Must have been a pretty bad team, right? But no! They won 89 games and finished second, just a game and a half behind the Reds. That 15 game homerless streak in July? They went 11-4 in those games.

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In the latest stable representation theory news, Andy Putman and (new Wisconsin assistant professor!) Steven Sam have just posted an exciting new preprint about the theory of representations of GL_n(F_p) as n goes to infinity; this is kind of like the linear group version of what FI-modules does for symmetric groups. (Or, if you like, our thing is their thing over the field with one element….!) This is something we had hoped to understand but got very confused about, so I’m looking forward to delving into what Andy and Steven did here — expect more blogging! In particular, they prove the Artinian conjecture of Lionel Schwartz. Like I said, more on this later.

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People made fun of that last scene where they take shrooms and go hiking in Big Bend. But I liked this last scene. It captures that feeling that, on the one hand, the past is past, but on the other hand, the past is always present, *all of it*, all layered on top of each other. As if the whole movie actually takes place over the course of about a second or two, in 18-year-old Mason’s mind, and we’re seeing the images that exist there in that span of time. I *think *all adults constantly have that feeling, right? That your entire adult life is sort of a mask, and you’re really 20-year-old you who’s traveled forward in time to see how it all turned out, and also you’re 15-year-old you, and 6-year-old you, and etc., all at once? You don’t actually even need shrooms for this!

Question: is it impossible to talk about a Richard Linklater movie without feeling like you’re executing a Linklater monologue pastiche?

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He starts with the following lovely observation, which was apparently in a 2007 paper of his but which I was unaware of. Suppose you make a maximalist conjecture about uniform growth of finitely generated linear groups. That is, you postulate the existence of a constant c(d) such that, for any finite subset S of GL_d(C), you have a lower bound for the growth rate

.

It turns out this implies Lehmer’s conjecture! Which in case you forgot what that is is a kind of “gap conjecture” for heights of algebraic numbers. There are algebraic integers of height 0, which is to say that all their conjugates lie on the unit circle; those are the roots of unity. Lehmer’s conjecture says that if x is an algebraic integer of degree n which is {\em not} a root of unity, it’s height is bounded below by some absolute constant (in fact, most people believe this constant to be about 1.176…, realized by Lehmer’s number.)

What does this question in algebraic number theory have to do with growth in groups? Here’s the trick; let w be an algebraic integer and consider the subgroup G of the group of affine linear transformations of C (which embeds in GL_2(C)) generated by the two transformations

x -> wx

and

x -> x+1.

If the group G grows very quickly, then there are a lot of different values of g*1 for g in the word ball S^n. But g*1 is going to be a complex number z expressible as a polynomial in w of bounded degree and bounded coefficients. If w were actually a root of unity, you can see that this number is sitting in a ball of size growing linearly in n, so the number of possibilities for z grows polynomially in n. Once w has some larger absolute values, though, the size of the ball containing all possible z grows exponentially with n, and Breuillard shows that the height of z is an upper bound for the number of different z in S^n * 1. Thus a Lehmer-violating sequence of algebraic numbers gives a uniformity-violating sequence of finitely generated linear groups.

These groups are all *solvable, *even metabelian; and as Breuillard explains, this is actually the hardest case! He and his collaborators can prove the uniform growth results for f.g. linear groups without a finite-index solvable subgroup. Very cool!

One more note: I am also of course pleased to see that Emmanuel found my slightly out-there speculations about “property tau hat” interesting enough to mention in his paper! His formulation is more general and nicer than mine, though; I was only thinking about profinite groups, and Emmanuel is surely right to set it up as a question about topologically finitely generated compact groups in general.

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Here’s one thing I liked about this movie. Every adult man in the movie talks to Mason about *responsibility. *Following up. Thinking about consequences of actions. It’s the verbal glue that holds all the men in the movie together.

But here’s the thing. Responsibility is a virtue, sure. But it turns out that good men and bad men believe in it just the same. You can’t tell who’s good by what they say. Mason’s abusive alcoholic stepdad tells him to live up to the commitments he makes. That’s good advice. Mason’s photography teacher, presented as someone who basically cares about him and means him well, tells him he can’t just do what he pleases if he wants to make art; he has to apply himself and learn technique. Also good advice. Not-necessarily-alcohol-abusing-but-drunk-and-checked-out stepdad #2 tells him he should call his mother if he’s going to be out all night because she worries. Also good advice! The manager at the cruddy restaurant where Mason works tells him he shouldn’t screw around chatting in the back when there are families waiting for their food. That’s good advice too! And the movie cleverly sets up the manager as a figure of fun (giving him a dorky polo shirt and a receding hairline) but then brings him back, in a sympathetic role, at Mason’s party, forcing the audience to say, yeah, the dorky guy was right, big ups for the dorky guy. Ethan Hawke’s second wife’s dad (following me here?) works similarly; the movie sets you up to see his gift of a gun to Mason as a piece of yokelism, but Mason visibly appreciates it, and what is the older man’s main piece of dialogue in the scene? A reminder that a gun is a serious thing and you have to use it with safety foremost in your mind. *Great* advice.

