You simply must meet Thomas. Thomas! — September 22, 2016

You simply must meet Thomas. Thomas!

The continuing Hamilton obsession reminds me: I’ve meant to read Dumas Malone’s six-volume biography of Jefferson for a long time; it’s supposed to be the definitive work on the man. I tried reading the first volume, but it was spending what seemed to me an excessive amount of time on Jefferson’s rural upbringing. That’s important to someone, surely; important when setting the stage for the famed philosopher’s veneration of rural life, surely; but not something I really need to read. So maybe I don’t need to read all six volumes. Maybe skip ahead to the time when he’s “off getting high [I always assumed it was ‘hot’] with the French”? Volumes 2 through 5 look like they cover the parts that most people would be concerned with, running from the Declaration through his time as president. Anyone interested in reading those four volumes with me?

As every schoolchild knows, Jefferson and Adams both died on the 50th anniversary of the signing of the Declaration of Independence, which would be July 4th of 1826. So from the end of Jefferson’s time as president until his death, there was a span of about 18 years. I’m sure he did fascinating things during that time, and I’m sure in particular that the letters he wrote would make for amazing reading…come to think of it, that time would span the War of 1812, and Jefferson was on one side of Virginia while Washington, D.C. burned, so surely he had interesting things to say. Regardless, volumes 2 through 5 are likely gripping reading, so let’s start by focusing on those.

James Madison also gets short shrift in Lin-Manuel Miranda’s play: offhand, I recall that Madison is mainly involved in uttering the hilarious single word “France”, convincing Jefferson to agree to the Compromise of 1790, and fielding Hamilton’s complaint that Madison is “useless as two shits.” But Madison is terribly important; my understanding is that he’s responsible for our government’s three-branch structure, in contrast to the monarchy that Hamilton wanted. That seems reasonably important. If nothing else, I’d like to read about the writing of the Federalist Papers, and the debate over the Constitution.

As always, I welcome people joining me in this reading.

Two math things — September 21, 2016

Two math things

  1. It’s a long-term goal of mine to understand the proof of the Prime Number Theorem. The PNT, for those who are unfamiliar, is that the number of primes less than or equal to N is approximately N/ln(N), with the approximation improving as N grows to infinity; the percent error of the approximation approaches zero as N grows. I found a really interesting paper that walks through a proof. (The paper won an award for math exposition.) I’ve only done a quick first read-through, but it seems interesting. On that first pass, I think I now get why we even bother with the von Mangoldt symbol. Baby steps. If anyone would like to read along with me, y’all are welcome to.

    One question I have is whether it’s mathematically impossible to find a function that exactly equals the number of primes less than or equal to a number. The N/ln(N) approximation is good, but it’s just an approximation with a known rate of error — and while the percent error drops to zero, the absolute error grows without bound. Is there a proof that a function which counts the exact number of primes less than N is impossible?

    (I could be more precise about this. Obviously the function which sums the number 1 over all primes p less than or equal to x is an exact function. But it’s obviously not what I’m looking for. There’s probably a formal way to describe exactly what I’m looking for it. It’s probably either “a function containing only a certain set of symbols” or “a function of at most O(log n)” or something.)

  2. If someone gives you the equation “ax = b”, you can solve that really easily with elementary algebra; the solution is x = b/a. Likewise if someone gives you an equation involving x-squared; the solution is the quadratic formula. The solutions get more and more complicated for x-cubed and the fourth power of x. There’s a theorem (Abel-Ruffini) which says that no solution using only addition, subtraction, multiplication, division, and root extraction (square roots, cube roots, etc.) is possible for the fifth power of x and higher in the general case. When I limit it to “the general case”, I mean that certain specific equations at higher powers may have solutions: x100-1=0 has the solution x=1. But the general equation ax5+bx4+cx3+dx2+ex+f=0 has no solution, nor do equations with higher powers.

    The question I’ve had for a while (apart from knowing enough Galois theory to know how to prove Abel-Ruffini) is what happens if you allow mathematical operations other than addition, subtraction, and the rest. What if you allow sines and cosines? Fourier series and their inverses? Bessel functions? Elliptic functions? The Wiki says that a certain kind of transformation turns the general quintic into a simpler quintic polynomial, which can then be solved using a Bring radical. Is the Bring radical the simplest function which can solve the general quintic?

