Monthly Archives: May 2012

Why Walker is winning

I tend to agree with Nate Silver, who thinks a victory by Tom Barrett in Tuesday’s recall election is fairly unlikely.  The Times’s coverage of Wisconsin politics has gotten a lot better since last February’s Capitol protests.  The NYTimes Mag feature from last Sunday is well-reported and well-written and told me some things I didn’t know.  But throughout there’s an air of puzzlement about the governor’s continued political viability that doesn’t seem warranted to me.

The feature is heavy on interviews with experienced Wisconsin political hands, both Democrats and Republicans, who are dejected about the Walker style of government and what it’s done to the state’s political culture.  I can easily imagine that it’s a depressing time to be a state legislator (and a downright dangerous time to be a Supreme Court justice) whatever party you belong to.

But I think the average Republican voter here likes Scott Walker just fine.  They like stripping collective bargaining rights just fine, and they like voter ID just fine.   And Republican voters make up half the population of Wisconsin.  Normal politics here is 5o-50; throw in the advantages of incumbency and whatever proportion of the voters disapprove of recalls on principle, and Barrett has a built-in disadvantage to overcome.  (That’s not even to mention the massive spending disparity in Walker’s favor.)  A Walker victory wouldn’t be very notable; what’s notable is the fact that a million recall petitions were signed in the first place, or that an unknown Madison judge came within a hairsbreadth of unseating an incumbent Supreme Court Justice.

That being said, the error bar here is pretty wide; not the sampling error in the polls, but the intrinsic uncertainty about who’s going to show up and vote in an election with no historic precedent.  Wisconsin Democrats surprised me and everybody else by getting a million recall petitions signed; maybe they’ll surprise me and everybody else by organizing a massive turnout on June 5.

And Barrett fans can take some comfort in the fact that I’ve been consistently wrong in every prediction I’ve made about Wisconsin politics.

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Lev Grossman — they asked him anything

Friend of the blog Lev Grossman did an AMA on reddit tonight about his novels The Magicians and The Magician King.  (I wrote about The Magicians here.)  Lots of good material but I especially liked this from Lev on Narnia:

You know how you — by which I mean me — love your parents, but you’re also kind of permanently angry at them, all the time? That’s how I feel about the Narnia books. I really do love them. I’ve tried to make my daughter read them about 100 times. But I feel so bitter about them too — about what they did and didn’t prepare me for in life.

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Knuth, big-O calculus, implicit definitions (difficulty of)

Don Knuth says we should teach calculus without limits.

I would define the derivative by first defining what might be called a “strong derivative”: The function f has a strong derivative f'(x) at point x if

f(x+\epsilon)=f(x)+f'(x)\epsilon+O(\epsilon^2)

I think this underestimates the difficulty for novices of implicit definitions.  We’re quite used to them:  “f'(x) is the number such that bla bla, if such a number exists, and, by the way, if such a number exists it is unique.” Students are used to definitions that say, simply, “f'(x) is bla.”

Now I will admit that the usual limit definition has hidden within it an implicit definition of the above kind; but I think the notion of limit is “physical” enough that the implicitness is hidden from the eyes of the student who is willing to understand the derivative as “the number the slope of the chord approaches as the chord gets shorter and shorter.”

Another view — for many if not most calculus students, the definition of the derivative is a collection of formal rules, one for each type of “primitive” function (polynomials, trigonometric, exponential) together with a collection of combination rules (product rule, chain rule) which allow differentiation of arbitrary closed-form functions.  For these students, there is perhaps little difference between setting up “h goes to 0″ foundations and “O(eps)” foundations.  Either set of foundations will be quickly forgotten.

The fact that implicit definitions are hard doesn’t mean we shouldn’t teach them to first-year college students, of course!  Knuth is right that the Landau notation is more likely to mesh with other things a calculus student is likely to encounter, simultaneously with calculus or in later years.  But Knuth seems to say that big-O calculus would be self-evidently easier and more intuitive, and I don’t think that’s evident at all.

