A Part of the Main

We may be confident that the Great American Poem will not be written, no matter what genius attempts it, until democracy, the idea of our day and nation and race, has agonized and conquered through centuries, and made its work secure.

But the Great American Novel—the picture of the ordinary emotions and manners of American existence … will, we suppose, be possible earlier.
—John William De Forest. “The Great American Novel.” The Nation 9 January 1868.

Things refuse to be mismanaged long.
—Theodore Parker. “Of Justice and the Conscience.” 1853.

 

“It was,” begins Chapter Seven of The Great Gatsby, “when curiosity about Gatsby was at its highest that the lights in his house failed to go on one Saturday night—and, as obscurely as it began, his career as Trimalchio was over.” Trimalchio is a character in the ancient Roman novel The Satyricon who, like Gatsby, throws enormous and extravagant parties; there’s a lot that could be said about the two novels compared, and some of it has been said by scholars. The problem with comparing the two novels however is that, unlike Gatsby, The Satyricon is “unfinished”: we today have only the 141, not-always-continguous chapters collated by 17th century editors from two medieval manuscript copies, which are clearly not the entire book. Hence, comparing The Satyricon to Gatsby, or to any other novel, is always handicapped by the fact that, as the Wikipedia page continues, “its true length cannot be known.” Yet, is it really true that estimating a message’s total length based only on a part of the whole is impossible? Contrary to the collective wisdom of classical scholars and Wikipedia contributors, it isn’t, which we know due to techniques developed at the behest of a megalomaniac Trimalchio convinced Shakespeare was not Shakespeare—work that eventually become the foundation of the National Security Agency.  

Before getting to the history of those techniques, however, it might be best to describe first what they are. Essentially, the problem of figuring out the actual length of The Satyricon is a problem of sampling: that is, of estimating whether you have, like Christopher Columbus, run up on an island—or, like John Cabot, smacked into a continent. In biology, for instance, a researcher might count the number of organisms in a given area, then extrapolate for the entire area. Another biological technique is to capture and tag or mark some animals in an area, then recapture the same number of animals in the same area some time later—the number of re-captured previously-tagged animals provides a ratio useful for estimating the true size of the population. (The fewer the numbers of re-captured, the larger the size of the total population.) Or, as the baseball writer Bill James did earlier this year on his website (in “Red Hot Start,” from 16 April), of forecasting the final record of a baseball team based upon its start: in this case, the “true underlying win percentage” of the Boston record given that the team’s record in its first fifteen games was 13-2. The way that James did it is, perhaps, instructive about possible methods for determining the length of The Satyricon.

James begins by noting that because the “probability that a .500 team would go 13-2 or better in a stretch of 15 games is  … one in 312,” while the “probability that a .600 team would go 13-2 in a stretch of 15 games is … one in 46,” it is therefore “much more likely that they are a .600 team than that they are a .500 team”—though with the caveat that, because “there are many more .500 teams than .600 teams,” this is not “EXACTLY true” (emp. James). Next, James finds the standard statistical measure called the standard deviation: that is, the amount by which actual team records distribute themselves around the .500 mark of 81-81. James finds this number for teams in the years 2000-2015 to be .070, a low number; meaning that most team records in that era bunched closely around .500. (By comparison, the historical standard deviation for “all [major league] teams in baseball history” is .102, meaning that there used to be a wider spread between first-place teams and last-place teams than there is now.) Finally, James arranges the possible records of baseball teams according to what mathematicians call the “Gaussian,” or “normal” distribution: that is, how team records would look were they to follow the familiar “bell-shaped” curve, familiar from basic statistical courses, in which most teams had .500 records and very few teams had either 100 wins—or 100 losses. 

