I have never listened to an album by

I think of myself as someone who’s listened to a lot of records, at least within the segment of music I pay most attention to (1977-2000 Anglosphere indie.)  But there are some weird holes.  I have never listened to an album, all the way through, by:

• Radiohead
• Sonic Youth
• Neutral Milk Hotel
• The Fall

These are meant to be in order from most to least surprising.   I know one song by Radiohead (“Creep,” natch) sort of know one song by the Fall (“Prole Art Threat,”) have certainly heard a few songs by Sonic Youth but couldn’t hum one (except I know there’s one where the lyric “I don’t think so” is central) and I’m not sure I’ve ever heard a song by Neutral Milk Hotel.

If you define “album” to exclude best-ofs and singles comps, one must add to this list New Order, the Smiths, Squeeze, Elvis Costello, the Ramones, and quite possibly Prince (I know I own one of his mid-80s records on cassette, but I’m not sure I’ve listened to it.)  And Joy Division, before I bought the box set.  Really!

I don’t own a U2 album, but it’s unthinkable that I didn’t at some point in college I didn’t hear one in toto.  I first listened to a Beck album (Odelay) last April.  Also, the only Guns N Roses album I’ve listened to all the way through is their covers record, The Spaghetti Incident. Their version of “New Rose” is completely successful.

Share your own surprising rock lacunae in comments.

2666

I read the bulk of Roberto Bolaño’s 2666 in late December, the last time the stomach flu rampaged through my house.  It’s a very good book to read in the middle of the night when you’re not sure whether or not you’re going to throw up.  The landscapes in the book — like the bathroom at 3am — are very brightly lit and clear, but also unsettlingly shifty.

(The last time I had food poisoning was in New Orleans on New Year’s Eve 1994, and I was reading Pale Fire; also entirely appropriate to the occasion, and in much the same way.)

The reason I bought 2666 wasn’t because I knew I was getting stomach flu, but because of my occasional worry that I’m too old to experience a new novel as a masterpiece. Rather: most of the time think I’m too old to experience a new novel as a masterpiece, and occasionally I consider this cause for worry.   And when that happens I buy and read the acknowledged masterpiece of the moment, to see if I can get those bumpers to light up one more time.

No lights this time.  But I was glad to have read this big, nauseous book.  Some comments below the fold — don’t proceed if (like me) you try to avoid prior knowledge of books you plan to read.

Revolution revisited

Update:  EMI had the song pulled from YouTube — sorry.  Hope you got to hear it!

It’s almost forty years since the Beatles broke up, but they still have the power to surprise.  I never really understood what the straight pop song “Revolution” and the tape-loop breakdown of “Revolution #9″ had to do with each other.  This just-leaked demo reveals them as two pieces of one many-jointed eleven-minute song.  (via ilX.)

She do the police in different voices

Whether Joss Whedon’s new show Dollhouse can be good surely depends, most of all, on whether Eliza Dushku is actor enough to convincingly portray a new character in the same body every week — or, if the arc of the show is as promised, each week a new character through which some slowly revealed constant character bleeds through, in the painful sense of the word “bleeds.”

After the first episode, I’m doubtful.  But then, the first episode — said to be a hurried compromise forced on Whedon by Fox, just as with Firefly — wasn’t very Whedonny at all.  Lots of chunky exposition, poorly delineated dramatis personae, quickly revealed and as quickly resolved “dark secrets.”  Very little snap, with the exception of a fine tough-cop men’s room scene that would win this year’s Best Men’s Room Scene Emmy if not for Madison rocker Shirley Manson’s star turn as a homicidal urinal — really! — on Sarah Connor Chronicles.

I can’t lie; I trust Joss.  I will watch.

My name is Blossom, I was raised in a lion’s den

Blossom Dearie is dead at 82.

I am not the kind of person who has opinions about jazz.  But there are a few things I think I’ll never tire of hearing:  “Well You Needn’t,” “So What,” and just about anything sung and played by Blossom Dearie.  If it is possible at all to belt out a song delicately, it was possible only for her.  Mrs. Q and I were lucky enough to see her play once, probably around 2000, in the strange Thai restaurant / jazz club that served as her regular stage in New York.

