Monthly Archives: June 2009

Why do commencement speakers lie so much?

So asks Robin Hanson at Overcoming Bias, a blog I like reading because it presents a smart, well-thought-out, likeable account of a style of thinking and valuation so utterly alien to my own that I can hardly believe human beings manage it.

Hanson objects to the speaker at his son’s graduation saying things like “Never let anyone tell you there is something you can’t do,” and “You’ll have setbacks, but never let them discourage you.”  He remarks:

I was embarrassed to be associated with such transparent falsehoods, but apparently I’m in a minority.  What obvious lies have you heard at commencement, and why do you think such lies were told?

Surely this is one of those questions only an economist could be puzzled about.  Lots of posters and commenters on Overcoming Bias seem to live in a weird Gricean dystopia in which every utterance is a mechanism for, and only for, modifying our degrees of belief about the truth-values of various propositions.  Which means, I guess, that every utterance that fails to do this is a “lie.”

Of course, lots of utterances — especially utterances produced in public, and directed at a heterogeneous audience — aren’t like this.  Love, for instance, is not “all you need” — oxygen, protein, and sunlight are at least as essential to life.  But the Beatles aren’t liars.  For each person in the commencement audience, there is indeed something they cannot do.  And that doesn’t make the commencement speaker a liar, either.  Commencement speeches, like songs, are mainly intended to produce feelings.  This is not worthless.  But now I’m puzzled, because Hanson obviously knows all this.  He is not — I assume — the kind of person who, when asked “Would you mind passing the salt?” answers “No, I wouldn’t,” and keeps the salt.

Anyway, comment if you too find Overcoming Bias interesting and alien, or if you find it interesting and mainstream and think I’m the alien.  That would be good to know.

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Mathematicians, a coffee table book from Princeton University Press

Just got in the mail a coffee-table book from PUP, which will appeal to you if you like looking at big photographic portraits of mathematicians while you drink your coffee.  I do!  The pictures, by Mariana Cook, are agreeable, but what really sells the book for me are the short essays that accompany the photos.

At least two of these would make good openings for novels. Pictured here,  Ed Nelson:

I had the great good fortune to be the youngest of four sons with a seven-year gap between my brothers and me, born into a warm and loving family.  This was in Georgia, in the depths of the Depression, where my father organized interracial conferences.  He was the sixth Methodist minister in lineal descent.  While driving he would amuse himself by mentally representing the license plate numbers of cars as the sum of four squares.

And Kate Okikiolu:

My mother is British, from a family with a trade-union background and a central interest in class struggle; she met my father, who is Nigerian, while both were students of mathematics in London.  My father was a very talented mathematician, and after my parents married, he went on to a position in the mathematics department of the University of East Anglia.  While I was growing up, the elementary school I attended was extremely ethnically homogeneous.  I was unable to escape from heavy issues concerning race, which my mother always explained in a political context.  My parents separated after my father resigned his university position to focus on his inventions, and my mother then finished her education and became a school mathematics teacher.

Less novelistic but very keenly observed is this, from the Vicomte Deligne, on the role of intuition in geometry:

You have more than one picture for each mathematical object.  Each of them is wrong but we know how each is wrong.  That helps us determine what should be true.

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More Iranian election statistics

It’s looking more and more as if the official Iranian election returns were at least partially fictional.  I wrote last week about one unconvincing statistical argument for fraud; now a short paper by Bernd Beber and Alexandra Scacco offers more numbers and makes a stronger case.

Keeping in mind that I like their paper a lot, let me say something about a part of it where I thought a bit more justification was needed.

Consider the following three scenarios for generating 116 digits that are supposed to be random:

  1. Digits produced by 116 spins of a spinner labeled 0,1,…,9.
  2. Final digits of vote totals from 116 Iranian provinces.
  3. Final digits of vote totals from U.S. counties.

Now consider the following possible outcomes:

  • A.  Each digit appears either 11 or 12 times.
  • B. 0 appears only 4% of the time, and the other digits appear roughly 10% of the time.
  • C.  7 appears 17% of the time, 5 appears only 4% of the time, other digits appear roughly 10% of the time.

Which outcome should make you doubt that the digits are truly random?

In scenario 1, I think B and C are suspicious; that level of deviation from the mean is more than you’d expect from random spins.  Outcome B would make you suspect the spinner was biased against landing on 0, and C would make you think the spinner was biased towards 7 and against 5.

