Mrs. Q: CJ, Christa [the babysitter] said you asked a lot of “Why” questions today!

CJ: Why did I?

Me: Whoa, that’s meta.

CJ: Why is it meta?

I was writing down some mathematical notes and encountered a grammatical intuition that confused me.

- “X, which is the bound given in (1.2), and which is sharp” sounds fine;
- “X, which is the bound given in (1.2), and is sharp” sounds weird;
- “X, which is the bound given in (1.2), and sharp” sounds awful.

I understand why the last one sounds awful; the two verbs, one of which expresses an identity and one a quality, aren’t parallel, despite looking the same. (I guess you could say ‘It depends what the meaning of the word “is” is.’) But why does the second one sound funny? Or am I wrong, and the first two both sound funny? And why does Larkin’s roughly equivalent formulation sound fine?

Elizabeth Alexander’s decision to deliver the inaugural poem in “poetry reading voice,” with careful little pauses to indicate line breaks, was a bad mistake — after Obama’s smooth, long lines, she sounded like Rain Man, or a William Shatner impersonator, or Rain Man impersonating William Shatner. But I thought the poem itself, “Praise Song For The Day,” was great.

I’m not sure anyone else thought so. Monica praised the poem very faintly. Adam Kirsch called it “bureaucratic,” which he meant as an insult. But is it? Some things are made to happen by heroic leaders. But others, equally important, get done by thousands of people in separate rooms, none with a global view, each one carrying out a small task thoughtfully and by the book. Poetry isn’t a thing of the latter kind, but poetry has to recognize that there *are* such things, and that they matter. As must the President. Steve Burt made this point in verse.

Back to Kirsch,who labels the opening

Each day we go about our business

as cliche, fairly — but seems to miss that the following lines

walking past each other, catching each other’s

eyes or not, about to speak or speaking.All about us is noise. All about us is

noise and bramble, thorn and din

stroll around the different aspects of the word “about,” poking at it, so that the *words* of the first line, or at least the word “about,” retroactively re-activate inside their dead phrase.

Alexander’s not afraid to tweak Obama a bit:

A farmer considers the changing sky.

reminding us (and him!) that “change,” too, is a real word, not just a slogan, and it might mean you’re about to lose your crop. And then this, my favorite part:

Sing the names of the dead who brought us here,

who laid the train tracks, raised the bridges,picked the cotton and the lettuce, built

brick by brick the glittering edifices

they would then keep clean and work inside of.

“Picked the cotton and the lettuce” is a graceful way of getting both 19th century African slaves and contemporary migrant farmers from Latin America into a single, eight-syllable frame. You can’t help comparing it with Maya Angelou’s dreary ethnocatalogue: “THE BLACK, THE JEW, THE HINDOO, THE CROAT….” I won’t defend “brick by brick” — glittering edifices are steel and glass office towers, not brick buildings. But the permeation of the workers through the building walls (with an implicit generation shift — the fathers are construction workers, the children disperse through the class structure, some becoming janitors and others deskworkers) is deft as hell — and she caps it off with the weird scrambly rhyme of “edifices” and “inside of,” and a cheeky sentence-ending preposition which seems to talk back — but respectfully! — to the schoolteacher five stanzas previous. Just as she talked back to the new President when she brought up the changing sky.

A lot is getting done in the rooms of this poem, piece by piece and without flourishes. It’s bureaucratic in the best way.

A paper by Yuhan Zha, posted on the arXiv yesterday under the unassuming title “A height inequality,” claims to prove the ABC conjecture via a notion of “quasi-arithmetic differential,” some kind of Arakelov-theoretic gadget which apparently allows you to mimic complex differential geometry well enough to imitate the proof of the function field case. Zha was a Ph.D. student of Fulton and a Harvard postdoc, so this presumably merits serious consideration. Has anybody out there given this a real read yet?

The result of Yuri Bilu and Pierre Parent that I blogged about last summer has appeared in a new, modified version on the arXiv. The authors discovered a mistake in the earlier version — their theorem on rational points on X^split(p) is now conditional on GRH, while they get an unconditional version for points on X^split(p^2). The dependence on GRH (Proposition 5.2 in the new version) is via explicit Chebotarev bounds; under GRH one has that if E/Q is a non-CM elliptic curve whose mod-p Galois representation lands in the normalizer of a split Cartan, then p << log (N_E)^(1+eps). The idea is that when E is not CM, one can find a nonzero Fourier coefficient a_l with l at most (log N_E)^(2+eps), which is required to reduce to 0 mod p; this immediately implies the desired bound on p. In the old version, the unconditional weaker bound p << (height(j(E)))^2, due to Masser, Wustholtz, and Pellarin, was sufficient; in the present version, it’s this bound that gives you control of X^split(p^2)(Q).

