Ribbit

 “‘The frog is almost five hundred million years old. Could you really say with much certainty that America, with all its strength and prosperity, with its fighting man that is second to none, and with its standard of living that is the highest in the world, will last as long as … the frog?’”
—Joseph Heller. Catch-22. (1961).
 … the fall of empires which aspired to universal dominion could be predicted with very high probability by one versed in the calculus of chance.
—Laplace. Theórie Analytique des Probabilities. (1814).

 

If sexism exists, how could it be proved? A recent lawsuit—Chen-Oster v. Goldman Sachs, Inc., filed in New York City on 19 May, 2014—aims to do just that. The suit makes four claims: that Goldman’s women employees make less than men at the same positions; that a “disproportionate” number of men have been promoted “over equally or more qualified women”; that women employees’ performance was “systematic[ally] underval[ued]”; and that “managers most often assign the most lucrative and promising opportunities to male employees.” The suit, then, echoes many of the themes developed by feminists over the past two generations, and in a general sense may perhaps be accepted, or even cheered, by those Americans sensitive to feminism. But those Americans may not be aware of the potential dangers of the second claim: dangers that threaten not merely the economic well-being of the majority of Americans, including women, but also America’s global leadership. Despite its seeming innocuousness, the second claim is potentially an existential threat to the future of the United States.

That, to be sure, is a broad assertion, and seems disproportionate, you might say, to the magnitude of the lawsuit: it hardly seems likely that a lawsuit over employment law, even one involving a firm so important to the global financial machinery as Goldman Sachs, could be so important as to threaten the future of the United States. Yet few today would deny the importance of nuclear weapons—nor that they pose an existential threat to humanity itself. And if nuclear weapons are such a threat, then the reasoning that led to those weapons must be at least as, if not more so, as important than the weapons themselves. As I will show, the second claim poses a threat to exactly that chain of reasoning.

That, again, may appear a preposterous assertion: how can a seemingly-minor allegation in a lawsuit about sexism have anything to do with nuclear weapons, much less the chain of logic that led to them? One means of understanding how requires a visit to what the late Harvard biologist Stephen Jay Gould called “the second best site on the standard tourist itinerary of [New Zealand’s] North Island—the glowworm grotto of Waitomo Cave.” Upon the ceiling of this cave, it seems, live fly larvas whose “illuminated rear end[s],” Gould tells us, turn the cave into “a spectacular underground amphitheater”—an effect that, it appears, mirrors the night sky. But what’s interesting about the Waitomo Cave is that it does this mirroring with a difference: upon observing the cave, Gould “found it … unlike the heavens” because whereas stars “are arrayed in the sky at random,” the glowworms “are spaced more evenly.” The reason why is that the “larvae compete with, and even eat, each other—and each constructs an exclusive territory”: since each larva has more or less the same power as every other larva, each territory is more or less the same size. Hence, as Gould says, the heaven of the glowworms is an “ordered heaven,” as opposed to the disorderly one visible on clear nights around the the world—a difference that not only illuminates just what’s wrong with the plaintiff’s second claim in Chen-Oster v. Goldman Sachs, Inc, but also how that claim concerns nuclear weapons.

Again, that might appear absurd: how can understanding a Southern Hemispheric cavern help illuminate—as it were—a lawsuit against the biggest of Wall Street players? To understand how requires another journey—though this one is in time, not space.

In 1767, an English clergyman named John Michell published a paper with the unwieldy title of “An Inquiry into the Probable Parallax, and Magnitude of the Fixed Stars, from the Quantity of Light Which They Afford us, and the Particular Circumstances of Their Situation.” Michell’s purpose in the paper, he wrote, was to inquire whether the stars “had been scattered by mere chance”—or, instead, by “their mutual gravitation, or to some other law or appointment of the Creator.” Since (according to Michell’s biographer, Russell McCommach), Michell assumed “that a random distribution of stars is a uniform distribution,” he concluded that—since the night sky does not resemble the roof of the Waitomo Cave—the distribution of stars must be the result of some natural law. Or even, he hinted, the will of the Creator himself.

So things might have stayed had Michell’s argument “‘remained buried in the heavy quartos of the Philosophical Transactions”—as James Forbes, the Professor of Natural Philosophy at Edinburgh University, would write nearly a century later. But Michell’s argument hadn’t; several writers, it seems, took his argument as evidence for the existence of the supernatural. Hence, Forbes felt obliged to refute an argument that, he thought, is “‘too absurd to require refutation.’” To think—as Michell did—that “a perfectly uniform and symmetrical disposition of the stars over the sky,” as Forbes wrote, “could alone afford no evidence of causation” would be “palpably absurd.” The reason Forbes thought that way, in turn, is the connection both to the Goldman lawsuit—and nuclear weapons.

Forbes made his point by an analogy to flipping a coin: to think that the stars had been distributed randomly because they were evenly spaced across the sky, he wrote, would be as ridiculous as the chances that “on 1000 throws [of a fair coin] there should be exactly 500 heads and 500 tails.” In fact, the Scotsman pointed out, mathematics demonstrates that in such a case of 1000 throws “there are almost forty chances to one [i.e., nearly 98%], that some one of the other possible events shall happen instead of the required one.” In 1000 throws of a fair coin, there’s less than a three percent chance that the flipper will get exactly 500 heads: it’s simply a lot more likely that there will be some other number of heads. In Gould’s essay about the Waitomo Cave, he put the same point like this: “Random arrays always include some clumping … just as we will flip several heads in a row quite often so long as we can make enough tosses.” Because the stars clump together, Forbes argued, that is evidence that they are randomly distributed—not of a benevolent Creator, like Michell thought. Forbes’ insight, in turn, about how to detect randomness, or chance, in astronomical data had implications far beyond the stars: in a story that would take much more space than this essay to tell, it eventually led a certain Swiss patent clerk to take up the phenomena called “Brownian motion.”

The clerk, of course, was Albert Einstein; the subject of his 1905 paper, “On the Movement of Small Particles Suspended In a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat,” was the tendency—“easily observed in a microscope,” Einstein remarks—for tiny particles to move in an apparently-spontaneous manner. What Einstein realized (as physicist Leonard Mlodinow put it in his 2008 book, The Drunkard’s Walk: How Randomness Rules Our Lives) was that the “jiggly” motion of dust particles and so on results from collisions between them and even smaller particles, and so “there was a predictable relationship between factors such as the size, number, and speed of the molecules and the observable frequency and magnitude of the jiggling.” In other words, “though the collisions [between the molecules and the larger particles] occur very frequently, because the molecules are so light, those frequent isolated collisions have no visible effects” for the most part—but once in a while, “when pure luck occasionally leads to a lopsided preponderance of hits from some particular direction,” there are enough hits to send the particle moving. Or, to put it another way, when the flip of a 1000 coins all come up heads, the particle will move. Put in that fashion, to be sure, Einstein’s point might appear obscure at best—but as Mlodinow goes on to say, it is no accident that this seemingly-minor paper became the great physicist’s “most cited work.” That’s because the ultimate import of the paper was to demonstrate the existence … of the atom. Which is somewhat of a necessity for building an atom bomb.

The existence of the atomic bomb, then, can be said to depend on the insight developed by Forbes: just how significant the impact of chance can be in the formation of both the very large (the universe itself, according to Forbes), and the very small (the atom, according to Einstein). The point both men attempted to make, in turn, is that the existence of order is something very rare in this universe, at any rate (whatever may be the case in others). Far more common, then, is the existence of disorder—which brings us back to Goldman Sachs and the existence of sexism.

It is the contention of the second point in the plaintiffs’ brief in Chen-Oster v. Goldman Sachs, Inc., remember, that there exists (as University of Illinois English professor Walter Benn Michaels has noted) a “‘“stark” underrepresentation’ [of women] in management” because “‘just 29 percent of vice presidents, 17 percent of managing directors, and 14 percent of partners’” are women. Goldman Sachs, as it happens, has roughly 35,000 employees—which, it turns out, is about 0.001% of the total population of the United States, which is 323 million. Of those 323 million, as of the 2010 Census women number about 157 million, compared to around 151 million men. Hence, the question to be asked about the Goldman Sachs lawsuit (and I write this as someone with little sympathy for Goldman Sachs) is—if the reasoning Einstein followed to demonstrate the existence of the atom is correct—then if the chances of landing exactly 500 heads, when tossing a coin 1000 times, is less than three percent, how much less likely is it that a sample of 35,000 people will exactly mirror the proportions of 323 million? The answer, it would seem, is rather low: it’s simply a lot more likely that Goldman Sachs would have something other than a proportionate ratio of men to women than the reverse, just as it it’s a lot more likely that stars should clump together than be equally spaced like the worms in the New Zealand cave. And that is to say that the disproportionate number of men in leadership in positions at Goldman Sachs is merely evidence of the absence of a pro-woman bias at Goldman Sachs, not evidence of the existence of a bias against women.

To which it might be replied, of course, that the point isn’t the exact ratio, but rather that it is so skewed toward one sex: what are the odds, it might be said, that all three categories of employee should all be similarly bent in one direction? Admittedly, that is an excellent point. But it’s also a point that’s missing from the plaintiffs’ brief: there is no mention of a calculation respecting the particular odds in the case, despite the fact that the mathematical techniques necessary to do those calculations have been known since long before the atomic bomb, or even Einstein’s paper on the existence of the atom. And it’s that point, in turn, that concerns not merely the place of women in society—but ultimately the survival of the United States.

After all, the reason that the plaintiffs in the Goldman Sachs suit do not feel the need to include calculations of the probability of the disproportion they mention—despite the fact that it is the basis of their second claim—is that the American legal system is precisely structured to keep such arguments at bay. As Oliver Roeder observed in FiveThirtyEight last year, for example, the justices of the U.S. Supreme Court “seem to have a reluctance—even an allergy—to taking math and statistics seriously.” And that reluctance is not limited to the justices alone: according to Sanford Levinson, a University of Texas professor of law and government interviewed by Roeder in the course of reporting his story, “top-level law schools like Harvard … emphasize … traditional, classical legal skills” at the expense of what Levinson called “‘genuine familiarity with the empirical world’”—i.e., the world revealed by techniques pioneered by investigators like James Forbes. Since, as Roeder observes, all nine current Supreme Court justices attended either Harvard or Yale, that suggests that the curriculum followed at those schools has a connection to the decisions reached by their judicial graduates.

