Steve Reads

(…as reported in the New York Times), it is perhaps appropriate to include a graphic which, while it doesn’t prove anything, is suggestive:

“BGP” here is Borders, “AMZN” is of course Amazon, and “BKS” is Barnes & Noble.

Borders’ market cap — the total value of its stock — is $67.1 million. Barnes & Noble’s is $838.49 million. Amazon’s is $55.44 billion. Granted, Amazon is not just a bookstore. But these numbers aren’t, I think, all that misleading.

While we’re on the topic of Amazon, it occurred to me the other day: there’s essentially nothing that makes Wal-Mart distasteful while making Amazon desirable. Both try to squeeze their suppliers as much as possible to get the cheapest prices for their customers. Both use their size as a weapon to get those low prices from their suppliers. Both are killing off neighborhood stores; it just happens that Wal-Mart does it rather more obviously than Amazon. Amazon would probably have labor troubles as well, if it had as many low-paid employees as Wal-Mart does.

And yet I buy from Amazon sometimes [1], while I wouldn’t be caught dead inside a Wal-Mart. This is partly an unconscious class thing: Wal-Mart is associated, among folks in my particular urban milieu (a friend calls us “SWPLs”, from Stuff White People Like), with trashy suburbs and poorer folks. Until recently, it hadn’t consciously occurred to me that that might be the issue, but I think it is.

That said, in both Amazon’s and Wal-Mart’s case we shouldn’t romanticize what came before. Amazon didn’t replace a nation of Harvard Book Stores; it replaced a nation of Barnes & Nobles and Borderses. B&N and Borders may have begun the trend of eliminating local bookstores [2], but they also eliminated Waldenbooks. Waldenbooks, in turn, had been a K-Mart property since 1984 (according to the Wikipedia). Likewise, Wal-Mart — at least in my limited experience — didn’t replace a nation of shopkeepers; it replaced a nation of K-Marts.

I have no real point here. I’d recommend that you buy books where you enjoy buying books. Everyone’s going to have his own tradeoff between price and localness. My cutoff is around $20: if the same book is $20 cheaper on Amazon, I’m likely to buy it there. I hope there comes a point when my income is such that I don’t pay attention to differences of that magnitude, but I’m not there yet.

Around here, the Harvard Book Store is such an institution, and adds such color to the area, that its disappearance would be an incalculable loss. It’s hard to imagine Harvard Square without that beautiful black-and-gold façade; I hope I never have to imagine it.

A friend suggested a couple years ago that all the damage had been done: the market-share division between Amazon and the rest of the world was about where it was going to settle. I was hopeful then. I’m less hopeful now. Electronic books look like a real killer; Amazon made waves recently when it noted that it sells more electronic books than it does hardcovers (new hardcovers, presumably). That market is only going to grow, and there’s no reason to think that the Harvard Book Stores of the world can compete there.

So I’m worried. All I can do is continue to buy local when possible, and hope for the best. I’m lucky to live in a town where a Harvard Book Store is even possible; most places aren’t nearly so lucky. And even the local-bookstore market has thinned dramatically around here in recent years. When Wordsworth, the Harvard Square institution, closed six years ago, its founder bitterly noted:

“In the 1980s … on Memorial Drive, you’d see people coming out of dorms and heading toward Harvard Square. In the 1990s, what you’d see in the windows of dorms was a Doppler effect of blue lights from computer screens, and you knew students were at their computer, hitting a key to order from Amazon.com. The only reason they’d come out of their dorms was to have Chinese food and mate.”

[1] — I normally get my books from the library. If I buy new books, I buy them from the Harvard Book Store just up the street. If I buy used books, I buy them off Amazon when they’re significantly cheaper than the Harvard Book Store’s copies. Also, Amazon’s used-book selection is just much better than any local store’s would be, particularly if I’m looking for obscure academic texts; HBS doesn’t carry those at all.

[2] — Those of us who grew up near Burlington, Vermont remember Chasman & Bem. In retrospect, it was a beautiful bookstore. At the time, I remember the service being terrible. If it were still around, and I still lived in Vermont, I’d be shopping there rather than at the Borders or Barnes & Noble up the street. It’s too late for that, though: Barnes & Noble moving in a couple miles up the street killed them off.

I visited my brother in Boston back in probably 1993 or 1994 and hit up a gorgeous bookstore with him in Faneuil Hall (the last time I actually hung out in Faneuil). I believe that was Waterstone’s, part of a British bookstore chain. It, too, is gone.

It is a very important and very modern error, says Karen Armstrong, to read the Bible as though it contained factual content. The Greeks knew that there were two kinds of knowledge, logos that concerns itself with facts, and mythos that concerns itself with things like love and courage and coping with hardship; the Greeks never confused these domains. Moving briskly through religious and philosophical history, Armstrong argues that no one confused these domains until the Scientific Revolution: Plato, Aristotle, Jesus, Augustine, Aquinas, Luther, Descartes, Pascal, and on and on — they all realized that there was a domain to which science would never properly have access. This separation seems to have disappeared in our modern scientific era, when all ideas are thought to be amenable to scientific analysis.

They also all realized that there was a realm of the literally unspeakable, which one could only reach through long study and ritual. The ritual was important: merely reading texts wouldn’t get you there. And the texts — for instance, the Bible and the Torah — don’t just stand on their own; they’re meant to be read along with a teacher. And they’re meant to be read metaphorically rather than literally (logos versus mythos again).

The reader will naturally wonder: if the Bible is meant to be read metaphorically, does that mean that Jesus did not literally perform the miracles and did not literally ascend to Heaven? She says explicitly that few people ever took the miracles literally, and in any case that they don’t matter to faith. Jesus, along with some other famous holy men, was probably very good at healing certain psychosomatic disorders, but she seems to argue that walking on the water and so forth are meant to be understood metaphorically.

What, then, of things like the Nicene Creed, which asserts that Christ “suffered, and … ascended into heaven”? Did he literally ascend into heaven, or metaphorically? Armstrong asserts that the ignorant Emperor Constantine forced this creed on Christians, who then returned to their homes and pretty much continued as they had, treating the whole thing as a metaphor. If not in the specifics, then in the general approach, Armstrong here meshes with what I know of Aquinas: when we say that God is a rock, we don’t literally mean that it’s a rock; we’re supposed to be able to identify what’s metaphor and what’s fact in the Bible.

Armstrong essentially contends that all religions, going as far back as Buddhism and Hinduism, have believed in an ineffable realm that’s only accessible through prayer and worship and charity. She contends that Christianity, Judaism, and Islam have all gone after the same basic peaceful approach to humanity. For example (p. 79):

In a famous Talmudic story, it was said that Hillel had formulated a Jewish version of Confucius’s Golden rule. One day, a pagan had approached Hillel and promised to convert to Judaism if Hillel could teach him the entire Torah standing on one leg. Hillel replied: “What is hateful to yourself, do not to your fellow man. That is the whole of the Torah and the remainder is but commentary. Go learn it.”

Here we have a line connecting Confucius and Judaism. Armstrong connects Judaism and Christianity, and Christianity and Islam, in the same way. They’re all essentially teaching us to be good to our neighbors, and all giving us a set of rituals to tap into the ineffable.

Armstrong’s writing is so clear, and her message of universal love so captivating, that you have to step out of it periodically and wonder if she’s missing a part of the story. Why do we have separate religions, if they’re all chasing after the same basic ineffable truths? (That’s the thing: she seems to be arguing that, if you follow the rituals of each religion, you’ll eventually land on the same ineffable truths.) Unless I misunderstand the New Testament, Christians really do believe that they’ve replaced Abraham’s covenant with a new one; Christianity isn’t just Judaism with a new face. Islam really did take over Constantinople and turn the Hagia Sophia from an Orthodox or Latin cathedral into a mosque. I certainly do hope that a message of universal love lies beneath every world religion, but then what have they all been fighting for?

In Armstrong’s eyes, the uglier parts of the various religions are perversions of the one true idea. She regrets Augustine’s doctrine of original sin:

…Original Sin, one of his less positive contributions to Western theology. He produced an entirely novel exegesis of the second and third chapters of Genesis, which claimed that the sin of Adam had condemned all his descendants to eternal damnation. Despite the salvation wrought by Christ, humanity was still weakened by what Augustine called “concupiscence,” the irrational desire to take pleasure in beings instead of God itself. It was expereinced most acutely in the sexual act, when our reasoning powers are swamped by passion, God is forgotten, and creatures revel shamelessly in one another. … Born in grief and fear, this doctrine has left Western Christians with a difficult legacy that linked sexuality indissolubly with sin and helped to alienate men and women from their humanity.