    So then my first question is: what’s the simplest set of functions you can add to addition, subtraction, multiplication, and division, such that the general quintic has a solution in this augmented set?

I don’t want to give Amtrak ideas on how to make things even worse, but… — September 13, 2016

I don’t want to give Amtrak ideas on how to make things even worse, but…

When I travel on Amtrak, I always use the Matt Yglesias hack: wait downstairs at Penn Station, rather than upstairs, because the Amtrak boarding process is insane.

I wonder whether Yglesias posted that observation about Penn with some fear that Amtrak would lock down the process and thereby kill the golden goose. It’s been several years now, and the enjoyable hack is still there, so perhaps there’s nothing to worry about.

I say the following with similar trepidation: if you want to avoid the incredibly stupid and pointless lines at South Station, just get on one stop farther along toward New York, at Back Bay; problem solved. There are no waiting lines, and people board trains the way they should — the same way they board subways.

Also, it looks like Amtrak is considering making the train system worse. Read this whole thread by a fellow whose Twitter description says that he is “Prone to live-tweeting transit plans.”

Periodic Jefferson Image reminder — September 7, 2016

Periodic Jefferson Image reminder

On one of the recent episodes of The Room Where It’s Happening (a podcast about Hamilton because, like I mentioned, I’m obsessed), they play a message from a caller who says, basically, “Wow, it sounds like Jefferson was a real bad guy. I’m glad I’m learning differently about him now.” Nothing wrong with hearing something different about a Founding Father, of course. But while we’re walking down that road anyway, I’d like to reiterate my love of a book called The Jefferson Image in the American Mind. It’s less about Jefferson the man (if memory serves, the book starts when Jefferson dies, or shortly before), and much more about what’s become of how we perceive him in the centuries since his death. That angle is, perhaps, as interesting as the man himself. You could, if you wanted, tell a coherent story of American governance as the playing-out of the Jeffersonian and Hamiltonian strains in American thought over 200-plus years. (Probably more valuable to tell the story of America as two centuries of trying to atone for our original sin of slavery, but sure: Jefferson/Hamilton is a good one.)

Depending upon the country’s self-perception, and depending upon what the ideology of the time called for, Jefferson’s image swung from socialist French fairy to Jacobin anarchist to father of freedom itself. It’s actually pretty funny.

A few years ago we had the David McCullough bio of John Adams, which landed pretty hard on the anti-Jefferson side. Now we have Hamilton (the musical) taking a few little jabs at Adams (“That poor man / They’re going to eat him alive!”). Opinions change. Seems kind of silly to commit yourself to a battle over personalities. Committing yourself to a historiographical battle is more interesting. But it’s still more interesting, I think, to understand the forces that these men put into play, and what those forces mean for the basic structure of American governance.

Recognizing the bubble I’m in — September 4, 2016

Recognizing the bubble I’m in

Very often I’m the least educated person in whatever group I’m in. At work I’m surrounded by computer-science PhDs. Among my friends and family, I’m one of the few without a graduate or professional degree. My cats have MBAs.

Yet that’s actually not the way the country looks, as a whole. In my age bracket — which is the most educated of all age brackets — about 36% of us have bachelor’s degrees, and less than 1 in 7 have advanced degrees. I’m sure you could slice the groups up more finely, such that my not having a graduate degree puts me in the minority — e.g., among white, upper-middle-class urbanites — but that’s just the point: I’m so used to such rarefied demographics that I don’t often realize how rarefied they are.

My hypothesis is that people with technical bachelor’s degrees (“STEM” degrees, as they say) tend to have advanced degrees less often than those outside of STEM careers. When I was in college, someone from the School of Computer Science pointed out that lifetime earnings for those with CS degrees rise if you get a master’s degree, then actually fall if you get a Ph.D.: during the 4-8 years when you could be earning a CS-master’s-level salary, you’re instead earning no income and collecting the Ph.D. And at the time, a computer-science Ph.D. confined you to whatever CS specialty you’d been working in; that’s probably less true today. So there may have been more incentive back then to go directly from the bachelor’s degree into industry.

