to figure out whether I have a Sabbath number.  Here’s the best chain I could make.

I once played guitar on “What Goes On” with my friend Jay Michaelson‘s band, The Swains, at Brownies.

Jay performed with Ezra Lipp “sometime in 2000,” he reports.

Lipp has played with Chris Robinson of the Black Crowes.

From here we use the Six Degrees of Black Sabbath tool, written by Paul Lamere at EchoNest (now part of the Spotify empire.)

The Black Crowes backed up Jimmy Page at a concert in 1999.

Page played with David Coverdale in Coverdale.Page.

David Coverdale was in Deep Purple with Glenn Hughes of Black Sabbath.

So my Sabbath number is 6, and my Erdos-Bacon-Sabbath number is 11.







Tagged , , , ,

i, you sneaky bastard

Childhood memory:  I learned that i is formally defined to be the square root of -1.  Well, I thought, that worked well, what about the square root of i?  Surely that must be yet a new kind of number.  I just had to check that (a+bi)^2 can never be i.  But whoa, you can solve that!  (sqrt(2)/2) + (sqrt(2)/2)i does the trick.  I was kind of bowled over by this.  i, you sneaky bastard — you anticipated my next move and got ahead of me!  I had no idea what “algebraically closed” meant, or anything like that.  But it was one of my first experience of the incredible power of the right definition.  Once the definition is right, you can just do everything.


Obscure novels that are great

I was thinking about the amazing and barely read here TRIOMF, by Marlene van Niekerk, and asked on Twitter:  what are novels you think are truly great and which nobody knows about?  Like, say, less than 10 Amazon reviews, to use an imperfect measure?

Tagged , ,

Imagine 33 percent

This, from the New York Times Book Review, bugged me:

There are 33 percent more such women in their 20s than men. To help us see what a big difference 33 percent is, Birger invites us to imagine a late-night dorm room hangout that’s drawing to an end, and everyone wants to hook up. “Now imagine,” he writes, that in this dorm room, “there are three women and two men.”

It’s not so bad that the reviewer was confused about percentages; it’s that she went out of her way to explain what the percentage meant, and said something totally wrong.

I figured the mistake was probably inherited from the book under review, so I checked on Google Books, and nope; the book uses the example, but correctly, as an example of how to visualize a population with 50% more women than men!

Tagged ,

Lipnowski-Tsimerman: How large is A_g(F_p)?

Mike Lipnowski and Jacob Tsimerman have an awesome new preprint up, which dares to ask:  how many principally polarized abelian varieties are there over a finite field?

Well, you say, those are just the rational points of A_g, which has dimension g choose 2, so there should be about p^{(1/2)g^2} points, right?  But if you think a bit more about why you think that, you realize you’re implicitly imagining the cohomology groups in the middle making a negligible contribution to the Grothendieck-Lefchetz trace formula.  But why do you imagine that?  Those Betti numbers in the middle are huge, or at least have a right to be. (The Euler characteristic of A_g is known, and grows superexponentially in dim A_g, so you know at least one Betti number is big, at any rate.)

Well, so I always thought the size of A_g(F_q) really would be around p^{(1/2) g^2}, but that maybe humans couldn’t prove this yet.  But no!  Lipnowski and Tsimerman show there are massively many principally polarized abelian varieties; at least exp(g^2 log g).  This suggests (but doesn’t prove) that there is not a ton of cancellation in the Frobenius eigenvalues.  Which puts a little pressure, I think, on the heuristics about M_g in Achter-Erman-Kedlaya-Wood-Zureick-Brown.

What’s even more interesting is why there are so many principally polarized abelian varieties.  It’s because there are so many principal polarizations!  The number of isomorphism classes of abelian varieties, full stop, they show, is on order exp(g^2).  It’s only once you take the polarizations into account that you get the faster-than-expected-by-me growth.

What’s more, some abelian varieties have more principal polarizations than others.  The reducible ones have a lot.  And that means they dominate the count, especially the ones with a lot of multiplicity in the isogeny factors.  Now get this:  for 99% of all primes, it is the case that, for sufficiently large g:  99% of all points on A_g(F_p) correspond to abelian varieties which are 99% made up of copies of a single elliptic curve!

That is messed up.


Tagged , , , , ,

Leibniz on music

Leibniz wrote:

Even the pleasures of sense are reducible to intellectual pleasures, known confusedly.  Music charms us, although its beauty consists only in the agreement of numbers and in the counting, which we do not perceive but which the soul nevertheless continues to carry out, of the beats or vibrations of sounding bodies which coincide at certain intervals.

Boy, do I disagree.  Different pleasures are different.

Tagged ,

Bobrowski-Kahle-Skraba on the null hypothesis in persistent homology

I really like persistent homology; it’s a very beautiful idea, a way to look for structure in data when you really don’t have any principled way to embed it in Euclidean space (or, even when it does come embedded in Euclidean space, to find the kind of structure that doesn’t depend too much on the embedding.)

But because I like it, I want to see it done well, so I have some minor complaints!

Complaint one:  Persistent homology, applied to H_0 only, is clustering, and we know a lot about clustering already.  (Update:  As commenters point out, this is really only so for persistent homology computed on the Vietoris-Rips complex of a point cloud, the “classical case…”!)  Not to say that the ideas of persistence can’t be useful here at all (I have some ideas about directed graphs I want to eventually work out) but my sense is that people are not craving new clustering algorithms.  I really like the work that tries to grapple with the topology of the data in its fullness; I was really charmed, for instance, by Ezra Miller’s piece about the persistent homology of fruit fly wings.  (There’s a lot of nice stuff about geometric probability theory, too — e.g., how do you take the “average” of a bunch of graded modules for k[x,y], which you may think of as noisy measurements of some true module you want to estimate?)

My second complaint is the lack of understanding of the null hypothesis.  You have some point cloud, you make a barcode, you see some bars that look long, you say they’re features — but why are you so sure?  How long would bars be under the null hypothesis that the data has no topological structure at all?  You kind of have to know this in order to do good inference.  Laura Balzano and I did a little numerical investigation of this years ago but now Omer Bobrowski, Matthew Kahle, and Primoz Skraba have proved a theorem!  (Kahle’s cool work in probabilistic topology has appeared several times before on Quomodocumque…)

They show that if you sample points from a uniform Poisson process on the unit cube of intensity n (i.e. you expect n points) the longest bar in the H_k barcode has

(death radius / birth radius) ~ [(log n)/(log log n)]^(1/k).

That is really short!  And it makes me feel like there actually is something going on, when you see a long barcode in practice.

Tagged , , , ,
%d bloggers like this: