## Outback Steakhouse with the alphabetical epicures

CJ and I joined the Eating in Madison A to Z crew again last month on a trip to the Outback Steakhouse, capping off a Father’s Day afternoon spent at Vitense Golfland.  Three and a half is too young for miniature golf, it turns out, but just right for Outback Steakhouse.

## Someone still loves you Meredith Salenger

Meredith Salenger went to college with me.  This was before Natalie Portman and the guy from Weezer came to town, and Meredith, who starred in The Journey of Natty Gann as a kid and moved up to leading young lady in a couple of teen movies, was as big a star as we had.  She lived in the same building as I did but we never exchanged a word, and to be honest I remember her as stuck-up and clubby.

So the other day I was Googling her name (because I routinely Google starlets of the ’80s?  No — because I was looking for commentary about the Orioles trade of Oscar Salazar for Cla Meredith, and when I started typing “meredith salazar” her name came up on the autocomplete) and I discovered an enjoyable series of posts by Scott Venci, who blogs about high school sports for the Green Bay Press-Gazette.  Venci, a Meredith Salenger fan from way back, somehow got hold of her e-mail address and decided to see if he could get her to do a phone interview for his blog.  His secondary goal was to propose marriage.

Well, Meredith Salenger is still single, but she did do the interview, and it’s good reading.  Part 1. Part 2. Part 3. Part 4.

Especially interesting:  what she gave up to go to Harvard, which for most people is a career enhancer.

“I thought, ‘OK. I’ll go to Harvard for four years, and when I get back I’ll keep having movies offered to me,” Salenger said. “I was young, and I didn’t know. Nobody in my family is in this business. It was never a question of whether I was going to go to college. But when I graduated, it was like, ‘Oh, wait. You’re not a name anymore.’ It was only four years, but it definitely affected my career.”

She comes off throughout as smart, reflective, and funny, and I’m sorry I thought she was stuck-up and clubby — unless of course she actually was stuck-up and clubby at the time, in which case I’m glad she isn’t any more.

If that’s not enough Meredith Salenger for you, here’s her twitter feed.

## “Deforming Galois Representations” is online, too

The hits just keep on coming, as Barry Mazur has now posted a scan of his paper, “Deforming Galois Representations,” from the long-unavailable Galois Groups over Q proceedings, on his homepage.  I didn’t link directly to the .pdf because there’s tons of other interesting stuff on Barry’s homepage to look at!

## Netflix Prize photo finish!

Two hours less than 30 days ago, the team of BellKor’s Pragmatic Chaos submitted the first entry to the Netflix Prize to exhibit a 10% improvement in performance over Netflix’s movie-recommendation algorithm.   That started the final clock for the competition — whoever’s ahead at 2:42 Eastern time today wins the \$1 million prize.

One of the really interesting lessons of the competition is that blendings of many algorithms seem to work better than any single algorithm, even when there’s no principled reason to do the blend.  It’s sort of a “wisdom of crowds of computer programs” effect.  As you can imagine, once BellKor’s Pragmatic Chaos (itself a blend of algorithms from two teams that have been leading through most of the competition) crossed the 10% threshold, just about everybody else realized their best — probably only — chance was to work together.

As of yesterday afternoon, a team called The Ensemble,  made up of — well, I can’t really tell how many previously separate competitors, but a lot — has achieved a 10.09% improvement.  BellKor’s Pragmatic Chaos is at 10.08%.  A hundredth of a percentage point might determine who gets the million.   Wow.

Is BPC sitting on a slightly better algorithm they’re planning to submit at the buzzer for the win?  Check the leaderboard later this afternoon to find out.

Update: Double wow.  No announcement yet, but it looks like BPC and The Ensemble both made submissions in the last hour of the contest; BGC made it to 10.09% but Ensemble, four minutes before closing time, bumped up to 10.10%.

Re-update: I didn’t read the rules carefully enough.  It looks like there’s another dataset (‘test dataset”), distinct from the one generating the public scores (“quiz dataset”) and the final winner will be the program that does best on the test dataset.  So the shifts in the lead, exciting as they are, aren’t necessarily relevant to the contest; we’ve got two algorithms which are essentially identically good and it ought to be a coin-flip which one does better in the final judgment.