But of course, outcome A is much more improbable (or so my mental calculation tells me) than either B or C.  So why does’t it arouse suspicion?  Because there’s no apparent mechanism by which a spinner could be biased to produce near-exactly uniformly distributed results like this.  Your prior degree of belief that the spinner is “fixed” to produce this behavior is thus really low, and so even after observing A your belief in the spinner’s fairness is left essentially unchanged.

In scenario 3, I don’t think any of the three outcomes should raise too much suspicion.  Yes, the probability of seeing deviations from uniformity as large as those in C in random digits is under 5%.  But we have a strong prior belief that U.S. elections aren’t crooked — in this case, I think it’s fair to say that scenarios A,B, and C are all evidence that the digits being faked, but not enough evidence to raise the very small prior to a substantial probablity of fraud.

Scenario 2, the one Beber and Scacco consider, is the most interesting.  Outcome C is the one they found.  In order to estimate the probability of fraud in a Bayesian way, given outcome C, you need three numbers:

  • The probability of seeing outcome C from random digits;
  • The probability of seeing outcome C from digits made up from whole cloth at the ministry;
  • The probability — prior to any knowledge of the election results — that the Iranian government would release false numbers.

The third question isn’t a mathematical one, but let’s stipulate that the answer is substantial — much larger than the analogous probability in the United States.

The first question is the one Beber and Scacco assess in their paper; they get an answer of less than 5%.  That sounds pretty damning — deviations like the “extra 7s” seen in the returns would arise less than 1 in 20 times from authentic election numbers.  In fact, outcomes A,B and C are all pretty unlikely to arise from random digits.

But outcome C is evidence for fraud only if it’s more likely to arise from fake numbers than real ones.  And here we have an interesting question.  Beber and Scacco observe that, in practice, people are bad at choosing random digits; when they try, they tend to pick some numbers more frequently than chance would dictate, and some less.  (Their cites for this include the interesting paper by Philip J. Boland and Kevin Hutchinson, Student selection of random digits, Statistician, 49(4): 519-529, 2000.)

So on these grounds it seems outcome C is indeed good evidence for faked data.  But note that the Boland-Hutchinson data doesn’t just say people are bad at picking random digits — it says they are bad in predictable ways at picking random digits.  Indeed, in each of their four trial groups, participants chose “0″ — which just doesn’t “feel random” — between 6.5% and 7.5% of the time, substantially less than the 10% you’d get from a random spinner.

So outcome B, I think, would clearly be evidence for fraud.  But outcome C is a little less cut-and-dried.  Just as it’s not clear what mechanism would make a fixed spinner prone to outcome A, it’s not clear whether it’s reasonable to expect a person trying to pick random numbers to choose lots of numbers ending in “7″.  In Boland and Hutchinson’s study, that digit came up just about exactly 10% of the time.

Here’s one way to get a little more info; let’s say we believe that people trying to imitate random numbers choose 0 less often than they should.  If the Iranian election digits had an overpopulation of 0, you might take this to be evidence against the made-up number hypothesis.

So I checked — and in fact, only 9 out of the 116 digits from the provincial returns, or 7.7%, are 0.  Point, Beber and Scacco.

In the end, it’ll take people with better knowledge of Iranian domestic politics — that is, people with more reliable priors — to determine what portion of the election numbers are fake.  But Beber and Scacco have convinced me, at least, that the provincial returns they studied are more consistent with made-up numbers than with real ones.

Here’s a post from Andrew Gelman’s blog in which Beber and Scacco explain what their tests reveal about the county-level election data.

Update: A more skeptical take on Beber and Scacco from Zach at Alchemy Today, who also makes the point that in order to get this question right it’s a good idea to think about the way in which people’s attempts to choose random numbers deviate from chance.  I think his description of Beber and Scacco’s reasoning as “bogus” is too strong, but his observation that the penultimate digits of the state totals for Obama and McCain are as badly distributed as the final digits of the Iran numbers is a good reminder to be cautious.

Re-update: Beber remarks on Zach’s criticisms here.

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The Orioles have two legitimate Rookie of the Year candidates and neither one of them is named Matt Wieters

I’m talking about Nolan Reimold, currently slugging .546 and leading all major-league rookies in OPS; and Brad Bergesen, who’s been the Orioles’ best starter this year at 23.  Higher-profile pitching prospects Rick Porcello and David Price have ERAs a little lower, but Bergesen looks better on home runs, walks, and strikeouts.  He is, as they say, “in the discussion.”

Here’s Tom on some Reimold heroics.