If the records of actual baseball teams follow such a distribution, James finds that “in a population of 1,000 teams with a standard deviation of .070,” there should be 2 teams above .700, 4 teams with percentages from .675 to .700, 10 teams from .650 to .675, 21 teams from .625 to .650, and so on, down to 141 teams from .500 to .525. (These numbers are mirrored, in turn, by teams with losing records.) Obviously, teams with better final records have better chances of starting 13-2—but at the same time, there are a lot fewer teams with final records of .700 than there are of teams going .600. As James writes, it is “much more likely that a 13-2 team is actually a .650 to .675 team than that they are actually a .675 to .700 team—just because there are so many more teams” (i.e., 10 teams as compared to 4). So the chances of each level of the distribution producing a 13-2 team actually grows as we approach .500—until, James says, we approach a winning percentage of .550 to .575, where the number of teams finally gets outweighed by the quality of those teams. Whereas in a thousand teams there are 66 teams who might be expected to have winning percentages of .575 to .600, thereby meaning that it is likely that a bit better than one of those teams might have start 13-2 (1.171341 to be precise), the chance of one of the 97 teams starting at 13-2 is only 1.100297. Doing a bit more mathematics, which I won’t bore you with, James eventually concludes that it is most likely that the 2018 Boston Red Sox will finish the season with .585 winning percentage, which is between a 95-67 season and a 94-68 season. 

What, however, does all of this have to do with The Satyricon, much less with the National Security Agency? In the specific case of the Roman novel, James provides a model for how to go about estimating the total length of the now-lost complete work: a model that begins by figuring out what league Petronius is playing in, so to speak. In other words, we would have to know something about the distribution of the lengths of fictional works: do they tend to converge—i.e., have a low standard deviation—strongly on some average length, the way that baseball teams tend to converge around 81-81? Or, do they wander far afield, so that the standard deviation is high? The author(s) of the Wikipedia article appear to believe that this is impossible, or nearly so; as the Stanford literary scholar Franco Moretti notes, when he says that he works “on West European narrative between 1790 and 1930,” he “already feel[s] like a charlatan” because he only works “on its canonical fraction, which is not even one percent of published literature.” There are, Moretti observes for instance, “thirty thousand nineteenth-century British novels out there”—or are there forty, or fifty, or sixty? “[N]o one really knows,” he concludes—which is not even to consider the “French novels, Chinese, Argentinian, [or] American” ones. But to compare The Satyricon to all novels would be to accept a high standard deviation—and hence a fairly wide range of possible lengths. 

Alternately, The Satyricon could be compared only to its ancient comrades and competitors: the five ancient Greek novels that survive complete from antiquity, for example, along with the only Roman novel to survive complete—Apuleius’ The Metamorphoses. Obviously, were The Satyricon to be compared only to ancient novels (and of those, only the complete ones) the standard deviation would likely be higher, meaning that the lengths might cluster more tightly around the mean. That would thereby imply a tighter range of possible lengths—at the risk, since the six ancient novels could all differ in length from The Satyricon much more than all the novels written likely would, of making a greater error in the estimate. The choice of which set (all novels, ancient novels) to use thereby is the choice between a higher chance of being accurate, and a higher chance of being precise. Either way, Wikipedia’s claim that the length “cannot be known” is only so if the words “with absolute certainty” are added. The best guess we can make can either be nearly certain to contain the true length within it, or be nearly certain—if it is accurate at all—to be very close to the true length, which is to say that it is entirely possible that we could know what the true length of The Satyricon was, even if we were not certain that we did in fact know it. 

That then answers the question of how we could know the length of The Satyricon—but when I began this story I promised that I would (eventually) relate it to the foundations of the National Security Agency. Those, I mentioned, began with an eccentric millionaire convinced that William Shakespeare did not write the plays that now bear his name. The millionaire’s name was George Fabyan; in the early 20th century he brought together a number of researchers in the new field of cryptography in order to “prove” Fabyan’s pet theory that Francis Bacon was the true author of the Bard’s work Bacon having been known as the inventor of the code system that bears his name; Fabyan thusly subscribed to the proposition that Bacon had concealed the fact of his authorship by means of coded messages within the plays themselves. The first professional American codebreakers thereby found themselves employed on Fabyan’s 350-acre estate (“Riverbank”) on the Fox River just south of Geneva, Illinois, which is still there today—and where American military minds found them on the American entry into World War One in 1917. 