Still, that exclusion might not be so troublesome were it limited merely to the legal machinery. But as Nick Robinson reported last year in the Buffalo Law Review, attorneys have “dominated the political leadership of the United States” throughout its history: “Since independence,” Robinson pointed out there, “more than half of all presidents, vice presidents, and members of Congress have come from a law background.” That then implies that if the leadership class of the United States is derived from American law schools, and American law schools train students to disdain mathematics and the empirical world, then it seems plausible to conclude that much of the American leadership class is specifically trained to ignore both the techniques revealed by Forbes and the underlying reality they reveal: the role played by chance. Hence, while such a divergence may allow plaintiffs like those in the Goldman case to make allegations of sexism without performing the hard work of actually demonstrating how it might be possible mathematically, it might also have consequences for actual women who are living, say, in a nation increasingly characterized by a vast difference between the quantifiable wealth of those at the top (like people who work for Goldman Sachs) and those who aren’t.

And not merely that. For decades if not centuries, Americans have bemoaned the woeful lack of performance of American students in mathematics: “Even in Massachusetts, one of the country’s highest-performing states,” Elizabeth Green observed in the latest of one of these reports in the New York Times in 2014, “math students are more than two years behind their counterparts in Shanghai.” And results like that, as the journalist Michael Lewis put the point several years ago in Vanity Fair, risk “ceding … technical and scientific leadership to China”—and since, as demonstrated, it’s knowledge of mathematics (and specifically knowledge of the mathematics of probability) that made the atomic bomb possible, that implies conversely that ignorance of the subject is a serious threat to national existence. Yet, few Americans have, it seems, considered whether the fact that students do not take mathematics (and specifically probability) seriously may have anything to do with the fact that the American leadership class explicitly rules such topics, quite literally, out of court.

Of course, as Lewis also pointed out in his recent book, The Undoing Project: A Friendship that Changed Our Minds, American leaders may not be particularly alone in ignoring the impact of probabilistic reasoning: when, after the Yom Kippur War—which had caught Israel’s leaders wholly by surprise—future Nobel Prize winner Daniel Kahneman and intelligence officer Zvi Lanir attempted to “introduce a new rigor in dealing with questions of national security” by replacing intelligence reports written “‘in the form of essays’” with “probabilities, in numerical form,” they found that “the Israeli Foreign Ministry was ‘indifferent to the specific probabilities.’” Kahneman suspected that the ministry’s indifference, Lewis reports, was due to the fact that Israel’s leaders’ “‘understanding of numbers [was] so weak that [the probabilities did not] communicate’”—but betting that the leadership of other countries continues to match the ignorance of our own does not particularly appear wise. Still, as Oliver Roeder noted for FiveThirtyEight, not every American is willing to continue to roll those dice: University of Texas law professor Sanford Levinson, Roeder reported, thinks that the “lack of rigorous empirical training at most elite law schools” requires the “long-term solution” of “a change in curriculum.” And that, in turn, suggests that Chen-Oster v. Goldman Sachs, Inc. might be more than a flip of a coin over the existence of sexism on Wall Street.

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Blind Shots

… then you are apt to have what one of the tournament’s press bus drivers
describes as a “bloody near-religious experience.”
—David Foster Wallace. “Roger Federer As Religious Experience.” The New York Times, 20 Aug. 2006.

Not much gets by the New York Times, unless it’s the non-existence of WMDs—or the rules of tennis. The Gray Lady is bamboozled by the racquet game: “The truth is,” says The New York Times Guide to Essential Knowledge, Third Edition, not only that “no one knows for sure how … the curious scoring system came about.” But in what might be an example of the Times’ famously droll sense of fun, an article by Stuart Miller entitled “Quirks of the Game: How Tennis Got Its Scoring System” not only does not provide the answer its title promises, but actually even only addresses its ostensible subject by merely noting that “No one can pinpoint exactly when and how” the ostensible subject of the piece came into existence. So much, one supposes, for reportorial tenacity. Yet despite the failure of the Times, in fact there is an explanation for tennis’ scoring system—an explanation that is so simple that while the Times’ inability to see why tennis is scored the way it is is amusing, also leads to disquieting thoughts about what else the Times can’t see. That’s because solving the mystery of why tennis is scored the way it is also could explain a great deal about political reality in the United States.

To be fair, the Times is not alone in its befuddlement: “‘It’s a difficult topic,’” says one “Steve Flink, an historian and author of ‘The Greatest Tennis Matches of All Time,’” in the “How Tennis Got Its Scoring System” story. So far as I can tell, all tennis histories are unclear about the origins of the scoring system: about all anyone knows for sure—or at least, is willing to put on paper—is that (as Rolf Potts put it in an essay for The Smart Set a few years ago) when modern lawn tennis was codified in 1874, it “appropriated the scoring system of the ancient French game” of jeu de paume, or “real tennis” as it is known in English. The origins of the modern game of tennis, all the histories do agree, lie in this older game—most of all, the scoring system.

Yet, while that does push back the origins of the system a few centuries, no one seems to know why jeu de paume adopted the system it did, other than to observe that the scoring breakdowns of 15, 30, and 40 seem to be, according to most sources, allusions to the face of a clock. (Even the Times, it seems, is capable of discovering this much: the numbers of the points, Miller says, appear “to derive from the idea of a clock face.”) But of far more importance than the “15-30-40” numbering is why the scoring system is qualitatively different than virtually every other kind of sport—a difference even casual fans are aware of and yet even the most erudite historians, so far as I am aware, cannot explain.

Psychologist Allen Fox once explained the difference in scoring systems in Tennis magazine: whereas, the doctor said, the “score is cumulative throughout the contest in most other sports, and whoever has the most points at the end wins,” in tennis “some points are more important than others.” A tennis match, in other words, is divided up into games, sets, and matches: instead of adding up all the points each player scores at the end, tennis “keeps score” by counting the numbers of games, and sets, won. This difference, although it might appear trivial, actually isn’t—and it’s a difference that explains not only a lot about tennis, but much else besides.

Take the case of Roger Federer, who has won 17 major championships in men’s tennis: the all-time record in men’s singles. Despite this dominating record, many people argue that he is not the sport’s Greatest Of All Time—at least, according to New York Times writer Michael Steinberger. Not long ago, Steinberger said that the reason people can argue that way is because Federer “has a losing record against [Rafael] Nadal, and a lopsided one at that.” (Currently, the record stands at 23-10 in favor of Nadal—a nearly 70% edge.) Steinberger’s article—continuing the pleasing simplicity in the titles of New York Times tennis articles, it’s named “Why Roger Federer Is The Greatest Of All Time”—then goes on to argue that Federer should be called the “G.O.A.T.” anyway, record be damned.

Yet weirdly, Steinberger didn’t attempt—and neither, so far as I can tell, has anyone else—to do what an anonymous blogger did in 2009: a feat that demonstrates just why tennis’ scoring system is so curious, and why it has implications, perhaps even sinister implications from a certain point of view, far beyond tennis. What that blogger did, on a blog entitled SW19—postal code for Wimbledon, site of the All-England Tennis Club—was very simple.

He counted up the points.

In any other sport, with a couple of exceptions, that act might seem utterly banal: in those sports, in order to see who’s better you’d count up how many one player scored and then count up how many the other guy scored when they played head-to-head. But in tennis that apparently simple act is not so simple—and the reason it isn’t is what makes tennis such a different game than virtually all other sports. “In tennis, the better player doesn’t always win,” as Carl Bialik for FiveThirtyEight.com pointed out last year: because of the scoring system, what matters is whether you win “more sets than your opponent”—not necessarily more points.

Why that matters is because the argument against Federer as the Greatest Of All Time rests on the grounds that he has a losing record against Nadal: at the time the anonymous SW19 blogger began his research in 2009, that record was 13-7 in Nadal’s favor. As the mathematically-inclined already know, that record translates to a 65 percent edge to Nadal: a seemingly-strong argument against Federer’s all-time greatness because the percentage seems so overwhelmingly tilted toward the Spaniard. How can the greatest player of all time be so weak against one opponent?

In fact, however, as the SW19 blogger discovered, Nadal’s seemingly-insurmountable edge was an artifact of the scoring system, not a sign of Federer’s underlying weakness. Of the 20 matches the two men had played up until 2009, the two men played 4,394 total points: that is, where one player served and the two volleyed back and forth until one player failed to deliver the ball to the other court according to the rules. If tennis had a straightforward relationship between points and wins—like baseball or basketball or football—then it might be expected that Nadal has won about 65 percent of those 4,394 points played, which would be about 2,856 points. In other words, to get a 65 percent edge in total matches, Nadal should have about a 65 percent edge in total points: the point total, as opposed to the match record, between the two ought to be about 2,856 to 1,538.

Yet that, as the SW19 blogger realized, is not the case: the real margin between the two players was Nadal, 2,221, and Federer, 2,173. Further, those totals included Nadal’s victory in the 2008 French Open final—which was played on Nadal’s best surface, clay—in straight sets, 6-1, 6-3, 6-0. In other words, even including the epic beating at Roland Garros in 2008, Nadal had only beaten Federer by a total of 48 points over the course of their careers: a total of less than one percent of all the points scored.

And that is not all. If the single match at the 2008 French Open final is excluded, then the margin becomes eight points. In terms of points scored, in other words, Nadal’s edge is about a half of a percentage point—and most of that percentage was generated by a single match. So, it may be so that Federer is not the G.O.A.T., but an argument against Federer cannot coherently be based on the fact of Nadal’s “dominating” record over the Swiss—because going by the act that is the central, defining act of the sport, the act of scoring points, the two players were, mathematically speaking, exactly equal.

Now, many will say here that, to risk making a horrible pun, I’ve missed the point: in tennis, it will be noted, not all acts of scoring are equal, and neither are all matches. It’s important that the 2008 match was a final, not an opening round … And so on. All of which certainly could be allowed, and reasonable people can differ about it, and if you don’t understand that then you really haven’t understood tennis, have you? But there’s a consequence to the scoring system—one that makes the New York Times’ inability to understand the origins of a scoring system that produces such peculiar results something more than simply another charming foible of the matriarch of the American press.

That’s because of something else that is unusual about tennis by comparison to other sports: its propensity for gambling scandals. In recent years, this has become something of an open secret within the game: when in 2007 the fourth-ranked player in the world, Nikolay Davydenko of Russia, was investigated for match-fixing, Andy Murray—the Wimbledon champion currently ranked third in the world—“told BBC Radio that although it is difficult to prove who has ‘tanked’ a match, ‘everyone knows it goes on,” according to another New York Times story, this one by reporter Joe Drape.

Around that same time Patrick McEnroe, brother of the famous champion John McEnroe, told the Times that tennis “is a very easy game to manipulate,” and that it is possible to “throw a match and you’d never know.” During that scandal year of 2007, the problem seemed about to break out into public awareness: in the wake of the Davydenko case the Association of Tennis Professionals, one of the sport’s governing bodies, commissioned an investigation conducted by former Scotland Yard detectives into match-fixing and other chicanery—the Environmental Review of Integrity In Professional Tennis, issued in May of 2008. That investigation resulted in four lowly-ranked players being banned from the professional ranks, but not much else.

