Category Archives: slate

Statistical chutzpah in the Indiana school grade-changing scandal

I wrote a piece for Slate yesterday about Tony Bennett, the former Indiana schools czar who intervened in the state’s school-grading system to ensure that a politically connected public charter got an A instead of a C.  (The AP’s Tom LoBianco broke the original story.)  Bennett offered interviewers an explanation for the last-minute grade change which was plainly contradicted by the figures in the internal e-mails LoBianco had obtained and released.  Presumably, Bennett figured nobody would bother to look at the actual numbers.  That is incredibly annoying.

Summary of what actually happened in Indiana, by analogy:

Suppose the syllabus for my math class said that the final grade would be determined by averaging the homework grade and the exam grade, and that the exam grade was itself the average of the grades on the three tests I gave. Now imagine a student gets a B on the homework, gets a D-minus on the first two tests, and misses the third. She then comes to me and says, “Professor, your syllabus says the exam component of the grade is the average of my grade on the three tests—but I only took twotests, so that line of the syllabus doesn’t apply to my special case, and the only fair thing is to drop the entire exam component and give me a B for the course.”

I would laugh her out of the office. Or maybe suggest that she apply for a job as a state superintendent of instruction.

 

 

 

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Natural logs and products of no primes

The e-mail you get after you write an article about number theory is very interesting.  For one thing, you’re reminded of phrasings which have one meaning among mathematicians, but a slightly different one outside the tribe.

The majority of the e-mail I’ve gotten about the bounded gaps piece concerns two questions of this kind:  I’ll answer them both here, in case other readers are following the link from Slate to the blog.

Q:  You say that the number of primes less than X is about X/log(X), but don’t you mean X/ln(X)?

A:  When mathematicians say “log” we mean the natural log, the thing which in some other contexts (e.g. Google’s search bar calculator) is denoted “ln.”  But mathematicians never say “ln.”  (To be honest, we kind of think the base-10 logarithm should be called “lu.”)

Q:  You say that every positive number is the product of primes, but this is not true for prime numbers themselves, which can’t be expressed as products.

A:  A prime number is indeed the product of prime numbers!  It is the product of just one prime number, itself.

What about 1?  It’s the product of zero prime numbers.

 

Make no mistake

Choire Sicha in Slate, in the course of correctly praising Ursula K. LeGuin, remarks:

The literary novel is, make no mistake, as much a pileup of inherited conventions as the worst werewolf cash-in. There are now thousands of young, MFA-toting writers, so many of them aping the weak generation of literary male novelists now in their 50s: pallid and insufferable teachers and idols, in light of the strong and inventive generation before them.

When you find yourself inserting “make no mistake” into an assertion, you should consider the possibility that you’re doing so because you subconsciously recognize that your assertion is not sufficiently well-justified.

Also:  Sicha packs an amazingly dense tangle of sexual politics into just a few sentences!  Literary fiction is stultifying because it’s tied to the cultural practices of men in their 50s.  But they aren’t real men like their forbears, they are instead weak and pallid!  (Katie Roiphe called and she wants her tendentious generalizations back.  But then while she was on the phone Camille Paglia cut in on call-waiting and then things got really ugly.)

And the people with MFAs don’t just have MFAs — they tote them!  Probably in a tote bag!  Probably while drinking some insufferable kind of coffee drink!

Literary fiction — even literary fiction written by MFA-toters — is a big, rich, complicated zone.  At the moment I am reading Peter Carey’s crazy Illywhacker – Carey is indeed a male of the old persuasion, but pallid he is not – and Heidi Julavits’s new book The Vanishers, which is unquestionably literary fiction but which has lots of psychic phenomena and astral travel in it.  It’s a delight.  And I started Justin Cronin’s vampire-apocalypse book The Passage, whose more “literary” parts are better than the other parts.  I was promised it would be as good as The Stand, a great book whose status as literature is an interesting thing to think about.

I keep meaning to write a post about the ways in which Stephen King and Jonathan Franzen have converged on each other as writers, and how this fact helped me think about what “literary” means w/r/t novels.  But there is no time to do it today, only time to snark about something I read in Slate.  There is a lesson here.

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Somewhere a dog barked

From Rosecrans Baldwin in Slate:

As a reader of novels and not much else, I keep a running list of authorial whims. Male writers of the Roth/Updike generation, for example, love the word cunt. Also, where novelists once adorned their prose with offhand French bon mots, Spanish now appears. Here’s another: Novelists can’t resist including a dog barking in the distance. I’ve seen it happen across the spectrum—Jackie Collins, William Faulkner, and Chuck Palahniuk: “There was no more rain, just an eerie stillness, a deathly silence. Somewhere a dog barked mournfully.” (American Star) “She did not answer for a time. The fireflies drifted; somewhere a dog barked, mellow sad, faraway.” (Light in August) “This is such a fine neighborhood. I jump the fence to the next backyard and land on my head in somebody’s rose bush. Somewhere a dog’s barking.” (Choke)

I checked The Grasshopper King, and nope:  no barking dogs.  There’s a ceramic dog, and one dog who howls (but who appears moments later, and is named) and finally, near the end, a talking dog.  Me 1, cliche 0.

In other Slate literary coverage, Dan Kois reviews Ben H. Winter’s novel The Last Policemana detective story set in a future where Earth is six months away from certain destruction by asteroid collision.  When I was in college I took Spike Lee’s screenwriting course, and my screenplay was roughly on the same theme. It was a meteor heading for the earth, not an asteroid, and the atmosphere was supposed to be roughly that of After Hours or Into the Night.  It was called Planet Earth.  Lee’s total commentary on the screenplay, written on page 3, was “Some parts I laughed, some parts I didn’t,” and he gave me an A-.