Specifically, they found Elizabeth Smith and William Friedman (who would later marry). During the war the couple helped to train several federal employees in the art of codebreaking. By 1921, they had been hired away by the War Department, which then led to spending the 1920s breaking the codes of gangsters smuggling liquor into the dry United States in the service of the Coast Guard. During World War Two, Elizabeth would be employed in breaking one of the Enigma codes used by the German Navy; meanwhile, her husband William had founded the Army’s Signal Intelligence Service—the outfit that broke the Imperial Japanese Navy’s “Purple” code (itself based on Enigma machines), and was the direct predecessor to the National Security Agency. William had also written the scientific papers that underlay their work; he had, in fact, even coined the word cryptanalysis itself.          

Central to Friedman’s work was something now called the “Friedman test,” but then called the “kappa test.” This test, like Bill James’ work, compared two probabilities: the first being the obvious probability of which letter a coded one is likely to be, which in English is in one in 26, or 0.0385. The second, however, was not so obvious, that being the chance that two randomly selected letters from a source text will turn out to be the same letter, which is known in English to be 0.067. Knowing those two points, plus how long the intercepted coded message is, allows the cryptographer to estimate the length of the key, the translation parameter that determines the output—just as James can calculate the likely final record of a team that starts 13-2 using two different probabilities. Figuring out the length of The Satyricon, then, might not be quite the Herculean task it’s been represented to be—which raises the question, why has it been represented that way? 

The answer to that question, it seems to me, has something to do with the status of the “humanities” themselves: using statistical techniques to estimate the length of The Satyricon would damage the “firewall” that preserves disciplines like Classics, or literary study generally, from the grubby no ’ccount hands of the sciences—a firewall, we are eternally reminded, necessary in order to foster what Geoffrey Harpham, former director of the National Institute for the Humanities, has called “the capacity to sympathize, empathize, or otherwise inhabit the experience of others” so “clearly essential to democratic citizenship.” That may be so—but it’s also true that maintaining that firewall allows law schools, as Sanford Levinson of the University of Texas remarked some time ago, to continue to emphasize “traditional, classical legal skills” at the expense of “‘finding out how the empirical world operates.’” And since that has allowed (in Gill v. Whitford) the U.S. Supreme Court the luxury of considering whether to ignore a statistical measure of gerrymandering, for example, while on the other hand it is quite sure that the disciplines known as the humanities collect students from wealthy backgrounds at a disproportionate rate, it perhaps ought to be wondered precisely in what way those disciplines are “essential to democratic citizenship”—or rather, what idea of “democracy” is really being preserved here. If so, then—perhaps using what Fitzgerald called “the dark fields of the republic”—the final record of the United States can quite easily be predicted.

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Stayin’ Alive

And the sun stood still, and the moon stayed,
until the people had avenged themselves upon their enemies.
—Joshua 10:13.

 

“A Sinatra with a cold,” wrote Gay Talese for Esquire in 1966, “can, in a small way, send vibrations through the entertainment industry and beyond as surely as a President of the United States, suddenly sick, can shake the national economy”; in 1994, Nobel laureate economist Paul Krugman mused that a “commitment to a particular … doctrine” can eventually set “the tone for policy-making on all issues, even those which may seem to have nothing to do with that doctrine.” Like a world leader—or a celebrity—the health of an idea can have unforeseen consequences; for example, it is entirely possible that the legal profession’s intellectual bias against mathematics has determined the nation’s racial policy. These days after all, as literary scholar Walter Benn Michaels observed recently, racial justice in the United States is held to what Michaels calls “the ideal of proportional inequality”—an ideal whose nobility, it so happens that Nobel Prize-winner Daniel Kahneman and his colleague Amos Tversky have demonstrated, is matched only by its mathematical futility. The law, in short, has what Oliver Roeder of FiveThirtyEight recently called an “allergy” to mathematics; what I will argue is that, as a consequence, minority policy in the United States has a cold.

