[E]valuation is nontrivial

You know how when you're in a debate with a smart person, and the debate wants to fragment -- you need some kind of tree structure to keep track of all the threads that the two of you have brought up, because some of them are irrelevant to the main point but still intriguing, and some of them neither of you are sure whether they'll be crucial or just trivial, and sometime what was irrelevant turns into its own fun conversation/debate?

Except usually you can't do all of this, because the debate is taking place in a linear format like blog (or, worse, Facebook) comment threads?

I had a moment feeling a little like that today when reading Massimo Pigliucci's report from the American Philosophical Association meeting in Philadelphia where he relates sitting through a panel stocked with followers of Ayn Rand. In general, this is an exercise not worth the investment of time, since no one except Objectivists takes Objectivist philosophy seriously. (Not least because Objectivist philosophers don't take any non-Objectivist philosophy seriously, and it's pretty bootless to try to have an academic discourse that way.)

Whiny little gits: on legislation by version control

There's an idea that's been rattling around my head for some time now, probably originally seeded by some internet forum discussion, and it's now been rattling long enough without me seeing any deadly objections that I figured I'd put it down on e-paper.

Problem-setting: legislative process. It's weird, and convoluted, and in many cases the rules of a legislative chamber allow changes to be made to a bill which the members need not be aware of. This was borne out recently in Congress when a single member inserted a provision at the behest of Citigroup, and there was no way to excise the provision from the final version which was submitted to both houses for an up-or-down vote, without jeopardizing the passage of the whole bill.

To zoom out a bit: voters don't care about, pay attention to, or understand process. That's OK, in one sense -- voters really are supposed to care about results, in theory, and are supposed to trust their representatives to get good at process. The problem comes in when advocacy organizations start scoring process moves as position-taking. For example, there's a funny little quirk in the Senate rules that if the majority fails to break a filibuster, the only way to try later to break the same filibuster is if someone changes their mind. What this means in practice is that the Majority Leader will vote to sustain the filibuster if he's sure the logjam won't break -- this way he can "change his mind" later if they can whip up the votes to get the bill through. But this exposes him to an advocacy organization scoring his vote as being on the wrong side of their favorite issue.

There's even the very basic existential question of "what does the law actually say?". How are we to know, under the current way of setting up legislation, if the text on the paper distributed to Congress is the same as the text which is digitally available on the website of the Library of Congress; or if either is identical to the text on the page signed by the President? And in case of a discrepancy, which is "the law"? Typos happen, and humans aren't optimized to catch them on paper.

Fen: Carrion Skies

This is not totally a bookmark.

Metal for winter

So, there's these Russians, and they have a band...


... and it makes me think of snow and ice and other things nice...

Blut Aus Nord

The two tracks currently available for streaming in promo for Blut Aus Nord's new album are... fucking amazing.




That is all.

If you don't have student loans, there's a high probability you're missing something

An opinion piece floated across my radar this morning; penned by one Jessica Slizewski, originally at XOJane and picked up at Time.com, it announces to the reader that I Don’t Have Student Loans and I Don’t Feel Bad for People Who Do. OK, so I'm being trolled. I don't care, I feel the need to retort.

Before I begin, I do feel compelled to state that, like Ms Slizewski, I strongly feel that the rent tuition is too damn high, and that student-loan debt overhang is having a nasty macroeconomic effect on the U.S. I also think that the structure of student-loan finance puts some perverse incentives on institutions of higher education; but that's neither here nor there.

Eluveitie and...

Metsatöll

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Týr

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Eluveitie

A universal algebraist proves Fodor's Lemma

In the last post, we mentioned Fodor's Lemma (in the context of an attempted proof that didn't end up working out). Well, my brain was idling the other evening, and decided that it needed to prove this lemma. Don't ask me why my brain does what it does.

Attention conservation notice: this post is written for someone with maybe a lower-level grad-school level of knowledge, or maybe upper-level undergrad, and who knows what a subalgebra is but doesn't necessarily know any logic.

More on the countable chain condition

We last met the ccc in the context of preserving cofinalities in forcing extensions; but the exercise that I gave the proof for was specifically about forcing. This week, I ran across a nice little exercise which doesn't explicitly mention forcing at all -- it's pure combinatorics -- but, at least for me, thinking about it using the forcing idea was the key to solving the problem.

Exercise 1: Let \( \mathbb{P} \) be a ccc poset, and let \( X = \{ x_i \colon i < \omega_1 \} \subseteq \mathbb{P} \) be a subset. Show that there exists an uncountable subset of \( X \) whose every pair are compatible.

At first glance, this looks completely obvious -- things are either compatible or incompatible, and you can't have more than countably many pairwise incompatible things. The problem, though, is that the compatibility relation need not be transitive -- just because you have an uncountable subset of \(X\) which is not an antichain does not mean that it satisfies the conclusion of the exercise.

What made this problem interesting to me was that I had to discard some of the heuristics that usually serve me well. In particular, a dependable heuristic when dealing with posets is duality: if something is true for all posets, then you should be able to turn your poset upside-down and it should still be true. However, the compatibility relation is not stable under duality! Most forcing posets have a single weakest condition; if you dualize, you get that every two conditions are compatible, which is clearly useless.

Alice and Bob visit the cardinal, Part II

(Part I of this post can be found here.)

Greetings, loyal blog readers! I'm afraid life took over for a bit after writing Part I, but we're now back in the peanut gallery watching Alice and Bob battle wits.