Perhaps however that papering-over should not be surprising, given the history of the game. As mentioned, today’s game of tennis owes its origins in the game of real tennis, or jeu de paume—a once-hugely popular game very well-known for its connection to gambling. “Gambling was closely associated with tennis,” as Elizabeth Wilson puts it in her Love Game: A History of Tennis, from Victorian Pastime to Global Phenomenon, and jeu de paume had a “special association with court life and the aristocracy.” Henry VIII of England, for example, was an avid player—he had courts built in several of his palaces—and, as historian Alison Weir has put it in her Henry VIII: The King and His Court, “Gambling on the outcome of a game was common.” In Robert E. Gensemer’s 1982 history of tennis, the historian points out that “monetary wagers on tennis matches soon became commonplace” as jeu de paume grew in popularity. Yet eventually, as historians of jeu de paume have repeatedly shown, by “the close of the eighteenth century … game fixing and gambling scandals had tarnished Jeu de Paume’s reputation,” as a history of real tennis produced by an English real tennis club has put it.

Oddly however, despite all this evidence directly in front of all the historians, no one, not even the New York Times, seems to have put together the connection between tennis’ scoring system and the sport’s origins in gambling. It is, apparently, something to be pitied, and then moved past: what a shame it is that these grifters keep interfering with this noble sport! But that is to mistake the cart for the horse. It isn’t that the sport attracts con artists—it’s rather because of gamblers that the sport exists at all. Tennis’ scoring system, in other words, was obviously designed by, and for, gamblers.

Why, in other words, should tennis break up its scoring into smaller, discrete units—so that  the total number of points scored is only indirectly related to the outcome of a match? The answer to that question might be confounding to sophisticates like the New York Times, but child’s play to anyone familiar with a back-alley dice game. Perhaps that’s why places like Wimbledon dress themselves up in the “pageantry”—the “strawberries and cream” and so on—that such events have: because if people understood tennis correctly, they’d realize that were this sport played in Harlem or Inglewood or 71st and King Drive in Chicago, everyone involved would be doing time.

That’s because—as Nassim Nicholas Taleb, author of The Black Swan: The Impact of the Highly Improbable, would point out—breaking a game into smaller, discrete chunks, as tennis’ scoring system does, is—exactly, precisely—how casino operators make money. And if that hasn’t already made sense to you—if, say, it makes more sense to explain a simple, key feature of the world by reference to advanced physics rather than merely to mention the bare fact—Taleb is also gracious enough to explain how casinos make money via a metaphor drawn from that ever-so-simple subject, quantum mechanics.

Consider, Taleb asks in that book, that because a coffee “cup is the sum of trillions of very small particles” there is little chance that any cup will “jump two feet” of its own spontaneous accord—despite the fact that, according to the particle physicists, that event is not outside the realm of possibility. “Particles jump around all the time,” as Taleb says, so it is indeed possible that a cup could do that. But in order to to make that jump, it would require that all the particles in the cup made the same leap at precisely the same time—an event so unlikely that the odds of it are longer than the lifetime of the universe. Were any of the particles in the cup to make such a leap, that leap would be canceled out by the leap of some other particle in the cup—coordinating so many particles is effectively impossible.

Yet, observe that by reducing the numbers of particles to less than a coffee cup, it can be very easy to ensure that some number of particles jump: if there is only one particle, the chance that it will jump is effectively 100%. (It would be more surprising if it didn’t jump.) “Casino operators,” as Taleb drily adds, “understand this well, which is why they never (if they do things right) lose money.” All they have to do to make money, on the other hand, is to refuse to “let one gambler make a massive bet,” and instead to ensure “to have plenty of gamblers make a series of bets of limited size.” The secret of a casino is that it multiplies the numbers of gamblers—and hence the numbers of bets.

In this way, casino operators can guarantee that “the variations in the casino’s returns are going to be ridiculously small, no matter the total gambling activity.” By breaking up the betting into thousands, and even—over the course of time—millions or billions of bets, casino operators can ensure that their losses on any single bet are covered by some other bet elsewhere in the casino: there’s a reason that, as the now-folded website Grantland pointed out in 2014, during the previous 23 years “bettors have won twice, while the sportsbooks have won 21 times” in Super Bowl betting. The thing to do in order to make something “gamable”—or “bettable,” which is to say a commodity worth the house’s time—is to break its acts into as many discrete chunks as possible.

The point, I think, can be easily seen: by breaking up a tennis match into smaller sets and games, gamblers can commodify, or make the sport “more bettable”—at least, from the point of view of a sharp operator. “Gamblers may be a total of $20 million, but you needn’t worry about the casino’s health,” Taleb says—because the casino isn’t accepting ten $2 million bets. Instead, “the bets run, say, $20 on average; the casino caps the bets at a maximum.” Rather than making one bet on a match’s outcome, gamblers can make a series of bets on the “games within the game”—bets that, as in the case of the casino, inevitably favor the house even without any match-fixing involved.

In professional tennis there are, as Louisa Thomas pointed out in Grantland a few years ago, every year “tens of thousands of professional matches, hundreds of thousands of games, millions of points, and patterns in the chaos.” (If there is match-fixing—and as mentioned there have been many allegations over the years—well then, you’re in business: an excellent player can even “tank” many, many early opportunities, allowing confederates to cash in, and still come back to put away a weaker opponent.) Anyway, just as Taleb says, casino operators inevitably wish to make bets as numerous as possible because, in the long run, that protects their investment—and tennis, what a co-inky-dink, has more opportunities for betting than virtually any sport you can name.

The august majesty of the New York Times, however, cannot imagine any of that. In their “How Tennis Got Its Scoring System” story, it mentions the speculations of amateur players who say things like: “The eccentricities are part of the fun,” and “I like the old-fashioned touches that tennis has.” It’s all so quaint, in the view of the Times. But since no one can account for tennis’ scoring system otherwise, and everyone admits not only that gambling flourished around lawn tennis’ predecessor game, jeu de paume (or real tennis), but also that the popularity of the sport was eventually brought down precisely because of gambling scandals—and tennis is to this day vulnerable to gamblers—the hypothesis that tennis is scored the way it is for the purposes of gambling makes much more sense than, say, tennis historian Elizabeth Wilson’s solemn pronouncement that tennis’ scoring system is “a powerful exception to the tendencies toward uniformity” that is so dreadfully, dreadfully common in our contemporary vale of tears.

The reality, of course, is that tennis’ scoring system was obviously designed to fleece suckers, not to entertain the twee viewers of Wes Anderson movies. Yet while such dimwittedness can be expected from college students or proper ladies who have never left the Upper East Side of Manhattan or Philadelphia’s Main Line, why is the New York Times so flummoxed by the historical “mystery” of it all? The answer, I suspect anyway, lies in some other, far more significant, sport that is played by with a very similar set of rules as tennis: one that equally breaks up the action into many more different acts than seem strictly necessary. In this game, too, there is an indirect connection between the central, defining act and wins and losses.

The name of that sport? Well, it’s really two versions of the same game.

One is called “the United States Senate”—and the other is called a “presidential election.”

Paper Moon

Say, it’s only a paper moon
Sailing over a cardboard sea
But it wouldn’t be make-believe
If you believed in me
—“It’s Only A Paper Moon” (1933).

 

As all of us sublunaries knows, we now live in a technological age where high-level training is required for anyone who prefers not to deal methamphetamine out of their trailer—or at least, that’s the story we are fed. Anyway, in my own case the urge towards higher training has manifested in a return to school; hence my absence from this blog. Yet, while even I recognize this imperative, the drive toward scientific excellence is not accepted everywhere: as longer-term readers may know, last year Michael Wilbon of ESPN wrote a screed (“Mission Impossible: African-Americans and Analytics”) not only against the importation of what is known as “analytics” into sports—where he joined arms with nearly every old white guy sportswriter everywhere—but, more curiously, essentially claimed that the statistical analysis of sports was racist. “Analytics” seem, Wilbon said, “to be a new safe haven for a new ‘Old Boy Network’ of Ivy Leaguers who can hire each other and justify passing on people not given to their analytic philosophies.” But while Wilbon may be dismissed because “analytics” is obviously friendlier to black people than many other forms of thought—it seems patently clear that something that pays more attention to actual production than to whether an athlete has a “good face” (as detailed in Moneyball) is going to be, on the whole, less racist—he isn’t entirely mistaken. Even if Wilbon appears, moronically, to think that his “enemy” is just a bunch of statheads arguing about where to put your pitcher in the lineup, or whether two-point jump shots are valuable, he can be taken seriously if he recognizes that his true opponent is none other than—Sir Isaac Newton.

Although not many realize it, Isaac Newton was not simply the model of genius familiar to us today as the maker of scientific laws and victim of falling apples. (A story he may simply have made up in order to fend off annoying idiots—a feeling with which, if you are reading this, you may be familiar.) Newton did, of course, first conjure the laws of motion that, on Boxing Day 1968, led William Anders, aboard Apollo 8, to reply “I think Isaac Newton is doing … the driving now” to a ground controller’s son who asked who was in charge of the capsule—but despite the immensity of his scientific achievements, those were not the driving (ahem) force of his curiosity. Newton’s main interests, as a devout Christian, were instead about ecclesiastical history—a topic that led him to perhaps the earliest piece of “analytics” ever written: an 87,000-word monstrosity the great physicist published in 1728.

Within the pages of this book is one of the earliest statistical studies ever written—or so at least Karl Pearson, called “the founder of modern statistics,” realized some two centuries later. Pearson started the world’s first statistics department in 1911, at the University College London; he either inaugurated or greatly expanded some half-dozen entire scientific disciplines, from meteorology to genetics. When Albert Einstein was a young graduate student, the first book his study group studied was a work of Pearson’s. In other words, while perhaps not a genius on the order of his predecessor Newton or his successor Einstein, Pearson was prepared to recognize a mind that was. More signifcantly, Pearson understood that, as he later wrote in the essay that furnishes the occasion for this one, “it is unusual for a great man even in old age to write absolutely idle things”: when someone immensely intelligent does something, it may not be nonsense no matter how much it might look it.

That’s what led Pearson, in 1928, to publish the short essay of interest here, which is about what could appear like the ravings of a religious madman, but as Pearson saw, weren’t: Newton’s 1728 The Chronology of Ancient Kingdoms amended, to which is prefixed: A Short Chronicle from the First Memory of Things in Europe to the Conquest of Persia by Alexander the Great. As Pearson understood, it’s a work of apparent madness that conceals depths of genius. But it’s also, as Wilbon might recognize (were he informed enough to realize it) it’s a work that is both a loaded gun pointed at African-Americans—and also, perhaps, a very tool of liberation.