“The concept that mathematics can be relevant to the study of law,” law professor Michael I. Meyerson observed in 2002’s Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution, “seems foreign to many modern legal minds.” In fact, he continued, to many lawyers “the absence of mathematics is one of law’s greatest appeals.” The strength of that appeal was on display recently in the 2011 Wisconsin case discussed by Oliver Roeder, Gill v. Whitford—a case that, as Roeder says, “hinges on math” because it involves the invention of a mathematical standard to measure “when a gerrymandered [legislative] map infringes on voters’ rights.” In oral arguments in Gill, Roeder observed, Chief Justice John Roberts said, about the mathematical techniques that are the heart of the case, that it “may be simply my educational background, but I can only describe [them] as sociological gobbledygook”—a derisory slight that recalls 19th-century Supreme Court Justice Joseph Story’s sneer concerning what he called “men of speculative ingenuity, and recluse habits.” Such statements are hardly foreign in the annals of the Supreme Court: “Personal liberties,” Justice Potter Stewart wrote in a 1975 opinion, “are not rooted in the law of averages.” (Stewart’s sentence, perhaps incidentally, uses a phrase—“law of averages”—found nowhere in the actual study of mathematics). Throughout the history of American law, in short, there is strong evidence of bias against the study and application of mathematics to jurisprudence.

Yet without the ability to impose that bias on others, even conclusive demonstrations of the law’s skew would not matter—but of course lawyers, as Nick Robinson remarked just this past summer in the Buffalo Law Review, have “dominated the political leadership of the United States.” As Robinson went on to note, “more than half of all presidents, vice presidents, and members of Congress have come from a law background.” This lawyer-heavy structure has had an effect, Robinson says: for instance, he claims “that lawyer-members of Congress have helped foster the centrality of lawyers and courts in the United States.” Robinson’s research then, which aggregates many studies on the subject, demonstrates that the legal profession is in a position to have effects on the future of the country—and if lawyers can affect the future of the country in one fashion, it stands to reason that they may have affected it in others. Not only then may the law have an anti-mathematical bias, but it is clearly positioned to impose that bias on others.

That bias in turn is what I suspect has led the Americans to what Michaels calls the theory of “proportional representation” when it comes to justice for minority populations. This theory holds, according to Michaels, that a truly just society would be a “society in which white people were proportionately represented in the bottom quintile [of income] (and black people proportionately represented in the top quintile)”—or, as one commenter on Michaels’ work has put it, it’s the idea that “social justice is … served if the top classes at Ivy League colleges contain a percentage of women, black people, and Latinos proportionate to the population.” Within the legal profession, the theory appears to be growing: as Michaels has also observed, the theory of the plaintiffs in the “the recent suit alleging discrimination against women at Goldman Sachs” complained of the ‘“stark” underrepresentation’ [of women] in management” because women represented “‘just 29 percent of vice presidents, 17 percent of managing directors, and 14 percent of partners’”—percentages that, of course, vary greatly from the roughly 50% of the American population who are women. But while the idea of a world in which the population of every institution mirrors the population as a whole may appear plausible to lawyers, it’s absurd to any mathematician.

People without mathematical training, that is, have wildly inaccurate ideas about probability—precisely the point of the work of social scientists Daniel Kahneman and Amos Tversky. “When subjects are instructed to generate a random sequence of hypothetical tosses of a fair coin,” wrote the two psychologists in 1971 (citing an earlier study), “they produce sequences where the proportion of heads in any short segment stays far closer to .50 than the laws of chance would predict.” In other words, when people are asked to write down the possible results of tossing a coin many times, they invariably give answers that are (nearly) half heads and half tails despite the fact that—as Brian Everitt observed in his 1999 book Chance Rules: An Informal Guide to Probability, Risk, and Statistics—in reality “in, say, 20 tosses of a fair coin, the number of heads is unlikely to be exactly 10.” (Everitt goes on to note that “an exact fifty-fifty split of heads and tails has a probability of a little less than 1 in 5.”) Hence, a small sample of 20 tosses has less than a twenty percent chance of being ten heads and ten tails—a fact that may appear yet more significant when it is noted that the chance of getting exactly 500 heads when flipping a coin 1000 times is less than 3%. Approximating the ideal of proportionality, then, is something that mathematics tells us is not simple or easy to do even once, and yet, in the case of college admissions, advocates of proportional representation suggest that colleges, and other American institutions, ought to be required to do something like what baseball player Joe DiMaggio did in the summer of 1941.