Maybe we could get students over the hump of implicit definitions by means of Frost:

Home is the place where, when you have to go there,

They have to take you in.

(Though it’s not clear the implied uniqueness in this definition is fully justified.)

If I were going to change one thing about the standard calculus sequence, by the way, it would be to do much more Fourier series and much less Taylor series.

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John Stuart Mill and scansion

There are lots of good reasons to read Henry Farrell and Cosma Shalizi’s network-theoretic defense of democracy against market fundamentalism on the one hand and hierarchic paternalism on the other.  But at the moment I just want to quote their quote of John Stuart Mill:

But the economical advantages of commerce are surpassed in importance by those of its effects which are intellectual and moral. It is hardly possible to overrate the value, in the present low state of human improvement, of placing human beings in contact with persons dissimilar to themselves, and with modes of thought and action unlike those with which they are familiar. Commerce is now what war once was, the principal source of this contact.

And I’m not even quoting the quote because the quote says something interesting, which it does — it’s just because scansion is on my mind, thanks to Paul Fussell, and I was struck by the grace of “Commerce is now what war once was.”  To write with authority you have to have good ideas, but you also have to pay attention to the sound of your words.  Writing is a formalization of sound, not a formalization of thought.

 

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RIP Paul Fussell

The Great War and Modern Memory is one of the finest books of literary criticism I’ve read, though I can’t say I’ve read many.  It was probably only when I read that book that I started to get a sense of literary criticism as a literary form in itself.  I took lots of English courses in college, but the kind where you read novels and poems, not books about novels and poems.

The copyright status here is questionable, but on the day of the man’s death it’s surely OK to link to a scanned copy of Fussell’s very funny essay on the ABM, or “Author’s Big Mistake” — the angry response to an uncomplimentary review.  It’s been years since I read this, and reading it again just now I think about 60% of the paragraphs demanded to be read aloud to Mrs. Q.

E.G.:

Imagine what mortification it is for an author to pass through crummy discount bookstores and see great piles of his masterpiece stacked up on the remainder tables, marked down from $14.95 to $1.95, and moving sluggishly even then.

This is lovely — the high style of “pass through” swooping down to “crummy,” the syntactic insult of using “his masterpiece” as a mass noun, and of course the quiet suggestion of feces provided by the phrase “great piles.”  Fussell was a g–d— pro, is what I’m trying to say, and I’m lucky to have come across him when I was learning to write.

Update:  But I will say that changing “sluggishly” to “slowly” would sacrifice only a little vividness, and would make the end of that sentence scan much more cleanly.  That’s the choice I would have made.

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David Brooks and impossible lifestyles

Brooks:

In Europe, workers across the Continent want great lifestyles without long work hours. They want dynamic capitalism but also personal security. European welfare states go broke trying to deliver these impossibilities.

This is a weird thing to say.  I’m no European, but I think what Continental folks mean by “great lifestyles” is not “a 3000 sq foot house” or “a new car every five years” but something more like “a flexible schedule with time to spend on family and travel.”  I think they would say, of us, “Workers across America want a great lifestyle with long work hours and two weeks vacation a year.  American families make themselves crazy trying to deliver these impossibilities.”  And they would be right.

 

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Should Harvard offer a “good enough, but no room” certificate?

There are people who think that the information conveyed by a Harvard diploma is almost entirely made up of the fact of admission to Harvard; that is, that Harvard graduates on average have no more skills than students who got into Harvard but chose to go somewhere else.

I’m not one of those people.  But it got me thinking — the fact of admission certainly conveys some information.  And there are unquestionably lots of students who the admission office feels are academically strong enough to attend Harvard, but who don’t make it into the entering class.

What would happen if the admissions office offered exactly this certification?  A signed piece of paper saying, “At age 17, student X had credentials which would have made academic success at Harvard very likely, had there been room.”  Would that be a valuable piece of paper for a 22-year-old to have?  Would it be in Harvard’s interest to offer a certain number of certificates of that kind?