She gives so little time to ideas like these that you’d almost forget there’s any content to each religion on its own. Instead, she focuses on the act of learning each religion, which universally involves studying alongside a teacher (rabbit, priest, imam, whatever) and performing charitable works. You’d almost forget that many thousands (millions?) of people have died from “perversions” of religion.

Armstrong’s gentle humanity — which wants to find the good in all religion — is endearing and infectious, and her scholarship is breathtaking: The Case For God covers a vast swath of intellectual history, from the authors of the Lascaux cave paintings up to the new atheists (Dawkins, Dennett, Hitchens). She’s made me want to go back and reread Augustine and Aquinas with an eye to metaphor rather than to factual content. Her description of Aquinas’s Summa is gripping intellectual history, and I quote it at length below the fold.

I haven’t yet established to my satisfaction whether the use of reason in religion — which Aquinas made most famous — even makes sense, and I’m not sure that Armstrong answers this question. Armstrong’s tool throughout The Case For God is apophatic theology, the method of defining God by what it is not: God is not a mortal man; God is not just an infinite version of you and me; God is not made of a substance at all; and so forth. One sees in this method something akin to the Zen Buddhist koans: a different state of understanding achieved by coming to grips with paradox.

Around the Scientific Revolution, religion undermined itself by trying to make something scientific of itself. God became something whose existence one could document; “He” eventually became something a lot like a human, only infinitely large and infinitely wise and infinitely patient and so forth. The metaphor fell away, as did the awestruck stance before a fundamentally ineffable thing. When God is understood in a factual way — “He” created the Universe some fixed number of years ago, and He reached down to smite Onan, and so forth — we lose both grandeur and believability. When compared to a scientific standard, of course the Bible will collapse; it was never meant to be read that way. By trying to appeal to the scientists, modern Christians have doomed their religion to be laughed at and discarded.

As I also read in Diarmaid MacCulloch’s The Reformation, Armstrong notes that the Catholic Church’s reaction against Galileo — and against the Copernican revolution — was really an unfortunate accident of timing: the Church had been losing to Protestants, and consequently tightened up their grip on dogma. Again, the Church should have no position on cosmology; the Bible can’t be read as a factual map of the Creation.

Then again, of course, a book like the Bible — or even a much shorter document like the Constitution — will be subject to changing interpretations as the years pass. Armstrong sounds like a strange kind of self-negating fundamentalist at points: the Bible’s, and the Torah’s, and the Koran’s meanings must change as each new learner understands it in context, but it was never meant to be understood in my one disfavored way. Essentially Armstrong is arguing that apophatic theology is one of the only ways to understand a religious text. She asserts with evidence that every important theologian has approached his or her book apophatically. Still, I’m sure she could have filled another book of the same size with theologians of the opposite stripe.

I’ve only scratched the surface of the evidence that Armstrong has amassed. The best thing I can say about it is that you really owe it to yourself to pick up The Case For God and devour it like I did. Armstrong’s brilliant writing is going to bring me back to theology to see if I can understand the masters better.

(more…)

(Attention conservation notice: Wherein I think out loud for about 900 words on the subject of acquired taste, with particular reference to espresso — not because that’s the most important example, but rather because it helps me make things a bit more concrete.)

I’ve had this nagging question in my head for a long, long time: how do you judge what something is “supposed” to taste like when it’s an acquired taste for most everyone?

This isn’t a rhetorical question; it may be reasonable to demand that, say, scotch taste a specific way. But there are a number of tastes that virtually no one enjoys when they’re young; black coffee and wine come to mind immediately. This may be just an American thing; I don’t want to universalize it too much. But childhood food tastes tend to the sweet. I’d hypothesize that sugar is not an acquired taste, but espresso is.

So what I’ve wondered for a while is: who decides what espresso is supposed to taste like? Some possible standards:

• It’s supposed to taste like what the average consumer likes, including those who at present don’t drink espresso. Imagine, for instance, that you gathered people at random off the street and put a number of different espressos in front of them. The best espresso, by this standard, is the one that the most people liked.

  The trouble here is obvious: you’re appealing to the average, and that may not be what defines “the best espresso.” The average person may, in Dave Barry’s words, not be able to distinguish between red wine and melted popsicles, but that doesn’t mean that melted popsicles are what wine is supposed to taste like.

• It’s supposed to taste like what those who’ve tasted many espressos say it should taste like. The trouble here is that their perception of what it should taste like may be colored by what the community they’re in says it should taste like. I seem to recall that French-roast coffee was all the rage 10 or 15 years ago; nowadays lightly-roasted coffees seem to be on the upswing. Does this mean that those coffees are objectively “what coffee is supposed to taste like,” or does it just mean that master baristas are driven by fads like everyone else?

• It’s supposed to taste like what those with highly perceptive senses — think Robert Parker, the “man with the million-dollar nose” — say it should taste like. The trouble here is a bit of the last bullet — the Parkers of the world probably spend their time conversing with like-minded folks — but also that it’s not clear how much I have to learn from someone whose palate is that finely honed. Yes, one day I hope to be able to register as much as Parker does when I quaff a fine wine, but in the meantime most of the subtlety is lost on me. Should I be drinking espresso that appeals to people with far different tastes from mine?

• There’s no right answer; it’s supposed to taste like whatever you like drinking. This is a fine standard, and in fact in some ways it’s probably ideal. But it does demand discipline from the drinker: if you’re going to make your own standards, you owe it to yourself to drink many different kinds of espresso (or wine, or scotch, or whatever) and decide which you like best.

All of these, I suspect, could be taken beyond the realm of food and into art or literature or comedy. What makes Andy Kaufman funny? Picasso is harder to get into than Thomas Kinkade; is the latter better than the former? I have less to say about those disciplines, because I know less about them.

In general, I certainly hope that interpersonal comparisons are possible. If they’re not, that makes life more boring; I find it fun to discuss food and literature and whatever, and you probably do too. I doubt you feel as though there’s an impassable wall between you and me that makes it impossible for us to compare foods. We read various critics; sometimes they call our attention to aspects we might not have noticed in books we’ve just read or coffee we’ve just drunk. Then we decide for ourselves whether the standards that they use to judge books or food work for us.

Is that the most we can say about acquired tastes? That there’s no right or wrong taste for espresso or wine or whatnot, but only whether someone else’s standard rings true for you? That doesn’t feel quite right to me, because it’s likely to be driven by fads. Fads are less a measure of what’s good than what’s popular. Yet I don’t want to go to the opposite side, either, and assert that there’s no right answer other than what you yourself enjoy; there are people who know more about a given product than I do, and I owe them some deference.

I decided to write all of this down after reading a piece about American espresso that crystallized a lot of what I’m wondering. The argument that American espresso is a different breed from what Italians like certainly makes a lot of sense to me. Though I’d want to see it confirmed empirically, by putting the same espressos in front of Americans and Italians and seeing whether there’s really as little overlap as Milos would suggest.

One fellow on Twitter is rather more decisive than I am in his feelings about Milos; he says, “This man is a dick with ears.”

The next time you hear someone say that the Social Security retirement age needs to go up because “back when Social Security was started, people weren’t expected to live much past retirement age,” first point out to them that the terminology is confusing: “life expectancy” means “life expectancy at birth.” Life expectancy at birth goes down if you die in the crib. What’s actually important, when setting the retirement age, is your life expectancy at age 65. Since we’ve made big strides on reducing child mortality, life expectancy at birth has gone way up; life expectancy at age 65 has only gone up by a little less than six years across all races and sexes, and has only gone up by a bit less than three years for black men. See the tables (with sources linked) below.

A couple other things to note:

• Suppose we’re in a recession when you’re in your late 60s. You get laid off. How likely do you think it will be that you’ll get re-hired? (Though as a friend mentioned the other night: employers may refuse to hire older folks because they know that their new employees will only be working until they hit 65; an increase in the retirement age might make employers think they can get a few more productive years out of them, thereby making age discrimination less of a problem.)

