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Sokal’s Hoax

Like many other scientists, I was amused when I heard about the prank played by the NYU mathematical physicist Alan Sokal, who late in 1994 submitted a sham article to the cultural studies journal Social Text. In the article Sokal reviewed various current topics in physics and mathematics, and, tongue in cheek, drew various cultural, philosophical, and political morals that he felt would appeal to fashionable academic commentators who question the claims of science to objectivity.

The editors of Social Text did not detect that Sokal’s article was a hoax, and they published it in the journal’s Spring/Summer 1996 issue.1 The hoax was revealed by Sokal himself in an article for another journal, Lingua Franca,2 in which he explained that his Social Text article had been “liberally salted with nonsense,” and in his opinion was accepted only because “(a) it sounded good and (b) it flattered the editors’ ideological preconceptions.” Newspapers and newsmagazines throughout the US and Britain carried the story, and Sokal’s hoax appeared likely to join the small company of legendary academic hoaxes, along with the pseudofossils of Piltdown man planted by Charles Dawson and the pseudo-Celtic epic Ossian written by James Macpherson. The difference is that Sokal’s hoax served a public purpose, to attract attention to what Sokal saw as a decline of standards of rigor in the academic community, and for that reason it was disclosed immediately by the author himself.

The targets of Sokal’s satire occupy a broad intellectual range. There are those “postmoderns” in the humanities who like to surf through avant-garde fields like quantum mechanics or chaos theory to dress up their own arguments about the fragmentary and random nature of experience. There are those sociologists, historians, and philosophers who see the laws of nature as social constructions. There are cultural critics who find the taint of sexism, racism, colonialism, militarism, or capitalism not only in the practice of scientific research but even in its conclusions. Sokal did not satirize creationists or other religious enthusiasts who in many parts of the world are the most dangerous adversaries of science,3 but his targets were spread widely enough, and he was attacked or praised from all sides.

Entertaining as this episode was, I could not immediately judge from press reports what it proved. Suppose that, with tongue in cheek, an economist working for a labor union submitted an article to The National Review, giving what the author thought were false economic arguments against an increase in the statutory minimum wage. What would it prove if the article were accepted for publication? The economic arguments might still be cogent, even though the author did not believe in them.

I thought at first that Sokal’s article in Social Text was intended to be an imitation of academic babble, which any editor should have recognized as such. But in reading the article I found that this is not the case. The article expresses views that I find absurd, but with a few exceptions Sokal at least makes it pretty clear what these views are. The article’s title, “Transgressing the Boundaries—Toward a Transformative Hermeneutics of Quantum Gravity,” is more obscure than almost anything in his text. (A physicist friend of mine once said that in facing death, he drew some consolation from the reflection that he would never again have to look up the word “hermeneutics” in the dictionary.) In fact I got the impression that Sokal finds it difficult to write unclearly.

Where the article does degenerate into babble it is not in what Sokal himself has written but in the writings of the genuine postmodern cultural critics he quotes. Here, for instance, is a quote that he takes from the oracle of deconstruction, Jacques Derrida:

The Einsteinian constant is not a constant, is not a center. It is the very concept of variability—it is, finally, the concept of the game. In other words, it is not the concept of something—of a center starting from which an observer could master the field—but the very concept of the game.

I have no idea what this is intended to mean.

I suppose that it might be argued that articles in physics journals are also incomprehensible to the uninitiated. But physicists are forced to use a technical language, the language of mathematics. Within this limitation, we try to be clear, and when we fail we do not expect our readers to confuse obscurity with profundity. It never was true that only a dozen people could understand Einstein’s papers on general relativity, but if it had been true, it would have been a failure of Einstein’s, not a mark of his brilliance. The papers of Edward Witten of the Institute for Advanced Study at Princeton, which are today consistently among the most significant in the promising field of string theory, are notably easier for a physicist to read than most other work in string theory. In contrast, Derrida and other postmoderns do not seem to be saying anything that requires a special technical language, and they do not seem to be trying very hard to be clear. But those who admire such writings presumably would not have been embarrassed by Sokal’s quotations from them.