In the last post, we talked about a fun game which Matt Baker used to prove the uncountability of the reals. (We'll call this the Nested-Intervals Game.) In his post about this game, he asked a question which (still weeks later) is vexing me:

Question 0: Does there exist a target set \(T\) such that neither player has a winning strategy for the Nested-Intervals Game targeting \(T\)?

On voter fraud

Dear Texas,

If you're so damn concerned about someone else showing up and voting under my name, sending voter registration cards as postcards seems awfully...casual, no?

Artery Metal

Nine Minutes


Nine minutes of local support. Have potential.

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Find Balance

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Silence The Messenger


Technically proficient screamcore

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Allegaeon


Worth the price of a ticket on their own.

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Upon This Dawning


Hey, if it gets screaming teenage girls to like death metal, who am I to complain?

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Chimaira

Alice and Bob visit the cardinal, part I

(Part II of this post can be found here.)

Speaking of diagonal arguments: I ran across the blog of one Matt Baker yesterday, who sketched out probably the easiest proof I've ever seen of the uncountability of the real line. He also included a question in his post, one that I have a strong intuition about the answer, but so far haven't been able to prove I'm right.

(NB: when I say easiest proof I've ever seen, I mean that I sat down at lunch with a colleague who hadn't seen math since her freshman year of calc, and we finished lunch with her pretty much all over that shit.)

Anyway, I thought I'd record that argument in case Baker's blog disappears or (as has happened twice today) I can't figure out search terms to find it again. The next post will discuss his question, the version of an answer I can prove, and what makes the full problem more difficult. I'll try to pitch the level of these posts (well, more this one than the next) at the level of my lunch colleague.

Today in pissy racism

A quick note for those keeping score at home: Kevin Williamson is still a race-baiting piece of shit:

[National Review] decided to send roving correspondent Kevin Williamson, who has some strong revisionist views on American racial politics, to East St. Louis, Illinois, to take in the local scene, and … oh, no:

East St. Louis, Ill. — "Hey, hey craaaaaacka! Cracka! White devil! F*** you, white devil!" The guy looks remarkably like Snoop Dogg: skinny enough for a Vogue advertisement, lean-faced with a wry expression, long braids. He glances slyly from side to side, making sure his audience is taking all this in, before raising his palms to his clavicles, elbows akimbo, in the universal gesture of primate territorial challenge. Luckily for me, he’s more like a three-fifths-scale Snoop Dogg, a few inches shy of four feet high, probably about nine years old, and his mom — I assume she’s his mom — is looking at me with an expression that is a complex blend of embarrassment, pity, and amusement, as though to say: “Kids say the darnedest things, do they not, white devil?”

The scene ends with an interminable sentence Williamson probably regards as “literary":

... my terminus in East St. Louis, where instead of meeting my Kurtz I get yelled at by a racially aggrieved tyke with more carefully coiffed hair than your average Miss America contestant.

There are a few lines in here that a good editor would cut but could be waved off as unwitting bad judgment — the Heart of Darkness reference, three fifths, making fun of the hair. But when the writer also decides the best comparison for a young black kid’s behavior is a monkey and to gratuitously question his parentage, there’s really not much question, is there?

Fundamental theorem on chain conditions

Continuing on our occasional theme of "problems suitable for a prelim exam".

Lo these many years ago, I took (and passed) the prelim exam in Logic at the CUNY Grad Center. (I think they call it a "qualifying exam" there, but whatever. "Subject exam", if you will.) Now, the course structure was all model theory the first semester (syntax and semantics of first-order logic, compactness theorem, various other applications of ultraproducts, quantifier elimination, ... maybe a couple of other things?) and most of the second semester was spent proving the soundness and completeness theorems for the first-order syntactic calculus, and then the Incompleteness Theorem(s). We had maybe a month or so left at the end of that time, which the professor offered to spend on set theory and computability theory, divided as we liked. None of us had strong feelings, so we dipped a toe in each and went on our merry. The structure of the prelim exam followed the structure of the course.

The point of the preceding story was, that I have seen prelim problems from model theory, but few from set theory or recursion theory. (I think that exam did have a problem on it requiring use of a finite injury argument, but that was one of the ones I skipped.)

Anyway: I was reading some set theory this week, just for fun, and the author said something like "... it is a basic fact that c.c.c. forcing preserves cardinals and cofinalities, ...", and I said to myself, self, if it's so basic, why can you never remember why this should be true? And down the rabbit hole I went.

It took a few tries before I came up with a proof, and I still haven't gone back to see if the proof of this theorem in Jech or Kunen is substantially different. But I like the proof I came up with, it seems natural, and I think, if a prelim course were to cover forcing (like a first-year course devoted only to set theory really should) that a problem like this would make a natural prelim problem.

Theorem: If \( \kappa \) is a cardinal, \( \lambda = \mathrm{cf}(\kappa) \), and \( \mathbb{P} \) satisfies the \( \lambda \)-chain-condition, then for any \(V\)-generic filter \( G \) over \( \mathbb{P} \), the cofinality of \( \kappa \) in \(V[G] \) is still \( \lambda \).

Proof: Let \(\gamma < \lambda \), and let \( \mathring{f} \) be a \( \mathbb{P}\)-name for a function from \( \gamma \) into \( \kappa \). We must show that \[ \mathbb{1} \vdash \exists \xi < \kappa \; \forall \alpha < \gamma \; \mathring{f}(\alpha) < \xi \]
Now fix some \( \alpha < \gamma \) for the moment: we know by the Truth Lemma that, if \( V[G] \models \mathring{f}(\alpha) =  \beta \), then for some \( p_{(\alpha, \beta)} \in G \), \( p_{(\alpha, \beta)} \vdash \mathring{f}(\alpha) = \beta \). For each \( \beta \) which could equal \( \mathring{f}(\alpha) \) in such a generic extension, fix such a \( p_{(\alpha, \beta)} \).

