“America’s Walking City”

Boston loves to call itself that, but I would like to observe a few reasons why that’s kind of nonsense:

  1. New York is obviously America’s real walking city. Sorry.
  2. If we’re being picky about it, Cambridge holds a better claim on being America’s walking city than Boston does. (Yes, that may be kind of cheating, given the student population here.)
  3. Follow Google’s directions from Central Square in Cambridge to Deep Ellum in Allston, and you will regret the day you ever thought of walking in Boston. (The presence of a rail yard along your route might begin to suggest the difficulty.)
  4. The intersection at Charles/MGH was just not meant for walkers. And there’s a series of ugly footbridge hacks around there to get you onto and off of the Esplanade. “A series of ugly hacks” defines a large part of Boston. (Sorry, I love this city, and I would like to raise a family here, but let’s be honest about this place.)
  5. The snow. It’s only been falling around here for 400 years or so. Give it another 400 and the city may figure out how to make sidewalks walkable in its presence.

Morris Kline, Mathematics for the Nonmathematician

Black background, white text. In the background is also half of the famous anatomical drawing, I think of da Vinci's.

Highly recommended, for a wide range of audiences. This book builds up mathematics from the most basic level, namely counting. More than that, though, it presents mathematics in historical, scientific, cultural, and artistic context. It proceeds through the history of mathematics, teaching theorems from geometry, arithmetic, algebra, and probability along the way. I’ve never really liked geometry, but this book made me find it fascinating. And not just the Euclidean geometry that we learn in high school; Mathematics for the Nonmathematician spends a lot of time explaining how Renaissance painters discovered the laws of perspective and based them on a rigorous geometry that they invented (namely projective geometry). I imagine my artist friends will be able to relate to this book in a way that they’ve never related to a math text before.

Then the sections on physics are astounding, and make me want to go learn the mechanics that I never really grasped in college.

Throughout, Kline sprinkles his historical discussions and his theorems with applications from as many fields as he can find. Without sacrificing much in rigor, Kline calculates the approximate distance to the moon and the Sun, and tells us how we could estimate the distance from Venus to the Sun without having to fly to Venus and set up a telescope there. He discusses the theory of optics that might have allowed the Greeks to design their famous parabolic mirror to light invading ships on fire. The volume of examples here is truly astounding, and make the book just endlessly fun.

Kline wants you to understand why mathematics is beautiful. Why, exactly, do people spend their time on this austere, arcane science? Why did the Greeks turn it into the foundation of true knowledge? And for that matter, were the Greeks as amazing as we’ve made them out to be, inventing branches of knowledge and ways of thinking that have persisted for thousands of years? (Short answer: yes.)

The Greeks believed that mathematics taught us the truth. To skip over a lot of careful explanation, Kline traces this belief from the Greeks to its demise in the 1800s. Mathematics teaches us what follows from certain axioms, but we can choose those axioms for the sake of convenience. We can invent different geometries if they’re useful to us; for that matter we can invent entirely new ways of adding numbers together if those are useful. (Kline has a particularly charming example of how you might build a system of arithmetic around baseball batting averages.) The gap between deduction, formerly thought to be the essence of infallible truth, and induction, formerly thought to be messy and error-prone, has narrowed somewhat. The axioms have to come from somewhere, and they don’t come from God. They come from humans, who pick axioms that seem to approximate some portion of the world around them. Given the axioms, we proceed step by step to certain conclusions; but the axioms are ours to create.

This is just such a fun book. I recommend it to anyone with the vaguest interest in how mathematics intersects with our world. And I thank my friend Paul for pointing me in this book’s direction.

I appreciate the sentiment, but this is basically false

“Your health care decisions are not your boss’s business,” said Senator Patty Murray, Democrat of Washington –New York Times story about a Democratic bill to override the Supreme Court’s Hobby Lobby decision

I’m as unhappy about the Hobby Lobby decision as anyone else, especially since the U.S. Conference of Catholic Bishops say they don’t object to insurance covering Viagra. There’s an obvious double standard, and I hate it.

