Category Archives: travel

I will gladly pay you Tuesday for a smørrebrød today

Back from this very interesting conference on homological stability at the University of Copenhagen.  First time in Denmark.

Two things that struck me — or rather, in a sense, one thing that struck me twice — a kind of relaxedness about money.  I wanted to rent a bike to see the city a bit on the conference half-day, but ended up only having an hour or so free.  I found a bike shop that offered daily bike rentals and asked if they rented by the hour; the proprietor said, don’t worry about it, just leave your driver’s license here and take the bike and we won’t charge you.

The next day, I stopped at the smørrebrød shop to get my morning smørrebrød, but was out of Danish cash, and found that my PIN-less US credit card was no good there.  And again, I got “don’t worry about it” — just take your smørrebrød now, said the smørrebrød-maker, and come back and pay me tomorrow.  Which is what I did.

Unthinkable behavior for a shop in the United States, or am I wrong?

Re bikes and smørrebrød:

  • Copenhagen is the only place I’ve ever seen where the dream of bikes as an equal part of traffic seems to be a reality.  It’s a true pleasure.  Also, my stereotype that Europeans don’t wear helmets isn’t quite right; I’d say about a quarter of the riders were helmeted, including lots of young, hip-looking people.
  • Smørrebrød!   They are little open-faced sandwiches on which you can put almost anything.  I got them for breakfast every morning and ate them as I walked to the university, even though I think eating smørrebrød at 8am and eating while walking in general are somewhat non-Danish things to do.  They served raw beef smørrebrød at the conference reception but for breakfast I didn’t go so wild; my favorite was the frikadeller, a meatball with a kind of creamy dill sauce on it.  There is a very enthusiastic smørrebrød blog  where you can learn more.  Also, Copenhagen’s most famous smørrebrød house now has an outpost in New York.

Update:  Hey, I should at least give the generous Danish shopkeepers credit by name!  The excellent smørrebrød I ate every morning were from Madmanden on Classensgade.  And the folks who let me borrow their bike free were at Cykelsmeden on Nørregade.

Via NPR, some smørrebrød:

F*** yeah belly lox

At the very end of yesterday’s NYC trip I was in midtown with an hour before I had to leave for the airport, so I did what anyone would do — took the 1 up to 79th street and dashed into Zabar’s to get a half-pound of belly lox in an insulated bag with an ice pack.

Belly lox is not the lox you get on a bagel at the bagel store, no way.  It’s not smoked, but salt-cured, from the fattiest part of the salmon.  It is salty, very salty.  It presents a resistance to the teeth, then snaps, then melts like butter in your mouth.  It’s something like a very briny top-quality sushi invented by Jews and sliced very thin.  Of all the things people claim they only do right in New York (pastrami, bagels, pizza, etc.) belly lox is the one they actually only do right — hell, as far as I know, only do at all — in New York.

You could have this on a bagel, but should you really dilute the majesty of belly lox with that much bread?  On the other hand, it’s too intense to eat more than a few bites of it plain.  Here’s the way I’m eating it — on an Ak-Mak cracker with a little cream cheese.  Holy hell, this is amazing.



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Dinner theater at EL Ideas

I was just in Chicago for a conference, and, having always meant to go to a highly touted experimental restaurant in the Chicago style, made a reservation — sorry, I mean “got tickets” — for EL Ideas.

To get this out of the way first — yes, the food was good.  Very, very good.  But I don’t actually want to talk about the food!  Lots of restaurants have good food.  What’s really interesting about EL Ideas is the way it merges the idea of “restaurant” with the idea of “theater.”

There’s no menu — each of the 24 diners eats the same thing at the same time, so that, as in a play, everyone in the room is having the same experience.  Before the meal begins, the chef/impresario/director/producer pops out from the kitchen to tell you that this isn’t going to be the usual stuffy expensive restaurant deal — he wants you to wander into the kitchen and ask what’s going on, he wants you to really get into it.  He warns that you should summon an Uber car rather than trying to walk home through the somewhat desolate neighborhood because if you did the latter “you might die.”  In other words:  we are the ones hip enough to be in this neighborhood, to feel a  little frisson of danger, though nothing you can’t dispel with an app!  (In fact, I cannot say the crowd looked notably hip — my dinner companions were younger than me, but most other people looked old and rich, one more thing EL Ideas has in common with the theater.)