• There’s a gap in life expectancy by income, which the figures by race and sex don’t necessarily capture. (Though since race and sex affect income — women and black people are paid less — the life-expectancy numbers based only on race and sex may already capture an income effect. What we want is are models that predict life expectancy as a function of race, sex, and income, holding each constant while the other varies.)

I’ve had a book in my queue for a while, namely Working Longer: The Solution to the Retirement Income Challenge, which seems to address these issues. I’ve had a visceral resistance to reading it — namely that if someone suggests I work later in life, I might suggest in response that they perform an anatomical sexual impossibility. But I’ll overcome that resistance and read it for you, out of affection.

There was recently a little tempest in a teapot on Twitter about some measure of how influential a Twitterer you are, which got me thinking about how silly a lot of these measures are. They remind me a lot of early baseball statistics: read one of the early books in the sabermetrics genre, like The Hidden Game Of Baseball, and you’ll find a lot of dudes with limited statistical training taking a little of x, and a little of y, adding it together, and finding that — hey, this looks like a good measure of something; let’s use it! There are worse ways to develop a measure of something, but there are also better ways. Subsequent sabermetricians developed better ways, using rigorous statistics.

These amateur Twitter ranks made me think of Google’s PageRank algorithm, which was based on years of work trying to measure influence in academic journals. The Google problem and the journal problem are quite similar: if a given journal, or a given journal article, have a lot of inbound “links” (that is, citations from other journals), that’s good — but only if the linking journals are themselves highly linked. A bunch of citations from garbage journals, or a bunch of inbound web links from spam sites, shouldn’t contribute anything to your journal’s or your website’s rank.

The math behind the basic PageRank algorithm is simple. Imagine that you’re an infinitely patient web surfer who jumps randomly from page to page: you start on some page, click on every link on that page, and do the same on every subsequent page. If you click on 10,000 links, and 500 of them go to CNN.com, then you’ve spent 5% of your time on CNN. If 1,000 of those links go to NYTimes.com, you’ve spent 10% of your time on the Times. The PageRank for a given site is the fraction of time that our hypothetical random web surfer spends, in the long term, on that site.

Specifically, imagine a big table listing the probability that one site links to another:

(In Google’s practice, this would be a square table with as many rows and as many columns as there are pages on the Internet. So imagine a table with billions of rows and as many columns.)

The probability in each cell is the probability that the domain in the same row links to the domain in the same column; so for instance, the probability that CNN links to Talking Points Memo is 0.25; it doesn’t link at all to the Times or to the Huffington Post. (These are purely made-up numbers.)

Imagine, again, that we’re a random web-surfer. We start at the Times‘s website, click somewhere, then click another link at random from where we’ve landed. So now we’re two clicks away from wherever we started. What’s the probability that we’d end up at Huffington Post after two clicks? Turns out that we can answer the question if we turn the table above into a mathematical object called a matrix. The matrix version of the table above looks like

This is called a “transition-probability matrix.” Since every row sums to one — because every page links to some other page, even if the page it links to is itself — it’s also called a “stochastic matrix.” It turns out — via the Chapman-Kolmogorov equation — that the probability of getting from one of those pages to another within two clicks is the square of the transition-probability matrix. Squaring such an odd-looking beast may seem weird, but it’s a well-defined operation called matrix multiplication. The square of that matrix looks like so:

which says that the probability of getting from Talking Points Memo to Huffington Post in two clicks is 0.075. Continue this process through many clicks and you’ll eventually approach what’s called the “stationary distribution” — the long-term probabilities of ending up in any given state, independently of where you started out. In this particular case, the stationary probabilities are

• CNN: about 0.285
• The Times: 0.4
• HuffPo: about 0.057
• TPM: about 0.257

The Times, then, would have the highest PageRank, followed by CNN, TPM, and HuffPo. Again, the interpretation of the PageRank is very simple: the long-term fraction of time that a random [1] web-surfer would spend on your page.

Of course Google needs to modify this basic approach somewhat. One assumes that there’s a lot of “secret sauce” baked into the actual PageRank algorithm — as opposed to this bare skeleton — that allows Google to respond to spammers more effectively.

Regardless, I suspect a Markov-chain approach like PageRank would apply with few modifications to Twitter. Your Twitter rank would go up the more retweets (someone on Twitter essentially forwarding your tweet on to his or her followers) or mentions (someone including your Twitter handle in his or her tweet) you get, but only if the people retweeting or mentioning you were themselves highly ranked. The essential metric would be the fraction of time that a random Twitter surfer would spend reading your tweets.

One might argue that having a lot of followers should increase your Twitter rank. This is debatable: are your followers actually valuable if they’re not mentioning you or voting for your tweets by retweeting them? I could see basing the Twitter rank on followers rather than tweets, in which case the interpretation would be “the fraction of time a random Twitter surfer, jumping from Twitter handle to Twitter handle, would spend on your account.” But that seems less promising than basing it on tweets.

In any case, the point is that PageRank has a simple interpretation based on probabilities. This is in contrast to all the gimmicky Twitter-ranking sites, whose point is to drive traffic to one site or another. It’s like we’re reinventing Google. Right now we’re at the Alta Vista of Twitter: the current competitors are less focused on searching and ranking, more focused on their “portal,” and ultimately less professional than what Google came up with by using actual math.

For much, much more on the mathematical details of PageRank, see Langville and Meyer’s Google's PageRank and Beyond: The Science of Search Engine Rankings. It’s a gem.

[1] — Specifically, someone surfing according to a Markov chain. This is a very simple way of modeling a sort of random process that has “no memory”: if you tell me the first, second, third, fourth, and fifth pages you clicked on, and ask me to guess what your sixth page will be, I can throw out all the information you gave me apart from the fifth page. Earlier states, that is, don’t matter in prediction of the future; only the most recent state matters.

There should be a category on bookstore shelves for “little, dense, incisive, ingenious books.” Exit, Voice, And Loyalty would be one; Herbert Simon’s The Sciences of the Artificial would be right next to it.

Hirschman here examines three methods for addressing an organization’s deterioration: “exit,” the option of leaving the organization, not buying its products anymore, etc.; “voice,” the option of sticking with the organization and protesting in the hopes of improving it; and “loyalty,” which is really more a property that encourages you to stay with the organization longer (thereby probably delaying exit and giving voice more of a chance). Normally we think of exit and voice as separate powers: exit is what you use in a market economy, while voice is what you use when dealing with a government (which is typically hard or even impossible to exit). Hirschman asks a simple question: how do these powers interact?

The interaction turns out to be fascinating. Consider parents dissatisfied with the performance of their children’s public school. The parents who are most focused on school quality are likely to leave first and put their kids in private schools, leaving behind only the less quality-focused parents who are less likely to speak up. So the exit option (parents abandoning the school) diminishes the use of the voice option (speaking up). This is likely to accelerate the school’s decline.

Or consider a product (maybe a brand of automobile is a canonical example here) whose quality has diminished over time. Again, exit is likely to be used before voice: the customers most concerned about quality will bail first. If too many customers bail too fast, the company won’t have enough time to fix the product before it’s gone out of business. Whereas if too many customers don’t bail out quickly enough, the company will never learn that its products need to improve. So one can postulate a certain optimal level of quality-sensitivity in customers: not too high to kill the company before it fixes things, but not so low that the company stagnates. Modeling this formally would naturally use an analogue of price elasticity; whereas price elasticity measures the percentage decrease in sales that results from small percentage increase in price, quality elasticity measures the percentage change in sales for a small percentage change in quality.

Indeed, one of the neat little accomplishments in this neat little book is that it uses formal economic models to study the interaction of exit, voice, and loyalty even when the context is, say, the decline of a government rather than that of a company. The indifference curves are mostly confined to appendices, and Hirschman’s writing is clear enough that normally you can get the gist just as easily — if less rigorously — from his words as from his charts.

A government would be a classic case where exit is basically unused: yes, you could leave the United States in protest — and some large fraction of our countrymen promise to move to Canada at every presidential election — but would you? So the main option available to you in a democracy is voice. Similarly, you’re likely to raise your voice in a political party before you’d exit it, particularly if the alternative party is far away from you ideologically.