In that year in which “the Blitzkrieg raged” (as the Rolling Stones would write later), the baseball player Joe DiMaggio achieved what Gould says is “the greatest and most unattainable dream of all humanity, the hope and chimera of all sages and shaman”: the New York Yankee outfielder hit safely in 56 games. Gould doesn’t mean, of course, that all human history has been devoted to hitting a fist-sized sphere, but rather that while many baseball fans are aware of DiMaggio’s feat, what few are aware of is that the mathematics of DiMaggio’s streak shows that it was “so many standard deviations above the expected distribution that it should not have occurred at all.” In other words, Gould cites Nobel laureate Ed Purcell’s research on the matter.

What that research shows is that, to make it a better-than-even money proposition “that a run of even fifty games will occur once in the history of baseball,” then “baseball’s rosters would have to include either four lifetime .400 batters or fifty-two lifetime .350 batters over careers of one thousand games.” There are, of course, only three men who ever hit more than .350 lifetime (Cobb, Hornsby, and, tragically, Joe Jackson), which is to say that DiMaggio’s streak is, Gould wrote, “the most extraordinary thing that ever happened in American sports.” That in turn is why Gould can say that Joe DiMaggio, even as the Panzers drove a thousand miles of Russian wheatfields, actually attained a state chased by saints for millennia: by holding back, from 15 May to 17 July, 1941, the inevitable march of time like some contemporary Joshua, DiMaggio “cheated death, at least for a while.” To paraphrase Paul Simon, Joe DiMaggio fought a duel that, in every way that can be looked at, he was bound to lose—which is to say, as Gould correctly does, that his victory was in postponing that loss all of us are bound to one day suffer.

Woo woo woo.

What appears to be a simple baseball story, then, actually has a lesson for us here today: it tells us that advocates of proportional representation are thereby suggesting that colleges ought to be more or less required not merely to reproduce Joe DiMaggio’s hitting streak from the summer of 1941, but to do it every single season—a quest that in a practical sense is impossible. The question then must be how such an idea could ever have taken root in the first place—a question that Paul Krugman’s earlier comment about how a commitment to bad thinking about one issue can lead to bad thinking about others may help to answer. Krugman suggested in that essay that one reason why people who ought to know better might tolerate “a largely meaningless concept” was “precisely because they believe[d] they [could] harness it in the service of good policies”—and quite clearly, proponents of the proportional ideal have good intentions, which may be just why it has held on so long despite its manifest absurdity. But good intentions are not enough to ensure the staying power of a bad idea.

“Long streaks always are, and must be,” Gould wrote about DiMaggio’s feat of survival, “a matter of extraordinary luck imposed upon great skill”—which perhaps could be translated, in this instance, by saying that if an idea survives for some considerable length of time it must be because it serves some interest or another. In this case, it seems entirely plausible to think that the notion of “proportional representation” in relation to minority populations survives not because it is just, but instead because it allows the law, in the words of literary scholar Stanley Fish, “to have a formal existence”—that is, “to be distinct, not something else.” Without such a distinction, as Fish notes, the law would be in danger of being “declared subordinate to some other—non-legal—structure of concern,” and if so then “that discourse would be in the business of specifying what the law is.” But the legal desire Fish dresses up in a dinner jacket, attorney David Post of The Volokh Conspiracy website suggests, may merely be the quest to continue to wear a backwards baseball cap.

Apropos of Oliver Roeder’s article about the Supreme Court’s allergy to mathematics, Post says in other words, not only is there “a rather substantial library of academic commentary on ‘innumeracy’ at the court,” but “it is unfortunately well within the norms of our legal culture … to treat mathematics and related disciplines as kinds of communicable diseases with which we want no part.” What’s driving the theory of proportional representation, then, may not be the quest for racial justice, or even the wish to maintain the law’s autonomy, but instead the desire of would-be lawyers to avoid mathematics classes. But if so, then by seeking social justice through the prism of the law—which rules out of court at the outset any consideration of mathematics as a possible tool for thinking about human problems, and hence forbids (or at least, as in Gill v. Whitford, obstructs) certain possible courses of action to remedy social issues—advocates for African-Americans and others may be unnecessarily limiting their available options, which may be far wider, and wilder, than anyone viewing the problems of race through the law’s current framework can now see.