Before each dish is presented, the chef gives a little introduction, during which you are supposed to be quiet — if you talk while the he’s talking, the chef warns, you might get thrown out.  Just like the theater.

You don’t exactly get a reservation here; you purchase the meal in advance, as with a ticket to a show.

And at the end everyone claps!

When I was younger, I used to go to plays a lot.  OK, not a lot.  But I probably saw three to five plays a year, and even then I think most people I knew weren’t going.  Now I never go to plays; for all I know, I may never see a play again.

But EL Ideas makes me think that there are things people want from plays, and these are things that people who never go to plays sense, consciously or not, that they still want, and so something wonderful happens — the theater, seemingly made extinct by other, nimbler forms of entertainment, spores out into the atmosphere and embeds itself in another cultural host.







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Let us now praise American Airlines

Did you ever wonder what would happen if your son left the carry-on suitcase he was pulling at the bottom of the jetway before getting on the plane, because that’s what we always do in Madison, but there wasn’t actually a gate-check tag on it?

It turns out that, at least if you do this in Tucson on American, and if you have a luggage tag with your name on it, they’ll cross-reference the name against their passenger record and correctly check the bag through to your final destination.





Brewers report

CJ and I took in a couple of Brewers games last weekend, both victories over the Pirates.  Perhaps the greatest pleasure was seeing Carlos Gomez do something that’s only been done a few dozen times in baseball history; after walking to lead off the bottom of the third, he stole second, then, with the pitcher up, stole third.  And then he broke for home.  A.J. Burnett uncorked a panic pitch that got away from Pittsburgh’s catcher and Gomez scored without a play.  He had stolen his way around the entire basepath!

Except he hadn’t.  Ordinarily, you’re credited with a steal of home if you’re off before the pitch; but official scorer Tim O’Driscoll ruled that the Brewers had been attempting a suicide squeeze, which means the play is scored as a wild pitch, not a stolen base.

Still, I know what I saw; an exhibition of brazenly aggressive baserunning, the likes of which I have not seen since college, when Tom Scocca used to run on me that way in Atari baseball, because it was really hard to make accurate throws in that game, and because all mercy and human feeling drained out of Scocca when he played Atari baseball.

More Brewers impressions:

  • About 60% of jerseys at a Brewers game are Ryan Braun jerseys.  Judging from the cheers he got, I’m pretty sure nobody in Milwaukee cares whether Braun used or is using PEDs.
  • The scoreboard at Miller Park displays OPS!  Very forward-looking.  On the other hand, there’s no out-of-town scoreboard on the outfield wall, which to me seems an unforgivable omission.
  • Once a year or so I think “hey, burger and brat on the same bun, that sounds like a pretty great sandwich,” and I order one.  Burger and brat on the same bun is not actually a great sandwich, but merely a meaty confusion.
  • American Science and Surplus is only about 10 minutes from Miller Park and is one of the most amazing stores I’ve ever seen.  You can buy typewriters there, or teflon hexagons in bulk, or sunglasses with hidden mirrors in the lenses so you can see behind you, or full-color posters depicting all the kinds of ulcers.  You can buy a 5-foot-long whisk for only 18 bucks.  Why didn’t I?
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Tufts made me a nice poster

I just had the extremely enjoyable experience of giving the Norbert Wiener lectures at Tufts.  I’m not sure my talks lived up to the awesomeness of this poster:


