In other words, the longer a game of chance continues the larger are the spells and runs of luck in themselves,
but the less their relative proportions to the whole amounts involved.
—John Venn. The Logic of Chance. (1888).
“A probability that is very small for a single operation,” reads the RAND Corporation paper mentioned in journalist Sharon McGrayne’s The Theory That Would Not Die, “say one in a million, can become significant if this operation will occur 10,000 times in the next five years.” The paper, “On the Risk of an Accidental or Unauthorized Nuclear Detonation,” was just what it says on the label: a description of the chances of an unplanned atomic explosion. Previously, American military planners had assumed “that an accident involving an H-bomb could never occur,” but the insight of this paper was that overall risk changes depending upon volume—an insight that ultimately depended upon a discovery first described by mathematician Jacob Bernoulli in 1713. Now called the “Law of Large Numbers,” Bernoulli’s thought was that “it is not enough to take one or another observation … but that a large number of them are needed”—it’s what allows us to conclude, Bernoulli wrote, that “someone who intends to throw at once three sixes with three dice, should be considered reckless even if winning by chance.” Yet, while recognizing the law—which predicted that even low-probability events become likely if there are many of them—considerably changed how the United States handled nuclear weapons, it has had essentially no impact on how the United States handles certain conventional weapons: the estimated 300 million guns held by its citizens. One possible reason why that may be, suggests the work of Vox.com founder Ezra Klein, is that arguments advanced by departments of literature, women’s studies, African-American studies and other such academic “disciplines” more or less openly collude with the National Rifle Association to prevent sensible gun control laws.
The inaugural “issue” of Vox contained Klein’s article “How Politics Makes Us Stupid”—an article that asked the question, “why isn’t good evidence more effective in resolving political debates?” According to the consensus wisdom, Klein says, “many of our most bitter political battles are mere misunderstandings” caused by a lack of information—in this view, all that’s required to resolve disputes is more and better data. But, Klein also writes, current research shows that “the more information partisans get, the deeper their disagreements become”—because there are some disagreements “where people don’t want to find the right answer so much as they want to win the argument.” In other words, while some disagreements can be resolved by considering new evidence—like the Strategic Air Command changed how it handled nuclear weapons in light of a statistician’s recall of Bernoulli’s work—some disagreements, like gun control, cannot.
The work Klein cites was conducted by Yale Law School professor Daniel Kahan, along with several co-authors, and it began—Klein says—by collecting 1,000 Americans and then surveying both their political views and their mathematical skills. At that point, Kahan’s group gave participants a puzzle, which asked them to judge an experiment designed to show whether a new skin cream was more or less likely to make a skin condition worse or better, based on the data presented. The puzzle, however, was jiggered: although many more people got better using the skin cream than got worse using the skin cream, the percentage of people who got worse using the skin cream against those who did not use it was actually higher. In other words, if you paid attention merely to numbers, the data might appear to indicate one thing, while a calculation of percentages showed something else. As it turns out, most people relied on the raw numbers—and were wrong; meanwhile, people with higher mathematical skill were able to work through the problem to the right answer.
Interestingly, however, the results of this study did not demonstrate to Kahan that perhaps it is necessary to increase scientific and mathematical education. Instead, Kahan argues that the attempt by “economists and other empirical social scientists” to shear the “emotional trappings” from the debate about gun control in order to make it “a straightforward question of fact: do guns make society less safe or more” is misguided. Rather, because guns are “not just ‘weapons or pieces of sporting equipment,’” but “are also symbols,” the proper terrain to contest is not the grounds of empirical fact, but the symbolic: “academics and others who want to help resolve the gun controversy should dedicate themselves to identifying with as much precision as possible the cultural visions that animate this dispute.” In other words, what ought to structure this debate is not science, but culture.
To many on what’s known as the “cultural left,” of course, this must be welcome news: it amounts to a recognition of “academic” disciplines like “cultural studies” and the like that have argued for decades that cultural meanings trump scientific understanding. As Canadian philosopher Ian Hacking put it some years ago in The Social Construction of What?, a great deal of work in those fields of “study” have made claims that approach saying “that scientific results, even in fundamental physics, are social constructs.” Yet though the point has, as I can speak from personal experience, become virtual commonsense in departments of the humanities, there are several means of understanding the phrase “social construct.”