That’s a proposal that appeared today on Citizen’s Briefing Book, the digg-style section of the Obama transition website where interested citizens can post, and vote on, suggestions for the new administration.

On first glance, this sounds good to me! Currently, the NSF has a successful graduate fellowship program, which each year awards a few dozen students full support for their Ph.D. study, along with a $30,000 annual stipend. These students are the very strongest math undergraduates in the country, and the large majority go to one of the top 5 programs.

What if, instead, the NSF gave ten times as many students a much smaller package? Say, enough to supplement a TA salary by $5,000 per year, and to offer one or two semesters of full support to be used during the dissertation year? That would make a big difference to a lot of students at state universities, who otherwise have limited time off from teaching.

The argument for using the money to fund a small number of full-tuition fellowships, I guess, is that budgets are limited even at Harvard and Princeton, and the NSF fellowships allow more students to train at top departments than otherwise would. From running graduate admissions at Princeton I know very well that many, many students who would succeed at Princeton get rejected in favor of even stronger applicants. But graduate admissions are limited by things besides money — primarily the time and attention of the faculty.

The justification for the huge stipend is even harder to imagine. It’s more than doubled since I was a grad student fellow in the mid-90s. If a student is deciding whether to go to grad school on financial grounds, $30K is the same as $15K — bubkes next to what a star math major can make in industry.

So what would happen if the NSF gave many small fellowships instead of a few big ones? The students at Harvard and Princeton would still be fully supported, maybe teaching one semester to get some classroom experience. Maybe some students who otherwise would have gone to Harvard and Princeton would go to Chicago or Columbia instead. And a *lot* of U.S. students at good places like Wisconsin would write better dissertations faster.

Of course, the effect would also include a big transfer of wealth from the top-5 math departments to my graduate students; so maybe my self-interest is showing here.

See also: I. Laba’s thoughtful post on Canada’s NSERC Discovery Grant program, and whether it should switch from it’s current “many small grants” model to a “few large grants” model like the current NSF Graduate Fellowship.

Wouldn’t it be good PR for the Henry Vilas Zoo to indicate on their website that **a huge awesome tiger lives there now? **I wouldn’t have known about it if my eye hadn’t fallen on a small sidebar in a discarded Wisconsin State Journal. But once I found out, I hustled CJ over there immediately. The new resident is a 9-year-old Amur tiger from Siberia (ancestrally, that is: this one’s actually from South Dakota.) What you immediately notice about the tiger — I mean, besides that it’s **huge and awesome**– is that it clearly likes padding around in the Wisconsin snow. Why doesn’t Vilas have more cold-weather animals? I’d be happy if I never spent another minute in the little house where the three giraffes spend all winter cooped up, glumly tugging hay out of the hay dispenser and every once in a while licking the walls for a change of pace. I’d assumed the two big ones were the parents of the little ones, but it turns out they’re three unrelated males, which is more depressing still — it’s like the world’s worst bachelor apartment, but even smellier.

CJ, I concede, loves the giraffes. But still — how about some caribou? Or some wolves? Wolves are **almost as awesome as tigers!**

Some things I learned while writing this post:

- Wall-licking in giraffes is apparently not uncommon in captive specimens, and is thought by some researchers to be cognate to OCD; the website attached to the book
*Stereotypic Animal Behavior*(G. Mason, ed.) has photos and videos of just about every popular zoo animal you can think of, compulsively freaking out. - The new Amur tiger isn’t the first; for years there was a breeding pair here. The three cubs were named Mendota, Monona, and Wingra; Mendota died during dental surgery in 2002 and the other two cubs moved to Utica. The father, Nicoli, died of old age in 2005, leaving the tiger enclosure empty. In early 2008, another female Amur, Mariette, was living in Vilas. Where she is now, and why she was never exhibited, I’m not sure; it might have had something to do wtih her sister, Tatiana, who escaped and killed a San Francisco zoogoer on Christmas 2007.
- Vilas has lions, giraffes, chimpanzees, and now a tiger, but is missing the other marquee zoo animal; an elephant. I figured out why. Three elephants have lived in Madison, and two of them were named Winkie. The first Winkie, in 1966, pulled a three-year-old girl into his enclosure and killed her. The replacement Winkie arrived later that year, and seriously injured zookeepers in 1977 and 1999. The next year, protests over Vilas’s substandard elephant housing got Winkie moved to an elephant sanctuary in Tennessee, where she killed one of her handlers in 2006.