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The Z-list

Did you know that Harvard sets aside about 20 places a year for students it wants to admit (i.e. students with whose parents or high school Harvard wants to maintain good relations) but who don’t quite make the academic cut?  These students — the so-called “Z-list” — are asked to take an extra year to burnish their credentials so that Harvard can admit them in good conscience.  This Crimson article from 2002 has much more.

I think the name “Z-list” is actually more insulting than the practice itself.

By the way, that Crimson article has some nice mild number-crunching in it — and the reporter, Dan Rosenheck, now writes about sports statistics for the New York Times.  His article this week about the college pitcher Stephen Strasburg is a fine piece of quantitative sportswriting.

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One paragraph of Oscar and Lucinda

Most of the way through this fine Peter Carey novel; about the book in general I don’t have much to say but that it superbly realizes the traditional novelistic virtues.  I wanted to highlight this passage, though, a bit of thought from a provincial bishop:

Dancer could not, of course he could not, have clergy who were notorious around the track, who lost their horses or their carriages because they heard a horse was “going to try.”  Sydney — a venal city — was too puritanical to allow such a thing.  But had you informed Dancer of this story after dinner, he would have found it funny.  He could find nothing in his heart against the races and he left that sort of raging to the Baptists or Methodists.  The true Church of England, he would have felt (but never said) was the Church of gentlemen.  Sometimes gentlemen incur debts.

Notes:  “of course he could not” in place of the standard “of course” is splendid.  Not sure why the doubled “horse” in the first sentence, or why “or” instead of “and” between Baptists and Methodists.  What I really like here is the closing.  If I’d written this paragraph I would have gone with the easier rhythm of “Gentlemen sometimes have debts.”  But Carey’s version — which is kind of hard to say, which can only be said aloud in the deliberate word-by-word manner Carey’s trying to suggest, and which does all the work of characterizing this bit player in the book — is massively better.

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On the Iranian election returns, in Slate

In today’s Slate I write about the claim that the official Iranian election returns are too linear to be true.

The graph (via Tehran Bureau) looks pretty amaing; but in fact, as I explain, it’s pretty much what you’d expect real election data to look like.

One point there wasn’t room for in the piece; if you look carefully at the chart above, you’ll see that the folks at Tehran Bureau got the election returns to fit the line y = 0.5238x – 742642 very well.  But in some sense that’s irrelevant, unless there’s some reasonable expectation that  clerical powers-that-be would want faked election numbers to follow a funny line with a negative y-intercept.  When R.A. Fisher went after Gregor Mendel, it wasn’t just because Mendel’s results looked suspiciously regular; it was because they looked suspiciously close to Mendel’s theoretical predictions.  If Mendel shaded the data, consciously or not, that’s the direction it would go.

I mean, I can fit a really nice quadratic in x to the Iranian election data — or, for that matter, U.S. election data — but absent any reason to posit a vast parabola-loving conspiracy, it’s just not that suspicious.

Update: (June 18)  Lots more material around the web about Iranian election stats.  A preprint on the arXiv claims the official numbers violate Benford’s law, but Andrew Gelman says no. On the other hand, via Mark Blumenthal at Pollster, I learn that Walter Mebane at Michigan finds some suspicious-looking irregularities in the town-level data.

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Speaking of Emmanuel Kowalski

How can I have forgotten to put his blog on my blogroll?  Well, it’s up there now — a great place for thoughtful posts on number theory both contemporary and historical, not to mention engaging diversions on mysterious symbols on slide rules and the important question of whether Grothendieck appears in the movie of Zazie dans le métro.

In Emmanuel’s most recent post, he reports on something I too should have mentioned; that the beautiful result of Bilu and Parent about rational points of X^split(p), whose original version fell prey to a subtle error, has apparently been corrected, and the original result is now once again independent of GRH.

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Math Midway this Sunday in Washington Square Park

If you’re in New York City and like math, consider stopping by the Math Midway, an interactive math exhibit running 10-6 this Sunday, June 14 as part of this year’s World Science Festival Street Fair. (The World Science Festival, despite its name, seems always to take place in New York.  Reminds me of a book I read at Emmanuel’s house, an Encyclopedie des Fromages du Monde which was in fact about the cheeses of France.)  Two more Greenwich Village recommendations from last week’s visit to New York: new Italian storefront restaurant Risotteria and Stephen Merritt’s musical adaptation of Coraline.

It seems that the people behind the Midway are planning to launch a full-scale museum of mathematics, to be called Math Factory and located somewhere in Greater New York.  Is this a good idea?

Update: I almost forgot my most important New York recommendation:  the Francis Bacon retrospective at the Met, which is even better than Risotteria and Coraline.

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