Then (with \(\alpha\) still fixed) it is clear that the \( p_{(\alpha, \beta)} \) are pairwise incompatible. Since \( \mathbb{P} \) satisfies the \( \lambda \)-chain condition, this collection of conditions has size \( \mu_\alpha < \lambda \), and hence \[ \left| \left\{ \beta < \kappa \colon \exists p \in \mathbb{P} \; p \vdash \mathring{f}(\alpha) = \beta \right\} \right| = \mu_\alpha < \lambda \]It follows that the set of possible range values of \( \mathring{f} \), namely \[ Y = \bigcup_{\alpha < \gamma} \left\{ \beta < \kappa \colon \exists p \in \mathbb{P} \; p \vdash \mathring{f}(\alpha) = \beta \right\} \]has cardinality no greater than \[ \sum_{\alpha < \gamma} \mu_\alpha \]

Now recall that \( \lambda \) is regular, so the sum of fewer than \( \lambda \) smaller cardinals \( \mu_\alpha \) must be less than \( \lambda \). It follows that \( Y \) is a bounded subset of \( \kappa \); say \( Y \) is bounded by \( \xi < \kappa \). Then \[ \mathbb{1} \vdash \forall \alpha < \gamma \; \mathring{f}(\alpha) < \check{\xi} \]

Spectral Lore: III

An absolutely gorgeous long (LONG!) album from one-man Greek outfit Spectral Lore. Too upbeat to be doom, too riffy to be folk metal, too little guitar masturbation to be progressive, not quite black enough to be black, but shares something with all of these...

Listen to it all of a piece, or not at all. This is not an album to sample an isolated track from

Lurr

Oh my.

I only now realized the joke in that the alien Lurr, from Futurama, is from the planet Omicron Persei Eight.

O. P. Eight.

And they're always watching TV there.

Hmmmmm. I see what you did there.

Candlelight Records sampler: "Legion III"

Hat tip to No Clean Singing for pointing to this sampler of tasty new metal. In particular, the last track, by UK band Xerath, is kinda addictive.

Vignettes of modernia

A crushed bottle of Five Hour Energy in the parking lot of Ikea.

At ten in the morning on a Saturday.

Knowledge Transfer

A quick note, stemming from discussions at the new job about depth of knowledge (on the part of elementary/middle school students and their teachers) and related questions. One of those related questions is knowledge transfer: the ability to take knowledge from one context and apply it in a related context. The first hurdle there, of course, is recognizing that the contexts are related; the second is knowing what to keep and what to change, as the contexts change.

A complicated link of half-remembered references brought me to a paper (PDF) by one Michelle Perry describing an experiment done with 4th and 5th graders. The children in the experiment were selected based on knowing basic arithmetic (addition and multiplication under 20) but not being able to correctly fill in a blank in a problem like

\[ 4 + 6 + 3 = \_\_ + 3 \]

which tests the conception of the \(=\) sign as a statement of equivalence (correct) or an instruction to go forth and compute (incorrect). Students were given either direct instruction in the procedure to follow (add up the left hand side and then subtract the known term on the right from that sum), or given a purely conceptual instruction with no explicit steps.

What is really interesting is the result: both groups did roughly as well on post-instructional assessment -- but only on the problems that used addition, and so were exactly analogous to the problem they'd been instructed on. The post-test, however, also included problems that required the same principle, but used multiplication instead:

\[ 3 \times 2 \times 3 = \_\_ \times 3\]

In these problems, the children who had been taught a procedure "followed" it by doing the multiplication on the left and then subtracting the known "term" on the right from the product! Around 40% of the children who had been taught the principle underlying the problem successfully transferred knowledge to the unfamiliar setting, compared to 10% of the "procedure" group.

The remainder of the study is interesting too: their results indicate that teaching concept-plus-procedure actually undercuts transfer: basically if you teach a concept and then immediately teach a procedure for it, students' conceptual understanding gets washed out by the procedural knowledge.

Be prepared

Note to self: when buying a can of beans to make into part of dinner, make sure that your new apartment has the use of a can opener.

TNC on Williamson

The Case for American History 

Today in [racially segregated] straw armies...

So Kevin Williamson, whom friends of the blog have met before, was tapped by noted white-supremacist rag National Review to deliver the [g]libertarian response to Ta-Nehisi Coates' address on the state of our racial union. Get an umbrella, folks, it's gonna get pissy in here.

We begin in the very first paragraph:

Mr. Coates’s beautifully written monograph is intelligent and sometimes moving, and the moral and political case he makes is not to be discounted lightly, but it is not a persuasive case for converting the liberal Anglo-American tradition of justice into a system of racial apportionment.

Now, if you're like me, you might be scratching your head what the everloving fuck Williamson is talking about. Is he referring to the actual justice system -- a system that in its colorblindness just happens to imprison black men an order of magnitude more frequently than white ones? Or is he referring to some more inchoate tradition of justice, like the one which greeted the returning veterans from World War II with flowers if they were black and federally subsidized mortgages if they were white?

You cannot read Coates' essay and not realize that the Anglo-American tradition has been one of racial apportionment since the 1600s. This is the entire point. Goods of great and lasting value have been apportioned, through private and market-oriented means as well as through public policy, in a racially lopsided way. Now, of course not every lopsided apportionment of goods is a crime, but Williamson can't even seem to get this far.