Here Hirschman consults a famous model by Harold Hotelling, metaphorically applied to ice-cream stands lined up along a beach. Imagine that beachgoers are distributed uniformly along the beach, and two ice-cream stands are trying to decide where to place themselves to capture the most customers. Imagine that the ice-cream stands initially start on opposite ends of the beach, but are free to relocate. The leftmost ice-cream stand realizes that if it moves a little bit toward the center, it can continue to pick up customers to its left (because those customers are still closer to the leftmost ice-cream stand than to the rightmost) while picking up those customers that lie less than halfway between the leftmost and rightmost stands. The rightmost stand realizes, similarly, that it can move to the center and continue picking up those customers to its right while picking up a few more in the middle. This process continues until both ice-cream stands are almost exactly at the middle, separated by a tiny sliver of distance.

Replacing the beach with some measure of political ideology, the conclusion is that it’s always in political parties’ interests to move to the center. There are initial obvious reasons why the analogy isn’t quite right. It’s not obvious that voters are uniformly distributed across the ideological spectrum, for one. For another, the Hotelling model assumes that customers don’t care about the cost of walking down the beach: they’ll pick the nearest stand, regardless of how far they have to walk to get there. In a political context, this would imply that voters don’t especially care which beliefs their parties hold; they just want the party to be “closer to me than the other party is.” Which isn’t obvious: perhaps people on the right or left ends of the political spectrum really want parties on the extremes, and will opt out of party politics altogether if they’re forced to pick among centrist alternatives.

Hirschman ends up rejecting the Hotelling model as it applies to political parties, for the reasons laid out above (more to the point: because it fails to work empirically). Here he’s rejecting what is apparently known as Hotelling’s Law, not to mention the median-voter theorem.

For such a small book and so few atoms (three, in fact: exit, voice, and loyalty), Hirschman’s is remarkably dense with interesting ideas. Highly recommended.

(…as we were), it helped me realize another thing that’s really annoying about Ann Patchett’s novel Run: it’s ripped directly from Common Ground, only it loses all of the latter’s majesty and honesty toward its characters, and replaces them with cheap sentimentality. One of the families that Lukas follows in Common Ground, for instance, ends up suffering a crime so horrifying that thinking about it has denied me sleep on a few occasions; Lukas depicts the crime matter-of-factly, because his whole project is to turn an honest eye on race and on cities. A ghastly crime simply wouldn’t fit within Patchett’s world; it’s not treacly enough for her, and Run is trying so hard to Say Something that it avoids being honest when it should.

I’d invite you to read Common Ground and then Run, and tell me that Patchett didn’t ape the former in writing the latter. It would be one thing if she’d aped it with any respect or skill; as it is, she colorized it and replaced the soundtrack with carnival music.

I’ve been horribly remiss in not writing a review of Lukas’s monumental Common Ground: A Turbulent Decade in the Lives of Three American Families. To say that it’s a book about Boston’s 1970s-era busing crisis is to be, at some level, accurate, but to miss the immense, teeming landscape that Lukas has painted. Common Ground is nothing less than a history of race in the United States. It is a landmark. It is among the two or three nonfiction books that you really must read, along with Caro’s Power Broker and Rhodes’s Making of the Atomic Bomb.

Common Ground views race through three lenses: the Divers, white pioneers into Boston’s South End; the Twymons, black and living in the South End projects; and the white Irish McGoffs of Charlestown. The Divers are what you might call yuppies, though it is to Lukas’s extreme credit that he would never let a character be reduced to a label. The Divers, in any case, are some of the brave white folks who ventured into the South End when it was no place for white people, to try to build a neighborhood and a community. The Twymons — mother and children — are not destined for a happy life in the projects. The McGoffs are right in the thick of — and active participants in — the most virulent Charlestown racism.

Lukas is sympathetic toward his characters, and has the gift of telling their stories exactly as they themselves would tell them. And like Love in the Time of Cholera, Lukas takes the time, at every moment when it’s necessary, to step back and explain a bit of history if it’s important to his characters. Time and again we pause from the present moment to learn about someone’s poor Irish ancestors, or someone’s slave grandparents. The effect is that we’re not just reading three stories; we’re reading a web of interconnections. Boston, which so often gets tamed into an abbreviated “There was the Boston Tea Party … and then MIT came! … And now we have software. … Let’s walk the Freedom Trail!”, gets rightfully recast as the “blooming, buzzing confusion” that it really is.

Along the way, we meet many, many people. Probably the two strongest characters are Louise Day Hicks, member of the Boston School Committee, daughter of an iconic judge, and symbol of virulent anti-busing racism; and Arthur Garrity, the judge who wrote the momentous decision mandating busing for Boston’s schools. Hicks comes across looking opportunistic, brilliant, and willing to attach herself to the most despicable ideas if they’d advance her career. Garrity stands aloof from the havoc that he arguably created, calmly resisting all efforts to avoid busing. These two wildly different people are beacons in the storm.

A blurb on Common Ground‘s cover by Studs Terkel, that master of ground-level history, says that it tells a truth about “all large American cities.” That is very true, but like most any attempt to describe Common Ground, this vastly understates the scope of its accomplishment. Common Ground tells the story of race in America as only a book about American cities can. Cities are the crucible where all of America’s problems get worked out — or not. If the problems get solved, they get solved here; if they fail, they fail here. Lukas documents the failure of American racial integration, and the arguably noble experiment that led to that failure.

I can’t emphasize enough, though, that one of the things that makes Common Ground so powerful is that, while Lukas may have set his sights on the stars, he knew that the only way to reach them was to start down in the dirt. At no point in Common Ground do you feel as though Lukas is trying to Make A Point. He probably is trying to do so, but he’s too disciplined a writer to give in to cheap moralizing or easy grandiosity. What’s grandiose in Common Ground are its people — each of them down in the shit with everyone else, surviving and maybe thriving as well as they possibly can. If their survival or their failure has any larger meaning, Lukas lets the characters and their history bring out that meaning.

American history has been, in large part, the history of race, the history of America’s original sin, and the history of its attempts to expiate that sin. In Common Ground, Lukas has condensed this history into the interrelated lives of a few Bostonians. In 200 years, Common Ground will be on the shelf along with a select few other books that mapped out where America came from and where it tried to go.

This book is selling very well and has initiated lots of conversations, so I can’t say that it’s a failure. Its authors are in high demand all over the place for their observations on the current economic crisis. Good for them. If I were a policymaker, I’d probably really like this book. As an educated lay reader, it turns out this isn’t the book for me.

It’s more of a compendium — an almanac, really — of financial statistics, with not very much narration layered atop. What it brings to the world is a large database of financial crises, painstakingly compiled from lots of sources. The data mostly span 200 years in the cases of banking crises and international defaults, reaching the full 800 years advertised in the subtitle only in the cases of things like hyperinflation or currency debasement. It’s interesting, but it’s not the kind of thing you want to take with you on a bus ride.

It is, with some justice, focused on the misbehavior of governments. We start out learning about government external defaults — reneging on debts owed to foreign governments. Reinhart and Rogoff note one outstanding puzzle: why do governments default when, in many cases, their debt-to-GDP or debt-to-revenue ratio is not terribly high (c. 10% or 20%)? If you examine also their internal defaults, Reinhart and Rogoff note that a lot of the puzzle goes away: governments often default to external partners when they can’t afford to pay their domestic creditors, either. But governments have an advantage over their domestic creditors in a way that they don’t over their external partners: they can put domestic creditors in jail, or kill them. It’s much harder to collect data on internal defaults, if only because such defaults will often be hidden beneath executions.

Governments have other tricks to get out of paying off their debts. One way is to hyperinflate the economy, thereby inflating their way out of debt. Another, similar way is to debauch the currency; this has been happening for hundreds, if not thousands of years, the earliest examples involving slicing tiny bits off gold and silver coins and decreeing that the coins are worth what uncut ones were. The invention of paper “fiat currency,” Reinhart and Rogoff note, has been a boon for rulers who want to inflate their money: it’s much easier to print more paper than it is to adulterate gold coins. No country has avoided defaulting on its debts by inflating its currency; the U.S. did so, rather stealthily, when it went off the gold standard after World War I.