Well? Why?

Osteria Papavero is a relatively new downtown Italian. Small friendly room, small reliable menu. A ladder with some vines slung over it gives the place a rustic feel, and at the moment there’s an agreeably modest Christmas tree in the corner. The other night, Mrs. Q and I started with ribolitta (not on the menu, but the place is quite accommodating to vegetarians who want more choices than the menu offers) and a plate of Italian cheeses, highlighted by Ubriaco — a spicy tongue-warming tannic kind of cheese, new to me, that spends most of its life drenched in wine, and tastes like it. Mrs. Q ordered tagliatini in black truffle sauce and I had a kind of elongated orrechiette whose name I forget, in a sausage and mushroom ragout. Both completely conventional and no less satisfying for that. You need places like this in town, places that do everything within tradition and with no mistakes. Ideally in a small friendly room. The French version of this is Sardine (except Sardine is in a big friendly room.) Oh, and Papavero isn’t very expensive; $60 for the two of us with coffee and dessert but no wine.

But I’m pretty sure you’re not eating there! Because it’s been mostly empty whenever we’ve gone.

Other remarks:

- A kind of trademark is fried bread in the breadbasket; salty and oily, it’s both delicious and the kind of thing you wouldn’t be shocked to be served at the state fair, which makes it a funny thing to be eating at a restaurant like this.
- The dessert was maybe the only challenging thing we ate: a very good chocolate tart which was interesting by virtue of not being very sweet.
- Our neighbor, a postdoc visiting from Italy, says Papavero is the only Italian restaurant in town that’s Italian.
- We brought a friend with celiac here once, and the chef was a perfect angel about preparing food that wouldn’t sicken her.

“Orphans” are things you meant to think about but which you’ve regretfully concluded are never going to rise to the top of the stack. Ideas you never finished having.

Blogging your orphans seems a good use of a math blog, or even a partial math blog like this one — at best, someone else will be able to tell you what’s interesting about your question, or even derive some interest from it themselves; and at worst, someone will be able to explain to you why your question is in fact *not* interesting, thus setting your mind at ease.

Anyway: the mention of Voronoi cells reminded me of a question that once vexed me about combinatorial geometry in R^2. The question actually arose from an article I wrote about Howard Rosenthal and Keith Poole, political scientists who use data from Congressional votes to map legislators onto low-dimensional Euclidean space. But their method doesn’t *really* specify points in R^n. When n = 1, for instance, what they get is not a set of 535 points on the real line, but an *ordering* of the 535 legislators along an axis representing liberalism at one end and conservatism at the other.

What’s really being recorded by the projection of Congress to R^2? I think it’s something like this — for each triple of legislators (x,y,z) you ask: is z to the left or the right of the ray that starts at x and proceeds towards y?

There are n! possible orderings of n points on the line. How many “orderings” are there of n points in the plane?

An algebraic combinatorist might phrase the question like this: Let M be a 3xn matrix with real entries, where the third column consists entirely of 1’s. Suppose every 3×3 minor of M is nonsingular. Then let f(M) be a function from the set of 3-tuples of distinct elements of [1..n] to the set {+1,-1}, where you assign to each 3-tuple (i,j,k) with i < j < k the sign of the determinant of the 3×3 matrix formed by rows i,j,k of M.

**Question:** As M ranges over 3xn matrices of the given form, how many different functions f(M) are there?

An obvious upper bound is 2^(n choose 3), but this is way too big. Note that if you replace “3” by “2”, the answer to the analogous question is n!.

As a geometer, I’d phrase the question in a different (but I think equivalent) way:

**Question:** Let X_n be the space of ordered n-tuples of points in R^2 such that no three points are collinear. How many components does X_n have?

Again, if you replace R^2 with R^1 and “no three points are collinear” with “no two points coincide,” you get n!.

Let a(n) be the answer to the questions above (which, if I am not confused, have the same answer.) Then a(3) = 2 and a(4) = 14, and I think maybe a(5) is 252 but I’m not really sure. Combinatorial geometers with a soft spot for orphans, tell me more!

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