A little further on, Williamson dances with an actual insight before losing the beat:

The most valuable aspect of Mr. Coates’s essay is as a corrective to the tendency to treat the systematic political and economic repression of black Americans as though it were a matter of distant history and a question that had been for the most part settled at Gettysburg, with a few necessary legislative reforms in the following century. The process of extirpating effective racism did not end in 1868 or in 1964; even assuming a zero racial handicap on a forward-going basis, we would expect it to take decades before the average economic differences between blacks and whites were to disappear. (If, indeed, we should expect them to disappear at all.)

Now, let's take a suggestion from that BBC piece about toilets and go through the thought-experiment of how this works in detail.

Under what conditions would we expect the economic distribution of whites and blacks to converge to each other, assuming that they have formal equality of access? One of the drivers of continued inequality is inherited wealth: if I am wealthy, then on average my children and grandchildren will be wealthy as well. Now, if I am white, what is the expectation that my children and grandchildren will be white? Here is where I think the models underlying Williamson's expectations might not match up with mine. Williamson, I suspect, models U.S. society going forward as a place of heavy racial intermixing, so that between those descendants of today's black people who benefit from hard work and entrepreneurship and those who marry into previously white money, the boundaries between the races blur and the overlapping distributions will coalesce.

I'm less optimistic. While I do see plenty of glorious miscegenation taking place, the drivers of de facto segregation in the U.S. are not gone even if everyone has formal access to the same suite of financial tools. And segregation -- in schools, in neighborhoods, in all these places -- is a countervailing force against this commingling of the descendants.

If segregation remains as powerful a fact as it is today, then we would expect the wealth distributions of white and black people not to converge, but precisely the opposite.

There is probably a vicious circle at work here: Even controlling for income, blacks are financially risk-averse compared with whites, which probably has something to do with the history that Mr. Coates cites; but this risk aversion has the long-term effect of leaving them worse off as they forgo higher returns on their savings

Worse off than what? Higher-return investment strategies are by definition higher-risk -- what Williamson is saying here is a direct denial of even weak forms of the efficient markets hypothesis. Unless he thinks that black people's risk-aversion takes the form of saving in the First People's Bank of Mattress, any approach to personal finance which beats inflation is either just as good as any other or improperly priced.

Hey, wait a minute. It couldn't possibly be the case that the personal-finance game is rigged against people with lower assets, could it?

Blacks probably should extend that skepticism, or even transfer it, to the welfare state. Mr. Coates does not spare the New Dealers, who enacted a raft of progressive policies that were in many cases designed to exclude or disadvantage African Americans. Contrary to the convenient myth related by our contemporary liberals, there was no substantial conflict between Democratic liberals and Democratic segregationists on most of the progressive agenda — the  progressives and the segregationists were, in the main, the same people, and the so-called conservative Democrats in the South were very enthusiastic about federal regulation of businesses, the minimum wage, social insurance, and welfare programs, so long as they could be structured in a way that would not benefit blacks very much. But Mr. Coates does not give much consideration to the possibility that a similar dynamic still is at work among our 21st-century progressives — not in the sense that white progressives see their own interests being in direct competition with those of black Americans, but in the sense that programs run for the theoretical benefit of the poor, who are disproportionately black, are in fact run for the benefit of the largely white upper-middle-class bureaucrats who are employed by them.

I smell piss. Piss, everywhere.

Listen, Kevin. We've been over this. It is impossible to be both a progressive and a segregationist, at least in the sense(s) the word "progressive" has been used in the post-Civil-War political context. Yes, the New Deal was a pretty raw deal for black people. The rising tide eventually lifted some nonwhite boats, but it's quite true that in order to get the damn thing on the books and in force, FDR needed the votes of his southern Democratic caucus.

But I can't figure why you are making this bait-and-switch to talk about how conservative Dems in the 1930s didn't hew close to the shibboleths of the modern conservative movement. Federal regulation of business, minimum wage, social insurance, and welfare programs can be net positives for a state economy. Now, conservatives love to accuse the latter three of these of impoverishing their nominal beneficiaries, but that case falls apart every time. (Hence the fallback position of "well, it inculcates a culture of poverty", which is both false and paternalistic bullshit. When there are jobs to be worked which pay better than welfare, people work them if they can get them.) But that's not even the case you're making here, since you pivot to "bureaucrats" without even the courtesy of telling us which programs you're imagining the bureaucrats are occupying, sucking up our precious bodily fluids.

Well, that's not quite true. Right after the last excerpt, you mention teachers' unions and how they're fighting school reform. Now, it's not clear what teachers' unions and bureaucrats have to do with each other, and it's very very unclear that turning the Washington D.C. school system over to Michelle Rhee was in the interests of anybody except Michelle Rhee and a whole bunch of fly-by-night charter schools. But seriously: what the hell point are you trying to make here? It's an incoherent mess.

We're almost done:

Blacks are disproportionately poor, and policies that encourage economic growth and robust employment, which is the only meaningful long-term anti-poverty program, should benefit blacks with roughly the same disproportion.

This is just simple mathematics: absent any structural amelioration of the reasons that some discrete subgroup of the population is disadvantaged, just growing the economy preserves disadvantage. A color-blind approach like this is both naive and counterproductive.

And this is, again, the whole case being made: that the assaults against black people in the U.S. have been public, sustained, and not racially neutral. It defies logic to think that a racially-neutral response could possibly work to counter this history.

Usage peeve

Dear internet and beyond:

The following is incorrect:

"Bob was reticent to discuss his benefits package."

What you meant there was

"Bob was reluctant to discuss his benefits package."