Yet—as any consideration of streaks and runs must, eventually, conclude—just because that is how things are at the moment is no reason to suspect that things will remain that way forever: as Gould says, the “gambler must go bust” when playing an opponent, like history itself, with near-infinite resources. Hence, Paul Simon to the contrary, the impressive thing about the Yankee Clipper’s feat in that last summer before the United States plunged into global war is not that after “Ken Keltner made two great plays at third base and lost DiMaggio the prospect of a lifetime advertising contract with the Heinz ketchup company” Joe DiMaggio left and went away. Instead, it is that the great outfielder lasted as long as he did; just so, in Oliver Roeder’s article he mentions that Sanford Levinson, a professor of law at the University of Texas at Austin and one of the best-known American legal scholars, has diagnosed “the problem [as] a lack of rigorous empirical training at most elite law schools”—which is to say that “the long-term solution would be a change in curriculum.” The law’s streak of avoiding mathematics, in other words, may be like all streaks. In the words of the poet of the subway walls,

Koo-koo …

Ka-choo.

Forked

Alice came to a fork in the road. “Which road do I take,” she asked.
“Where do you want to go?” responded the Cheshire Cat.
“I don’t know,” Alice answered.
“Then,” said the Cat, “it doesn’t matter.”
—Lewis Carroll. Alice’s Adventures in Wonderland. (1865).

 

At Baden Baden, 1925, Reti, the hypermodern challenger, opened with the Hungarian, or King’s Fianchetto; Alekhine—the only man to die still holding the title of world champion—countered with an unassuming king’s pawn to e5. The key moment did not take place, however, until Alekhine threw his rook nearly across the board at move 26, which appeared to lose the champion a tempo—but as C.J.S. Purdy would write for Chess World two decades, a global depression, and a world war later, “many of Alekhine’s moves depend on some surprise that comes far too many moves ahead for an ordinary mortal to have the slightest chance of foreseeing it.” The rook move, in sum, resulted in the triumphant slash of Alekhine’s bishop at move 42—a move that “forked” the only two capital pieces Reti had left: his knight and rook. “Alekhine’s chess,” Purdy would write later, “is like a god’s”—an hyperbole that not only leaves this reader of the political scientist William Riker thankful that the chess writer did not see the game Riker saw played at Freeport, 1858, but also grateful that neither man saw the game played at Moscow, 2016.

All these games, in other words, ended with what is known as a “fork,” or “a direct and simultaneous attack on two or more pieces by one piece,” as the Oxford Companion to Chess defines the maneuver. A fork, thereby, forces the opponent to choose; in Alekhine’s triumph, called “the gem of gems” by Chess World, the Russian grandmaster forced his opponent to choose which piece to lose. Just so, in The Art of Political Manipulation, from 1986, University of Rochester political scientist William Riker observed that “forks” are not limited to dinner or to chess. In Political Manipulation Riker introduced the term “heresthetics,” or—as Norman Schofield defined it in 2006—“the art of constructing choice situations so as to be able to manipulate outcomes.” Riker further said that  “the fundamental heresthetical device is to divide the majority with a new alternative”—or in other words, heresthetics is often a kind of political fork.

The premier example Riker used to illustrate such a political forking maneuver was performed, the political scientist wrote, by “the greatest of American politicians,” Abraham Lincoln, at the sleepy Illinois town of Freeport during the drowsy summer of 1858. Lincoln that year was running for the U.S. Senate seat for Illinois against Stephen Douglas—the man known as “the Little Giant” both for his less-than-imposing frame and his significance in national politics. So important had Douglas become by that year—by extending federal aid to the first “land grant” railroad, the Illinois Central, and successfully passing the Compromise of 1850, among many other achievements—that it was an open secret that he would run for president in 1860. And not merely run; the smart money said he would win.

Where the smart money was not was on Abraham Lincoln, a lanky and little-known one-term congressman in 1858. The odds against the would-be Illinois politician were so long, in fact, that according to Riker Lincoln had to take a big risk to win—which he did, by posing a question to Douglas at the little town of Freeport, near the Wisconsin border, towards the end of August. That question was this: “Can the people of a United States Territory, in any lawful way, against the wish of any citizen of the United States, exclude slavery from its limits prior to the formation of a state constitution?” It was a question, Riker wrote, that Lincoln had honed “stilletto-sharp.” It proved a knife in the heart of Stephen Douglas’ ambitions.