But really. Here’s reality:

  1. By ‘Your health care decisions’, what Murray means is ‘what your insurer is required to pay for.’ Let’s be clear on that, because you can still go ahead and pay for contraception on your own. Again, I’d like to see insurance plans pay for contraception, but let’s be clear on what “Your health care decisions” means.
  2. Your health-care decisions, by that standard, are never entirely up to you. Insurance pays for some things and not for others.
  3. This would still be true even if — as I would prefer — we had a single-payer health system. The government would still pay for some things and not pay for other things.

I think it’s hopelessly muddled to frame this in the language of “your health-care decisions”. What the big debate is about is simply this: what do we believe that the our insurers — whether it’s the government or a private insurer — should be required to pay for? That’s an ethical and economic decision. And our insurers will sometimes make decisions at variance with our own ethics. And that sucks. Those on the other side would, presumably, say that it sucks when they need to go against their ethics to pay for something that they consider objectionable. My response to that would be: how far are you willing to take that? If my religion forbids male doctors from palpating naked female patients unless the doctor is married to the patient, are you willing to deny coverage in that case? Are you willing to make female patients seek out female doctors if they want the insurer to pay for it?

Indeed, I think I need to read more on the Religious Freedom Restoration Act and the Hobby Lobby decision, because I’m confused why religion here doesn’t excuse just about everything. SCOTUS describes the RFRA as follows:

The [RFRA --SRL] prohibits the “Government [from] substantially burden[ing] a person’s exercise of religion even if the burden results from a rule of general applicability” unless the Government “demonstrates that application of the burden to the person—(1) is in furtherance of a compelling governmental interest; and (2) is the least restrictive means of furthering that compelling governmental interest.” 42 U. S. C. §§2000bb–1(a), (b). As amended by the Religious Land Use and Institutionalized Persons Act of 2000 (RLUIPA), RFRA covers “any exercise of religion, whether or not compelled by, or central to, a system of religious belief.” §2000cc–5(7)(A).

I’m tempted to find some excellent regulatory arbitrage out of this, whereby I can make a lot of money by hiding fraud under cover of religion. More than that, though, I find it offensive that I have to pay, through my taxes, for wars that I don’t agree with. Did the government use the least restrictive means of furthering its compelling government interest in destabilizing Iraq when it taxed me? Okay, arguably yes. Was the government’s decision to require coverage of contraception 1) not in furtherance of a compelling governmental interest? Or was it 2) not the least restrictive means of furthering that interest? I guess I need to read the decision.

So anyway: yes, this sucks, and it conflicts with my ethics. Let’s be clear that this is an ethical objection, not an objection — as Murray would have it — about someone interfering in your health decisions. Someone’s always going to interfere in your health decisions.

Zia Haider Rahman, In the Light of What We Know

The view out an airplane window. The passenger taking the photo is sitting a few rows back from the wing on the right side of the aircraft.

Hm. People seem to love this book. I’m told (though I’ve not read it yet) that The New Yorker gave In the Light of What We Know a review brimful of superlatives. (I guess it would be James Wood’s review, which I’ll read when I’m done here.) And there are a lot of good things to say about this book. You know that feeling you get when you read Anna Karenina, that Tolstoy was just paying much more attention than you were when you attended the same cocktail party? And that when Tolstoy got home to set his thoughts to paper, he was able to delicately pick apart his own thoughts to explain to his own satisfaction what he had just seen? Well, imagine that Tolstoy came knocking on your door after 10 years away from you, clothes in tatters and several months’ growth of beard hanging from his face. You sit down with an audio recorder between you, press record, and just listen to Tolstoy talk for weeks and months. Oh, and by the way, your father — you, the guy with the audio recorder — happens to be a Tolstoy-level intellect, who also happens to be a theoretical physicist.