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Jonah Lehrer, Niall Ferguson, the lecture economy

They apparently had the same problem — their brand was “person who writes books” but their actual business model became “person who gives lectures for five-figure fees.”  The demands of the two roles are very different.

Ideally, a public lecture should be an advertisement inducing people to read your book and engage with your argument presented in full.  What a disaster if the book becomes an advertisement for the lecture instead.

Update:  Stuff on this theme is all over the place today:  here’s Daniel Drezner on “Intellectual Power and Responsibility in an Age of Superstars” and Justin Fox on “the rage against the thought-leader machine.”  Both pieces are great.

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The much-deserved death of the perfect 10

Slate just re-posted my 2008 article in praise of the new gymnastics scoring system.  I stand by it.

“The new ‘open-ended’ scoring system was designed in part to prevent us from outgrowing the rules,” international gymnastics judge Judy Schalk told me via e-mail. Before the new system, just about all elite competitors performed routines difficult enough to bring the start value up to a 10.0; sailing over that threshold earned you no more points than barely clearing it. With the new system, gymnasts have the incentive to keep making their routines tougher and more complex. In every other sport, the competitors in Beijing are superior to their predecessors and get better scores to prove it. Why should gymnastics be the only sport without world records?
With the new system, gymnastics comes into compliance with the Olympic motto. That’s “faster, higher, stronger,” not “more graceful, more beautiful, closer to perfect.” It’s no coincidence that the Olympic sports that have historically chased the latter ideal are the same ones in which the women’s game overshadows the men’s: gymnastics and figure skating.
Figure skating ditched the perfect 6.0 after crooked judging in the 2002 Salt Lake City Olympics embarrassed the sport. The old scoring system already had many discontents, most famously great French champion Surya Bonaly, who showed her disdain for the judges at the 1998 Olympics by landing a backflip on one skate. It was illegal, it carried a mandatory deduction, and she was the only woman in the world who could do it.

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I say two sentences about the World Series on NPR

Transcript and recording here.

This was based on a much longer conversation.  I’ll just add that yes, not only do wild card teams not always get blown out, they sometimes win!  The larger point stands, though — if the pennant winners are drawn somewhat uniformly from the best four teams in the league, you’re more likely to have a mismatched World Series than you were in olden times, when the pennant winner was usually the best team in its league.

Here’s my old Slate piece on why the World Series should be stopped when one team goes up 3-0, but should go to best of 9 if the first six games split 3-3.

If you like Mike Pesca’s voice and you like smart sports talk, I highly recommend Slate’s Hang Up and Listen podcast.

 

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Revenge of the intersentence double space

Farhad Manjoo, in Slate, delivers a spirited attack on double-spacers like me.  Apparently the intersentence double space is irrational and unbeautiful.  My readers mostly disagree, and more importantly, so does LaTeX.  This argument reminds me of books I used to read as a kid about the forthcoming rationalization of English spelling.  The inventor of the Dewey Decimal System, Melville Dewey — excuse me, Melvil Dui — was a big player here.  Anyway, it didn’t happen.  Our lumpy, irrational language, with its silent gh and its intersentence lacunae, trundles on its own track.

 

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Narcissistic personality disorder, the NRC rankings, and finite metric spaces in Slate

I have a piece in Slate today about the classification of personality disorders in the new DSM, and the NRC graduate school rankings.  OK, they don’t really let me mention finite metric spaces in Slate.  But that’s what’s going on behind the lines, and it’s a problem I’ve been wrestling with.  Let’s say you have a finite metric space M; that is, a finite set of points with assigned distances between them.  Now there’s a whole world of algorithms (multidimensional scaling and its many cousins) to embed M in a Euclidean space of some reasonably small dimension without messing up the metric too much.  And there’s a whole world of heirarchical clustering algorithms that embed M in the set of leaves of a tree.

But I don’t really know a principled way to decide which one of these things to do.

Stuff there wasn’t room for in the piece — I should have mentioned Ian Hacking’s book Mad Travelers, which gives a very rich humanistic account of the process by which categories of mental illness are generated.  And when I talked about the difficulty of crushing a finite metric down to one dimension, I should have linked to Cosma Shalizi’s “g, a statistical myth”

 

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Reader survey: how seriously do you take expected utility?

Slate reposted an old piece of mine about the lottery, on the occasion of tonight’s big Mega Millions drawing.  This prompted an interesting question on Math Overflow:

I have often seen discussions of what actions to take in the context of rare events in terms of expected value. For example, if a lottery has a 1 in 100 million chance of winning, and delivers a positive expected profit, then one “should” buy that lottery ticket. Or, in a an asteroid has a 1 in 1 billion chance of hitting the Earth and thereby extinguishing all human life, then one “should” take the trouble to destroy that asteroid.

This type of reasoning troubles me.

Typically, the justification for considering expected value is based on the Law of Large Numbers, namely, if one repeatedly experiences events of this type, then with high probability the average profit will be close to the expected profit. Hence expected profit would be a good criterion for decisions about common events. However, for rare events, this type of reasoning is not valid. For example, the number of lottery tickets I will buy in my lifetime is far below the asymptotic regime of the law of large numbers.

Is there any justification for using expected value alone as a criterion in these types of rare events?

This, to me, is a hard question.  Should one always, as the rationality gang at Less Wrong likes to say, “shut up and multiply?” Or does multiplying very small probabilities by very large values inevitably yield confused and arbitrary results?

UpdateCosma Shalizi’s take on lotteries and utilities, winningly skeptical as usual.

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