As English professor Michael Bérubé has remarked, much of that work can be traced as “following the argument Heidegger develops at the end of the first section of Being and Time,” where the German philosopher (and member of the Nazi Party) argued that “we could also say that the discovery of Neptune in 1846 cold plausibly be described, from a strictly human vantage point, as the ‘invention’ of Neptune.” In more general terms New York University professor Andrew Ross—the same Ross later burned in what’s become known as the “Sokal Affair”—described one fashion in which such an argument could go: by tracing how a “scientific theory was advanced through power, authority, persuasion and responsiveness to commercial interests.” Of course, as a journalistic piece by Joy Pullmann—writing in the conservative Federalist—described recently, as such views have filtered throughout the academy they have led at least one doctoral student to claim in her dissertation at the education department of the University of North Dakota that “language used in the syllabi” of eight science classes she reviewed
reflects institutionalized STEM teaching practices and views about knowledge that are inherently discriminatory to women and minorities by promoting a view of knowledge as static and unchanging, a view of teaching that promotes the idea of a passive student, and by promoting a chilly climate that marginalizes women.
The language of this description, interestingly, equivocates between the claim that some, or most, scientists are discriminatory (a relatively safe claim) and the notion that there is something inherent about science itself (the radical claim)—which itself indicates something of the “cultural” view. Yet although, as in this latter example, claims regarding the status of science are often advanced on the grounds of discrimination, it seems to escape those making such claims just what sort of ground is conceded politically by taking science as one’s adversary.
For example, here is the problem with Kahan’s argument over gun control: by agreeing to contest on cultural grounds pro-gun control advocates would be conceding their very strongest argument: the Law of Large Numbers is not an incidental feature of science, but one of its very foundations. (It could perhaps even be the foundation, because science proceeds on the basis of replicability.) Kahan’s recommendation, in other words, might not appear so much as a change in tactics as an outright surrender: it’s only in the light of the Law of Large Numbers that the pro gun-control argument is even conceivable. Hence, it is very difficult to understand how an argument can be won if one’s best weapon is, I don’t know, controlled. In effect, conceding the argument made in the RAND paper quoted above is more or less to give up on the very idea of reducing the numbers of firearms, so that American streets could perhaps be safer—and American lives protected.
Yet another, and even larger-scale problem with taking the so-called “cultural turn,” as Kahan advises, however, is that abandoning the tools of the Law of Large Numbers does not merely concede ground on the gun control issue alone. It also does so on a host of other issues—perhaps foremost of them on matters of political representation itself. For example, it prevents an examination of the Electoral College from a scientific, mathematically-knowledgable point of view—as I attempted to do in my piece, “Size Matters,” from last month. It may help to explain what Congressman Steve Israel of New York meant when journalist David Daley, author of a recent book on gerrymandering, interviewed him on the practical effects of gerrymandering in the House of Representatives (a subject that requires strong mathematical knowledge to understand): “‘The Republicans have always been better than Democrats at playing the long game.’” And there are other issues also—all of which is to say that, by attacking science itself, the “cultural left” may literally be preventing government from interceding on the part of the very people for whom they claim to speak.
Some academics involved in such fields have, in fact, begun to recognize this very point: all the way back in 2004, one of the chiefs of this type of specialist, Bruno Latour, dared to ask himself “Was I wrong to participate in the invention of this field known as science studies?” The very idea of questioning the institution of that field can, however, seem preposterous: even now, as Latour also wrote then, there are
entire Ph.D. programs … still running to make sure that good American kids are learning the hard way that facts are made up, that there is no such thing as natural, unmediated, unbiased access to truth, that we are always prisoners of language, that we always speak from a particular standpoint, and so on, while dangerous extremists are using the very same argument of social construction to destroy hard-won evidence that could save our lives.
Indeed. It’s actually to the point, in fact, that it would be pretty easy to think that the supposed “left” doesn’t really want to win these arguments at all—that, perhaps, they just wish to go out …
With a bang.