But it gets better, because the perceptiveness of a Tolstoy gets thrown at a very specific set of concerns, namely Bangladeshi and Afghan immigrants to London and to the American financial system at the height of the bubble. Again, imagine Tolstoy being transported to the United States during the Cold War. Just imagine the cultural and economic divides separating Lev Tolstoy, gentleman farmer and anarchist Christian, from the world around him. Consider how strangely Americans then would treat him. And consider what magic Tolstoy’s diaries would contain.

This, then, is at least 70% of In the Light of What We Know. Our narrator’s long-lost friend, Zafar, appears at the narrator’s door. Our narrator’s marriage is falling apart, yet the narrator’s monstrous, modern, sterile, granite-countertopped apartment offers enough space to keep him and his wife nicely separated. His career is also falling apart; he’s the scapegoat at his structured-finance firm when the subprime-mortgage market is imploding. Zafar has just returned from Afghanistan. We’re given to understand that lurking within Zafar is a capacity for shocking violence. We’re given to understand many things; this is the storyteller’s gift of laying down suspense. So the first downer to note is that Rahman never really delivers on these promises. It’s considered churlish these days, I think, to expect resolution from a modern novel, so churlish perhaps I am. Regardless, you should expect no resolution.

You also shouldn’t expect to learn much about anyone other than Zafar. It’s expected, of course, that you’d understand him; his monologue is almost the entirety of the book. You won’t understand the narrator. You won’t understand the narrator’s wife, who is to all intents and purposes a nonentity. You will not understand Emily, the woman for whom Zafar feels a tortured love. This last is the real shame of the novel; Zafar, our Tolstoy, plumbs the depths of everyone else’s psyche, but Emily remains untouched. We hardly hear a word out of her mouth, by construction: Emily sits passively mute almost from the first moment we meet her. We’re given to understand that she is cold and almost robotic in her movements through life — as though she has a checklist that only she knows; if only Zafar could get access to that checklist, perhaps he could understand her. He never will have access to that checklist, of course, so cold and unfeeling she remains. All that binds her and Zafar is, it seems, a passionate physical love. This is supposed to appease the audience, I suppose — maybe we imagine Sharon Stone from the Basic Instinct days, able to condemn men to servitude with a deliberate crossing and uncrossing of her legs. Alas, Emily is the hole in the middle of the story, and it’s a hole that Rahman pretty clearly deliberately left unfilled.

Rahman hints early on that Gödel’s Incompleteness Theorem — viz., that in any formal system, there are theorems which are true but which cannot be proved — will play an important part in the book. Anyone with a bit of mathematical training will, I think, recoil at this suggestion; probably no other part of mathematics has been so much the playground of mathematically illiterate cranks than has Gödel’s Theorem. I always think of Hilary Putnam here:

Strictly speaking, all Gödel’s theorem shows is that, in any particular consistent axiomatizable extension of certain finitely axiomatizable subtheories of Peano arithmetic, there are propositions of number theory that can neither be proved nor disproved.

Not the most earth-bending theorem, when phrased that way, is it? It’s not even clear that it applies to anything that you or I care about; a negligible fraction of what we care about in our day to day lives is part of a formal system. Will the sun rise tomorrow? That’s an empirical question whose answer may rest on subatomic physics (theories that allow us to predict when the Sun’s nuclear fuel will run out), let’s say. It’s quite clear that the answer, or its nonexistence, has nothing at all to do with whether Peano arithmetic is complete.

So it’s both a blessing and a curse that Rahman never really does anything with Gödel. It’s a blessing, because I just don’t expect novelists to treat Gödel with the care that he deserves; and it’s a curse, because Rahman clearly believes that Gödel belongs somewhere within his novel, and always threatens to drag him in from the margins.

The resulting novel is, frankly, kind of a muddle. If Zafar had just been the Virgil to our Dante, exploring the minds of those he passed on the streets of London, what we’d have is a deeply penetrating work of social analysis. As it is, we have some of that, plus some math, plus some purely perfunctory characters, plus an ending that’s meant to be shocking but feels, instead, like Rahman was in a hurry to wrap up.