The purpose of the section of the Chronology that concerned Pearson—there are others—was what Pearson called “a scientific study of chronology”: that is, Newton attempted to reconstruct the reigns of various kings, from contemporary France and England to the ancient rulers of “the Egyptians, Greeks and Latins” to the kings of Israel and Babylon. By consulting ancient histories, the English physicist compiled lists of various reigns in kingdoms around the world—and what he found, Pearson tells us, is that “18 to 20 years is the general average period for a reign.” But why is this, which might appear to be utterly recondite, something valuable to know? Well, because Newton is suggesting that by using this list and average, we can compare it to any other list of kings we find—and thereby determine whether the new list is likely to be spurious or not. The greater the difference between the new list of kingly reigns and Newton’s calculations of old lists, in short, the more likely it is that the new list is simply made up, or fanciful.

Newton did his study because he wanted to show that biblical history was not simply mythology, like that of the ancient Greeks: he wanted to show that the list of the kings of Israel exhibited all the same signs as the lists of kings we know to have really existed. Newton thereby sought to demonstrate the literal truth of the Bible. Now, that’s not something, as Pearson knew, that anyone today is likely much to care about—but what is significant about Newton’s work, as Pearson also knew, is that what Newton here realized was that it’s possible to use numbers to demonstrate something about reality, which was not something that had ever really been done before in quite this same way. Within Newton’s seeming absurdity, in sum, there lurked a powerful sense—the very same sense Bill James and others have been able to apply to baseball and other sports over the past generation and more, with the result that, for example, the Chicago Cubs (managed by Theo Epstein, Bill James’ acolyte) last year finally won, for the first time in more than a century, the final game of the season. In other words, during that nocturnal November moonshot on Chicago’s North Side last year, Sir Isaac Newton was driving.

With that example in mind, however, it might be difficult to see just why a technique, or method of thinking, that allows a historic underdog finally to triumph over its adversaries after eons of oppression could be a threat to African-Americans, as Michael Wilbon fears. After all, like the House of Israel, neither black people nor Cubs fans are unfamiliar with the travails of wandering for generations in the wilderness—and so a method that promises, and has delivered, a sure road to Jerusalem might seem to be attractive, not a source of anxiety. Yet, while in that sense Wilbon’s plea might seem obscure, even the oddest ravings of a great man can reward study.

Wilbon is right to fear statistical science, that is, for a reason that I have been exploring recently: of all things, the Voting Rights Act of 1965. That might appear to be a reference even more obscure than the descendants of Hammurabi, but in fact not so: there is a statistical argument, in other words, to be derived from Sections Two and Five of that act. As legal scholars know, those two sections form the legal basis of what are known as “majority minority districts”: as one scholar has described them, these are “districts where minorities comprise the majority or a sufficient percentage of a given district such that there is a greater likelihood that they can elect a candidate who may be racially or ethnically similar to them.” Since 1965, such districts have increasingly grown, particularly since a 1986 U.S. Supreme Court decision (Thornburg v. Gingles, 478 U.S. 30 (1986) that the Justice Department took to mandate their use in the fight against racism. The rise of such districts are essentially why, although there were fewer than five black congressmen in the United States House of Representatives prior to 1965, there are around forty today: a percentage of congress (slightly less than 10%) not much less than the percentage of black people in the American population (slightly more than 10%). But what appears to be a triumph for black people may not be, so statistics may tell us, for all Americans.

That’s because, according to some scholars, the rise in the numbers of black congressional representatives may also have effectively required a decline in the numbers of Democrats in the House: as one such researcher remarked a few years ago, “the growth in the number of majority-minority districts has come at the direct electoral expense of … Democrats.” That might appear, to many, to be paradoxical: aren’t most African-Americans Democrats? So how can more black reps mean fewer Democratic representatives?

The answer however is provided, again perhaps strangely, by the very question itself: in short, by precisely the fact that most (upwards of 90%) black people are Democrats. Concentrating black voters into congressional districts, in other words, also has the effect of concentrating Democratic voters: districts that elect black congressmen and women tend to see returns that are heavily Democratic. What that means, conversely, that these are votes that are not being voted in other districts: as Steven Hill put the point for The Atlantic in 2013, drawing up majority minority districts “had the effect of bleeding minority voters out of all the surrounding districts,” and hence worked to “pack Democratic voters into fewer districts.” In other words, majority minority districts have indeed had the effect of electing more black people to Congress—at the likely cost of electing fewer Democrats. Or to put it another way: of electing more Republicans.

It’s certainly true that some of the foremost supporters of majority minority districts have been Republicans: for example, the Reagan-era Justice Department mentioned above. Or Benjamin L. Ginsberg, who told the New York Times that such districts were “‘much fairer to Republicans, blacks and Hispanics” in 1992—when he was general counsel of the Republican National Committee. But while all of that is so—and there is more to be said about majority minority districts along these lines—these are only indirectly the reasons why Michael Wilbon is right to fear statistical thought.

That’s because what Michael Wilbon ought to be afraid of about statistical science, if he isn’t already, is what happens if somebody—with all of the foregoing about majority minority districts in mind, as well as the fact that Democrats have historically been far more likely to look after the interests of working people—happened to start messing around in a fashion similar to how Isaac Newton did with those lists of ancient kings. Newton, remember, used those old lists of ancient kings to compare them with more recent, verifiable lists of kings: by comparing the two he was able to make assertions about which lists were more or less likely to be the records of real kings. Nowadays, statistical science has advanced over Newton’s time, though at heart the process is the same: the comparison of two or more data sets. Today, through more sophisticated techniques—some invented by Karl Pearson—statisticians can make inferences about, for example, whether the operations recorded in one data set caused what happened in another. Using such techniques, someone today could use the lists of African-American congressmen and women and begin to compare them to other sets of data. And that is the real reason Michael Wilbon should be afraid of statistical thought.

Because what happens when, let’s say, somebody used that data about black congressmen—and compared it to, I don’t know, Thomas Piketty’s mountains of data about economic inequality? Let’s say, specifically, the share of American income captured by the top 0.01% of all wage earners? Here is a graph of African-American members of Congress since 1965:

Chart of African American Members of Congress, 1967-2012
Chart of African American Members of Congress, 1967-2012

And here is, from Piketty’s original data, the share of American income captured etc.:

Share of U.S. Income, .01% (Capital Gains Excluded) 1947-1998
Share of U.S. Income, .01% (Capital Gains Excluded) 1947-1998

You may wish to peruse the middle 1980s—perhaps coincidentally, right around the time of Thornburg v. Gingles both take a huge jump. Leftists, of course, may complain that this juxtaposition could lead to blaming African-Americans for the economic woes suffered by so many Americans—a result that Wilbon should, rightly, fear. But on the other hand, it could also lead Americans to realize that their political system, in which the number of seats in Congress are so limited that “majority minority districts” have, seemingly paradoxically, resulted in fewer Democrats overall, may not be much less anachronistic than the system that governed Babylon—a result that, Michael Wilbon is apparently not anxious to tell you, might lead to something of benefit to everyone.

Either thought, however, can lead to only one conclusion: when it comes to the moonshot of American politics, maybe Isaac Newton should still—despite the protests of people like Michael Wilbon—be driving.

All Even

George, I am an old man, and most people hate me.
But I don’t like them either so that makes it all even.

—Mr. Potter. It’s A Wonderful Life (1946).

 

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Because someone I love had never seen it, I rewatched Frank Capra’s 1946 It’s A Wonderful Life the other night. To most people, the film is the story of how one George Bailey comes to perceive the value of helping “a few people get outta [the] slums” of the “scurvy little spider” of the film, the wealthy banker Mr. Potter—but to some viewers, what’s important about the inhabitants of Bedford Falls isn’t that they are poor by comparison to Potter, but instead that some of them are black: the man who plays the piano in the background of one scene, for instance, or Annie, the Bailey family’s maid. To Vincent Nobile, a professor of history at Rancho Cucamonga’s Chaffey College, the casting of these supporting roles not only demonstrates that “Capra showed no indication he could perceive blacks in roles outside the servant class,” but also that Potter is the story’s villain not because he is a slumlord, but because he calls the people Bailey helps “garlic eaters” (http://historynewsnetwork.org/article/1846). What makes Potter evil, in other words, isn’t his “cold monetary self-interest,” but because he’s “bigoted”: to this historian, Capra’s film isn’t the heartwarming story of how Americans banded together to stop a minority (rich people) from wrecking things, but instead the horrifying tragedy of how Americans banded together to stop a minority (black people) from wrecking things. Unfortunately, there’s two problems with that view—problems that can be summarized by referring to the program for a football game that took place five years before the release of Capra’s classic: the Army-Navy game of 29 November, 1941.

Played at Philadelphia’s Franklin Memorial Stadium (once home of the NFL’s Philadelphia Eagles and still the home of the Penn Relays, one of track and field’s premier events), Navy won the contest 14-6; according to Vintage College Football Programs & Collectibles (collectable.wordpress.com [sic]), the program for that game contains 212 pages. On page 180 of that program there is a remarkable photograph. It is of the USS Arizona, the second and last of the American “Pennsylvania” class of super-dreadnought battleships—a ship meant to be, according to the New York Times of 13 July 1913, “the world’s biggest and most powerful, both offensively and defensively, superdreadnought ever constructed.” The last line of the photograph’s caption reads thusly:

It is significant that despite the claims of air enthusiasts, no battleship has yet been sunk by bombs.”

Slightly more than a week later, of course, on a clear bright Sunday morning just after 8:06 Hawaiian time, the hull of the great ship would rest on the bottom of Pearl Harbor, along with the bodies of nearly 1200 of her crew—struck down by the “air enthusiasts” of the Empire of the Sun. The lesson taught that morning, by aircraft directed by former Harvard student Isoroku Yamamoto, was a simple one: that “a saturation attack by huge numbers of low-value attackers”—as Pando Daily’s “War Nerd” columnist, Gary Brecher, has referred to this type of attack—can bring down nearly any target, no matter how powerful (http://exiledonline.com/the-war-nerd-this-is-how-the-carriers-will-die/all/1/). (A lesson that the U.S. Navy has received more than once: in 2002, for instance, when during the wargame “Millennium Challenge 2002” Marine Corps Lieutenant General Paul K. Riper (fictionally) sent 16 ships to the bottom of the Persian Gulf with the creative use of, essentially, a bunch of cruise missiles and several dozen speedboats loaded with cans of gasoline driven by gentlemen with, shall we say, a cavalier approach to mortality.) It’s the lesson that the cheap and shoddy can overcome quality—or in other words that, as the song says, the bigger they come, the harder they fall.