The final category of “financial folly” that Reinhart and Rogoff tackle are the banking crises. The world thought we’d figured out how to avoid these — through banking-insurance systems like the FDIC — until the “shadow banking” system did us in during the current crisis.

In all these cases, Reinhart and Rogoff make a thorough, detailed case that there is nothing new under the sun: the crises that we had hundreds of years ago are the same ones we have now and the same ones we’ll probably have hundreds of years from now. There’s some slight hope that economic knowledge really will improve our policies, but it’s only slight.

Being largely a compendium of charts — typically one every other page, or more — the biggest sin this book commits is that the charts are just not that readable. My kingdom for some bolding in the chart captions; as it was, my eye flailed around on every chart, trying to pick out the things I was supposed to read. Each chart came with a hefty caption, detailing the many sources where its numbers came from. Each chart was subtly different: raw billions, percent of GDP, counts of crises since some specified time. Tons and tons of charts to read, yet the amount of time devoted to designing the charts was clearly much less than that devoted to the book’s overall design — which is gorgeous. (I let Princeton University Press know, by way of Twitter, how beautiful this book is; they thanked me, and told me that they’d pass along the good word to their designer. I’m happy to hear that; I don’t imagine book designers get much credit, usually.)

If you’re a policymaker, you probably want to read this book. Though I wonder if your time would be better spent with something like Dean Baker’s Plunder and Blunder; it’s short, and it contains a few rules of thumb to detect bubbles: principally price-to-earnings ratios above a certain threshold and property values growing very much at all. This Time Is Different seems like it will turn out to be more useful for the data it’s compiled, which others will put to use preventing future bubbles. It may not be a practical tool on its own.

(Attention Conservation Notice: 1,200 words trying, and failing, to explain why The Kids Are All Right is boring and trite and self-satisfied and annoying. The bulleted list below contains the full plot of the movie. Most of the judgments I pass on the film are outside the bullets, so you may just want to read the non-bulleted bits.)

I sat and stared at the screen for a long while, trying to explain what was so … un-awesome about The Kids Are All Right. Somehow that turned out to be really hard. If you take only one thing away from this review, please take away that The Kids Are All Right is super-overrated, and that I don’t understand why people are into it.

Maybe I’ll get some traction on explaining its lack of goodness if I just make a bulleted list of what happens in the movie. I’m going to summarize basically the entire plot here, so there will be spoilers aplenty. Don’t read on if you intend to see the movie.

I will include bolded question marks (like “?“) whenever some part of the movie just puzzled me.

• There’s a boy (“Laser”) and a girl (“Joni”) and their lesbian mothers, played by Annette Bening and Julianne Moore.
• The boy does some coke. He’s hanging out with a Bad Dude.
• Laser tells Joni that he wants to meet the sperm donor who was … uh … involved in their creation.
• Joni has to make the call because she’s older than Laser is (she’s 18, he’s 15), and … I guess you need to be an adult in order to make this sort of phone call? (?)
• Joni digs through her moms’ filing cabinet to find the sperm bank’s number, she calls that number, the sperm bank gets in touch with the donor, and they agree to meet.
• The sperm donor, Laser, and Joni meet. Things are a little hesitant and awkward at first. Laser thinks the donor is too self-satisfied. Joni likes him.
• Meanwhile, Laser is spending more time with a Bad Dude. The Bad Dude leads Laser into all kinds of trouble, the first bit of which is that they find the moms’ porn collection. It features men having sex. Earlier, we’ve seen the moms start getting it on while they watch dude porn. (?)
• The moms have been suspicious that Laser and the Bad Dude are gay together. After they catch Laser and his Bad Dude friend with the porn, they sit him down to have an Intervention and ask if he’s gay. It turns out he’s not gay. Laser asks why they watch dude porn when they are lesbians. They explain that it’s complicated, but it has to do with how female sexuality is internal, so they sometimes need to watch externalized sexuality. Or something. (?) Even within the world of the film, that explanation made no sense: the moms seemed confused why they themselves enjoyed it, and they couldn’t explain it clearly to their kids. Clearly the director, Lisa Cholodenko, didn’t expect the audience to understand the explanation, so it’s puzzling to me why she included it.
• The moms discover that their kids have met the sperm donor. The moms decide to meet him too. So everyone gets together for a terribly awkward dinner, wherein Annette Bening asks him, “So … when did you know you wanted to be in the food-service industry?” (He runs a restaurant. It seems successful. He also seems like a stoner.)
• The kids continue to hang out with him. Laser plays basketball with him. Eventually they get close enough that the donor can tell Laser that the Bad Dude is no good, and that Laser should stop hanging out with him. Laser takes umbrage at this.
• Shortly thereafter, Laser and the Bad Dude are walking along in a Bad Part Of Town, and they happen upon an old mangy stray dog. Laser gets down on one knee and starts to pet him. The Bad Dude insists that Laser hold the dog while the Bad Dude pees on the dog (?). Laser says no. The Bad Dude calls Laser a pussy. Laser shoves the Bad Dude and calls him a dick. The Bad Dude punches Laser. Thus ends the friendship of Laser and the Bad Dude. The sperm-donor dad has thereby proven his bona fides. Laser and the dad can now be friends.
• Julianne Moore’s character is trying to start a career as a landscape designer. She’s unsure of herself. The sperm-donor dad, Paul, invites her to help design the backyard at his house.
• Needless to say, eventually they bone. Even though she’s lesbian. (?)
• Annette Bening finds out about the sex. She is devastated.
• Paul tries to visit the Lesbian House to make amends. Annette Bening tells him to go and make his own family and get out of hers. That is the last we see of Paul. Other movies would have thought that Paul was maybe more important than that, and wouldn’t have dropped his character so artlessly.
• The painful process of reconciliation continues between Bening and Moore. Moore gives a little tearful speech to her family about how much marriage sucks, and how it’s so easy to take your partner for granted, and so yeah, sorry, cry cry cry. This is the scene that they’ll show when The Kids Are All Right is nominated for an Oscar; mark my words.
• The moms drive their daughter to college to start her freshman year. She asks them to leave her room because she’s been chafing under their grip (been going to parties, drinking, trying to make herself into a hypersexualized being that she probably isn’t), spends some time alone, and then semi-desperately comes looking for them after thinking they’ve abandoned her and gone home. She thereby proves that she’s still mamas’ little girl. Everyone has a big reconciling group hug, moms get back in the car and head home, Joni goes off to college, all is well, fade to black.

I think what bugs me most about this is that if it didn’t feature lesbians, it would be an utterly boring movie about the perils of a boring domestic life. But we all know what a boring domestic life is like; we live that life every day. What this movie contributes to that storyline is … lesbians. Its entire premise is basically “See? Lesbians have complicated lives too.” But this is not a discovery.

As for the portrayal of lesbians: throughout The Kids Are All Right and afterward, my ladyfriend and I agreed that there hadn’t been any actual lesbians involved in the making of the film. The web tells me that Lisa Cholodenko is, herself, actually lesbian, so my lady and I were wrong. What this movie teaches us, in any case, is that a) lesbians like watching guy porn, b) lesbians sometimes need to have sex with a penis, c) lesbian problems are just like straight-couple problems.

And throughout the movie, it’s a bunch of self-satisfied upper-middle-class Californians eating healthy, delicious meals in jaw-droppingly gorgeous homes and kitchens. The kids and the lesbian moms all sit down together every night to share dinner like a good, happy, boring domestic family. We’re watching any number of 1950s sitcoms, re-enacted with lesbians and dude porn.

Having written all this, it still doesn’t feel like I’ve captured the utter annoying banality of this movie, but I’ll have to let it go. The Kids Are All Right is transcendently boring; all descriptions of its banality are condemned to understate just how trite it is.

Here’s what I don’t get. Ideally, in a well-run society of intelligent people, you need to advance arguments for your position. You can’t just wave your arms up and down, claim “It’s not right!” and expect that to be the end of it. And your own personal disgust isn’t grounds for anything. When you enter the public sphere, you’re supposed to present arguments.

