Monthly Archives: February 2008

The moduli space of chords: Dmitri Tymoczko on “Geometry and Music”, Friday 7 Mar, 2:30pm

The next installment of the “Math And…” seminar is coming next week:

7 Mar 2008, 2:30 PM, Birge 145: Dmitri Tymoczko (Princeton University, music)

Title: “Geometry and Music.”

In my talk, I will explain how to translate the basic concepts of music theory into the language of contemporary geometry. I will show that musicians commonly abstract away from five types of musical transformations, the “OPTIC transformations,” to form equivalence classes of musical objects. Examples include “chord,” “chord type,” “chord progression,” “voice leading,” and “pitch class.” These equivalence classes can be represented as points in a family of singular quotient spaces, or orbifolds: for example, two-note chords live on a Mobius strip whose boundary acts like a mirror, while four-note chord-types live on a cone over the real projective plane. Understanding the structure of these spaces can help us to understand general constraints on musical style, as well as specific pieces. The talk will be accessible to non-musicians, and will exploit interactive 3D computer models that allow us to see and hear music simultaneously.

The interactive 3D computer models are made by Dmitri’s program Chord Geometries, which you can download from his website. Or you can just watch the sample movies, and see what the opening of “Smoke on the Water” looks like on a Mobius strip. Dmitri comes by his mathematical know-how familially; his younger sister is the algebraic geometer Julianna Tymoczko (with whom I wrote this paper about diameters of finite groups) and his father was the philosopher of mathematics Thomas Tymoczko.

I’ve booked a big room, and the talk is open to the public, so if the abstract sounds interesting to you, please come!

On the other hand, perhaps the abstract puts you off by means of words like “real projective plane.” Well, it’s written for mathematicians; maybe it’s worth explaining in more down-to-earth language about what a guy like Dmitri means by “the space of chords,” or, as an algebraic geometer like me might put it, the moduli space of chords. Explanation below the fold: it’s essentially a brief version of an article called “The Idea of a Moduli Space” that I wrote for Imagine magazine when I was a grad student.

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My piece in Wired: The Netflix Prize

Last month I wrote an article for Wired about the Netflix Prize; a competition to develop a better algorithm for recommending movies, with $1 million from Netflix as the incentive. This kind of problem is immensely hard: the set of ratings submitted by Netflix users is huge, but very sparse (most users haven’t rented most movies) and very noisy (people make mistakes, their tastes change with time, multiple people may be rating on one account.) So to be able to massage this data into a decent set of movie recommendations is a formidable task — as you probably already know from the typically unsatisfactory performance of the recommendation engines that Netflix, Amazon, and so on, use now.

Anyway, the article’s now online; I write a bit about the mathematical techniques that the experts in the area use to attack this genre of problem, and one very interesting non-mathematician with a different and nearly as successful approach.

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Kiss this guy

More lyrics according to CJ. The Annie Lennox song “Walking on Broken Glass,” is called “Walking Down so Fast.” In Joe Jackson’s “It’s Different for Girls,” the line “No, not love, she said” is rendered by CJ (more poignantly, in his conceptual universe) as “No, no lunch, you said.”

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Orioles numerology

It’s still ice pellet season in Madison, but in Florida it’s baseball time — the Orioles open their spring training schedule next Thursday against the Marlins. So it seems a good time to advertise the most awe-inspiring Orioles completism project I’ve ever encountered: Orioles Numerology, which provides capsule summaries of every Oriole, ordered by uniform number. At #1 we have, of course, the great Al Bumbry and current star Brian Roberts — but I’d forgotten that in between there was Tony Tarasco, fixed forever in memory on the warning track, staring straight upward, disbelieving, as fan Jeffrey Maier hauled a “home run” over the fence for the Yankees in the 1996 ALCS. And at the end, #88, Albert Belle, who’d worn #8 before moving to a team where that number meant Ripken and Ripken only. I hadn’t remembered that the number was first worn by banjo-hitting infielder Rene Gonzales. The proprietors of the site have some bad things to say about Belle, but if not for an unexpected injury he’d have been the best Oriole of the 21st century. More Albert Belle and less Rene Gonzales would look pretty good right now.

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A^4 + B^2 = C^n

Mike Bennett, Nathan Ng, and I posted a paper recently about solutions to the equation

A^4 + B^2 = C^n (*)

in relatively prime integers (A,B,C). There are infinitely many solutions to this equation when n = 2 or 3; for example,

1089^4 + 1549034^2 = 15613^3.