I’d strongly recommend using a well-sharpened X-Acto knife to slice out the final 50-75 pages. Read up to there, enjoy the time you spent with Zafar, and move along.

P.S.: The New Yorker writes

For years, Zafar has been obsessed with the Austrian mathematician Kurt Gödel’s Incompleteness Theorem: “Within any given system, there are claims which are true but which cannot be proven to be true.” The elegant proof hangs over this novel like an intellectual rainbow.

No, the proof does not. And the fact that the review says this makes me wonder if its author is aware of how the proof is constructed. I doubt the reviewer believes that Gödel-numbering is somehow a leitmotif for this novel.

Why can’t my portfolio exactly match the full market?

So far as I understand the conceptual basis for a lot of theorems in finance, one of the ideas seems to be reasonably straightforward: if some type of investment — domestic equities, foreign equities, bonds, housing, whatever — were systematically higher-yielding than some other type of investment, then everyone would just invest in the higher-yielding category and wipe out the difference in yield. So in the long run, you’d expect yields across asset classes to equilibrate.

Yes, this is based on assumptions, which might well be false. But let’s assume that it’s roughly true. Then the usual argument says that you can’t beat the market, and you’ll never do better than to diversify your portfolio. But note carefully what “diversify” means here. It doesn’t just mean “invest in all 500 stocks in the S&P 500″. There’s a whole lot more market out there! That is, there are a lot more asset classes than just large industrial stocks of the sort that the S&P traffics in. Even within the class of U.S. stocks, there are larger indexes like the Wilshire 5000. Or there’s the set of stocks tracked by the Vanguard Total Stock Market Index Fund. And then there are foreign stocks. And then government bonds. And municipal bonds. And corporate bonds.

But there’s still a lot more market out there. Some asset classes are harder to invest in than others, like houses. Wouldn’t it be cool if you could buy housing across many worldwide markets? It’s a little weird to imagine exactly how that would work, though large property owners do own a shocking amount of property across many cities. So in our imagined perfectly diversified portfolio, we’d have a bunch of housing. And we’d also have a lot of unlisted stocks. And we’d have some private equity. And we’d own some mines. Because again, the principle behind the diversification is that if everyone already knew that some asset class yielded outsized returns, they’d already be investing in it. The only way to beat the market in such a case is to know something that others don’t — to avoid some asset class that you know yields lower returns than the rest of the world thinks it does, or to invest in an asset class that others are systematically avoiding. In principle, I can’t see any reason why your buddy Doug’s new venture doesn’t count as an asset class for the purposes of this argument.

So here’s my question: how do I, J. Random Small Investor, get my portfolio fully diversified across all possible asset classes? One of Piketty’s observations in his masterwork is that the wealthy are able to obtain systematically above-market returns, in no small part because they can invest in asset classes that you and I don’t have access to. And in one example he gives — the Harvard endowment — it helps that the Harvard Corporation spends $100 million every year to manage $30 billion in assets. You and I could probably also do very well as investors if we spent all day every day managing our investments, and if we had a staff to do it, and if we had enough money to play with that we could offset some losing bets with more winning bets.

But that argument isn’t convincing to me, because we do have that ability; this is why we hire mutual funds. Apparently the Vanguard Total Stock Market Index Fund has $190 billion in assets. Granted, that particular fund won’t be investing in obscure corners of the asset universe, but why doesn’t Vanguard set up a fund that’s truly diverse across all asset classes, draw many billions of dollars from investors like me, and earn the same returns as the Harvard endowment or Bill Gates?

One possible answer is that regulation forbids them from investing in risky asset classes (like hedge funds or complicated swaps) if non-rich guys like me are on the other end of the trade. Is there some other reason I’m missing why wealthy people must earn higher returns than mutual funds do?