"Reticent" means "silent" or "disinclined to talk much". I suppose you could make a case for saying "Bob was reticent on the subject of his benefits package", though in my experience the word refers more to a broad character trait (think the strong, silent type) than it does to any particular decision to talk or not.

Thank you, have a wonderful holiday, and get off my lawn.

Don't stop! I yield!

Riffing on the topic I touched on a few weeks ago, of questions on high-pressure exams, I wanted to share some thoughts about a fun programming problem that I'm not sure makes a great interview question -- but maybe that's an argument for why it does.

The problem was mentioned in a thread about programming interview questions.

Consider the digits 123456789, in that order. Now consider the value of the expression resulting from inserting + or * between some of those digits: for example, you could insert + after 2 and 4 and * after 1 and 8, resulting in

>>> 1*2+34+5678*9
<<<   51148

or insert + after 3, 6, and 8, resulting in

>>> 123+456+78+9
<<<   666

Write a program which prints out all the expressions of this kind which evaluate to 2003. (Hint: there are exactly four.)

Matt Walsh Project I: Homeschooling

I'm going to start this series off light: responding to a post where my disagreements aren't with the main thrust, but with side (snide) comments.

In The Two Absolutely Worst Arguments Against Homeschooling, Walsh actually goes over ground that formed my very, very first paper in undergrad. Yes, Virginia, we've really been having the same damn arguments since the early oughts -- actually longer, since I think all the research that I cited in that paper was from the nineties and before. (Full disclosure: I was homeschooled for part of my K-12 career.)

Nostalgia aside, here are the two arguments he's referring to, in response to a reader email:

2. Homeschooled kids aren't properly socialized.

This one was known to be false very early on. I mean, yes, we've all known someone who was homeschooled and turned out -- weird. It's even possible that ordinary schooling (whether of the public or private variety) might have helped that person turn out a lot less weird (as it probably did for me). This, however, is not actually data in support of the contention. This is what is known as "availability bias": weird people stick out, whereas people who are well-socialized don't. You'd never ask someone who didn't stick out how they got to be that way: it's just the default that you interact fluently with people.

And it was known all the way back in the nineties that adults who came from a homeschooling background looked pretty similar to adults who'd come up through regular schooling. If I'm recalling correctly, some of the studies noticed a measurable trend that children in homeschooling, and adults who had been homeschooled, were more comfortable dealing with people who were older than them than with those their own age. I don't remember if that effect was robust over time, but it makes sense. (In regular school, you're mostly being socialized by people your own age; you take your cues from them, you adapt your language to theirs, etc. In a homeschooling situation, cues come from your parents and the other parents in the clique as much as or more than others your own age.)

Now, as I mentioned, some of Walsh's side comments are less reasonable:

Sure, you can probably tell me about a homeschooled kid you met once who was totally weird and awkward and stuff, but I could see your anecdote and raise you school shooters, the bullying epidemic, youth suicide rates, a youth culture utterly dominated by cliques, fads, and trends, and then this:

[beerbong.jpg]

Well adjusted adults?

Go to a college campus — any college campus — and tell me again how these public schooled ladies and gentlemen are such well adjusted adults.

For God’s sake, Dan, they literally cannot socialize without inhaling a barrel of urine-flavored light beer ahead of time.

I’m not claiming that homeschoolers don’t use smart phones or beer bongs, but I am saying that an overwhelming preponderance of our society has been exclusively public schooled, and if public school helped ‘socialize’ us, you’d think we’d see SOME positive results SOMEWHERE.

Look, you'll get no disagreement from me that Natty Light is terrible stuff. But note how Walsh moves the goalposts from "well socialized" to "well adjusted adults"? Anyone who claims that most college students, from whatever background, are well adjusted adults needs their head examined, but that's not the claim here. In college, one has a few years to learn that, even if no one's looking over one's shoulder, there are limits to what a person can do. The hangover doesn't care whether you have an exam tomorrow. That paper isn't going to write itself. No one's going to crack the whip over your head -- and parental whip-cracking isn't just done by homeschooling parents.

Those students in [beerbong.jpg] don't look poorly socialized to me. They look like they've socially sorted themselves into a social group that is reinforcing their behavior. There are plenty of other students on that campus who are partying in a more sane manner, and some who aren't partying at all, no matter when that picture was taken.

One becomes a well-adjusted adult by learning one's own limits, taking responsibility for what one is responsible for, and finding answers to the existential questions and insecurities that plague every teenager with a brain. Some people do that with four years of college. Some people flunk out, or make a baby they didn't intend to and find out the hard way that they don't offer baby loans like they do student loans. Some people forego college altogether (although the expected value of that decision ain't so hot these days). But the only way to become an adult is to practice being an adult, out from the supervision of parents and guardians, and neither homeschooling nor regular schooling can offer that. (Don't talk about boarding school. That's a whole 'nother conversation.)

1. We should keep our kids in public school in order to help ‘the system.’

This was the proposition that I was writing that first undergrad paper in response to. Well, more precisely, I was arguing against an improved statement, something like "Homeschooling is unacceptable because it undercuts the role of the school in producing good citizens."

I'm not at all sympathetic to the proposition in the form Walsh quotes it: take it away, Matt:

Is this really a priority for parents? When my wife and I make a decision for our family, should we stop first and ask, “wait, but will this help the system?”

Would you REALLY put the welfare of ‘the system’ over that of your own children?

I’d hope that you wouldn’t, and I’d hope that this line of logic is unique to you, but I know that it isn’t. I’ve heard it before. I’ve heard it so often, in fact, that I’m starting to think I’m the strange one for having absolutely no desire to make my children martyrs for some bureaucratic machine.