Related question:  can a student who gets into Harvard, but goes to a lower-ranked school (say, for financial or family reasons) put on their CV that they were admitted to Harvard, but declined?  Something about that strikes me as strange.  But why?  Isn’t it useful information for a potential employer?

(Note:  obviously the above applies with any elite university in place of “Harvard.”)

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How to compute arctangent if you live in the 18th century

Michael Lugo wrote a great post, following an idea of Andrew Gelman, about what would have happened if Pythagoras had known linear regresson.  Punchline:  he would have found a linear formula for the hypotenuse with an R^2 of 0.9995, and would surely not have seen any need to pursue the matter any further!

I thought this was mostly just a joke, until the mail brought me a copy of the very interesting A Wealth of Numbers from Princeton University Press, an anthology of popular writing about math stretching from the 16th century to the present.

From Hugh Worthington’s 1780 textbook, The Resolution of Triangles:

THE THIRD CASE is, the sides being given, to find the angles, and the rule is as follows.  “Half the longer of the two legs added to the hypotenuse, is always in proportion to 86, as the shorter leg is to its opposite angle.”

In modern language:  given a right triangle with legs a and b, and hypotenuse 1, how do you find the angle x adjacent to a?  Nowadays we would just say “x = arctan b/a.”  But this kind of computation was presumably not so easy in 1780.  Instead, Worthington offers the approximation

b/x = (a/2 + 1) / 86

which (after converting to radians, as good manners requires) gives

x = (86*pi/180) b / (a/2 + 1)

Of course, when the hypotenuse is set to 1, we have b = sin x and a = cos x.  So the approximation is

x = (86*pi/180) (sin x) / (cos x / 2 + 1).

This turns out to be a pretty awesome approximation!

How do you think they came up with this?

 

 

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The Scarlet Plague

I really like world-destroyed-by-disease novels and I really like Jack London and I was really happy to learn that Jack London wrote a world-destroyed-by-disease novel, The Scarlet Plague, which you can buy here.  It’s a quick, really enjoyable read, but not without heft.

London is really interested in the tension between the cultivated and the uncultivated.  The narrator, a former professor of English literature at Berkeley, longs for the civilized life of the past, but recognizes that cultivation and refinement breed weakness, while the oppression visited on the impoverished masses of pre-plague America had generated a cruel strength.  Here’s the vegetal version:

“With my horse and dogs and pony, I set out. Again I crossed the San Joaquin Valley, the mountains beyond, and came down into Livermore Valley. The change in those three years was amazing. All the land had been splendidly tilled, and now I could scarcely recognize it, ‘such was the sea of rank vegetation that had overrun the agricultural handiwork of man. You see, the wheat, the vegetables, and orchard trees had always been cared for and nursed by man, so that they were soft and tender. The weeds and wild bushes and such things, on the contrary, had always been fought by man, so that they were tough and resistant. As a result, when the hand of man was removed, the wild vegetation smothered and destroyed practically all the domesticated vegetation.”

And the human version, which comes a little earlier in the book:

“In the midst of our civilization, down in our slums and labor-ghettos, we had bred a race of barbarians, of savages; and now, in the time of our calamity, they turned upon us like the wild beasts they were and destroyed us.”

But London complicates this story.  In a typical apocalypse book, the reader would be invited to reflect on the personal qualities of the narrator that led him to be among the few survivors.  London insists we do no such thing:

“In the morning I was alone in the world. Canfield and Parsons, my last companions, were dead of the plague. Of the four hundred that sought shelter in the Chemistry Building, and of the forty-seven that began the march, I alone remained—I and the Shetland pony. Why this should be so there is no explaining. I did not catch the plague, that is all. I was immune. I was merely the one lucky man in a million—just as every survivor was one in a million, or, rather, in several millions, for the proportion was at least that.”

