Monthly Archives: June 2010

Thank God for Pittsburgh

Tom is right about Terry Crowley but wrong that the Orioles are “the worst team of 2010 and potentially the worst team of modern times.”  The Pirates are 4.5 games ahead of us, sure.  But they’ve scored the same putrid number of runs we have and allowed 20 more.  They’re a titanically crappy team that’s lucky enough to be playing .350 ball.  What’s more, they’re doing it in the NL Central, not the AL East; the Orioles have played 68% of their games against winning teams, as against 56% for the Bucs.  And the winning teams in our division include the three best in baseball.

None of this will be much comfort if we actually lose 120 games.  But I don’t think we will!

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Men in science

This from Katherine Reynolds Lewis in Slate, in an interesting article about why men lie to social scientists about how much childcare they do:

Take Jorge Torrico, 29, a bank manager who lives in Burke, Va., with his wife, Yoonji Kim, and their two toddler sons. Coming into marriage, his idealistic goal was to be an affectionate father and equal partner with his wife. They both work, and he figured that whenever the inevitable child-care emergency arose, they would decide who could handle it on the spot. But when it’s Torrico’s turn, he encounters astonishment from some colleagues who “can’t conceptualize that the father is the one taking responsibility for some of these things: the doctor’s appointment, taking care of the sick child.” Once, he was without child care and had to take his son to a monthly team meeting at work, held in the early evening. One peep from the preschooler, and Torrico was admonished not to bring him again. “The workplace doesn’t really accept the modern-day father,” he concluded.

I’ll say this for academia; fathers deal with a lot less of this nonsense than they do in the quote, real, unquote, world.  Nobody in the department blinks if I have to leave early to pick up CJ from day care, or stay home with him because he’s sick; or if I bring him to number theory seminar, or a faculty meeting, because preschool is off for the day.  I wonder if academic moms reading this feel the same way.

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In which John Tierney continues to annoy me: featuring reader survey!

John Tierney has annoyed me before on the subject of women in science.  And now he’s back, this time recapping the conventional wisdom that math departments like mine are 90% male because of the inborn boyish math power we men possess.  He styles this as “daring.”  The chutzpah!

Anyway, this time around he presses some perfectly respectable social science into service.  Here’s a fact:  more boys than girls get perfect scores on the math SAT.  And a recent study by Jonathan Wai, et al found that that among students who scored over 700 on the math SAT in 7th grade — just 1/10,000 of their sample — boys outnumbered girls by about 13 to 1 in the 1980s, a figure which dropped to 4:1 by the early 1990s and has stayed roughly constant since.

Now here’s how the standard — oops, sorry, I mean “daring” — argument goes:  mathematicians surely possess a math aptitude among the top 1 in 10,000 of the population.  That segment of the population is mostly men, as proven by science.  Ergo, most mathematicians should be men.

A mistake here, or at least a potential mistake, is thinking of success in mathematics as something driven by a variable called “aptitude”, which can be measured on a scale — as if getting tenured at Harvard were something like getting a 10 million on the math SAT.  Wai et al find that girls make up a substantial majority of extremely high 7th grade scorers in the English and writing sections of the exam.  Should one conclude on aptitudinal grounds women should be a majority among English professors?  It’s easy to mistake your operationalizations for reality, as when Wai et al write:

Giving the SAT-M in the 7th grade allows individual differences in the extreme right tail of the distribution (i.e., the top 1% which includes over one third of the ability range) to be captured adequately

I can think of lots of things they might mean by “one third of the ability range” but none which have any content.

Not that I’m saying it’s meaningless to ace the SAT before getting your driver’s license.  It’s a vanishingly small proportion of people who get a 700 on the math SAT at 13.  But I’d think it would be a very small proportion of mathematicians too!  If 10% of mathematicians were extreme child math prodigies, and those extreme child math prodigies are 80% boys, one hasn’t gone far towards explaining why US math research faculties are overwhelmingly male.

There’s actually an empirical question here which I know nothing about.  So let’s contribute to my know-nothingness by undertaking a brutally unscientific survey.  If you’re a working mathematician — say, a Ph.D. student in good standing or a faculty member at a university — did you score above 700M on the SAT when you were 13 or younger?  Since I think it’s a fairly small proportion of the world that takes the exam that early, let’s ask a more widely applicable question as well:  if you took the SAT as a senior in high school, did you get 800 on the math section?  (If you answer this, you might mention whether you took the exam before or after the 1995 recentering.)

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Adverb placement and probability

Just a weird and somehow illuminating syntactic trip-up:  per the odds of the moment at 538, it is correct to say both that

England, the United States, and Slovenia will all probably advance

and

England, the United States, and Slovenia will definitely not all advance.

There’s no paradox here, just a reminder to take care about the ambiguity in English-language descriptions of probabilities.

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My name is Cesar Izturis and I’m slugging .244

How amazing would Izturis’s defense have to be to make up for his hitting this season?  Like, let’s say he was so good that he could play both shortstop and third base and the Orioles could stick four guys in the outfield.  Would that make him an average player overall?

In other weak hitting news, CJ and I went to the Mallards today to see the home team beaten 2-1 by the Waterloo Bucks.  Bad:  intermittent rain.  Good:  surprisingly tasty grilled cheese sandwich from Maynard’s Slide-In Grill.