There were also plenty of jobs available to those with just the bachelor’s degree when I graduated from college back in 2000; had I graduated a year or two later, I would’ve entered the job market just after the bust. So that’s a second hypothesis: that the prevalence of advanced degrees rose when the economy tanked in 2001 and again when it collapsed in 2009. We can provisionally rule out that hypothesis by looking at the same Census Bureau table: the rate of advanced-degree attainment in the 25-to-34 age bracket is about the same as among the next-oldest cohort. Perhaps some people in the younger cohort are still getting their advanced degrees, so perhaps we have to wait a few years to compare apples to apples.

Some friends and I got in a similar discussion recently about the prevalence of Jews in the broader population. It feels like everyone I know and love is Jewish. But even within Boston, which is said to be the second-most-Jewish city in the United States, only 6% of residents are Jewish.

Again, I want to start cutting the data to explain the prevalence of Jews in my friend group. Does the percentage rise among white upper-middle-class Bostonians? But again, working to cut the data that way only argues for the point: I live in a bubble, and you have to establish a very specific bubble before the people I see around me match up to what’s in the bubble.

Lie-Bot saying 'The End! No moral.' to Philippe in an Achewood strip after telling Philippe a horrifying bedtime story. Lie-Bot then turns out the light, leaving a terrified Philippe to try to go to sleep.

Moving To Opportunity in Boston —

Moving To Opportunity in Boston

Much has been written about the benefits that can flow from helping people in poor neighborhoods move to wealthier neighborhoods (see, e.g., Yglesias). Today, Alon Levy on Twitter retweets Tony Dutzik, who shares an article from the Boston Globe about the difficulties that this sort of program faces in the Boston area. Wealthy suburbs like Newton resist providing affordable housing; instead we get this:

It was just three years ago that he withheld federal housing funds for a nine-unit development for the chronically homeless planned for a long-decommissioned fire station in Waban, a wealthy village on the west end of town where the locals play tennis at The Windsor Club in the summer and sled at Brae Burn Country Club in the winter.

“We live in a community where our kids walk to school,” one neighbor said at a public hearing on the project, “and I want to know why we shouldn’t be worried.” Another suggested that the prospective tenants might be more comfortable, “I hate to say this, but in Waltham.”

The article opens with the story of one woman whom any neighborhood would pretty clearly be honored to house:

It took some time, but Brito managed to find a subsidized apartment in a better-off community. Much better off, in fact: Lexington, a suburb of gracious Colonials and lofty SAT scores about 15 miles northwest of Boston.

Brito has to take a bus and two subways to get to her job in the city now. But the lengthy commute is worth it, she says. Her daughter can play alone in the backyard without fear. And her son, who just started his senior year at Lexington High, is considering St. John’s University in New York. Many of her old neighbors in the city aren’t faring so well. “Some people,” she said, “their environment swallows them.”

She’s willing to sacrifice a lot to make a better life for her family. Isn’t this what we’re supposed to be encouraging?

The intuition is that a neighborhood has every right to determine its makeup, including who gets to live there. In the United States, membership in the suburbs, with their good public schools and quality housing stock, is determined by ability to pay. Growing up in Vermont, we fought over Act 60, which tried to rectify some of the imbalances between wealthy and poor towns by redistributing some of the property-tax money from wealthy towns to poor ones. Naturally those towns which couldn’t afford to spend a lot on their schools drew the ire of wealthier towns: “We [in the wealthier towns] shouldn’t be penalized because we value our schools more.” In this model, the wealthier towns were paragons of virtue, willing to scrimp and save for their kids; it wasn’t just that the wealthier towns had set up a financial wall around themselves.