## “Le Groupe Fondamental de la Droite Projective Moins Trois Points” is now online

The three papers that influenced me the most at the beginning of my mathematical career were “Rational Isogenies of Prime Degree,” by my advisor, Barry Mazur; Serre’s “Sur les représentations modulaires de degré 2 de $\text {Gal}({\overline {\Bbb Q}}/{\Bbb Q})$;” and Deligne’s 200-page monograph on the fundamental group of the projective line minus three points.  The year after I got my Ph.D. I used to carry around a battered Xerox of this paper wherever I went, together with a notebook in which I recorded my confusions, questions, and insights about what I was reading.  This was the paper where I learned what a motive was, or at least some of the things a motive should be; where I first encountered the idea of a Tannakian category; where I first learned the definition of a Hodge structure, and what was meant by “periods.” Most importantly, I learned Deligne’s philosophy about the fundamental group:  that the grand questions proposed by Grothendieck in the “Esquisse d’un Programme” regarding the action of Gal(Q) on the etale fundamental group $\pi := \pi_1^{et}(\mathbf{P}^1/\overline{\mathbf{Q}} - 0,1,\infty)$ were simply beyond our current reach, but that the nilpotent completion of $\pi$ — which seems like only a tiny, tentative step into the non-abelian world! — nonetheless contains a huge amount of arithmetic information.  My favorite contemporary manifestation of this philosophy is Minhyong Kim’s remarkable work on non-abelian Chabauty.

Anyway:  Deligne’s article appears in the MSRI volume Galois Groups over Q, which is long out of print; I bought a copy at MSRI in 1999 and I don’t know anyone who’s gotten their hands on one since.  Kirsten Wickelgren, a young master of the nilpotent fundamental group, asked me the obvious-in-retrospect question of whether it was possible to get Deligne’s article back in print.  I talked to MSRI about this and it turns out that, since Springer owns the copyright, the book can’t be reprinted; but Deligne himself is allowed to make a scan of the article available on his personal web page.  Deligne graciously agreed:  and now, here it is, a publicly available .pdf scan of “Le Groupe Fondamental de la Droite Projective Moins Trois Points.”

Enjoy!

## Efficient markets and the digits of pi

John Quiggin had a good post yesterday on Crooked Timber about the various flavors of the Efficient Market Hypothesis, which according to Quiggin is a piece of shuffling zombie social science that won’t die no matter how many flaming sticks you jam through its skull.

The weakest form of the EMH is the so-called “random walk hypothesis” that the future behavior of a stock price is independent from its prior behavior.  If that’s the case, no amount of staring at charts is going to help you beat the market.  The random walk hypothesis is pretty well-supported by the data we have; a really nice popular account is Burton Malkiel’s A Random Walk Down Wall Street, one of the mathiest bestsellers I know of.  It makes a great present for anyone in need of a good rationale for not paying attention to their investments.

Quiggin writes

The success of the random walk hypothesis showed that the existence of predictable price patterns in markets with rational and well-informed traders was logically self-contradictory.

But this doesn’t seem quite right.  The EMF, even in its weakest form, holds that the current price of a stock is a best estimate arrived at by an aggregate of profit-maximizing investors with knowledge of the stock’s previous price:  if there were a reliable way to use previous prices to determine that tomorrow’s price would be Y, then the investors would figure that out, and today’s going price would be Y as well.

But the random walk hypothesis is much weaker.  It makes no claim about the etiology of stock prices.  It’s compatible with EMF, but it’s compatible with plenty of other models too — for instance, the one in which stock prices really are a random walk, where the price at time t+1 is the price at time t plus, let’s say, a normally distributed random variable X.  Such a market would be as impossible to beat as a roulette wheel — but evidently not because stock prices are best estimates of the future price of the stock, or of the underlying value of the company, or of anything at all.  (Fellow mathematician David Speyer makes a similar point in the comments at CT.)

You can dress this up a bit:  suppose price(t+1) – price(t) is the random variable X + [(.001) x t'th digit of pi] – (.045).   Unless something very weird is going on with the digits of pi, this version of the stock market would also satisfy the random walk hypothesis.  But unlike the pure random walk it’s a market where you can make some money; if I’m lucky enough to have access to the “digits of pi” rule, I can make a small average profit.  So the random walk hypothesis can hold for markets that are neither efficient nor unbeatable.