Is everyone here already reading “Pedestrian Observations”?

No? Then I would like to direct your favorable attention to “What elites do instead of providing services”. The analysis in there of why the very wealthy and very powerful prefer big, grand showpieces rather than workaday, functional infrastructure is brilliant, and seems to me quite right — devastatingly right. Please go read, then subscribe.

Shorter Great Divergence

Detail of _Guangzhou Factories, 1855-1856_, Sunqua, oil on canvas. Once in a very great while, I find something that I swear is an extended academic joke. I don’t mean “joke” in the sense that it’s unserious; I mean that the delivery of the whole thing is conducted with a tongue very forcefully rammed into a cheek. Maybe the best example of such a thing is Leo Harrington’s talk proposing an analogy between Hegelian logic and some topics in group theory. There’s just no way he’s serious there, but I’ll be damned if the man ever cracks a smile.

Pomeranz’s The Great Divergence is deadly serious. What could be more serious than a discussion of why the West won? The whole discussion is so often laden with moralistic Gregory Clark-style musings, and very often the whole exercise seems like an excuse to praise white people.

Which is why Pomeranz is so funny, to me at least. Throughout the book (I’m about halfway done) I hear him humming gently in the background, “It’s the slavery, stupid”. The rest of the book is very rigorous academic garb for that very simple idea.

I’m absolutely certain that I undervalue the importance of slavery to literally every bit of American history. That’s why constantly reminding myself, via something like Ta-Nehisi Coates’s reparations piece, is so vital.

The somewhat longer story, from Pomeranz, is that many nations were running up against fundamental labor and land constraints in the 1700s, and that Western Europe eliminated those constraints, respectively, by a) enslaving Africans and bringing them to the Americas, and b) taking over North America and killing all the native people there.

I really do hear Pomeranz saying throughout, in as measured a way as possible, “You are ignoring the biggest story of at least the last half-millennium if you ignore these.” That’s what I hear when he politely swats down one story, namely that white people had developed a habit of consumer acquisitiveness which started with increased consumption of sugar and tea. I hear Pomeranz quietly saying, “Interesting that you focus on the consumers of the sugar. Where do you think Western Europe got all that sugar?

Thus far the bulk of the argument has been to show that the data don’t show any significant differences between Chinese culture and the Western European one; and to the extent that there are any such differences, they tend to tilt in China’s favor. Pomeranz shows that the Chinese government was no more resistant to urbanization than the British one; that it wasn’t any more insistent that women stay out of the workforce; and so forth.

That’s all by way of ideological thicket-clearing. Presumably the next steps in the argument from here cut to the heart of the matter and show that only slavery and extermination of the indigenous population are of the right magnitude to explain why the West rose when it did. Pomeranz has also hinted that the Chinese government’s remonetizing silver when it did was well-timed with the Spanish government’s mining of silver in the New World; it prolonged foreign investment when that infrastructure was needed. And part of that story is an interesting one about how long-distance trade requires sophisticated banking: if your goods disappear long before you receive payment for them, and if that payment ultimately comes from someone thousands of miles away, you need some strong guarantees that you’ll get your money; these guarantees, in turn, probably require strong institutions that allow people to trust each other; and so on down the line. Presumably Pomeranz will show at some point that these institutions were just as strong in China (which has famously had a strong central government since well before the time of Christ) as they were in the West.

This scope of argument can often make me experience vertigo. You’re explaining the growth of an entire civilization, after all, even while you’re pulling in the very worst acts that we’ve ever perpetrated against other humans. Pomeranz doesn’t often let us get lost staring at the stars, because — bless him — he is off in the weeds. He has to be: if people are going to argue that there’s something vital in the bourgeois souls of white folk — something which allowed white people to rise to take the mantle of leadership over the benighted races — then there are probably just about two options:

  1. Engage with this on its own vague level, pointing out that the Chinese are so good people; or
  2. Try to find data that can concretely address these sorts of claims.