It’s a lesson that applies to more than merely the physical plane, as the Irish satirist Jonathan Swift knew: “Falsehood flies, and the Truth comes limping after,” the author of Gulliver’s Travels wrote in 1710. What Swift refers to is how saturation attacks can work on the intellectual as well as physical plane—as Emory University’s Mark Bauerlein (who, unfortunately for the warmth of my argument’s reception, endorsed Donald Trump in this past election) argued, in Partisan Review in 2001, American academia has over the past several generations essentially become flooded with the mental equivalents of Al Qaeda speedboats. “Clear-sighted professors,” Bauerlein wrote then, understanding the conditions of academic research, “avoid empirical methods, aware that it takes too much time to verify propositions about culture, to corroborate facts with multiple sources, to consult primary documents, and to compile evidence adequate to inductive conclusions” (http://www.bu.edu/partisanreview/books/PR2001V68N2/HTML/files/assets/basic-html/index.html#226). Discussing It’s A Wonderful Life in terms of, say, the economic differences between banks like the one owned by Potter and the savings-and-loan run by George Bailey—and the political consequences therein—is, in other words, hugely expensive in terms of time and effort invested: it’s much more profitable to discuss the film in terms of its hidden racism. By “profitable,” in other words, I mean not merely because it’s intrinsically easier, but also because such a claim is much more likely to upset people, and thus attract attention to its author: the crass stunt once called épater le bourgeois.

The current reward system of the humanities, in other words, favors those philosopher Isaiah Berlin called “foxes” (who know a great many things) rather than “hedgehogs” (who know one important thing). To the present defenders of the humanities, of course, such is the point: that’s the pro-speedboat argument noted feminist literary scholar Jane Tompkins made so long ago as 1981, in her essay “Sentimental Power: Uncle Tom’s Cabin and the Politics of American Literary History.” There, Tompkins suggested that the “political and economic measures”—i.e., the battleships of American political discourse—“that constitute effective action for us” are, in reality, merely “superficial”: instead, what’s necessary are “not specific alterations in the current political and economic arrangements, but rather a change of heart” (http://engl651-jackson.wikispaces.umb.edu/file/view/Sentimental+Power.pdf). To those who think like Tompkins—or apparently, Nobile—discussing It’s A Wonderful Life in terms of economics is to have missed the point entirely: what matters, according to them, isn’t the dreadnought clash of, for example, the unit banking system of the antebellum North (speedboats) versus the branch banking system of the antebellum South (battleships) within the sea of the American economy. (A contest that, incidentally, not only did branch banking largely win in 1994, during Bill Clinton’s administration, but a victory that in turn—because it helped to create the enormous “too big to fail” interstate banks of today—arguably played no small role in the crash of 2008). Instead, what’s important is the seemingly-minor attack of a community college teacher upon a Titanic of American culture. Or, to put the point in terms popularized by Silicon Valley: the sheer BS quality of Vincent Nobile’s argument about It’s A Wonderful Life isn’t a bug—it’s a feature.

There is, however, one problem with such tactics—the same problem described by Rear Admiral Chuichi (“King Kong”) Hara of the Imperial Japanese Navy after the Japanese surrender in September 1945: “We won a great tactical victory at Pearl Harbor—and thereby lost the war.” Although, as the late American philosopher Richard Rorty commented before his death in his Achieving Our Country: Leftist Thought in Twentieth Century America, “[l]eftists in the academy” have, in collaboration with “the Right,” succeeded in “making cultural issues central to public debate,” that hasn’t necessarily resulted in a victory for leftists, or even liberals (https://www.amazon.com/Achieving-Our-Country-Leftist-Twentieth-Century/dp/0674003128). Indeed, there’s some reason to suppose that, by discouraging certain forms of thought within left-leaning circles, academic leftists in the humanities have obscured what Elizabeth Drew, in the New York Review of Books, has called “unglamorous structural questions” in a fashion ultimately detrimental not merely to minority communities, but ultimately all Americans (http://www.nybooks.com/articles/2016/08/18/american-democracy-betrayed/).

What Drew was referring to this past August was such matters as how—in the wake of the 2010 Census and the redistricting it entailed in every state in the Union—the Democrats ended up, in the 2012 election cycle, winning the popular vote for Congress “by 1.2 per cent, but still remained in the minority, with two hundred and one seats to the G.O.P.’s two hundred and thirty-four.” In other words, Democratic candidates for the House of Representatives got, as Katie Sanders noted in Politifact in 2013, “50.59 percent of the two-party vote” that November, but “won just 46.21 percent of seats”: only “the second time in 70 years that a party won the majority of the vote but didn’t win a majority of the House seats” (http://www.politifact.com/truth-o-meter/statements/2013/feb/19/steny-hoyer/steny-hoyer-house-democrats-won-majority-2012-popu/). The Republican advantage didn’t end there: as Rob Richie reported for The Nation in 2014, in that year’s congressional races Republicans won “about 52 percent of votes”—but ended “up with 57 percent of seats” (https://www.thenation.com/article/republicans-only-got-52-percent-vote-house-races/). And this year, the numbers suggest, the Republicans received less than half the popular vote—but will end up with fifty-five percent (241) of the total seats (435). These losses, Drew suggests, are ultimately due to the fact that “the Democrats simply weren’t as interested in such dry and detailed stuff as state legislatures and redistricting”—or, to put it less delicately, because potentially-Democratic schemers have been put to work constructing re-readings of old movies instead of building arguments that are actually politically useful.

To put this even less delicately, many people on the liberal or left-wing side of the political aisle have, for the past several generations, spent their college educations learning, as Mark Bauerlein wrote back in 2001, how to “scoff[…] at empirical notions, chastising them as ‘näive positivism.’” At the same time, a tiny minority among them—those destined to “relax their scruples and select a critical practice that fosters their own professional survival”—have learned, and are learning, to swim the dark seas of academia, taught by their masters how to live by feeding upon the minds of essentially defenseless undergraduates. The lucky ones, like Vince Nobile, manage—by the right mix of bowing and scraping—to land some kind of job security at some far-flung outpost of academia’s empire, where they make a living entertaining the yokels; the less-successful, of course, write deeply ironic blogs.

Be that as it may, while there isn’t necessarily a connection between the humanistic academy’s flight from what Bauerlein calls “the canons of logic” and the fact that it was so easy—as John Cassidy of The New Yorker observed after this past presidential election—for so many in the American media and elsewhere “to dismiss the other outcome [i.e., Trump’s victory] as a live possibility” before the election, Cassidy at least ascribed the ease with which so many predicted a Clinton victory then to the fact that many “haven’t been schooled in how to think in probabilistic terms” (http://www.newyorker.com/news/john-cassidy/media-culpa-the-press-and-the-election-result). That lack of education, which extends from the impact of mathematics upon elections to the philosophical basis for holding elections at all (which extends far beyond the usual seventeenth-century suspects rounded up in even the most erudite of college classes to medieval thinkers like Nicholas of Cusa, who argued in 1434’s Catholic Concordance that the “greater the agreement, the more infallible the judgment”—or in other words that speedboats are more trustworthy than battleships), most assuredly has had political consequences (http://www.cambridge.org/us/academic/subjects/politics-international-relations/texts-political-thought/nicholas-cusa-catholic-concordance?format=PB&isbn=9780521567732). While the ever-more abstruse academic turf wars between the sciences and the humanities might be good for the ever-dwindling numbers of tenured college professors, in other words, it’s arguably disastrous, not only for Democrats and the populations they serve, but for the country as a whole. Although Clarence, angel second class, says to George Bailey, “we don’t use money in Heaven”—suggesting the way in which American academics swear off knowledge of the sciences upon entering their secular priesthood—George replies, “it comes in real handy down here, bub.” What It’s A Wonderful Life wants to tell us is that a nation whose leadership balances so precariously upon such a narrow educational foundation is, no matter what the program says, as vulnerable as a battleship on a bright Pacific morning.

Or a skyscraper, on a cloudless September one.

Stormy Weather

They can see no reasons …
—“I Don’t Like Mondays” 
The Boomtown Rats.
The Fine Art of Surfacing. 1979.

 

“Since Tuesday night,” John Cassidy wrote in The New Yorker this week, “there has been a lot of handwringing about how the media, with all its fancy analytics, failed to foresee Donald Trump’s victory”: as the New York Times headline had it, “How Data Failed Us in Calling an Election.” The failure of Nate Silver and other statistical analysts in the lead-up to Election Day rehearses, once again, a seemingly-ancient argument between what are now known as the sciences and the humanities—an argument sometimes held to be as old as the moment when Herodotus (the “Father of History”) asserted that his object in telling the story of the Greco-Persian Wars of 2500 years ago was “to set forth the reasons why [the Greeks and Persians] wage war on each other.” In other words, Herodotus thought that, to investigate war, it was necessary to understand the motives of the people who fought it—just as Cassidy says the failure of the press to get it right about this election was, Cassidy says, “a failure of analysis, rather than of observation.” The argument both Herodotus and Cassidy are making is the seemingly unanswerable one that it is the interpretation of the evidence, rather than the evidence itself, that is significant—a position that seems inarguable so long as you aren’t in the Prussian Army, dodging Nazi bombs during the last year of the Second World War, or living in Malibu.

The reason why it seems inarguable, some might say, is because the argument both Herodotus and Cassidy are making is inescapable: obviously, given Herodotus’ participation, it is a very ancient one, and yet new versions are produced all the time. Consider for instance a debate conducted by English literature professor Michael Bérubé and philosopher John Searle some years ago, about a distinction between what Searle called “brute fact” and “social fact.” “Brute facts,” Bérubé wrote later, are “phenomena like Neptune, DNA, and the cosmic background radiation,” while the second kind are “items whose existence and meaning are obviously dependent entirely on human interpretation,” such as “touchdowns and twenty-dollar bills.” Like Searle, most people might like to say that “brute fact” is clearly more significant than “social fact,” in the sense that Neptune doesn’t care what we think about it, whereas touchdowns and twenty dollar bills are just as surely entirely dependent on what we think of them.

Not so fast, said Bérubé: “there’s a compelling sense,” the professor of literature argued, in which social facts are “prior to and even constitutive of” brute facts—if social facts are the means by which we obtain our knowledge of the outside world, then social facts could “be philosophically prior to and certainly more immediately available to us humans than the world of brute fact.” The only way we know about Neptune is because a number of human beings thought it was important enough to discover; Neptune doesn’t give a damn one way or the other.