Stronger versions of the EMH hold that the market price already takes into account, not only the previous prices of the stock, but also publicly available information about the stock.  So what would happen if I let my secret investing strategy slip out?  This isn’t a rhetorical question; I’m authentically curious about what the rational-investor model would say about a market in which prices are publically revealed to have been governed, up until now, by some completely deterministic but “random-looking” sequence like the digits of pi.

## Reader survey: do you follow the arXiv?

For about a year now I’ve been following the math.AG and math.NT postings to the arXiv through Google Reader.  The good side of this is that you find out very quickly about papers in areas of special interest to you.  The downside, I guess, is that it can be sort of distracting; you sit down to work, you flip through the latest listings, maybe there’s one paper that’s interesting enough to read through the introduction and think about a bit, and before you know it the morning’s gone.

On balance, I like following the arXiv and intend to keep doing it.  But I have no sense of whether this is a standard practice, the way it used to be a standard practice (and maybe still is!) to go down to the library and flip through the latest issues of your favorite journals.

So:  do you follow the arXiv?  If so, what do you get out of it?

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## White Sox 12, Orioles 8

I like Jim Thome a lot, and in the abstract I am happy to have had the chance to see him hit a 450 foot home run, but in practice I’d prefer it not to have been against the Orioles with the bases loaded.

In keeping with the general tenor of the season, this was a game where the Orioles played badly but in which there was much to like. Adam Jones hit a home run that was both timely and authoritative (albeit less so than Thome’s, in both respects.) Brian Roberts set down the finest bunt single I’ve seen in person. Maybe best of all was Kam Mickolio, who pitched an inning and two thirds of scoreless relief, making some good hitters look bad and getting out of a jam when he needed to. Big storky guy who kind of flails the ball over to the plate, but somehow it snaps right in smartly. He has a future on this team.

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## One Paragraph of The Dwarf

Twice in my life I have read novels by unknown-to-me Nordic authors simply because they won the Nobel Prize, and in both cases they were really, really great.  The first was Independent People, by Halldór Laxness.  The second, which I’ve just finished, was Pär Lagerkvist’s short novel The Dwarf, in Alexandra Dick’s translation.  Looks like I’ll have to try Knut Hamsun.

Here’s the opening paragraph.  The impression this gives of the book is exactly correct.

I am twenty-six inches tall, shapely and well proportioned, my head perhaps a trifle too large.  My hair is not black like the others’, but reddish, very stiff and thick, drawn back from the temples and the broad but not especially lofty brow.  My face is beardless, but otherwise just like that of other men.  My eyebrows meet.  My bodily strength is considerable, particularly if I am annoyed.  When the wrestling match between Jehoshaphat and myself I forced him onto his back after twenty minutes and strangled him.  Since then I have been the only dwarf at this court.

The prevailing critical take about The Dwarf seems to read it as a meditation on evil, but I don’t think that’s quite right — it’s much more like a meditation on childishness. What’s going on here is something like this.  We find the innocence and freedom of childhood attractive, but this is only because actual children are small and weak.  Lagerkvist takes the mental qualities we associate with children — first and foremost an incomprehension,  verging on horror, of adult appetites and their satisfaction, but also impulsivity, stubbornness, and moral rigidity — and imparts them to a being with the power to do something about them. The result is something like psychopathy.  Or, if you want, evil.

(As for the first paragraph  — just note that the dwarf’s height is given in inches only, not feet and inches, like that of an infant.  And that the story told is a compressed little fantasy of sibling rivalry.)

The Dwarf is from 1945, the height of the psychoanalytic era.  So my guess is that the question implicit in the book, “What happens when a furious child is working the gears of an adult body?” was meant to be taken literally.

## Madison Science Pub at Brocach, July 26

A couple of weeks ago at the farmer’s market I ran into some undergrads who were doing science demonstrations on Capitol Square.  I tried to get CJ to drop the ball into the beaker and displace some liquid, but he was too shy.  While I was there, another guy wandered by to see what was happening — turned out he too was in the science popularization biz, and is running a series of science pub nights at Brocach downtown.  This July 26, the guest is  UW bio-anthro prof John Hawks, an expert in population genetics of early humans.

As it happened, CJ demanded we eat lunch at Brocach the same day.  I’d never been in there before and wasn’t sure if it was OK to bring him in, but in fact the place is packed with strollers at Saturday lunchtime, and they have a kids’ menu.  I had the corned beef hash, which was good, but — and coming from me, this means a lot — too big.

If you were a mathematician and you were going to talk at a science pub, what would you talk about?