Lincoln was, of course, explicitly against slavery, and therefore thought that territories could ban slavery prior to statehood. But many others thought differently; in 1858 the United States stood poised at a precipice that, even then, only a few—Lincoln among them—could see. Already, the nation had been roiled by the Kansas-Nebraska Act of 1854; already, a state of war existed between pro- and anti-slavery men on the frontier. The year before, the U.S. Supreme Court had outlawed the prohibition of slavery in the territories by means of the Dred Scott decision—a decision that, in his “House Divided” speech in June that same year, Lincoln had already charged Douglas with conspiring with the president of the United States, James Buchanan, and Supreme Court Chief Justice Roger Taney to bring about. What Lincoln’s question was meant to do, Riker argued, was to “fork” Douglas between two constituencies: the local Illinois constituents who could return, if they chose, Douglas to the Senate in 1858—and the larger, national constituency that could deliver, if they chose, Douglas the presidency in 1860.

“If Douglas answered yes” to Lincoln’s question, Riker wrote, and thereby said that a territory could exclude slavery prior to statehood, “then he would please Northern Democrats for the Illinois election”—because he would take an issue away from Lincoln by explicitly stating they shared the same opinion. If so, he would take away one of Lincoln’s chief weapons—a weapon especially potent in far northern, German-settled, towns like Freeport. But what Lincoln saw, Riker says, is that if Douglas said yes he would also earn the enmity of Southern slaveowners, for whom it would appear “a betrayal of the Southern cause of the expansion of slave territory”—and thusly cost him a clean nomination for the leadership of the Democratic Party as candidate for president in 1860. If, however, Douglas answered no, “then he would appear to capitulate entirely to the Southern wing of the party and alienate free-soil Illinois Democrats”—thereby hurting “his chances in Illinois in 1858 but help[ing] his chances for 1860.” In Riker’s view, in other words, at Freeport in 1858 Lincoln forked Douglas much as the Russian grandmaster would fork his opponent at the German spa in 1925.

Yet just as that late winter game was hardly the last time the maneuver was used in chess, “forking” one’s political opponent scarcely ended in the little nineteenth-century Illinois farm village. Many of Hillary Clinton’s supporters in 2016 now believe that the Russians “interfered” with the American election—but what hasn’t been addressed is how the Russian state, led by Putin, could have interfered with an American election. Like a vampire who can only invade a home once invited, anyone attempting to “interfere” with an election must have some material to work with; Lincoln’s question at Freeport, after all, exploited a previously-existing difference between two factions within the Democratic Party. If the Russians did “interfere” with the 2016 election, that is, they could only have done so if there already existed yet another split within the Democratic ranks—which, as everyone knows, there was.

“Not everything is about an economic theory,” Hillary Clinton claimed in a February of 2016 speech in Nevada—a claim common enough to anyone who’s been on campus in the past two generations. After all, as gadfly Thomas Frank has remarked (referring to the work of James McGuigan), the “pervasive intellectual reflex” of our times is the “‘terror of economic reductionism.’” The idea that “not everything is about economics” is the core of what is sometimes known as the “cultural left,” or what Penn State University English professor (and former holder of the Paterno Chair) Michael Bérubé has termed “the left that aspires to analyze culture” as opposed to “the left that aspires to carry out public policy.” Clinton’s speech largely echoed the views of that “left,” which—according to the late philosopher Richard Rorty, in the book that inspired Bérubé’s remarks above—is more interested in “remedies … for American sadism” than those “for American selfishness.” It was that left that the rest of Clinton’s speech was designed to attract.

“If we broke up the big banks tomorrow,“ Clinton went on to ask after the remark about economic theory, “would that end racism?” The crowd, of course, answered “No.” “Would that end racism?” she continued, and then called again using the word “sexism,” and then again—a bit more convoluted, now—with “discrimination against the LGBT community?” Each time, the candidate was answered with a “No.” With this speech, in other words, Clinton visibly demonstrated the arrival of this “cultural left” at the very top of the Democratic Party—the ultimate success of the agenda pushed by English professors and others throughout the educational system. If, as Richard Rorty wrote, it really is true that “the American Left could not handle more than one initiative at a time,” so that “it either had to ignore stigma in order to concentrate on money, or vice versa,” then Clinton’s speech signaled the victory of the “stigma” crowd over the “money” crowd. Which is why what Clinton said next was so odd.