Let’s grant that neighborhoods have the right to control their makeup. (This principle arguably is what helped Cambridge fight off the Inner Belt, though that’s really a story of neighborhood-versus-state rather than neighborhood-versus-newcomers.) Still, this principle conflicts with the right of people to live wherever they want to live, so long as those people follow the laws and generally make good citizens of themselves. Most of us would bristle at openly declaring that a community is allowed to exclude people based purely on their wealth, but that’s how we’ve organized our cities and our suburbs. Even more of us, I think, would bristle at the thought that children, in particular — people who have no choice in these matters — should have their choices constrained by their parents’ wealth.

One answer might be that this sort of financial wall around the suburbs creates aspirations: if you work hard enough and earn enough money, you too will be able to afford to live in Lexington and send your kids to school there. “Every American believes that he may one day be rich” is one of the common stories about why Americans hate the estate tax, even though it applies to the tiniest sliver of Americans; the story goes that we all think, “That could one day be me,” even though, statistically, that will not one day be me.

I’m a libertarian on this point. I believe that the barriers to moving to a new city ought to be minimal (follow the laws and pay your taxes, basically), as should the barriers to moving to a new country; I’m all for open borders. But I doubt either of these things will happen in my lifetime.

One solution that the Boston area has come up with is METCO, whereby children from poor areas can be bused out to schools in wealthier areas. I suppose this neuters some of the suburban opposition: there’s less concern that poorer folks will endanger their pristine suburban neighborhoods, because the poorer folks will go back to Roxbury, Dorchester, and Mattapan at the end of the school day.

Another option is to recognize that many of the financial walls around the suburbs come from zoning rules: forbidding multi-family buildings and requiring setbacks, among many others. Once we recognize this, start to chip away at those rules:

A bill approved earlier this month by the Legislature’s Joint Committee on Housing would confront that problem head-on. The bill would require that every city and town plan for multifamily housing and designate areas where it is allowed as-of-right. It would also require every community to allow single-family homes clustered on modest lots in compact, walkable neighborhoods surrounded by open space. Cities and towns would be compensated for any net increases in school costs that result from their approval of multifamily and cluster developments.

(via Matt Yglesias)

Another alternative, which I’ll never tire of citing, comes from then-Harvard professor, now-Senator Elizabeth Warren’s book The Two-Income Trap, wherein she advises severing the link between “nice place to live” and “place with the good schools.” Ethically, this seems obvious to me: my children shouldn’t be allowed to get a good education solely because they were lucky enough to be born to middle-class white parents; they should be allowed to get a good education because they are American citizens, in the same way that their citizenship entitles them to protection against foreign invasion regardless of their parents’ income. But this is likely a minority viewpoint.

There’s a hand-wavy hope that the problem will solve itself as wealthy people move back into the cities. The mechanism by which this happens is always vague. Will the wealthy people who move back into the cities largely disconnect themselves from public infrastructure? Will they take Uber everywhere, for instance, rather than ride the subway, and send their kids to private schools rather than to the neighborhood comprehensive? Will they even have kids, or will the wealthy people be largely retirement-age boomers or childless married couples? And as the wealthy people move in, will the poor people be priced out? If so, then the we’ll see the wealthy people improve the public schools, but only for their own benefit — not for the benefit of those who really need the help. In short, assuming that the disconnected actions of wealthy people alone will take care of the problem seems to be praying for a micro solution to a macro problem.

My great fear is that rising inequality will only make this problem worse: the wealthy and the poor will inhabit increasingly disconnected islands, and the wealthy won’t even acknowledge that the problems of poverty are their problems too.

Oh, and Barbarian Days — September 3, 2016

Oh, and Barbarian Days

I don’t know how I neglected to include Barbarian Days among the reviews. It’s great, and quite different from anything I’ve ever read. I wouldn’t have expected to care at all about a book by a guy who has devoted much of his life to surfing, but I ended up caring very much about this book. It’s a remarkable combination of technical surfing discussion that verges into the poetic (when have you ever read poetic technical writing?), plus the story of Finnegan’s own life. As he ages, he remains in love with surfing, but also comes to realize that there’s a larger world out there, and that he should stop just being a beach bum. The book becomes sort of the punchline: the man who was at the beach most days before the sun came up becomes the sort of man who can write a memoir like this. It’s magnificent.