I'm opposed to the argument even in the modified form I gave above. I do think that it's an important role of the school to instill shared values -- school, in other words, is not just about academics. Homeschoolers agree with me: overwhelmingly, they're not choosing to homeschool because the public school is academically weak, but because it's teaching evolution, or sex ed, or won't burn the copies of Harry Potter in the school library. Homeschooling is all about whose values get passed on to kids; and part of being a free society is that, if one feels strongly enough that the values embodied by some social institution are antithetical to one's own, one generally doesn't have to interact with or take advantage of that social institution.

(There are a few exceptions, of course. One can't simply decline to interact with the judicial system because one has problems with the values of that system. I have a deep problem with the lower value placed on black people's lives and welfare by the judicial system, but I can't just not show up to court when subpoenaed, even if I think the prosecution is unjust. One can't simply decline to interact with the IRS because one's values place a high premium on not paying taxes.)

Thinking that "the system" is unjust is a core right in a democracy [1]. Declining to abet an unjust system is a corollary right.

That all being said: society still has the right to set its own parameters of acceptable speech and ideas. Not that one who transgresses these parameters should be formally sanctioned under the power of the state, but there is plenty of room for people to exclude and privately sanction those who hold, say, bigoted views. One of the big goals of public school is training students what society now views as beyond the pale -- especially when they might not get it at home.

What I'm saying here is, don't dismiss too quickly the notion that the public may have an interest in students not being homeschooled, since those who are may be out of step with what society at large sees as the ideas one can or cannot hold while still being a full member in good standing.

From my own (progressive) position, for example, someone who literally wants to replace the separation of church and state with established state religion cannot be a member of American society in full good standing. It's just not possible. Likewise someone who advocates for child labor, or someone who wants to undo gender equality of the franchise. I don't want the government taking any action against holders of such ideas -- but I absolutely want them to be treated by their fellow citizens as objects of public distrust and scorn. I absolutely want them to be unelectable, unworthy of public trust.

In other words, while I don't think Argument 1 represents any kind of case for a public policy banning homeschooling, I do think that there's a case implicitly for the following: If you are considering homeschooling on the grounds that the values embodied in the public schools are incompatible with your own, you must be thereby ready for others, who do subscribe to those values that you dislike, to treat you as withdrawing from your own full membership in the shared social project that they are undertaking. Homeschooling is an "exit" strategy, with a (possible, implicit) future "voice" strategy to be undertaken by the former child after they are grown. And exit strategies  are not how democracy is designed to operate. Exit strategies are a business-world response to disagreements.

OK, this response has gone on long enough, so I'll skip over the silliness at the beginning of Walsh's post about teacher's unions. (As always is my response to someone who ignorantly complains about being "unable to fire" union members: why you you hate the free market? It took two parties to sign that contract, and now you want to go back on it? That ain't how this shit works.)

[1] I'm using "democracy" in the broad sense here: a system of government in which those in power derive that power from the people; and are accountable to the people for its use; and can be removed from office for abuse of that power, either through ordinary means (elections) or other (extraordinary, but spelled out in law) means. There's also a narrow sense of the word (in which every decision is put to general vote by the people) which obviously doesn't apply to the U.S. Both meanings are correct. Get over it.

Introducing the Matt Walsh Project

I have conservative friends. This should not be a surprise, but it can be anyway -- it's one of the ways that the Internet imitates modern life, that we are able to sequester ourselves into little enclaves (more on this in the next post). And it's also true that the overlap between self-identified conservatives and horrible (racist, sexist/gay-bashing/trans*-bashing, nativist, warmongering, etc.) people is nontrivial. When people in my life cross those lines too far or too often, they don't stay in my life, but simply self-identifying as conservative doesn't cut you off on its own. (Neither does being an idiot -- I'm dumb plenty often myself, and even more often don't have the relevant facts at my disposal.)

All of which is to say, that I have some conservative friends, despite the fact that I'm about as far away from being a conservative as one can be and still have real representation in the American political system. And many of those friends are on Facebook. And they share things.

Frequently, very stupid things. (Conservative imagememes are... well, they're embarrassingly dumb.)

Occasionally, less stupid things.

Very occasionally, things that are wrong, but deserve an answer.

And I've noticed one blog that people link to, that has an abnormally high incidence of the last category. And, oddly enough, this is a blog that doesn't seem to get picked up by (for example) Memeorandum, or to be on the radar of the liberal blogosphere, even though clearly conservatives share it around.

(It's really not all that odd that Walsh doesn't get much Memeorandum love -- Memeorandum's algorithm values people glomming onto existing stories, and it doesn't look like that's how he blogs. I'm not sure, since I don't have his RSS in my feedly or anything, and it's not relevant.) I'm not even really sure who Walsh is, aside from a blogger; his site banner has a picture of him in a radio studio, but his bio doesn't link to any radio show. Regardless: his words speak for themselves, and who he is in real life isn't really my problem.

Anyway: I'm setting myself the project of writing responses to Walsh's posts, when (a) they float across my own social networks (I'm not going to go looking for them), and (b) they've got enough wrong in them to warrant my time.

(NB: my time fluctuates in value. This month, it ain't worth much, so marginal wrong might get my time.)

I've got two to start with. One is a bit old, but the wrong factor is high, and it's on a topic that I have strong feelings about. The other got posted this week, and its level of wrong is actually pretty low; it was just enough to get my lazy ass writing about it.

Black metal is good for the nonsoul

This is absolutely a bookmark (h/t Heavy Blog Is Heavy):


I'll be too busy watching hockey tonight to listen to this, but it sounds right up my alley.