The next line of Clinton’s speech went like this: “Would that”—i.e., breaking up the big banks—“give us a real shot at ensuring our political system works better because we get rid of gerrymandering and redistricting and all of these gimmicks Republicans use to give themselves safe seats, so they can undo the progress we have made?” It’s a strange line; in the first place, it’s not exactly the most euphonious group of words I’ve ever heard in a political speech. But more importantly—well, actually, breaking up the big banks could perhaps do something about gerrymandering. According to OpenSecrets.org, after all, “72 percent of the [commercial banking] industry’s donations to candidates and parties, or more than $19 million, went to Republicans” in 2014—hence, maybe breaking them up could reduce the money available to Republican candidates, and so lessen their ability to construct gerrymandered districts. But, of course, doing so would require precisely the kinds of thought pursued by the “public policy” left—which Clinton had already signaled she had chosen against. The opening lines of her call-and-response, in other words, demonstrated that she had chosen to sacrifice the “public policy” left—the one that speaks the vocabulary of science—in favor of the “cultural left”—the one that speaks the vocabulary of the humanities. By choosing the “cultural left,” Clinton was also in effect saying that she would do nothing about either big banks or gerrymandering.

That point was driven home in an article in Fivethirtyeight this past October. In “The Supreme Court Is Allergic To Math,” Oliver Roeder discussed the case of Gill v. Whitford—a case that not only “will determine the future of partisan gerrymandering,” but also “hinges on math.” At issue in the case is something called “the efficiency gap,” which calculates “the difference between each party’s ‘wasted’ votes—votes for losing candidates and votes for winning candidates beyond what the candidate needed to win—and divide that by the total number of votes cast.” The basic argument, in other words, is fairly simple: if a mathematical test determines that a given arrangement of legislative districts provides a large difference, that is evidence of gerrymandering. But in oral arguments, Roeder went on to say, the “most powerful jurists in the land” demonstrated “a reluctance—even an allergy—to taking math and statistics seriously.” Chief Justice John Roberts, for example, said it “may simply be my educational background, but I can only describe [the case] as sociological gobbledygook.” Neil Gorsuch, the man who received the office that Barack Obama was prevented from awarding, compared “the metric to a secret recipe.” In other words, in this case it was the disciplines of mathematics and above all, statistics, that are on the side of those wanting to get rid of gerrymandering, not those analyzing “culture” and fighting “stigma”—concepts that were busy being employed by the justices, essentially to wash their hands of the issue of gerrymandering.

Just as, in other words, Lincoln exploited the split between Douglas’ immediate voters in Illinois who could give him the Senate seat, and the Southern slaveowners who could give him the presidency, Putin (or whomever else one wishes to nominate for that role) may have exploited the difference between Clinton supporters influenced by the current academy—and those affected by the yawning economic chasm that has opened in the United States. Whereas academics are anxious to avoid discussing money in order not to be accused of “economic reductionism,” in other words, the facts on the ground demonstrate that today “more money goes to the top (more than a fifth of all income goes to the top 1%), more people are in poverty at the bottom, and the middle class—long the core strength of our society—has seen its income stagnate,” as Nobel Prize-winning economist Joseph Stiglitz put the point in testimony to the U.S. Senate in 2014. Furthermore, Stiglitz noted, America today is not merely “the advanced country … with the highest level of inequality, but is among those with the least equality of opportunity.” Or in other words, as David Rosnick and Dean Baker put the point in November of that same year, “most [American] households had less wealth in 2013 than they did in 2010 and much less than in 1989.” To address such issues, however, would require precisely the sorts of intellectual tools—above all, mathematical ones—that the current bien pensant orthodoxy of the sort represented by Hillary Clinton, the orthodoxy that abhors sadism more than selfishness, thinks of as irrelevant.

But maybe that’s too many moves ahead.