Now, granted, sometimes — often — personal disgust sells things. It shouldn’t, but it does. I’m convinced that the fundamental belief underlying opposition to gay marriage, for instance, is that opponents believe anal sex between men is disgusting. (If the gay-marriage debate were about lesbians’ right to marry, I doubt it would be nearly this acrimonious.) There have been lots of purported “arguments” over the years against gay marriage, but none of them amount to anything at all. “Marriage is about raising children”: sure, but what about childless couples? “But won’t this lead to pedophilia and bestiality?”: obviously not, because obviously we only support marriage between consenting adults. And so forth. The problem with these arguments isn’t that they’re wrong, it’s that they’re incredibly wrong. They’re remarkably simple to swat down. It’s so simple to swat them down that they don’t even count as arguments. They’re not arguments; they’re reflexes. They’re meant to make other people raise their fists in agreement; they’re culturally evocative totems, not arguments. I’m not obliged to respond to your culturally evocative totem, and you’re not obliged to respond to mine. We’re only obliged to respond to arguments made in good faith. And so far as I can tell, no one has made any such arguments against gay marriage.

Nor have they made any such arguments against the “mosque” in lower Manhattan. The only “argument” I’ve seen is essentially that the wound from 9/11 is too raw, and that the area around Ground Zero is holy in some way. But clearly the “mosque”‘s opponents would have no problem with a Christian or Jewish (or Buddhist, or Zoroastrian) place of worship in that area. So the fundamental argument against the mosque, so far as I can tell, is that Muslims as collectively guilty for 9/11.

That’s it, right? Everyone knows that that’s the subtext beneath the entire dispute. If you can find some other, deeper reason why the “mosque” shouldn’t be built there, let me know, but I’ve certainly not seen it. And when Newt Gingrich says that “There should be no mosque near Ground Zero in New York so long as there are no churches or synagogues in Saudi Arabia”, it’s clear that he means exactly what I’ve suggested. All Muslims are responsible for 9/11, so there’s some kind of global quid pro quo that requires the Muslims everywhere to pay for the crimes of Muslims anywhere.

Put that way, I hope everyone would acknowledge that it’s a profoundly stupid, offensive, and false proposition. A tweet asking whether, since Tim McVeigh was Catholic, no churches should be allowed near the Murrah Federal Building sums it up as well as anything could.

And that’s it. That’s all they’ve got.

The debate became immediately confused, like they always do, by the meta issue of how this will affect [choose your favorite politician] in [choose your favorite upcoming race], or more specifically whether this will make Democrats look like pussies on what should be a morally clear issue (answer: yes). But all of that is immaterial. And doesn’t it just needlessly exhaust you? It exhausts me. There are a lot of things to think about in this life. There are a lot of things to get mad about. There are a lot of arguments to have about a lot of really important things. Becoming a morally aware adult, it turns out, is really hard.

If a lot of people are upset about the “mosque” in lower Manhattan, that is their business. If so many people are upset about it that it will cause some politicians to lose their jobs because they’re insensitive to others’ concerns, it is the politicians’ business to care about that. It is not my business to care about that. It is my business, as a rational member of a democratic society, to look at the arguments put forward against the Cordoba House and judge them on their merits. And there are no arguments. Shouldn’t that settle it?

Forgive me if this is an oversimplification of how democracies work. It certainly is. There’s a time and a place to engage in spirited rat-fucking. Other times, you just have to claw through the confusion on these issues, acknowledge that they really have no argument, and move on.

Here’s my dime-store understanding of Keynes (which tells me, by the way, that I need to go reread the General Theory):

• Companies aren’t investing because they expect that in the near future, customers won’t be buying. They expect this for the completely justified reason that customers aren’t buying right now.
• So companies don’t put their money into new factories and new machines and so forth. Instead they put it in the bank.
• So they don’t hire new workers to man the new machines.
• Now there’s less money in the pockets of the workers. So they buy less.
• So rational companies look ahead and see more of the same: nobody’s buying, so they won’t be investing.
• And so on down the drain.

So the government steps in to halt the self-fulfilling prophecy. The government hires workers to pave the roads, build bridges, paint murals, etc. They give those workers, let’s say, $10,000 apiece. Since they’re largely on the poorer end of the economic ladder, they spend most of that money on food and other necessities. Let’s say they spend 80% of what the government pays them. So they spend $8,000 of that $10,000. Someone else has then earned $8,000; assuming the recipient is situated similarly to the spender, 80% of that $8,000 then becomes new spending. And so forth. The initial $10,000 becomes $50,000 through this process of multiplication. (In general, if people spend r% of what they earn, the initial investment gets multiplied by 100/(100-r).)

Now companies expect that things will be different. They expect that next quarter will look a lot like this one, and this one turned out not to be too bad. So they invest. They hire more workers. Those workers spend money. That money gets multiplied, as above. The pump has been primed, the economy is rolling again, and yay.

Here’s my question, though: shouldn’t we expect companies to know that the good times won’t last? Companies must be expected to know that business will only keep moving so long as the government is supplying the jobs, right? Likewise, those employees working at government-provided jobs know that their jobs — paving roads, building bridges, painting murals — are only temporary. To the extent that they have any control over it, they’re going to try to save that money for a rainy day; they know that a rainy day is just around the corner.

The only honest way I can see out of this is for the government to credibly commit to a certain amount of continuous job-creation until the economy has reached some pre-determined goal (GDP increasing by a 3% annualized rate per quarter or whatever). Once the economy is moving on its own, the government promises to stop making work; until then, it’ll do everything it can. This creates the right expectations.

On the basis of this argument, including the bit about the multiplier, I don’t see what the difference — from the perspective of getting the economy moving — would be between a) the government mailing $10,000 checks to a million newly unemployed people, and b) the government creating jobs for a million newly unemployed people. In both cases you’re putting money in the unemployed folks’ pockets, and you expect that they’ll spend roughly the same fraction in each case.

Obviously there are non-stimulus reasons to prefer employment to mailing a check: work is good for people’s self-esteem, crime goes down when people are occupied, and in any case we should be spending money to fix things that need fixing. But toward the goal of setting expectations about the future, the cash and the work seem identical.

So is there any stimulus explanation for not just giving people a check? And, to get to the earlier question: is the idea of a one-time stimulus — any one-time stimulus — just doomed from the start? If you don’t set the expectation that you’ll pay whatever is needed, for however long it’s needed, won’t minimally rational economic actors be too cautious about spending what they have?

If you’ve read any of David Mitchell’s earlier books, specifically Cloud Atlas, I imagine you’ll think — like I did — that The Thousand Autumns of Jacob de Zoet takes place over literally a thousand years. I should burst that bubble for you now: it doesn’t. Somewhere in the middle of the book, you learn that Japan is the land of a thousand autumns.

To your and my surprise, then, this is a completely straightforward novel. I think Mitchell may have been compelled to convince the world that, yes, he can write novels that start one place, end another place, and don’t try to mess with your mind. He does it very well, as it turns out.

The title character lands in the Dutch outpost on Dejima, just off the coast of Nagasaki. (Right here, I expected that by the end of the book we would be in Nagasaki when the Bomb fell in 1945. The book starts [and, as it turns out, ends] in the 1700s, so I was immediately puzzled: how will Time-Traveling David Mitchell hit 1,000 autumns when we only have a couple hundred years to play with? Honestly, this left me with an odd feeling of anxiety.) He’s been beckoned there to help clean up the books: Dutch authorities believe that there’s been some mischief in the import/export accounting, and de Zoet is just the sort of upright man to clean things up.

Stop here and, being a good economist, consider the incentives. How much luck is a morally upright man going to have in such corrupt circumstances? If everyone’s in on taking a little out of every shipment, our hero will certainly have to be politically astute to avoid dashing his career (if not himself) on the rocks. He’s on a lonely island, surrounded by people he may very well make his enemies. The suspense of watching de Zoet wend his way through this battlefield is where the bulk of the book’s ample charm comes from.

There’s also, of course, a love interest: de Zoet falls curiously in love with a nurse whose face is mysteriously disfigured. I was going to go into some more detail about the difficulties they face in getting together, but I think I won’t. They face difficulties aplenty, needless to say, and the source of those difficulties turns out — as the story goes on — to be horrifying. If I said anything more, I’d risk giving away some of Thousand Autumns‘s captivating plot twists.

It’s an absolutely riveting book; I couldn’t put it down. I might gripe that the ending is too pat (it’s almost as though Mitchell is responding sarcastically to those who believed he couldn’t write a more-standard novel), but that’s small beer: go grab a copy and be absorbed for the next few hours.