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Four Tucson notes

  • As far as I can tell, Cafe Poca Cosa is still the best restaurant in the city.
  • Front page news during our stay:  the state has outlawed the Tucson school system’s Mexican American Studies program.
  • Downtown Tucson is an interesting case study for people interested in urban cores.  Grand old theaters, lots of vacant buildings, Cafe Poca Cosa, and strangely specific yet apparently operational businesses (Ace Rubber Stamps, Wig-O-Rama.)  Almost nobody on the street at 5pm on a Wednesday.  On the other hand, no sense of blight.  Is Tucson considered a successful downtown renewal, a failed one, or something in between?
  • The only Republican campaign signs I saw in Tucson were for Ron Paul, and there were quite a few of them.  Remark:  this is also true of Madison.
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Music Hack Day

Andrew Bridy, Lalit Jain, Ben Recht and I spent the weekend in Cambridge at Music Hack Day, organized by the Echo Nest and sponsored by just about every company you can think of that cares about both music and technology.  We hacked in a somewhat different spirit than most of the folks there; for us, the Million Song Dataset isn’t a tool for app-building, but a playground where we can test ideas about massive networks and information retrieval.

(Re app-building:  Bohemian Rhapsicord.  Chrome-only.)

We’ve actually been playing with the MSD for a few weeks, and I’ll probably post some of those results later, but let’s start with what we did this weekend.  We wanted to see what aspects of the rules of melody we could find in the dataset.  Which notes like to follow which other notes?  Which chords like to follow which other chords?  If you took piano lessons as a kid you already know the answers to these questions.  Which is kind of the point!  When you start to dig into a giant dataset, the first thing you’d better do is check that it can tell you the things you already know.

We quickly found out that getting a handle on the melodies wasn’t so easy.  The song files in the MSD aren’t transcribed from scores, and they don’t have notes:  there’s pitch data, but it’s in the form of chromata; these keep good track of how the energy of a song segment is distributed across frequency bands, but they don’t necessarily correspond well to notes.  (For instance, what does the chroma of a drum hit sound like?)  We found that only about 2% of the songs in the sample had chromata that were “clean” enough to let us infer notes.

But here’s the good thing about a million — 2% of a million is still a lot!  Actually, to save time, we only analyzed about 100,000 songs — but that still gave us a couple of thousand songs’ worth of chroma to work with.  We threw out all the songs Echo Nest thought were in minor keys, and transposed everything to C.  Then we put all the bigrams, or pairs of successive notes, in a big bag, and computed the frequency of each one in the sample.  And this is what we saw:

Pretty nice, right?  The size of the circle represents the frequency of the note.  C (the tonic) and G (the dominant) are the most common notes, just as they should be.  And the notes that are actually in the C-major scale are noticably more frequent than those that aren’t.  The arrow from note x to note y represents the probability that the note following an x will be y; the thicker and redder the arrow, the greater the transition probability.  These, too, look just as they should.  The biggest red arrow is the one from B to C, which is because a major seventh (correction from commenter: a leading tone) really wants to resolve to tonic.  And the strong “Louie Louie” clique joining C,F, and G is plain to see.

Once you have these numbers, you can start to play around.  Lalit wrote a program that generated notes by random-walking along the graph above: the resulting “song” sounds kind of OK!  You can hear it at the end of our 2-minute presentation:

Once you have this computation, you can do all kinds of fun things.  For example, which songs in the database have the most “unusual” melodies from the point of view of this transition matrix?  It turns out that many of the top scorers are indeed songs whose key Echo Nest has misclassified, or which are in keys (like blues scale) that Echo Nest doesn’t recognize.  There’s also a lot of stuff like this:

Not exactly “Louie Louie.”  Low scorers often sound like this Spiritualized song, with big dynamic shifts but not much tonal stray from the old I-IV-V (and in this case, I think it’s mostly the big red I-V)

A relevant paper:  “Clustering beat-chroma patterns in a large music database,” by Thierry Bertin-Mahieux, Ron Weiss, and Daniel Ellis.

Here I am talking linear algebra with Vladimir Viro, who built the amazing Music N-gram Viewer.

DSC_0179 by thomasbonte, on Flickr

Note our team slogan, a bit hard to read on a slant:  “DO THE STUPIDEST THING FIRST.”