Evan Soltas on the gender pay gap

Soltas:

"Look, I understand why Perry and Biggs have to respond to me and... I would agree with them that the 23-percent number reflects more than discrimination. But if they are going to try to explain away the pay gap, they're going to need to try a bit harder than this... When I actually ran the numbers, I found a persistent pay gap on the order of 4 percent to 10 percent, accounting for a battery of things -- frankly, everything that I could think of, and everything labor economists usually consider -- occupation, work experience, education, race, marital status, children, union membership, geographic location, and weekly hours.

(Nil)Potent problems

Somehow, every year about this time, I start thinking about preliminary exams. (Also known at other institutions as subject exams, qualifying exams, etc.: the dreaded first hurdle of staying in grad school.) Specifically, I start thinking about questions that would be appropriate to ask on such exams, in difficulty, length, and subject matter.

Now, I'm going to avoid my usual rant about the content of most prelims in algebra -- this post isn't about prelims per se, and besides that, the problem I want to talk about is one that I emphatically wish algebra prelims wouldn't test! But it's a fun little argument nevertheless.

Today in features, not bugs

The House GOP: :

The proposal, which Republicans voted for in the House Ways and Means Committee earlier this month, would alter the definition of full time employment under the Affordable Care Act from 30 hours a week to 40 hours a week and exempt more businesses from penalties for not offering employer-based insurance or lower the overall penalty burden. Under existing law, employers with more than 50 workers pay a penalty if their full-time employees (defined as working an average of 30 hours a week) receive subsidized coverage in the law’s health care exchanges. CBO concluded that the GOP proposal would lead to the very same problems Republicans have identified in Obamacare. H.R.2575 would reduce the number of people receiving employment-based coverage by 1 million, increase “the number of people obtaining coverage through Medicaid” or the health care exchanges by between 500,000 and 1 million, and raise the budget deficits by $73.7 billion. The ranks of the uninsured would also grow by “less than 500,000 people.”

Until the Republican Party learns to choose their desired policy outcomes first and structure their legislation around achieving those outcomes, no one has any business voting for them at any level.

To-Read list, Harlem Renaissance edition

I have to confess a deep ignorance of even the canonical works of the Harlem Renaissance; somehow, the curators of my educational experience skipped that chapter of American letters. And it's my own damn fault for not deciding to work through even one of these books in the last five years, or (even worse) during the three before that, when I was actually working in Harlem!

I will say that my leisure reading patterns have more broadly been what I think of as "light", which of course matches no one else's understanding of that term. Leaving entirely aside the math books that I've read for fun, I've chewed through everything Iain Banks has written that I can get my hands on, most of A Song of Ice and Fire (I had to return A Dance with Dragons to the library before I finished it -- no, seriously, someone recalled it out from under me), some Salman Rushdie, and also some nonfiction too. But it's certainly happened that I've taken out a book and gotten bogged down early, not because I wasn't enjoying it, but because it required my full faculties and I was reading for diversion rather than self-improvement.

So I've been wanting to change the face of my to-think list, and I think the end of my Ph.D. and the concomitant life changes should enable that, if I'm serious. So I'm glad to run across this recommendation from The Humanist, of two Harlem Renaissance authors, both women, whose work has been unjustly forgotten.

And just in case that link goes offline:
Ann Petry, The Narrows
Ann Petry, The Street
Nella Larsen, Quicksand

This is absolutely a bookmark.

A couple of weeks ago, I ran across this service -- I think it was actually an ad, and I never click on ads, but there you have it. The basic idea is that you set up an account for your discretionary spending, get a debit card for that account, and --here's the brilliant part -- the account smoothes out your cash flow and displays an available balance of less than is actually in the account.

Anyway, read through the site, liked the concept, closed the window.

Forgot the name.

And tried to google it today, and no fucking combination of search terms hits. Until finally the same inline ad shows up in my search results.

So, for my bookmarking pleasure: Simple Finance

Road rage imprecations

Ms Heel-Filcher to bad driver on the freeway: "I hope you hit 'reply all' by mistake."

Oh Slate, you're being igorant again

I didn't stay up last night to finish watching the women's downhill final, but that's OK. It's not a sports movie, it's sports; I'm watching for the thrill of the game, not on the edge of my seat to see if the American someone in particular won.

Anyway, I wake up this morning and find this nonsense on my Facebook feed:

But it’s still weird that the race had to end like this, because the timekeepers know who really won. The official timing for all Olympic events is supervised by the Swatch Group, through its divisions Omega Watches and Swiss Timing... and today Swiss Timing can measure every race in every event with such precision that there should never be any question about who won. The International Luge Federation, for example, times its races down to 1/1000^th of a second. So does speedskating. Why can’t the FIS do the same?

Well, it can, and it does. That’s the weird thing. The official FIS rule book for international ski competitions says competitors’ times “must be immediately and automatically sequentially recorded on printed strips to at least the 1/1000th (0.001) precision.” As Bill Pennington reported today in the New York Times, the clock in the official timing booth on the downhill ski slope actually exceeds that standard, measuring skiers’ times to 1/10000^th of a second. So even though the women’s downhill was scored as a tie, “in the timing control booth, three people—the head timer, a backup timer and a computer operator—saw who won the race according to the timing data.”

Incorrect, Justin. At least three people saw the raw numbers assigned by the timing mechanism to the two skiers. But that's not the same thing as seeing who won. And why is that? Because even though the timing booth may record a number with 4 decimal places, does not mean that this number is correct to all those places.