There’s great promise in this book, which it fails to live up to. It offers too little mathematics to appeal to even recreational mathematicians, and more mathematics than non-mathematically-inclined readers would be able to stomach. At the same time, it offers basically no interesting theology. It does, on the other hand, spend loads of time name-dropping Russian and French mathematicians for no good reason, and tells us all about persecution of academics during the Soviet era. It ought to be called “Russian Mathematicians: Some Things That Happened To Them For 75 Years Or So.”

The book’s fundamental assertion is that religious mysticism in Russia helped fuel the Russians’ great mathematical discoveries, and drove Russia ahead of France by the early part of the 20th century. That’s fine as far as it goes, but it obviously needs more than just some correlation to prove it. All Graham and Kantor have to offer is correlation: this one episode of mysticism happened, and this other episode of Russian mathematical flowering happened. We’re meant to conclude that the one caused the other.

It’s seemed to me, on the other hand, that at least since the great Kolmogorov, Russians have been particularly fond of abstraction for its own sake. This has allowed them to go off in mathematical directions of which the French daren’t dream. Did the Russian talent for abstraction drive their mathematical accomplishments as much as mysticism did? It seems to me that there could be many causes for the Russian mathematical flowering; Graham and Kantor focus on just one.

The reason they focus on just the one is that they’re interested in a particular Russian sect of Christianity, persecuted before and during the Soviet era, called the Name Worshippers. The Name Worshippers apparently believed that one could reach a trance-like state and come closer to god by repeating a particular prayer endlessly. The mathematics of infinity, pioneered by George Cantor, seemed to them a natural fit, for reasons that Graham and Kantor never make clear.

Cantor is most famous for his demonstration that certain infinities are larger than others — an idea that is very hard for many people to stomach, but which is rather easy to demonstrate and utterly commonplace in mathematics today. It was Bertrand Russell, I believe, who used a very straightforward example to demonstrate this. Suppose, said Russell, that you have a village in which a) every man has exactly one wife, b) every wife has exactly one husband, and c) no one marries outside the town. Then it doesn’t matter whether there are finitely many or infinitely many people in the town — you can be certain that there are just as many women as men. Mathematicians say that there is a “bijection” between the set of men in the town and the set of women in the town. If, on the other hand, there were an unmarried woman in the town and no unmarried men, then you could conclude that there were more women than men.

That’s where Cantor starts, in a discussion of very general objects called “sets.” A set is a collection of things bearing some properties in common — say, the set of all people alive and standing within the legal boundaries of Cambridge, Massachusetts at 11:28:00 a.m. on August 12, 2010, along with their couches. Two sets have the same “cardinality” if there exists a bijection between them. Cantor goes on to establish that can exist no bijection between the set of integers and the set of real numbers — that is, that the real numbers (rational numbers plus irrational numbers) is larger than the set of integers. He uses a very clever trick called the diagonal argument in which he first supposes that there does exist a bijection between the reals and the integers, then shows that such a bijection always leaves out some real numbers. It is unavoidably true that there are more reals than integers, which is to say that the reals are larger. Which is a special case, finally, of the assertion that some infinities are larger than others.

A lot of mathematicians at the time had trouble with this argument; abstract objects like sets seemed so far removed from the world of human experience that there were bound to be weird paradoxes and strange infinities. Better to stick with objects that were indubitably real, like the integers, and leave the abstract madness out of mathematics. Graham and Kantor blame French and German unwillingness to embrace abstraction for their falling behind the Russians. (The German mathematician Leopold Kronecker is famous for saying that God created the integers and that all else is the work of man.) It was Germans, Russians, and Hungarians, however — the German Gauss, the Russian Lobachevsky, and the Hungarian Bolyai — who had discovered non-Euclidean geometries 40 or 50 years before. Doesn’t this show two things? First, Germans and Hungarians were capable of letting their imaginations roam free, by casting off the Euclidean restraints that humanity had held sacred for 2000 years; they didn’t need Russian mysticism to make it happen. Second, did the Russian Lobachevsky need mysticism to achieve his breakthroughs? If not, then much of Graham and Kantor’s book reduces to “Some Russians needed mysticism. Others did not.” It becomes a documentary about an interesting coincidence, rather than something with any causal importance. Graham and Kantor clearly believe (see the final chapter in particular) that the Name-Worshipping episode is important to the development of mathematics, whereas to me it looks like a coincidence.

Returning to our story, though: the Russian Cantor’s set theory revolutionized all of mathematics. You can’t do serious mathematics now without encountering axioms posed in terms of sets. Look at the definition of a “topology”, for instance. Or what defines a “measure” (a mathematical generalization that covers ideas like “distance” and “weight” and “volume” and many others). You can compute the probability that a billion coin tosses in a row will all come up heads using only finite mathematics; but if you want to answer complicated questions like “what is the probability that a Brownian-motion path is continuous?” [1], you need infinities.

Graham and Kantor name-drop mathematicians and mathematical concepts, but rarely try to explain them; they gesture generally toward “functions of Baire class n” on a few occasions, without ever making it clear what these things are or why we should care. One gathers that a Baire class has something to do with discontinuous functions (the most pathological example of which is f(x) = 1 when x is rational, f(x) = 0 when x is irrational). And on a few occasions, Graham and Kantor suggest that the Russians found discontinuous functions freeing — that continuous functions somehow confine human will. Forgive me if I see absolutely no connection between the two. Graham and Kantor don’t help clarify what the connection might be.

So we get mathematical terms without mathematical understanding, and mysticism that’s mostly mystification. I could do without this book.

P.S.: I see that my friend Cosma Shalizi has also reviewed Naming Infinity, but I’ve not read his review yet.

[1] — Brownian motion shows up all over the place. It’s named after Robert Brown, who was studying the motion of pollen particles in water. Einstein used it to help estimate Avogadro’s number. Being physical objects, it’s reasonable to argue that pollen particles must move continuously (i.e., if they go from point A to point B, they must move through every point between A and B — they can’t just jump from one to the other). So then, if Brownian motion is an accurate model for the motion of pollen particles, you’d want to show that the probability of a Brownian-motion path’s being continuous is 1 — that is, that if you picked a Brownian-motion path “at random,” that you’d never pick a path wherein the pollen particle takes discontinuous jumps.

There are obviously infinitely many paths that a particle of pollen could follow; in fact, there are uncountably many paths. One is then forced, when judging models with the appropriate degree of skepticism, to hit up against Cantor’s infinities.

Basiclally nothing bad can come of waiting a week to form an opinion on something.

Hence I’m going to take my time to learn about the Verizon-Google net-neutrality proposal. My friend James Grimmelmann has given me a pile of links to read and people to look up, which I’ll do before I make up my mind.

My friend Carl a while ago expressed some confusion about why he’d ever want to get a smart phone. It’s a reasonable question: carrying a computer on your person at all times is remarkably distracting. If you don’t send text messages, it may seem pointless.

This morning, as I edited the details on a calendar entry on my phone, it struck me that that’s the main thing I couldn’t do without. I enjoy when my phone rings to tell me that I have some event coming in an hour. I enjoy editing events on the phone and knowing that they’ll be synced up with the Google Mind, so that I’ll see the same information right away if I visit the Google Calendar website.

You might justify getting a smart phone by the sheer efficiency of the thing: if you’re carrying an iPod and a phone, why not combine them into one device (manufactured by Apple or otherwise)? Nowadays that efficiency argument seems weaker to me: if it helps me avoid spending endless time online, I’d prefer to have an iPod separate from a dumb phone. But then, iPod+camera+telephone+texting device? I wouldn’t want to carry four separate devices. And it’s really great to have a camera on me at all times. Taking photos and then uploading them immediately to some public service is something I don’t need; people can wait an hour or two to take a look at the food I just ate in a nice restaurant. So it’s not the instant nature of the photos that makes camera phones valuable; it’s being able to take photos at all.

The aggregate effects of omnipresent technology are interesting. For instance, some guy exposed himself on the T the other day, and Twitter helped catch him. That wouldn’t have been possible without omnipresent camera phones and (to a lesser degree) omnipresent social networking on mobile phones. We’re all carrying cameras nowadays; that has to have a marked effect on lots of things (think “police brutality”).