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In which I stop by NYU and get categorified by Kazhdan

I had the good luck to be in New York on Friday when David Kazhdan gave an unscheduled lecture at NYU about categorification and representations of finite groups.  For people like me, who spend most of our days dismally uncategorified, the talk was a beautiful advertisement for categorification.

Actually, the first twenty minutes of the talk were apparently a beautiful advertisement for the Langlands program, but I got lost coming from the train and missed these.  As a result, I don’t know whether the results described below are due to Kazhdan, Kazhdan + collaborators, or someone else entirely.  And I missed some definitions — but I think I can transmit Kazhdan’s point even without knowing them.  You be the judge.

It went something like this:

Let G be a reductive split group over a finite field k and B a Borel. Then C[G(k)/B(k)] is a representation of G(k), each of whose irreducible constituents is a unipotent representation of G(k).  (Note:  the definition of “unipotent representation” is one that I missed but it comes from Deligne-Lusztig theory.)

When G = GL_n, all unipotent representations of G appear in C[G(k)/B(k)], so this procedure gives a very clean classification of unipotent representations — they are precisely the constituents of C[G(k)/B(k)].  Equivalently, they are the direct summands of the center of the Hecke algebra C[B(k) \G(k) / B(k)].  For more general G (e.g. Sp_6, E_8) this isn’t the case.  Some unipotent representations are missing from C[G(k)/B(k)]!

Where are they?

One category-level up, naturally.

(see what I did there?)

OK, so:  instead of C[B(k)\G(k)/B(k)], which is the algebra of B(k)-invariant functions on G(k)/B(k), let’s consider H, the category of B-invariant perverse l-adic sheaves on G/B.  (Update:  Ben Webster explained that I didn’t need to say “derived” here — Kazhdan was literally talking about the abelian category of perverse sheaves.)  This is supposed to be an algebra (H is for “Hecke”) and indeed we have a convolution, which makes H into a monoidal category.

Now all we have to do is compute the center of the category H.   And what we should mean by this is the Drinfeld center Z(H).  Just as the center of an algebra has more structure than the algebra structure — it is a commutative algebra! — the Drinfeld center of a monoidal category has more structure than a monoidal category — it is a braided monoidal category.  It’s Grothendieck Group K_0(Z(H)) (if you like, its decategorification) is just a plain old commutative algebra.

Now you might think that if you categorify C[B(k)\G(k)/B(k)], and then take the (Drinfeld) center, and then decategorify, you would get back the center of C[B(k)\G(k)/B(k)].

But you don’t!  You get something bigger — and the bigger algebra breaks up into direct summands which are naturally identified with the whole set of unipotent representations of G(k).

How can we get irreducible characters of G(k) out of Z(H)?  This is the function-sheaf correspondence —  for each object F of Z(H), and each point x of G(k), you get a number by evaluating the trace of Frobenius on the stalk of F at x.  This evidently yields a map from the Grothendieck group K_0(Z(H)) to characters of G(k).

To sum up:  the natural representation C[G(k)/B(k)] sometimes sees the whole unipotent representation theory of G(k), but sometimes doesn’t. When it doesn’t, it’s somewhat confusing to understand which representations it misses, and why.  But in Kazhdan’s view this is an artifact of working in the Grothendieck group of the thing instead of the thing itself, the monoidal category H, which, from its higher categorical perch, sees everything.

(I feel like the recent paper of Ben-Zvi, Francis and Nadler must have something to do with this post — experts?)

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Always eat at restaurants with Cochon in the name

This heuristic has served me well at Au Pied de Cochon in Montreal, and at Le Cochon Dingue in Quebec.  Wednesday night it was a winner again in New Orleans.  Since some of my readers may still have a New Orleans dinner or two ahead of them, let me recommend Cochon — no more than a 15 minute walk from your special session.  If you’ve just got a lunch left, their afternoon deli Cochon Butcher is also supposed to be good (and is also covered by my heuristic.)


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