“Is the distinction between social facts and brute facts,” Bérubé therefore asks, “a social fact or a brute fact?” (Boom! Mic drop.) That is, whatever the brute facts are, we can only interpret them in the light of social facts—which would seem to grant priority to those disciplines dealing with social facts, rather than those disciplines that deal with brute fact; Hillary Clinton, Bérubé might say, would have been better off hiring an English professor, rather than a statistician, to forecast the election. Yet, despite the smugness with which Bérubé delivers what he believes is a coup de grâce, it does not seem to occur to him that traffic between the two realms can also go the other way: while it may be possible to see how “social facts” subtly influence our ability to see “brute facts,” it’s also possible to see how “brute facts” subtly influence our ability to see “social facts.” It’s merely necessary to understand how the nineteenth-century Prussian Army treated its horses.

The book that treats that question about German military horsemanship is called The Law of Small Numbers, which was published in 1898 by one Ladislaus Bortkiewicz: a Pole who lived in the Russian Empire and yet conducted a study on data about the incidence of deaths caused by horse kicks in the nineteenth-century Prussian Army. Apparently, this was a cause of some concern to military leaders: they wanted to know whether, say, if an army corp that experienced several horse kick deaths in a year—an exceptional number of deaths from this category—was using bad techniques, or whether they happened to buy particularly ornery horses. Why, in short, did some corps have what looked like an epidemic of horse kick deaths in a given year, while others might go for years without a single death? What Bortkiewicz found answered those questions—though perhaps not in a fashion the army brass might have liked.

Bortkiewicz began by assembling data about the number of fatal horse kicks in fourteen Prussian army corps over twenty years, which he then combined into “corp years”: the number of years together with the number of corps. What he found—as E.J. Gumbel pus it in the International Encyclopedia of the Social Sciences—was that for “over half the corps-year combinations there were no deaths from horse kicks,” while “for the other combinations the number of deaths ranged up to four.” In most years, in other words, no one was killed in any given corps by a horse kick, while in some years someone was—and in terrible years four were. Deaths by horse kick, then, were uncommon, which meant they were hard to study: given that they happened so rarely, it was difficult to determine what caused them—which was why Bortkiewicz had to assemble so much data about them. By doing so, the Russian Pole hoped to be able to isolate a common factor among these deaths.

In the course of studying these deaths, Bortkiewicz ended up independently re-discovering something that a French mathematician, Simeon Denis Poisson, had already, in 1837, used in connection with discussing the verdicts of juries: an arrangement of data now known as the Poisson distribution. And as the mathematics department at the University of Massachusetts is happy to tell us (https://www.umass.edu/wsp/resources/poisson/), the Poisson distribution applies when four conditions are met: first, “the event is something that can be counted in whole numbers”; second, “occurrences are independent, so that one occurrence neither diminishes nor increases the chance of another”; third, “the average frequency of occurrence for the time period in question is known”; and finally “it is possible to count how many events have occurred.” If these things are known, it seems, the Poisson distribution will tell you how often the event in question will happen in the future—a pretty useful feature for, say, predicting the results of an election. But that what wasn’t was intriguing about Bortkiewicz’ study: what made it important enough to outlast the government that commissioned it was that Bortkiewicz found that the Poisson distribution “may be used in reverse”—a discovery ended up telling us about far more than the care of Prussian horses.

What “Bortkiewicz realized,” as Aatish Bhatia of Wired wrote some years ago, was “that he could use Poisson’s formula to work out how many deaths you could expect to see” if the deaths from horse kicks in the Prussian army were random. The key to the Poisson distribution, in other words, is the second component, “occurrences are independent, so that one occurrence neither diminishes nor increases the chance of another”: a Poisson distribution describes processes that are like the flip of a coin. As everyone knows, each flip of a coin is independent of the one that came before; hence, the record of successive flips is the record of a random process—a process that will leave its mark, Bortkiewicz understood.

A Poisson distribution maps a random process; therefore, if the process in question maps a Poisson distribution, then it must be a random process. A distribution that matches the results a Poisson distribution would predict must also be a process in which each occurrence is independent of those that came before. As the UMass mathematicians say, “if the data are lumpy, we look for what might be causing the lump,” while conversely, if  “the data fit the Poisson expectation closely, then there is no strong reason to believe that something other than random occurrence is at work.” Anything that follows a Poisson distribution is likely the result of a random process; hence, what Bortkiewicz had discovered was a tool to find randomness.

Take, for example, the case of German V-2 rocket attacks on London during the last years of World War II—the background, as it happens, to novelist Thomas Pynchon’s Gravity’s Rainbow. As Pynchon’s book relates, the flying missiles were falling in a pattern: some parts of London were hit multiple times, while others were spared. Some Londoners argued that this “clustering” demonstrated that the Germans must have discovered a way to guide these missiles—something that would have been highly, highly advanced for mid-twentieth century technology. (Even today, guided missiles are incredibly advanced: much less than ten percent of all the bombs dropped during the 1991 Gulf War, for instance, had “smart bomb” technology.) So what British scientist R. D. Clarke did was to look at the data for all the targets of V-2s that fell on London. What he found was that the results matched a Poisson distribution—the Germans did not possess super-advanced guidance systems. They were just lucky.

Daniel Kahneman, the Israeli psychologist, has a similar story: “‘During the Yom Kippur War, in 1973,’” Kahneman told New Yorker writer Atul Gawande, he was approached by the Israeli Air Force to investigate why, of two squads that took to the skies during the war, “‘one had lost four planes and the other had lost none.’” Kahneman told them not to waste their time, because a “difference of four lost planes could easily have occurred by chance.” Without knowing about Bortkiewicz, that is, the Israeli Air Force “would inevitably find some measurable differences between the squadrons and feel compelled to act on them”—differences that, in reality, mattered not at all. Presumably, Israel’s opponents were bound to hit some of Israel’s warplanes; it just so happened that they were clustered in one squadron and not the other.

Why though, should any of this matter in terms of the distinction between “brute” and “social” facts? Well, consider what Herodotus wrote more than two millennia ago: what matters, when studying war, is the reasons people had for fighting. After all, wars are some of the best examples of a “social fact” anywhere: wars only exist, Herodotus is claiming, because of what people think about them. But what if it could be shown that, actually, there’s a good case to be made for thinking of war as a “brute fact”—something more like DNA or Neptune than like money or a home run? As it happens, at least one person, following in Bortkiewicz’ footsteps, already has.

In November of 1941, the British meteorologist and statistician Lewis Fry Richardson published, in the journal Nature, a curious article entitled “Frequency of Occurrence of Wars and Other Quarrels.” Richardson, it seems, had had enough of the endless theorizing about war’s causes: whether it be due to, say, simple material greed, or religion, or differences between various cultures or races. (Take for instance the American Civil War: according to some Southerners, the war could be ascribed to the racial differences between Southern “Celtics” versus Northern “Anglo-Saxons”; according to William Seward, Abraham Lincoln’s Secretary of State, the war was due to the differences in economic systems between the two regions—while to Lincoln himself, perhaps characteristically, it was all due to slavery.) Rather than argue with the historians, Richardson decided to instead gather data: he compiled a list of real wars going back centuries, then attempted to analyze the data he had collected.

What Richardson found was, to say the least, highly damaging to Herodotus: as Brian Hayes puts it in a recent article in American Scientist about Richardson’s work, when Richardson compared a group of wars with similar amounts of casualties to a Poisson distribution, he found that the “match is very close.” The British scientist also “performed a similar analysis of the dates on which wars ended—the ‘outbreaks of peace’—with the same result.” Finally, he checked another data set concerning wars, this one compiled by the University of Chicago’s Quincy Wright—“and again found good agreement.” “Thus,” Hayes writes, “the data offer no reason to believe that wars are anything other than randomly distributed accidents.” Although Herodotus argued that the only way to study wars is to study the motivations of those who fought them, there may in reality be no more “reason” for the existence of war than the existence of a forest fire in Southern California.

Herodotus, to be sure, could not have seen that: the mathematics of his time were nowhere near sophisticated enough to run a Poisson distribution. Therefore, the Greek historian was eminently justified in thinking that wars must have “reasons”: he literally did not have the conceptual tools necessary to think that wars may not have reasons at all. That was an unavailable option. But through the work of Bortkiewizc and his successors, that has now become an option: indeed, the innovation of these statisticians has been to show that our default assumption ought to be what statisticians call the “null hypothesis,” which is defined by the Cambridge Dictionary of Statistics to be “the ‘no difference’ or ‘no association’ hypothesis.” Unlike Herodotus, who presumed that explanations must equal causes, we now assume that we ought to be first sure that there is anything to explain before trying to explain it.

In this case, then, it may be that the “brute fact” of the press’ Herodotian commitment to discovering “reasons” that explains why nobody in the public sphere predicted Donald Trump’s victory: because the press is already committed to the supremacy of analysis over observation, it could not perform the observations necessary to think Trump could win. Or, as Cassidy put it, when a reporter saw the statistical election model of choice “registering the chances of the election going a certain way at ninety per cent, or ninety-five per cent, it’s easy to dismiss the other outcome as a live possibility—particularly if you haven’t been schooled in how to think in probabilistic terms, which many people haven’t.” Just how powerful the assumption of the force of analysis over data can be is demonstrated by the fact that—even despite noting the widespread lack of probabilistic thinking—Cassidy still thinks it possible that “F.B.I. Director James Comey’s intervention ten days before the election,” in which Comey announced his staff was still investigating Clinton’s emails, “may have proved decisive.” In other words, despite knowing something about the impact of probability, Cassidy still thinks it possible that a letter from the F.B.I. director was somehow more important to the outcome of this past election than the evidence of their own lives were to million of Americans—or, say, the effect of a system in which the answer to the question where outweighs that of how many?

Probabilistic reasoning, of course, was unavailable to Herodotus, who lived two millennia before the mathematical tools necessary were even invented—which is to say that, while some like to claim that the war between interpretation and data is eternal, it might not be. Yet John Cassidy—and Michael Bérubé—don’t live before those tools were invented, and yet they persist in writing as if they do. While that’s fine, so far as it is their choice as private citizens, it ought to be quite a different thing insofar as it is their jobs as journalist and teacher, respectively—particularly in the case, as say in the 2016 election, when it is of importance to the continued health of the nation as a whole that there be a clear public understanding of events. Some people appear to think that continuing the quarrels of people whose habits of mind, today, would barely qualify them to teach Sunday school is something noble; in reality, it may just be a measure of how far we have yet to travel.

 

The Color of Water

No one gets lucky til luck comes along.
Eric Clapton
     “It’s In The Way That You Use It”
     Theme Song for The Color of Money (1986).