Responsibility talk isn’t really about being a good man or a bad man; it’s just about being a man. Mason’s biological father gives him a talk about birth control (at this point, Mason is about 13, and hasn’t had a girlfriend yet, I think) which is a fine model of the “This is serious, but I’m gonna be funny, but also, remember, I’m serious” approach. I’m sure a lot of dads of younger kids were taking notes.

But of course the context of this talk is that Mason Sr. himself didn’t use birth control, whence Mason! Who he then — contra all the responsibility talk — ran out on, before the movie even starts.

So it’s unfair, right, that I’m giving him credit for this speech? And for that matter, isn’t it unfair and kind of creepily patriarchal that I’m casting responsibility as part of being a *man*, as opposed to part of being an adult?

So the movie is working exactly to bring that into the light and then oppose it, I think. Because who *actually* lives up to commitments and acts responsible is Mason’s mother. He hears about responsibility from his dad, and every other man in the world. But he learns it from his mom.

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Here’s a passage from Craig Shirley’s *Reagan’s Revolution:*

Even its ‘red light’ district was festooned with red, white, and blue bunting, as dancing elephants were placed in the windows of several smut peddlers.

And from Perlstein:

The city’s anemic red-light district was festooned with red, white and blue bunting; several of the smut peddlers featured dancers in elephant costume in their windows.

Shirley:

Whenever he flew, Reagan would sit in the first row so he could talk to people as they boarded the plane. On one occasion, a woman spotted him, embranced him, and said, “Oh Governor, you’ve just got to run for President!” As they settled into their seats, Reagan turned to Deaver and said, “Well, I guess I’d better do it.”

Perlstein:

When Ronald Reagan flew on commercial flights he always sat in the front row. That way, he could greet passengers as they boarded. One day he was flying between Los Angeles and San Francisco. A woman threw her arms around him and said “Oh, Governor, you’ve got to run for president!” “Well,” he said, turning to Michael Deaver, dead serious, “I guess I’d better do it.”

The second passage is cited to Shirley, the first isn’t. But I don’t think it matters! You shouldn’t paraphrase someone else’s book sentence by sentence, even if you cite them. If you’re going to say exactly what they said, you should quote them.

Is this plagiarism? It is, at the very least, *patchwriting: *“restating a phrase, clause, or one or more sentences while staying close to the language or syntax of the source.” Mark Liberman at LanguageLog has a long, magisterial post about patchwriting in Perlstein’s book, pointing out some places where Shirley himself patchwrites from the New York Times.

I once came across a magazine article whose lede was patchwritten from an article of my own. I talked to a few trusted friends about how to handle it. Uniformly, they said: it’s not nice, but it’s not plagiarism, and you shouldn’t accuse the other author of stealing your stuff. In the end, I alerted the other author to the issue without accusing her, and she apologized, saying she’d done it in a hurry and didn’t realize it was so close. Which is probably true.

So I guess it’s not plagiarism and Shirley is not going to win his $25 million lawsuit against Perlstein. But I don’t really like it and I think when we do journalism we should strive to write our own stuff.

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The group’s president, Peter Wood, called the framework politically biased. One of his many complaints is about immigration: “Where APUSH sees ‘new migrants’ supplying ‘the economy with an important labor force,’ others with equal justification see the rapid growth of a population that displaces native-born workers from low-wage jobs and who are also heavily dependent on public services and transfer payments.”

Here’s the full text of the relevant bullet point in the standards.

The new migrants affected U.S. culture in many ways and supplied the economy with an important labor force, but they also became the focus of intense political, economic, and cultural debates.

You can decide for yourself whether the standard sweeps under the rug the fact that many people wish there were fewer immigrants. But shouldn’t Newsweek print the whole sentence, instead of letting its readers rely on selective quotes? Why do I have to look this stuff up myself?

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If one is to believe the account given in

Eine Frau,Sascha saw Hanka’s photograph by chance, probably one of the photographs that still exist today, and immediately informed the dismayed husband: “I will take your wife away!” A few days later Hanka appeared, still rather weak from her abortion—and it was love at first sight.”

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Where do people not want the book? Lowest sales per capita are in Miami. They also have little use for me in Los Angeles, Atlanta, and Houston. Note that for reasons of time I only looked at the 30 MSAs that sold the most copies of the book; going farther down that list, there are more pretty big cities where the book is unpopular, like Tampa, Charlotte, San Antonio, and Orlando.

It would be interesting to compare the sales figures, not to population, but to overall hardcover book sales. But I couldn’t find this information broken down by city.

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