Texting is an interesting phenomenon: as has gotten a lot of notice recently, people are using their phones for voice calls a lot less nowadays, and replace those calls with quick texts. I certainly use my phone that way: for most anyone other than my girlfriend, I make initial arrangements for outings via email, then send little texts as the time approaches: “I’ll be 20 mins late”; “I’m there”; etc. These don’t take away from real in-person socializing at all; I certainly feel like my social life is better than it was 10 years ago when cell phones and texting weren’t so omnipresent.

When I hang out with my girlfriend’s 13-year-old son, I realize that this sort of what does it all mean conversation will be completely gone in 15 years, and that the 13-year-old would look at me as though I were the world’s dumbest man if I tried to have it with him now. Kids text much more than they speak on the phone. Period. We can try to shake our fists at the sea on this issue, but it would be incredibly pointless to do so. (Likewise, arguing against MP3s and in favor of physical media, or inveighing against casual file sharing between friends, has long since become the most wasteful use of your time. People share MP3s. Period. We may be unhappy about this because it denies artists some money, but it is a fact.)

One thing I definitely don’t miss from the dumb-phone era is that silly thing where you lose your phone and then email all your friends, “Hi, I lost my phone. Please send me your contact information.” That is totally played out. I sync all my contacts to Google now; if I lose my phone or get a new one or wipe and reinstall the OS, I take 30 seconds to create a new Google account on the phone, then start it syncing. Within a couple minutes I have all my contacts and all my calendar entries on the device. I enjoy that very much.

“Contacts” here also includes a lot of businesses; for some of those businesses I only have a physical address. It’s awfully handy, for someone with a sense of direction as bad as mine is, living in a non-Euclidean city like Boston, to be able to use a map, compass, GPS, and Google Maps to find my way from wherever I am to a favorite café.

The rest of what’s on my phone count as nice-to-haves. It’s nice to be able to write email from my phone, but I can certainly wait until I get in front of a full computer for that. It’s nice to have a web browser, so that I can settle some point of curiosity in the middle of a conversation; but as I think we’re all discovering, it would be a lot better for society in general if we put the phones away during any outing. So I’d actually contend that a mobile browser turns out to be a slightly net negative. Having Facebook and Twitter apps on the phone is probably a net negative: they’re little distracting games.

I’d say, then, that the main reasons to get a smart phone are

• never again needing to bother your friends with requests for contact information
• your calendar and contacts, available at all times and synced with an external service
• not needing to carry a separate camera, iPod, and phone

Everything else is nice to have, or actively harmful to your attention span.

I’ve certainly found that having a mobile computer has reduced my attention span. When I’m reading a book, I typically pull out my iPhone every few minutes: email, Facebook, Twitter, repeat. Sometimes I put my iPhone and laptop in another room while I’m reading. When I go on vacations, I leave all technology behind and bring a stack of books with me. (My lovely girlfriend, bless her heart, realizes that all I want to do on vacation is read books and spend time with her, and she’s more than willing to accommodate me on both.)

These reactions to my own distraction are possible because I remember when it was otherwise. I’m very curious how life will be for Stephanie’s sons, who didn’t exist before the Web and who became conscious entities during the era of the cell phone. They may not realize that a world with longer periods of focus is even possible or desirable.

Lest you think that I’m going to predict doom and gloom, I’m not going to. When I read John Ruskin, I saw an earlier generation of this descent-into-darkness brand of pessimism. Ruskin saw his beloved pastoral England destroyed by mass production and the dark satanic mills, and assumed that cities would always be destructive to the human soul. It’s possible that he was right: maybe, if you transplanted me back into late-18th-century England, I’d be brought to tears by the beauty of that lost world. Granted, though, that macro changes often bear no resemblance to the desires of any individual actor, I think people tend to adapt the world around them to what they want. The city I live in now serves my needs pretty well.

In 150 years or so, I suspect the techno-pessimists of today (like George Packer) will look a lot like Ruskin: correct in some points, maybe tragic in their correctness, but shortsighted and naïve and futile.

Jerzy Neyman is one of those epochal researchers who developed tools that working scientists use every day, without necessarily knowing that they’re doing so. In 200 years they’ll still be using his tools, and he’ll have descended even more into the obscurity of constant use: mathematicians don’t need to write “quadratic reciprocity (Gauss, 1801)”; likewise, even when people have forgotten that it’s the Neyman-Pearson Lemma, they’ll still be using the Neyman-Pearson Lemma.

What this famous lemma gives us is a rigorous reason to use the particular statistical methods that we’d been using on intuitive grounds previously. It shows that in a certain well-defined sense, the best statistical test we can use is one based on likelihood ratios. A likelihood ratio, in turn, is the ratio of two probabilities: the probability that the data you see before you would have arisen under one hypothesis, divided by the probability that it would have arisen under another hypothesis. [1]

Neyman’s work laid the foundations of mathematical statistics, in the sense of deriving statistical results with the rigor of mathematicians. The decades following Neyman and Pearson’s work saw probability theory become rigorously grounded in measure theory, and saw statistics rigorously grounded in probability theory. And it saw statistical methods applied to countless problems well beyond gambling and agriculture. Neyman was at the center of all of this: he started what quickly became the world’s greatest center of statistical research, at Berkeley, and applied rigorous methods all the way from the foundations of statistics up to the structure of galaxies. He was, by any measure, an awe-inspiring scientist.

Constance Reid managed to catch Neyman while he was still alive. She interviewed him every Saturday toward the end of his life, and published the book soon after he died. Her biography isn’t scholarly, in the sense of digging very far into the content of his work. I think it’s fairer to call it an “academic” biography: it spends most of its time following Neyman’s university career, the conferences he organized, and the spats he got into with other statistical luminaries — principally the legendary R.A. Fisher, whose immortality in genetics is just as assured as it is in statistics. Fisher doesn’t come out looking very good under Reid’s lens: he’s bitter, condescending, egomaniacal, imperious, and unwilling to brook even the slightest disagreement on his work.

Reid has a bit of a fine line to toe: go into too much detail about the content of Neyman’s work and she’s likely to alienate general readers; go into too little detail and she’ll alienate technical readers. (Neyman: From Life is published by Springer-Verlag, the canonical publisher of math textbooks, so it’s clear that she has a technical audience in mind.) I think she stays too far on the non-technical side: we learn a lot about the conferences Neyman traveled to and the bureaucratic dust-ups he started at Berkeley, but very little about what, exactly, got Fisher and him so angry at each other. Was it that Fisher came from an earlier era when intuitive derivations of statistical results were acceptable? Was it that Fisher found Neyman’s methods appropriate for large samples but useless for small ones? Did it have something to do with “fiducial inference,” which is a Fisher innovation that I’ve never seen anyone explain clearly? (Check out its Wikipedia entry and try to explain to me what “fiducial inference” even means.) It’s not always clear that Reid herself knows the answers to these questions, and from time to time she describes Neyman glossing over some details during their interviews; he may not have thought much of her technical chops either.

That’s really a small gripe, of course: most people really will not need the kind of intellectual biography that I hoped to find. Instead they’ll meet a statistician who’s still unfairly productive in his 80s, whom the university can’t possibly let go of without forfeiting hundreds of thousands of dollars in grant money and a world-renowned conference every year. [2] Neyman seems like a perfectly lovable mensch, ambling about with his cigarettes, prodding students into doing math at the blackboard, and traveling everywhere with his “long-time collaborator and constant companion”, Professor Betty Scott.

(Reid’s coverage of Neyman’s private life is hilariously restrained. It would seem, on the basis of a few hints from others throughout the book, that Neyman was something of a ladies’ man. Reid seems to have shied away from asking Neyman’s wife what she thought about this; either that, or she avoided writing any of it down.)

Reid’s book has certainly rekindled my love for mathematical statistics, which I enjoyed studying so much at Carnegie Mellon. I’m definitely going to revisit the subject now that I’m older and maybe marginally smarter.

[1] — Here I simply must link to Cosma Shalizi’s clever derivation of the Neyman-Pearson Lemma on economic grounds.

[2] — The full text of the Proceedings of the Berkeley Symposia on Mathematical Statistics and Probability is available online? That’s several thousand pages. It contains many groundbreaking papers, among them the one in which Charles Stein introduced what we now call Stein’s Paradox. Amazing.