Orioles 35th round draft pick Jeremy Lucas went 0 for 3 and is now batting .182 on the year.  Watching amateur baseball makes you feel like hitting is a lot harder than defense, actually.  The Bucks, after 12 games, have yet to hit a home run.  The Mallards now have 4.  These guys can make a diving catch, they can stop a line drive, they can turn the double play.  But they can’t seem to make solid contact with a pitched ball, except by chance.    If you want a vision of the Northwoods League, imagine a foul ball smacking into the backstop — forever.

CJ pitched against the radar gun in the kids’ zone and was clocked at 10mph.  I ballooned with pride.  Double digits, kid.

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In which I try to find a way to follow the Orioles without crying

Does anybody know who the best prospect in baseball is, just in case somebody you know might have first pick in the 2011 draft?  Somebody who seemed finally, after years of self-sabotage, to be turning things around and doing things right, but who can’t catch a break and seems hated by the powers above?  Oh, wait, I forgot, I was supposed to do this without crying.

Anyway, per baseballrumormill it’s Rice 3B Anthony Rendon.  Well, the last time we drafted a slugging 3B it worked out all right.

Sorry, my mistake, the last time we drafted a slugging 3B it was Bill Rowell, who’s currently hitting .236 in his third year of A ball.

No, I’m fine, I just got something in my eye.

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Happy birthday, Dick Gross

Just returned from Dick Gross’s 60th birthday conference, which functioned as a sort of gathering of the tribe for every number theorist who’s ever passed through Harvard, and a few more besides.  A few highlights (not to slight any other of the interesting talks):

  • Curt McMullen talked about Salem numbers and the topological entropy of automorphisms of algebraic surfaces (essentially the material discussed in his 2007 Arbeitstagung writeup.)  In particular, he discussed the fact that the logarithm of Lehmer’s number — conjecturally the “simplest” algebraic integer — is in fact the smallest possible positive entropy for an automorphism of a compact complex surface.  Here’s a question that occurred to me after his talk.  If f is a Cremona transformation, i.e. a birational automorphism of P^2, then there’s a way to define the “algebraic entropy” of f, as follows:   the nth iterate of f is given by two rational functions (R_n(x,y),S_n(x,y)), you let d_n be the maximal degree of R_n and S_n, and you define the entropy to be the limit of (1/n) log d_n.  Question:  do we know how to classify the Cremona transformations with zero entropy?  The elements of PGL_3 are in here, as are the finite-order Cremona transformations (which are themselves no joke to classify, see e.g. work of Dolgachev.)  Are there others?
  • Serre spoke about characters of groups taking few values, or taking the value 0 quite a lot — this comes up when you want, e.g., to be sure that two varieties have the same number of points over F_p for all but finitely many p, supposing that they have the same number of points for 99.99% of all p.  The talk included the amusing fact that a character taking only the values -1,0,1 is either constant or a quadratic character.  (But, Serre said, there are lots of characters taking only the values 0,3 — what are they, I wonder?)
  • Bhargava talked about his new results with Arul Shankar on average sizes of 2-Selmer groups.  It’s quite nice — at this point, the machine, once restricted to counting orbits of groups acting on the integral points of prehomogenous vector spaces, is far more general:  it seems that the group of people around Manjul is getting a pretty good grasp on the general problem of counting orbits of bounded height of the action of G(Z) on V(Z), where G is a group over Z (even a non-reductive group!) and V is some affine space on which G acts.  With the general counting machine in place, the question is:  how to interpret these orbits?  Manjul showed a list of 70 representations to which the current version of the orbit-counting machine applies; each one, hopefully, corresponds to some interesting arithmetic enumeration problem.  It must be nice to know what your next 70 Ph.D. students are going to do…

Dick has a lot of friends — the open mike at the banquet lasted an hour and a half!  My own banquet story was from my college years at Harvard, where Dick was my first-year advisor.  One time I asked him, in innocence, whether he and Mazur had been in graduate school together.  He fixed me with a very stern look.

“Jordan,” he said, “as you can see, I am a very old man.  But I am not as old as Barry Mazur.

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What if political scientists covered the news?

Any scientist who has ever written for the popular press has experienced the tension between the academic’s natural inclination to say “here’s what we know, here’s what we might know, here’s what we don’t know” and the demands of journalistic convention that you offer something more like “A says X, B says Y, I have a Ph.D. and here’s who’s right.”  Christopher Beam has a brilliant comic take on this in Slate (which, by the way, is the most open of all general-interest magazines to the academic way of speaking.)

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Coulis fail

I like an artful swirl of sauce on the plate as much as the next high-end diner, but a cheesecake should not appear to have just skidded to a halt.

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Reader survey: what open question would you ask Dick Gross?

I’m speaking on an “open problems” panel in honor of Dick Gross’s 60th birthday.  I’ve got 10 minutes.  I think I know what I’m going to say, but I was just informed that the panel is to be allowed to run late if audience interest demands it.  So I thought it would be good to stock up a little more material.  And it occurred to me this might be a good opportunity to blogsource!  So, readers:  if you were going to promote an open problem in front of Dick Gross and his wellwishers, what would it be?

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