You probably can guess that I prefer 2. to 1., despite the paucity of the data. I’d rather believe a small number of things based on the little bits of truth that we can polish here and there, than believe a lot of transparently self-serving metaphysical bollocks about the superiority of white people. So when Pomeranz goes off in the weeds on these sorts of things, I think we’re obliged to follow him.

This is probably the third time I’ve tried to make my way through The Great Divergence, though, because the weeds have — I admit — thrown me off in the past. I’m over that now; I find the book fascinating, because its eyes really are focused on the stars even while it’s digging in the dirt. If you bear that in mind while you’re reading Pomeranz, I think you’ll appreciate it as much as I now do.

My paranoid backup scheme

Inspired, I think, by Marco Arment, I trebly back up my computers:

  1. To a Time Capsule at home.
  2. Via SuperDuper to an external hard drive that sits at work. (I couldn’t really tell you how this differs from just using dd(1), other than that it has a nice UI, only copies the diffs, and seemingly makes the external disk bootable. In any case, it’s great.)
  3. In the cloud to Backblaze.

I have my laptop set to automatically back up to the cloud at all times, and my girlfriend’s laptop set to do the same. Then I use the Backblaze iPhone app to periodically ensure that all my backups are up to date. It’s awesome. The best backup is the one you never have to think about, and I definitely don’t have to think about this one.

…and if you decide to use Backblaze, too, I can get a cut. It’s great. I would never recommend a product I didn’t use enthusiastically, and I wholeheartedly recommend Backblaze.

(As it happens, I also wholeheartedly recommend my Time Capsule and SuperDuper, but they offer me no way to get filthy rich, like Backblaze does.)

Ten-cent economic hypothesis of the day, keeping-up-with-the-Joneses edition

This Matt Yglesias post (about a Houston-area day spa for babies [sic]) makes me wonder if the following has been formalized appropriately. Imagine some microeconomic decision like how large a house to buy. Some part of that decision will come from your actual desire to own a larger or smaller home. Some part will come from zoning (maybe you can’t buy a 1000-square-foot ranch-style home in the gated community). And some part will come from a pointless arms race between neighbors: I need to have a larger house than you, and you need to have a larger one than me, and so we proceed, more and more garishly.

That last motive is a collective-action problem: I don’t actually care where I end up, so long as I end up ahead of you; you, of course, think the same way. This is an arms race, in other words. During the Cold War, neither the Soviet Union nor the U.S. wanted to build up a nuclear arsenal; they were both forced to, because neither side could credibly commit to the other that it would disarm. So it is, I think, with housing. If there were some way to forcibly disarm both of us — if there were a single superpower, to continue the analogy, with a monopoly on violence that could bring both the Soviet Union and the United States to heel, well then the problem would be solved.

As it happens, we have such a superpower in the United States. It’s called the U.S. government, and it has a magical power called “taxation”. Imagine if we taxed the wealthy to such an extent that they no longer had the choice to participate in housing arms races and could only buy ordinary-sized homes. In some sense they might not mind this: if the point is to get ahead of your neighbor, and your neighbor is getting taxed at the same high level as you are, you’re both reasonably happy with the situation. Of course, you’d be happier if you both had more money, but by stipulation you were already forced to throw money into a zero-sum pursuit of larger homes; now you’re just forced to throw money to the federal government.

I don’t claim that wealthy people would raise no tantrums at all if they were forced to pay higher taxes, but I do wonder whether much consumption among the wealthy is fundamentally about this sort of wasteful arms race.

There’s probability ε, for some very small ε, that economists haven’t already run through this idea. … Indeed, a moment’s Googling suggests that I’m talking about a positional good; Veblen’s (“conspicuous consumption”) name comes up, as I should have expected. Time to read some Veblen.

What I’m looking for, though, is a formal estimate of how much economic waste goes into the pursuit of positional goods, and maybe a theory of optimal taxation based around it. I wonder if any of you lovely people have seen such a thing.