 

 

The greenish tint to the Olympic pool wasn’t the only thing fishy about the water in Rio last month: a “series of recent reports,” Patrick Redford of Deadspin reported recently, “assert that there was a current in the pool at the Rio Olympics’ Aquatic Stadium that might have skewed the results.” Or—to make the point clear in a way the pool wasn’t—the water in the pool flowed in such a way that it gave the advantage to swimmers starting in certain lanes: as Redford writes, “swimmers in lanes 5 through 8 had a marked advantage over racers in lanes 1 through 4.” According, however, to ESPN’s Michael Wilbon—a noted African-American sportswriter—such results shouldn’t be of concern to people of color: “Advanced analytics,” Wilbon wrote this past May, “and black folks hardly ever mix.” To Wilbon, the rise of statistical analysis poses a threat to African-Americans. But Wilbon is wrong: in reality, the “hidden current” in American life holding back both black Americans and all Americans is not analytics—it’s the suspicions of supposedly “progressive” people like Michael Wilbon.

The thesis of Wilbon’s piece, “Mission Impossible: African-Americans and Analytics”—published on ESPN’s race-themed website, The Undefeated—was that black people have some kind of allergy to statistical analysis: “in ‘BlackWorld,’” Wilbon solemnly intoned, “never is heard an advanced analytical word.” Whereas, in an earlier age, white people like Thomas Jefferson questioned black people’s literacy, nowadays, it seems, it’s ok to question their ability to understand mathematics—a “ridiculous” (according to The Guardian’s Dave Schilling, another black journalist) stereotype that Wilbon attempts to paint as, somehow, politically progressive: Wilbon, that is, excuses his absurd beliefs on the basis that analytics “seems to be a new safe haven for a new ‘Old Boy Network’ of Ivy Leaguers who can hire each other and justify passing on people not given to their analytic philosophies.” Yet, while Wilbon isn’t alone in his distrust of analytics, it’s actually just that “philosophy” that may hold the most promise for political progress—not only for African-Americans, but every American.

Wilbon’s argument, after all, depends on a common thesis heard in the classrooms of American humanities departments: when Wilbon says the “greater the dependence on the numbers, the more challenged people are to tell (or understand) the narrative without them,” he is echoing a common argument deployed every semester in university seminar rooms throughout the United States. Wilbon is, in other words, merely repeating the familiar contention, by now essentially an article of faith within the halls of the humanities, that without a framework—or (as it’s sometimes called), “paradigm”—raw statistics are meaningless: the doctrine sometimes known as “social constructionism.”

That argument is, as nearly everyone who has taken a class in the departments of the humanities in the past several generations knows, that “evidence” only points in a certain direction once certain baseline axioms are assumed. (An argument first put about, by the way, by the physician Galen in the second century AD.) As American literary critic Stanley Fish once rehearsed the argument in the pages of the New York Times, according to its terms investigators “do not survey the world in a manner free of assumptions about what it is like and then, from that (impossible) disinterested position, pick out the set of reasons that will be adequate to its description.” Instead, Fish went on, researchers “begin with the assumption (an act of faith) that the world is an object capable of being described … and they then develop procedures … that yield results, and they call those results reasons for concluding this or that.” According to both Wilbon and Fish, in other words, the answers people find depends not the structure of reality itself, but instead on the baseline assumptions the researcher begins with: what matters is not the raw numbers, but the contexts within which the numbers are interpreted.

What’s important, Wilbon is saying, is the “narrative,” not the numbers: “Imagine,” Wilbon says, “something as pedestrian as home runs and runs batted in adequately explaining [Babe] Ruth’s overall impact” on the sport of baseball. Wilbon’s point is that a knowledge of Ruth’s statistics won’t tell you about the hot dogs the great baseball player ate during games, or the famous “called shot” during the 1932 World Series—what he is arguing is that statistics only point toward reality: they aren’t reality itself. Numbers, by themselves, don’t say anything about reality; they are only a tool with which to access reality, and by no means the only tool available: in one of Wilbon’s examples Stef Curry, the great guard for the NBA’s Golden State Warriors, knew he shot better from the corners—an intuition that later statistical analysis bore out. Wilbon’s point is that both Curry’s intuition and statistical analysis told the same story, implying that there’s no fundamental reason to favor one road to truth over the other.

In a sense, to be sure, Wilbon is right: statistical analysis is merely a tool for getting at reality, not reality itself, and certainly other tools are available. Yet, it’s also true that, as statistician and science fiction author Michael F. Flynn has pointed out, astronomy—now accounted one of the “hardest” of physical sciences, because it deals with obviously real physical objects in space—was once not an observational science, but instead a mathematical one: in ancient times, Chinese astronomers were called “calendar-makers,” and a European astronomer was called a mathematicus. As Flynn says, “astronomy was not about making physical discoveries about physical bodies in the sky”—it was instead “a specialized branch of mathematics for making predictions about sky events.” Without telescopes, in other words, astronomers did not know what, exactly, say, the planet Mars was: all they could do was make predictions, based on mathematical analysis, about what part of the sky it might appear in next—predictions that, over the centuries, became perhaps-startlingly accurate. But as a proto-Wilbon might have said in (for instance) the year 1500, such astronomers had no more direct knowledge of what Mars is than a kindergartner has of the workings of the Federal Reserve.

In the same fashion, Wilbon might point out about the swimming events in Rio, there is no direct evidence of a current in the Olympic pool: the researchers who assert that there was such a current base their arguments on statistical evidence of the races, not examination of the conditions of the pool. Yet the evidence for the existence of a current is pretty persuasive: as the Wall Street Journal reported, fifteen of the sixteen swimmers, both men and women, who swam in the 50-meter freestyle event finals—the one event most susceptible to the influence of a current, because swimmers only swim one length of the pool in a single direction—swam in lanes 4 through 8, and swimmers who swam in outside lanes in early heats and inside lanes in later heats actually got slower. (A phenomena virtually unheard of in top level events like the Olympics.) Barry Revzin, of the website Swim Swam, found that a given Olympic swimmer picked up “a 0.2 percent advantage for each lane … closer to [lane] 8,” Deadspin’s Redford reported, and while that could easily seem “inconsequentially small,” Redford remarked, “it’s worth pointing out that the winner in the women’s 50 meter freestyle only beat the sixth-place finisher by 0.12 seconds.” It’s a very small advantage, in other words, which is to say that it’s very difficult to detect—except by means of the very same statistical analysis distrusted by Wilbon. But although it is a seemingly-small advantage, it is enough to determine the winner of the gold medal. Wilbon in other words is quite right to say that statistical evidence is not a direct transcript of reality—he’s wrong, however, if he is arguing that statistical analysis ought to be ignored.

To be fair, Wilbon is not arguing exactly that: “an entire group of people,” he says, “can’t simply refuse to participate in something as important as this new phenomenon.” Yet Wilbon is worried about the growth of statistical analysis because he views it as a possible means for excluding black people. If, as Wilbon writes, it’s “the emotional appeal,” rather than the “intellect[ual]” appeal, that “resonates with black people”—a statement that, if it were written by a white journalist, would immediately cause a protest—then Wilbon worries that, in a sports future run “by white, analytics-driven executives,” black people will be even further on the outside looking in than they already are. (And that’s pretty far outside: as Wilbon notes, “Nate McMillan, an old-school, pre-analytics player/coach, who was handpicked by old-school, pre-analytics player/coach Larry Bird in Indiana, is the only black coach hired this offseason.”) Wilbon’s implied stance, in other words—implied because he nowhere explicitly says so—is that since statistical evidence cannot be taken at face value, but only through screens and filters that owe more to culture than to the nature of reality itself, therefore the promise (and premise) of statistical analysis could be seen as a kind of ruse designed to perpetuate white dominance at the highest levels of the sport.

Yet there are at least two objections to make about Wilbon’s argument: the first being the empirical observation that in U.S. Supreme Court cases like McCleskey v. Kemp for instance (in which the petitioner argued that, according to statistical analysis, murderers of white people in Georgia were far more likely to receive the death penalty than murderers of black people), or Teamsters v. United States, (in which—according to Encyclopedia.com—the Court ruled, on the basis of statistical evidence, that the Teamsters union had “engaged in a systemwide practice of minority discrimination”), statistical analysis has been advanced to demonstrate the reality of racial bias. (A demonstration against which, by the way, time and again conservatives have countered with arguments against the reality of statistical analysis that essentially mirror Wilbon’s.) To think then that statistical analysis could be inherently biased against black people, as Wilbon appears to imply, is empirically nonsense: it’s arguable, in fact, that statistical analysis of the sort pioneered by people like sociologist Gunnar Myrdal has done at least as much, if not more, as (say) classes on African-American literature to combat racial discrimination.

The more serious issue, however, is a logical objection: Wilbon’s two assertions are in conflict with each other. To reach his conclusions, Wilbon ignores (like others who make similar arguments) the implications of his own reasoning: statistics ought to be ignored, he says, because only “narrative” can grant meaning to otherwise meaningless numbers—but, if it is so that numbers themselves cannot “mean” without a framework to grant them meaning, then they cannot pose the threat that Wilbon says they might. In other words, if Wilbon is right that statistical analysis is biased against black people, then it means that numbers do have meaning in themselves, while conversely if numbers can only be interpreted within a framework, then they cannot be inherently biased against black people. By Wilbon’s own account, in other words, nothing about statistical analysis implies that such analysis can only be pursued by white people, nor could the numbers themselves demand only a single (oppressive) use—because if that were so, then numbers would be capable of providing their own interpretive framework. Wilbon cannot logically advance both propositions simultaneously.

That doesn’t mean, however, that Wilbon’s argument—the argument, it ought to be noted, of many who think of themselves as politically “progressive”—is not having an effect: it’s possible, I think, that the relative success of this argument is precisely what is causing Americans to ignore a “hidden current” in American life. That current is could be described by an “analytical” observation made by professors Sven Steinmo and Jon Watts some two decades ago: “No other democratic system in the world requires support of 60% of legislators to pass government policy”—an observation that, in turn, may be linked to the observable reality that, as political scientists Frances E. Lee and Bruce Oppenheimer have noted, “less populous states consistently receive more federal funding than states with more people.” Understanding the impact of these two observations, and their effects on each other would, I suspect, throw a great deal of light on the reality of American lives, white and black—yet it’s precisely the sort of reflection that the “social construction” dogma advanced by Wilbon and company appears specifically designed to avoid. While to many, even now, the arguments for “social construction” and such might appear utterly liberatory, it’s possible to tell a tale in which it is just such doctrines that are the tools of oppression today.

Such an account would be, however—I suppose Michael Wilbon or Stanley Fish might tell us—simply a story about the one that got away.

Striking Out

When a man’s verses cannot be understood … it strikes a man more dead than a great reckoning in a little room.
As You Like It. III, iii.

