Monthly Archives: March 2009

Eat this today — tacos al pastor pizza at Ian’s

While we’re on the subject of glorious culinary syncretism, I want to endorse in the strongest possible terms today’s special pizza at Ian’s:  a “tacos al pastor” pie with juicy chunks of marinated pork, fried onions, and pineapple over mozarella cheese and tomato-chipotle sauce.  It’s one of their finest achievements and I believe it’s today only.  Ian’s stays open until 3am, so there should be plenty of time to get down there if you’re out of state or something.

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Pastrami fried rice, or: is there Chinese food in Mountain Brook?

I still don’t know what the largest U.S. city without a Chinese restaurant is, but I know it’s bigger than I thought.   I posted an Ask Metafilter question, which yielded a great candidate:  Mountain Brook, AL, a toney bedroom suburb of Birmingham, with just over 20K residents and no Chinese restaurant, per Google and someone who lived there as recently as 2001.

Another inspired suggestion was the Chasidic enclave of Kiryat Joel, NY, whose 2009 population is probably close to 25,000.  Kiryat Joel is technically a village within the town of Monroe, so I’m not sure it should count.

The thing is, I’m actually kind of surprised there’s no Chinese restaurant in Kiryat Joel.  Every other Orthodox neighborhood I’ve been in has a glatt kosher Chinese place!  Admittedly, they’re usually really bad — but they’re also always really full.  I have fond memories of Mei Garden in Highland Park, NJ, a popular dinner spot after the Rutgers number theory seminar.  Really just one fond memory — the food in general was terrible, but the pastrami fried rice was majestic.  This is the kind of conceptual leap that eclipses its inspiration, like a cover version that makes the original song unnecessary.

Apparently Mei Garden isn’t the only place making pastrami fried rice, but they might have been the first.

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Two estimation questions

It\’s apparently customary, when being interviewed for a job in the consulting industry, to be asked to estimate various numerical quantities:  how many cars are rented each week in the United States?  What proportion of the total mass of American citizens is made up of males?  I think that in asking these questions the interviewer is testing your ability to carry out rapid approximate quantitative reasoning, or, alternatively, to make confident assertions about whose truth you\’re almost completely ignorant — both important skills in that line of work.

Anyway, here are two questions.  I know the answer to the first one, and will reveal it tomorrow.  Put your unreasonably confident answers in comments!

  1. What is the total number of living alumni (all degrees) of UW-Madison?
  2. What is the population of the largest U.S. city without a Chinese restaurant?

Update: (24 Mar)  Commenter QXW is in the lead on question 2, observing that the city of Rye, NY (pop. 14,955) has no Chinese restaurants per Google Maps.  Can it really be true?

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Blogging is good for math, or: Kakeya problems over finite fields

New paper on the arXiv by me, Richard Oberlin, and Terry Tao:  “Kakeya set and maximal conjectures for algebraic varieties over finite fields.” The paper got started in an interesting way.  I read about Dvir’s proof of the finite field Kakeya set conjecture on Terry’s blog.  To an algebraic geometer the proof is extremely striking — it uses so little algebraic geometry that one thinks (encouraged by one’s natural prejudices) “surely a little more algebraic geometry will lead to even better results!”  I had some back and forth with Terry in the comments on his post, then posted a little more about the problem on this blog, learning much more about the problem from the comments I received from Terry and others.

That got me, Terry, and Richard started thinking about whether the polynomial method could be used to get the Kakeya maximal conjecture over finite fields.  It’s something rather distant from the usual problems I work on (apart from my periodic and so far fruitless obsession with the cap set problem.)  The paper simply wouldn’t exist if it weren’t for blogging and the opportunities it provides for fast, informal idea-sharing between multiple mathematicians in different specialties and physical locations.

Terry has ably described the main thrust of the paper over at his place; the idea is that we use the “polynomial method” of Dvir, together with some methods from harmonic analysis, to prove the finite-field analogue of the Kakeya maximal conjecture — very imprecisely, this says that if f is a function on F_p^n with small norm and L is a set of lines such that f|l has large norm for every l in L, then L itself can’t cover too many different directions.  Of course, L can be big — a function which is big on a single hyperplane is big on tons of distinct lines.

As I said, Terry explained that part on his blog, so let me say a little something about the extension from functions on F_p^n to functions on an arbitrary variety over F_p.  There’s some content here even if you only care about functions on vector spaces!

For instance:  Dvir’s theorem says that a subset E of F_p^2 containing a line in every direction must have at least cp^2 points.  Essentially the same argument tells you that if E contains a conic with an asymptote in every direction, then again |E| > cp^2.  From the result in our paper, on the other hand, one can show easily that if E contains a conic with an asymptote along every horizontal line, then again |E| > cp^2.

Why is the last problem along the same lines as the first two?  In the second problems, we are asking E to contain a conic in every asymptotic direction; that is, E contains (the affine F_p-points of) a set of conics C whose union covers the F_p-points of the line at infinity.