Here she performs the Dave Frishberg classic “I’m Hip” (no video)

A TV appearance, singing “Surrey with the Fringe on the Top”:

And what might be her most famous vocal performance, “Figure Eight” from Schoolhouse Rock:

February linkdump

• The Virginia Quarterly Review has made most of its archive freely available online.  Have a look at David Wyatt’s overthought yet strangely readable analysis of Star Wars mythology from 1982, post-Empire but pre-Jedi: “Star Wars is also a nearly apocalyptic summing up of the tradition of film; it gives us back the history of movies as if that history were over.” (via MetaFilter)
• Dada Math at Williams sounds fun.
• If you like rock and are kind of nerdy about it, there is nothing more fun than a few hours spent in the bowels of a college radio station, reading the years of annotations layered in stickers all over the records.  If you don’t have access to such bowels right now, the Phoenix was able to obtain and scan a 1984 notebook from WHRB’s Record Hospital.
• New modes of web-enabled mathematical exposition are popping up everywhere.  If Yu-Gi-Oh has its own wiki, why not A^1 homotopy theory?

In which I am away from my desk

Back late last night from a brief trip to Chicago, where I visited Steve and Monica at the AWP and worked out (I hope!) the last details on a project with Ben McReynolds.  I usually bring my laptop when I travel.  But just before leaving, it occurred to me that the amount of downtime on this trip was so small that there was no point in carrying around the extra weight in my backpack all day.

At this point, I immediately started feeling anxious about not seeing my e-mail for two days.  The anxiety was an even more powerful argument for not bringing my laptop.  It’s important to stay sure you can quit any time you want.

I’ve now gone about 45 hours without looking at my e-mail, the longest stretch in quite some time.  Is this unusual?  What’s the longest you’ve been away from your e-mail in the past year?

Thurston on proof and progress in mathematics

I must have read Thurston’s excellent essay “On proof and progress in mathematics,” when it came out, but I don’t have any memory of it.  I re-encountered it the other day while playing with Springer’s eBook service, and flipping through the chapters of the recent collection 18 Unconventional Essays on the Nature of Mathematics.

Thurston makes a passionate case against theorem-proving as the measure of a mathematician’s contribution:

In mathematics,it often happens that a group of mathematicians advances with a certain collection of ideas. There are theorems in the path of these advances that will almost inevitably be proven by one person or another. Sometimes the group of mathematicians can even anticipate what these theorems are likely to be. It is much harder to predict who will actually prove the theorem,although there are usually a few “point people”who are more likely to score. However, they are in a position to prove those theorems because of the collective efforts of the team.The team has a further function,in absorbing and making use of the theorems once they are proven. Even if one person could prove all the theorems in the path single-handedly,they are wasted if nobody else learns them.

There is an interesting phenomenon concerning the “point”people.  It regularly happens that someone who was in the middle of a pack proves a theorem that receives wide recognition as being significant. Their status in the community—their pecking order—rises immediately and dramatically.When this happens,they usually become much more productive as a center of ideas and a source of theorems.Why? First,there is a large increase in self-esteem, and an accompanying increase in productivity. Second, when their status increases,people are more in the center of the network of ideas—others take them more seriously. Finally and perhaps most importantly, a mathematical breakthrough usually represents a new way of thinking,and effective ways of thinking can usually be applied in more than one situation.

This phenomenon convinces me that the entire mathematical community would become much more productive if we open our eyes to the real valuesin what we are doing. Jaffe and Quinn propose a system of recognized roles divided into “speculation”and “proving”. Such a division only perpetuates the myth that our progress is measured in units of standard theorems deduced. This is a bit like the fallacy of the person who makes a printout of the first 10,000 primes. What we are producing is human understanding. We have many different ways to understand and many different processes that contribute to our understanding. We will be more satisfied, more productive and happier if we recognize and focus on this.

Thurston concludes with some very interesting and frank reminiscences, including some regrets, about the way certain parts of topology bent around his gravitational field in the 70s and 80s.

By the way, some libraries have stopped buying new physical books from Springer in favor of access to the e-books.  If you’re at an institution that’s gone this route, tell me about it in comments!

Sifting and winnowing

“Sifting and winnowing” is the UW term for the intellectual work we all do, which is supposed to be simultaneously in service to Truth and to The People Of Wisconsin.  Today we got a rare chance.  A guy called the math department in order to settle an argument with his girlfriend:  is zero an even number, an odd number, or not a number?