 

There’s a story sometimes told by the literary critic Stanley Fish about baseball, and specifically the legendary early twentieth-century umpire Bill Klem. According to the story, Klem is working behind the plate one day. The pitcher throws a pitch; the ball comes into the plate, the batter doesn’t swing, and the catcher catches it. Klem doesn’t say anything. The batter turns around and says (Fish tells us),

“O.K., so what was it, a ball or a strike?” And Klem says, “Sonny, it ain’t nothing ’till I call it.” What the batter is assuming is that balls and strikes are facts in the world and that the umpire’s job is to accurately say which one each pitch is. But in fact balls and strikes come into being only on the call of an umpire.

Fish is expressing here what is now the standard view of American departments of the humanities: the dogma (a word precisely used) known as “social constructionism.” As Fish says elsewhere, under this dogma, “what is and is not a reason will always be a matter of faith, that is of the assumptions that are bedrock within a discursive system which because it rests upon them cannot (without self-destructing) call them into question.” To many within the academy, this view is inherently liberating: the notion that truth isn’t “out there” but rather “in here” is thought to be a sub rosa method of aiding the political change that, many have thought, has long been due in the United States. Yet, while joining the “social construction” bandwagon is certainly the way towards success in the American academy, it isn’t entirely obvious that it’s an especially good way to practice American politics: specifically, because the academy’s focus on the doctrines of “social constructionism” as a means of political change has obscured another possible approach—an approach also suggested by baseball. Or, to be more precise, suggested by the World Series of 1904 that didn’t happen.

“He’d have to give them,” wrote Will Hively, in Discover magazine in 1996, “a mathematical explanation of why we need the electoral college.” The article describes how one Alan Natapoff, a physicist at the Massachusetts Institute of Technology, became involved in the question of the Electoral College: the group, assembled once every four years, that actually elects an American president. (For those who have forgotten their high school civics lessons, the way an American presidential election works is that each American state elects a number of “electors” equal in number to that state’s representation  in Congress; i.e., the number of congresspeople each state is entitled to by population, plus two senators. Those electors then meet to cast their votes in what is the actual election.) The Electoral College has been derided for years: the House of Representatives introduced a constitutional amendment to abolish it in 1969, for instance, while at about the same time the American Bar Association called the college “archaic, undemocratic, complex, ambiguous, indirect, and dangerous.” Such criticisms have a point: as has been seen a number times in American history (most recently in 2000), the Electoral College makes it possible to elect a president without a majority of the votes. But to Natapoff, such criticisms fundamentally miss the point because, according to him, they misunderstood the math.

The example Natapoff turned to in order to support his argument for the Electoral College was drawn from baseball. As Anthony Ramirez wrote in a New York Times article about Natapoff and his argument, also from 1996, the physicist’s favorite analogy is to the World Series—a contest in which, as Natapoff says, “the team that scores the most runs overall is like a candidate who gets the most popular votes.” But scoring more runs than your opponent is not enough to win the World Series, as Natapoff goes on to say: in order to become the champion baseball team of the year, “that team needs to win the most games.” And scoring runs is not the same as winning games.

Take, for instance, the 1960 World Series: in that contest, as Lively says in Discover, “the New York Yankees, with the awesome slugging combination of Mickey Mantle, Roger Maris, and Bill ‘Moose’ Skowron, scored more than twice as many total runs as the Pittsburgh Pirates, 55 to 27.” Despite that difference in production, the Pirates won the last game of the series (in perhaps the most exciting game in Series history—the only one that has ever ended with a ninth-inning, walk-off home run) and thusly won the series, four games to three. Nobody would dispute, Natapoff’s argument runs, that the Pirates deserved to win the series—and so, similarly, nobody should dispute the legitimacy of the Electoral College.

Why? Because if, as Lively writes, in the World Series “[r]uns must be grouped in a way that wins games,” in the Electoral College “votes must be grouped in a way that wins states.” Take, for instance, the election of 1888—a famous case for political scientists studying the Electoral College. In that election, Democratic candidate Grover Cleveland gained over 5.5 million votes to Republican candidate Benjamin Harrison’s 5.4 million votes. But Harrison not only won more states than Cleveland, but also won states with more electoral votes: including New York, Pennsylvania, Ohio, and Illinois, each of whom had at least six more electoral votes than the most populous state Cleveland won, Missouri. In this fashion, Natapoff argues that Harrison is like the Pirates: although he did not win more votes than Cleveland (just as the Pirates did not score more runs than the Yankees), still he deserved to win—on the grounds that the total numbers of popular votes do not matter, but rather how those votes are spread around the country.

In this argument, then, games are to states just as runs are to votes. It’s an analogy that has an easy appeal to it: everyone feels they understand the World Series (just as everyone feels they understand Stanley Fish’s umpire analogy) and so that understanding appears to transfer easily to the matter of presidential elections. Yet, while clever, in fact most people do not understand the purpose of the World Series: although people think it is the task of the Series to identify the best baseball team in the major leagues, that is not what it is designed to do. It is not the purpose of the World Series to discover the best team in baseball, but instead to put on an exhibition that will draw a large audience, and thus make a great deal of money. Or so said the New York Giants, in 1904.

As many people do not know, there was no World Series in 1904. A World Series, as baseball fans do know, is a competition between the champions of the National League and the American League—which, because the American League was only founded in 1901, meant that the first World Series was held in 1903, between the Boston Americans (soon to become the Red Sox) and the same Pittsburgh Pirates also involved in Natapoff’s example. But that series was merely a private agreement between the two clubs; it created no binding precedent. Hence, when in 1904 the Americans again won their league and the New York Giants won the National League—each achieving that distinction by winning more games than any other team over the course of the season—there was no requirement that the two teams had to play each other. And the Giants saw no reason to do so.

As legendary Giants manager, John McGraw, said at the time, the Giants were the champions of the “only real major league”: that is, the Giants’ title came against tougher competition than the Boston team faced. So, as The Scrapbook History of Baseball notes, the Giants, “who had won the National League by a wide margin, stuck to … their plan, refusing to play any American League club … in the proposed ‘exhibition’ series (as they considered it).” The Giants, sensibly enough, felt that they could not gain much by playing Boston—they would be expected to beat the team from the younger league—and, conversely, they could lose a great deal. And mathematically speaking, they were right: there was no reason to put their prestige on the line by facing an inferior opponent that stood a real chance to win a series that, for that very reason, could not possibly answer the question of which was the better team.

“That there is,” writes Nate Silver and Dayn Perry in Baseball Between the Numbers: Why Everything You Know About the Game Is Wrong, “a great deal of luck involved in the playoffs is an incontrovertible mathematical fact.” But just how much luck is involved is something that the average fan hasn’t considered—though former Caltech physicist Leonard Mlodinow has. In Mlodinow’s book, The Drunkard’s Walk: How Randomness Rules Our Lives, the scientist writes that—just by virtue of doing the math—it can be concluded that “in a 7-game series there is a sizable chance that the inferior team will be crowned champion”:

For instance, if one team is good enough to warrant beating another in 55 percent of its games, the weaker team will nevertheless win a 7-game series about 4 times out of 10. And if the superior team could be expected to beat its opponent, on average, 2 out of each 3 times they meet, the inferior team will still win a 7-game series about once every 5 matchups.

What Mlodinow means is this: let’s say that, for every game, we roll a one-hundred sided die to determine whether the team with the 55 percent edge wins or not. If we do that four times, there’s still a good chance that the inferior team is still in the series: that is, that the superior team has not won all the games. In fact, there’s a real possibility that the inferior team might turn the tables, and instead sweep the superior team. Seven games, in short, is just not enough games to demonstrate conclusively that one team is better than another.

In fact, in order to eliminate randomness as much as possible—that is, make it as likely as possible for the better team to win—the World Series would have to be much longer than it currently is: “In the lopsided 2/3-probability case,” Mlodinow says, “you’d have to play a series consisting of at minimum the best of 23 games to determine the winner with what is called statistical significance, meaning the weaker team would be crowned champion 5 percent or less of the time.” In other words, even in a case where one team has a two-thirds likelihood of winning a game, it would still take 23 games to make the chance of the weaker team winning the series less than 5 percent—and even then, there would still be a chance that the weaker team could still win the series. Mathematically then, winning a seven-game series is meaningless—there have been just too few games to eliminate the potential for a lesser team to beat a better team.

Just how mathematically meaningless a seven-game series is can be demonstrated by the case of a team that is only five percent better than another team: “in the case of one team’s having only a 55-45 edge,” Mlodinow goes on to say, “the shortest statistically significant ‘world series’ would be the best of 269 games” (emp. added). “So,” Mlodinow writes, “sports playoff series can be fun and exciting, but being crowned ‘world champion’ is not a very reliable indication that a team is actually the best one.” Which, as a matter of fact about the history of the World Series, is simply a point that true baseball professionals have always acknowledged: the World Series is not a competition, but an exhibition.

What the New York Giants were saying in 1904 then—and Mlodinow more recently—is that establishing the real worth of something requires a lot of trials: many, many different repetitions. That’s something that, all of us, ought to know from experience: to learn anything, for instance, requires a lot of practice. (Even if the famous “10,000 hour rule” New Yorker writer Malcolm Gladwell concocted for this book, Outliers: The Story of Success, has been complicated by those who did the original research Gladwell based his research upon.) More formally, scientists and mathematicians call this the “Law of Large Numbers.”

What that law means, as the Encyclopedia of Mathematics defines it, is that “the frequency of occurence of a random event tends to become equal to its probability as the number of trials increases.” Or, to use the more natural language of Wikipedia, “the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.” What the Law of Large Numbers implies is that Natapoff’s analogy between the Electoral College and the World Series just might be correct—though for the opposite reason Natapoff brought it up. Namely, if the Electoral College is like the World Series, and the World Series is not designed to find the best team in baseball but instead be merely an exhibition, then that implies that the Electoral College is not a serious attempt to find the best president—because what the Law would appear to advise is that, in order to obtain a better result, it is better to gather more voters.

Yet the currently-fashionable dogma of the academy, it would seem, is expressly-designed to dismiss that possibility: if, as Fish says, “balls and strikes” (or just things in general) are the creations of the “umpire” (also known as a “discursive system”), then it is very difficult to confront the wrongheadedness of Natapoff’s defense of the Electoral College—or, for that matter, the wrongheadedness of the Electoral College itself. After all, what does an individual run matter—isn’t what’s important the game in which it is scored? Or, to put it another way, isn’t it more important where (to Natapoff, in which state; to Fish, less geographically inclined, in which “discursive system”) a vote is cast, rather than whether it was cast? The answer in favor of the former at the expense of the latter to many, if not most, literary-type intellectuals is clear—but as any statistician will tell you, it’s possible for any run of luck to continue for quite a bit longer than the average person might expect. (That’s one reason why it takes at least 23 games to minimize the randomness between two closely-matched baseball teams.) Even so, it remains difficult to believe—as it would seem that many today, both within and without the academy, do—that the umpire can continue to call every pitch a strike.