But there’s nothing special about P^2 and the line at infinity; in fact, as our result shows, the same kind of theorem holds with P^2 replaced by an arbitrary variety X and the line at infinity with an arbitrary hypersurface W in X.  For instance, one might take X to be P^2 blown up at the point [1:0:0], and W the exceptional divisor; then a set of conics whose union covers the F_p-points of W is precisely a set C of conics in the affine plane such that every horizontal line is an an asymptote for some conic in C.

Major league honkbal

Once again, in dramatic fashion, the Dutch baseballers give the Dominican club the finger like it was a leaky dike.  After a tense pitchers duel, the Netherlands go into the bottom of the 11th down 1-0.  Rob de Jong doubles to lead it off.  Then clutch Eugene Kingsale comes through with an RBI single (eenhonkslag), scoring the baserunner (honkloper)  to tie the game.  Dancing off the bag, basestealing threat Eugene Kingsale draws the throw, which sails wide of DR first baseman (eerste honkman) Manny Aybar, at which point alert Eugene Kingsale scampers all the way to third (derde honk).  The next batter, Yurrendell de Caster, hits a sharp grounder that Aybar gloves but can’t keep — and exultant Eugene Kingsale cruises home to end the game.  The Dutch advance to round 2, the Dominicans go home.

For more fun-to-say honkbal terms, see here and here.

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Dance, dance, dance, dance, dance to sports radio

They were interviewing Billy Beane on the sports talk station this morning.  “What music are you listening to lately?” Dan Patrick asked him.  “A little Joy Division,” said Billy Beane.

I have a new favorite team in the AL West.  Until Ken Griffey, Jr. announces that “Debris Slide” is his new walk-up song, that is.

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Two wise men I know

Allen Kornblum, founder and publisher of Coffee House Press, interviewed on the future of the book industry. Eric Walstein, mentor to a generation of little kids in Maryland who liked math, tells the Washington Post we’re using calculators wrong.

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Newton…. for the ladies

Just read an interesting paper by Robin Valenza, an English professor at U Chicago:  “Fiction and the Factual, or, Why Were There no Female Mathematical Geniuses in Eighteenth-Century England?”  Two things I enjoyed learning from this paper:

  • There was a book called Sir Isaac Newton’s Philosophy Explain’d For the Use of the Ladies in Six Dialogues on Light and Colours. After its first mention, Valenza abbreviates the title winningly as Newton…For the Ladies.
  • A popular form of entertainment in eighteenth-century England was provided by traveling showmen with Leyden jars, who went from town to town giving electric shocks to people who paid for the privilege.  Here’s Elizabeth Carter, translator of Newton…For the Ladies, in a 1747 letter:

Was you ever electrified? We have an itinerant philosopher here, who knocks people down for the moderate consideration of sixpence, and men, women, and children are electrified out of their senses. This is at present the universal topic of discourse. The fine ladies forget their cards and scandal to talk of the effects of electricity. The squires flock out of the villages to bring themselves and their dogs to be electrified; and the very boys and girls in the streets break their teeth with long hard words in describing the wonders of ‘tricity. For fear, however, that the mere love of philosophy should not gain him a sufficient number of spectators, this High Dutch conjuror is likewise possessed of a curious puppet-show, where I suppose the whole system of electricity is exhibited by Punch, who I believe would explain it just as well as any body else, for all the philosophers seem marvelously perplexed on this subject.

Netherlands magic, feel it happen!

In this sad era you take good Orioles news wherever you can find it.  Today, the Netherlands national team shocked the mighty Dominicans 3-2 in the World Baseball Classic.  Longtime Oriole Sidney Ponson pitched four solid innings and, longtime Oriole Eugene Kingsale (well, he was on the team for five years, though he racked up only about a half-seasons’ worth of playing time in all) scored what turned out to be the deciding run, reaching on a dribble of a single, advancing on an error, and scoring on a wild pitch.  Not exactly Earl Weaver style, but if your lineup is such that a 33-year-old Eugene Kingsale is your leadoff man, you gotta think small-ball.  Nice to see these guys in the orange and black again, even if the orange is representing the the House of Oranje-Nassau and not the Maryland state bird.

By the way, Sidney Ponson had a respectable career but is far from the greatest Dutch ballplayer; that would be Bert Blyleven, born in Zeist, and now the pitching coach for the Dutch national team.

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19th century “algorithms”

Emmanuel observes in the comments to the last post that the use of “algorithm” in the Felix Klein lecture predates by a few decades the earliest OED cite for the modern sense of that word; but adds, correctly, that it’s not at all clear Klein has the modern sense in mind.

Fortunately, the Cornell collection is fully searchable, and sortable by date!  So one instantly finds that the earliest mention of “algorithm” among the digitized monographs is from J.R. Young’s 1843 text “Theory and solution of algebraical equations of the higher orders”:

in what is clearly its contemporary usage.  No scare quotes, either.  What’s more, only a handful of texts in the Cornell collection predate this one; so this use of “algorithm” could well be a lot older.

I’ve written the OED, as Emmanuel suggested.  Let’s remember to check back in twenty years and see if the entry is changed!

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