By contrast, what Mike, Nathan and I prove is that for n > 3, there are no solutions to (*).

(CORRECTION:  Mrs. Q points out that I need to say “relatively prime nonzero integers” above — otherwise there are solutions like 0^4 + 1^2 = 1^n.)

More math below the fold:

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Oh my God, if he comes over here I’ll just die

Last week in DC we had dinner with a friend of ours who works in policy and journalism. I think he’s been in Washington a bit too long. As soon as we sat down, he drew us close and whispered “OK, don’t freak out, don’t look over there, but that guy in the grey suit at the table behind us? He’s a former Deputy Undersecretary of State.

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In which we hit the big (blog) time on Eating in Madison A to Z

A few weeks ago Mrs. Q, CJ, and I had the great pleasure of eating dinner with Nichole and JM, the alphabetically omnivorous proprietors of Eating in Madison A to Z. Their report on our meal at Oaxacan newcomer La Mestiza is up now. I stand by it, except for one thing — they call the pickled vegetables “delightfully hot” while I would go with something more like “too spicy for anyone who orders their Thai food medium or below.”

Another nice feature of their review: it taught me the word molcajete. I think of myself as a man who knows his guacamole, but this was new vocab for me.

I’ll be reading the rest of the “La”s carefully — I still haven’t found a real standout Mexican restaurant in Madison, though Tacqueria El Pastor is certainly satisfactory.

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The [Viennagram:]

We just came back from Mrs. Q.’s cousin’s bar mitzvah in my ancestral home of Montgomery County, Maryland. There I learned that Mrs. Q’s cousin (not the bar mitzvah, another cousin. There are a lot of cousins) has moved from Lakeville, MA to Providence to try and make it in the world of dissonant, brass-driven avant-garde rock music with his band The [Viennagram:]. And I think they might make it! This is great stuff, with a kind of extraterrestrial 1940s sound, and a lot of chanting. The only thing I can really compare them to is the geniuses of Man Man (deliverers of the best Madison rock show of 2007.)

Coincidentally, I also have cousins in Lakeville, and one of them also decided to make it as a rock star, and is now reasonably famous, most recently playing bass behind Natalie Merchant for six shows last month in New York.

Watch The [Viennagram:] play an outdoor show while being pelted by, and eventually repelting, rotten fruit:

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Read my book free

When it started up, Google Books had spotty coverage for literary fiction. But I’m happy to report that they now offer The Grasshopper King well, not the full text, but all of the first chapter, and enough of the rest to get a sense of the book.

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Obama, glitter, Wisconsin

Monica hits the front page of the Guardian, which reports on the art-auction party she threw for Barack Obama in New York in advance of Super Tuesday. Monica tells me that artist Aaron Sinift is still selling his glitter Obamas at $240 per: $80 goes to the artist, $160 to BO. This blog doesn’t endorse candidates, but it does endorse art; and let me just say that Obama looks great in glitter. In fact, since WordPress has upped its storage limit to 3 gigs, I don’t have to just say it — I can show it!


Monica probably doesn’t want her e-mail address on this blog, so if you want one of these (I hear they make excellent Valentines) write me and I’ll write her.

I’m glad the Democratic race is still undecided; I’ve never lived in a state with a meaningful primary before. I took CJ out to lunch today (at the very welcome newcomer Pizza Brutta on Monroe) and was very much hoping BO and HRC would cram themselves into the banquette on either side and cover CJ with kisses. Didn’t happen. But we’re still 10 days away.

From the linked Guardian piece above, here’s Monica campaigning in Iowa:

We had volunteered to go door to door for Obama in Mason City, Iowa, prior to the Iowa Democratic primary caucuses. Mason City is very rural, surrounded by small pig farming communities. Weather at some points was well below zero. I knocked at one man’s house – I guess it was 7:30 in the evening – and he answered the door wearing only a pair of Y-front jockey underwear. He was probably 60-something, Republican. I asked him if he would vote for Obama and he asked me if I would marry him. I said no and he said no, so I went on my way.

But there’s a big question unanswered here. Did Mr. Y-Front Hog Wrangler want to know if Monica would marry Obama? Or was this a proposal? Two very different stories. Either one works as a “meet cute” scene for a romantic comedy of the opposites-attract type.

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