This is something we were all supposed to learn in middle-school or high-school science: that any measuring device in any experiment is reliable within a certain tolerance, but is useless for distinguishing variations smaller than that tolerance. This is known as the "precision" of the instrument. If the instrument reports numbers in decimal notation, one normally distinguishes between those digits which are known to be correct, and those which are uncertain. (If the tolerance within which the equipment can measure is \( \varepsilon \), and \[ 10^{-e} > \varepsilon \geq 10^{-e-1} \]then the digit corresponding to \( 10^{-e} \) is the first uncertain digit.)

Note that the same piece of equipment may have different reliable precision in different experiments. Think about luge: the timing gate is extremely small and the profile of the athlete is very uniform (they're coming in toes-first), so an additional order of magnitude might be warranted. Or maybe, the true tolerance is only half of the true tolerance for skiing, but that's still enough to warrant one fewer digit in the official time.

Think about it this way: the FIS' decision to truncate to two decimal places means that, in their judgement, it is possible for the timing mechanism to report skier A's time as X.035 and skier B's time as X.037, while skier B actually made it down the course in less time. This is not an absurd judgement, and awarding these skiers a tie is actually more scientifically literate than pushing for the ghost in the Swatch machine.

Liveblogging the Veritas Forum

21:30 And we're done. I think two things kinda say it all: more of the audience questions were appropriate for a preacher than for a scientist; and the book table on the lobby was packed with every desperate attempt to make theism intellectually respectable published in the last twenty years. Veritas indeed.

21:25 I made my way to the mike line and asked about personhood being an emergent phenomenon. In particular, since she had gone out of her way to dismiss the very idea in less than a sentence, my question is, do you have the scientific basis for such a rejection? Result: total deflection. I mean, yes, it's also interesting that other humans ascribe person-ness to dumb routines, which is why the Turing Test is less powerful than it first appears, but answer the damn question.

20:58 Did she just approvingly mention Killing Jesus? As in, Bill Fucking O'Reilly?

20:50 Oh, and apparently the Bible instructs us not to self-promote. Or at least not to do the research you already did last year.

20:45  Now Picard and Spickard are sitting down for Q&A. His first questions are about religion.

20:37 ...And she came from an "atheist faith" to a Christian faith. Lovely.

20:36 Ah, now we see the reveal. Imagine an alien race which stumbles across inductions for building a radio. Lo and behold, it's more than its components: there's music too! And it's an emergent phenomenon! Personhood is analogous to the music "emerging" from a radio.

20:29 We've now seen two going on three multimedia clips; yet for some reason the products didn't bother to figure out how to connect the laptop's sound to the PA.

20:13 Picard opens by polling the room about their beliefs on whether human beings are "just" machines. She says she used to. Very few in the audience raise their hands. (The room, by the way, is FULL.)

20:11 A student brings the room to order. Picard's research sounds well worth doing.

The guest of honor: Rosalind Picard of MIT.

The local host: Anderson Spickard. The Third. Captain, I detect no warning signs of incipient douchebaggery.

Elbow grease

Random thought of the morning:

It is a fact that there exist electric cookware appliances which are completely submersible and dishwasher-safe. (We have such a beast -- a fondue pot that Ms. Heel-Filcher got for Christmas a couple of years back.)

In view of this, it is time and past time for there to exist a dishwasher-safe miniature grill. Get on that, George Foreman.

Proof by Contradiction

I spent one morning at the JMMs this week in a session on the Introduction-To-Proofs course (aka the Bridge course). I enjoyed the session; it contained some good techniques to include, some good warnings of things to avoid, etc. Such a course always includes learning about proof by contradiction.

Now, I have a bit of a thing about proof by contradiction. It's not that it's invalid; it's that, at least in classical logic, you can always transform a proof by contradiction into a proof by contraposition; in any case, while I'm not a constructivist and think that intuitionistic logic is mostly a curiosity, it's nice to have a proof which provides an implicit algorithm, when such a thing exists.

So today on the train I was puzzling over a little bit of boolean-algebra arithmetic which Tom Jech uses in his exposition of forcing. (I'm supervising an undergrad who wants to learn forcing, and the boolean-valued-model approach is so much nicer than the poset-only approach.) I tried to prove it forwards six ways to Sunday, and nothing seemed to work. So, remembering what we all tell students in Bridge courses, I turned it around and tried to prove it by contradiction, and that took all of six lines. I still don't see a direct proof that's not an artificial translation of the contradiction/contraposition result; if you know one, put it in the comments!

Theorem: Recall that in boolean algebras, the implication operation \( v_1 \Rightarrow v_2 \) is defined as \( v_2 \lor \neg v_1 \). If \(x,y,z \) belong to a boolean algebra \( \mathbf{B} \) and \( x \land y = x \land z \), then \( x \leq ( y \Leftrightarrow z) \).

Proof: Suppose otherwise. Then we can find elements \( x, y, z \) in a boolean algebra \( \mathbf{B} \) so that
\[ x > y \Rightarrow z = x \land ( z \lor (\neg y)) \]
Now observe that
\[ x \land ( z \lor (\neg y)) = (x \land z) \lor (x \land \neg y) = (x \land z) \lor (x \land y) \lor (x \land \neg y) = (x \land z) \lor x \geq x \]
Overall, \( x > x \), a contradiction.

Forcing Fraisse

Maybe it's just because it's three in the morning, but this little throwaway exercise in some lecture notes (pdf) of David Marker made my night:

Two models \( \mathcal{M} \) and \( \mathcal{N} \) are \( \infty \)-back-and-forth equivalent iff there is a forcing extension of the universe in which they are isomorphic.

Mind. Blown. And the proof is obvious.