His girlfriend won.

Laza and Kuznetsov on cubic fourfolds

By chance, Wisconsin had two seminars about cubic fourfolds on consecutive days last week, by means of which I learned much more about cubic fourfolds than I had in my life up to now.  Summary follows — based on my understanding of what was said, so all mistakes belong to me and not the speakers.

Radu Laza talked about his work on the moduli space of cubic fourfolds. One way you can study families of varieties is via the period map, which sends a variety X to the Hodge structure on H^i(X), for some degree i. It follows from a 1985 theorem of Claire Voisin that the period map from the space of cubic fourfolds X to Hodge structures on H^4(X) is injective; so the moduli space of cubic fourfolds is a subvariety of the moduli space of Hodge structures of the right shape, which is a nice 20-dimensional ball quotient. Laza goes further, computing the precise image of the period map, and thus giving a very clean description of the moduli space.

Alexander Kuznetsov gave a talk the following day on the rationality of cubic fourfolds.  Some cubic fourfolds are rational; for instance, if X is a cubic fourfold containing two skew planes P and Q, then you get a map from P x Q to X sending (p,q) to the third point of intersection of the line pq with X, and this map is birational.  The generic cubic fourfold, on the other hand, is conjectured to be non-rational; but I believe that no example of a provably non-rational cubic fourfold is known.

Kuznetsov’s idea is to approach this problem from the viewpoint of the derived category.  The derived category of a smooth cubic fourfold has a “semi-orthogonal decomposition” into a bunch of simple pieces, which don’t depend on X,  and one interesting piece, a subcategory we call A_X.  The category A_X isn’t a birational invariant, but it does behave nicely under basic birational operations — when you blow up a smooth subvariety Z of X (necessarily of dimension 0,1, or 2) you find that A_X simply “picks up a copy of A_Z.”  In particular, if X is birational to P^4, A_X must be “made out of” pieces coming from derived categories of varieties of dimension at most 2.  Kuznetsov believes this criterion can be used in practice to obstruct the rationality of X.

If this sounds familiar, it’s because it’s explicitly modeled on the Clemens-Griffiths obstruction to rationality of a cubic threefold Y.  There, the role of A_X is played by the intermediate Jacobian J(Y); and Clemens and Griffiths prove that if J is not isomorphic to the Jacobian of a curve, Y can’t be rational.  A critical role is played here by the semistability of the category of principally polarized abelian varieties; this doesn’t hold for triangulated categories, but Kuznetsov believes that a suitable version of semistability should apply to some class of categories including A_X.

If X is a cubic fourfold, the Fano variety F(X) parametrizing lines in X is again a fourfold, and is deformation equivalent to the Hilbert scheme parametrizing pairs of points on a K3.  This fact is omnipresent in Laza’s work, and it shows up for Kuznetsov too:  it turns out that in the cases where X is known to be rational (for instance, the infinite families produced by Brendan Hassett in his thesis) the Fano variety is not just a deformation of, but actually is, the Hilbert scheme Hilb^2 S for some K3 surface S.  And in this case, Kuznetsov’s A_X is nothing but the derived category D^b(S).

This might lead one to ask whether one could make a conjecture that dispensed with derived categories entirely (though I feel guilty and antique for suggesting that this might be a good thing!) and guess that X is rational exactly when F(X)  is Hilb^2 of a K3 surface S.  I think would be pretty close to a kind of Hodge-theoretic criterion for rationality, as in the cubic threefold case.

But if I understand correctly, Kuznetsov doesn’t think it can be that simple.  There is a divisor in the moduli space of cubic fourfolds which is naturally identified with the moduli space of K3 surfaces of some given degree.  Hassett shows that on this 19-dimensional variety there is a countable union of 18-dimensional families of rational cubic fourfolds.  Kuznetsov says that if X is a point on this divisor, and S the corresponding K3, that A_X is not the derived category D^b(S), but a twisted derived category D^b(S,alpha) for some Brauer class alpha on S which is generically nonvanishing (but vanishes on Hassett’s locus.)   And this twist, he believes, obstructs rationality — though without a good enough “semistability” property for the categories involved, nothing can yet be proved.