I think this makes the book more interesting.  All the narrator’s learning and culture doesn’t help him — but it doesn’t hurt him either.  He is no braver, no cleverer, no wiser, and no stronger than his fallen companions.   London’s plague isn’t a cleansing flood that kills a sick society and reduces the species to its ablest core.  It’s a random sample.  And the civilization that humans will build after the plague won’t be any better than what came before.  Or worse.  It will be the same:

“The gunpowder will come. Nothing can stop it—the same old story over and over. Man will increase, and men will fight. The gunpowder will enable men to kill millions of men, and in this way only, by fire and blood, will a new civilization, in some remote day, be evolved. And of what profit will it be? Just as the old civilization passed, so will the new. It may take fifty thousand years to build, but it will pass. All things pass. Only remain cosmic force and matter, ever in flux, ever acting and reacting and realizing the eternal types—the priest, the soldier, and the king. Out of the mouths of babes comes the wisdom of all the ages. Some will fight, some will rule, some will pray; and all the rest will toil and suffer sore while on their bleeding carcasses is reared again, and yet again, without end, the amazing beauty and surpassing wonder of the civilized state.”

We are the plague, and the plagued.

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Why not?

Twenty-three years later, is it still too soon to ask?

Maybe so.  But with a quarter of the season in the books, and Baltimore holding the best record in the American League, who can resist?  Rany Jazayerli in Grantland points out that the 21st-century Orioles have started strong before, only to fade in the late going.  But I’m not sure that tradition applies to the new-model Orioles.  Jazayerli writes, “2010 is the only season this century in which the Orioles played better at the end of the season than at the beginning,” a strange thing to say considering that the Orioles went 15-13 last September against a steady stream of contenders, finishing it off by coming from behind against the Red Sox and ending their season, in what will forever be known as The “M@#$$f@#$@$ sh#@, take your a#% home” Game.  Camden Depot looks back at the 2005 team, the last Oriole squad to be this good this deep into the season.  We all know how that turned out.

Could 2012 be different?  To answer that, you have to understand why the Orioles have played so much better than projected.  Who’s overperforming?  Adam Jones.  Matt Wieters.  Jason Hammel.  Wei-Yin Chen.  The entire bullpen.  To a lesser extent, Chris Davis and Robert Andino and even Jake Arrieta, whose ugly ERA masks a real improvement in his control.  Who’s doing worse than expected?  Basically just Mark Reynolds and the bench.  (Before the season I thought the bench would be much improved this year, but among the new spare parts only Wilson Betemit has really contributed.)

So the Orioles have been lucky with performance, and have been lucky in wins even above their performance, outpacing their Pythagorean winning percentage by 3 games (though to some extent this may just reflect excellent relief performance.)

The good news is, a lot of the overperformers are exactly the kind of players who might be experiencing an actual improvement, not just good luck.  Wieters and Adam Jones were prized prospects with obvious potential who’ve never quite put it all together in the major leagues, and who are now, at 26, entering their prime years.  If you were to carve out a single class of players prone to have breakout seasons, that’s it.  Chen came from Japan — it’s always hard to predict how pitchers will transition from Asia, and while Chen is almost certainly not going to maintain a 2.45 ERA, there’s every reason to believe he was way underestimated.  Arrieta is 26, too, and if he can keep up his current peripherals, I can easily see him finishing the season with a 4 or 4.5 ERA; not sterling, but it would have made him the best starter on last year’s team.  Matusz has been inconsistent and mediocre this year, which is to say he has massively improved from last year, and there’s every reason to think 2011 was the outlier.

Hammel, on the other hand, is more likely to revert to his previous well-established level, and the bullpen simply can’t keep performing as it has been.  (Looking at these guys, though, I’m impressed by how many middle relievers with pretty serious credential the Orioles quietly put together on the cheap.  Lindstrom is the only one who really, truly can’t be considered a potential elite reliever.)

Altogether, I think improvement over projection from Jones, Wieters, and Chen alone could make this team about 6 wins better, which means they project as about a .470 team on talent.  If they play .470 ball the rest of the way, they finish 83-79.  I’d take that!

 

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