Part of Sokal’s hoax was his description of developments in physics. Much of his account was quite accurate, but it was heavily adulterated with howlers, most of which would have been detected by any undergraduate physics major. One of his running jokes had to do with the word “linear.” This word has a precise mathematical meaning, arising from the fact that certain mathematical relationships are represented graphically by a straight line.4 But for some postmodern intellectuals, “linear” has come to mean unimaginative and oldfashioned, while “nonlinear” is understood to be somehow perceptive and avant-garde. In arguing for the cultural importance of the quantum theory of gravitation, Sokal refers to the gravitational field in this theory as “a noncommuting (and hence nonlinear) operator.” Here “hence” is ridiculous; “non-commuting”5 does not imply “nonlinear,” and in fact quantum mechanics deals with things that are both noncommuting and linear.

Sokal also writes that “Einstein’s equations [in the general theory of relativity] are highly nonlinear, which is why traditionally trained mathematicians find them so difficult to solve.” The joke is in the words “traditionally trained.” Einstein’s equations are nonlinear, and this does make them hard to solve; but they are hard for anyone to solve, especially someone who is not traditionally trained. Continuing with general relativity, Sokal correctly remarks that its description of curved space-time allows arbitrary changes in the space-time coordinates that we use to describe nature. But he then solemnly pronounces that “the π of Euclid and the G of Newton, formely thought to be constant and universal, are now perceived in their ineluctable historicity.” This is absurd—the meaning of a mathematically defined quantity like pi cannot be affected by discoveries in physics, and in any case both pi and G continue to appear as universal constants in the equations of general relativity.

In a different vein, Sokal pretends to give serious consideration to a crackpot fantasy known as the “morphogenetic field.” He refers to complex number theory as a “new and still quite speculative branch of mathematical physics,” while in fact it is nineteenth-century mathematics and has been as well established as anything ever is. He even complains (echoing the sociologist Stanley Aronowitz) that all of the graduate students in solid-state physics will be able to get jobs in that field, which will be news to many of them.

Sokal’s revelation of his intentional howlers drew the angry response that he had abused the trust of the editors of Social Text in his credentials as a physicist, a complaint made by both sociologist Steve Fuller and English professor Stanley Fish.^6 The editors of Social Text also offered the excuse that it is not a journal in which articles are submitted to experts for evaluation, but a journal of opinion.7 Maybe under these circumstances social was naughty in letting the editors rely on his sincerity, but the article would not have been very different if Sokal’s account of physics and mathematics had been entirely accurate. What is more revealing is the variety of physics and mathematics bloopers in remarks by others that Sokal slyly quotes with mock approval. Here is the philosopher Bruno Latour on special relativity:

How can one decide whether an observation made in a train about the behavior of a falling stone can be made to coincide with the observation of the same falling stone from the embankment? If there are only one, or even two, frames of reference, no solution can be found…. Einstein’s solution is to consider three actors….

This is wrong; in relativity theory there is no difficulty in comparing the results of two, three, or any number of observers. In other quotations cited by Sokal, Stanley Aronowitz misuses the term “unified field theory.” The feminist theorist Luce Irigaray deplores mathematicians’ neglect of spaces with boundaries, though there is a huge literature on the subject. The English professor Robert Markley calls quantum theory nonlinear, though it is the only known example of a precisely linear theory. And both the philosopher Michael Serres (a member of the Académie Franç’aise) and archpostmodernist Jean-François Lyotard grossly misrepresent the view of time in modern physics. Such errors suggest a problem not just in the editing practices of Social Text, but in the standards of a larger intellectual community.

It seems to me though that Sokal’s hoax is most effective in the way that it draws cultural or philosophical or political conclusions from developments in physics and mathematics. Again and again Sokal jumps from correct science to absurd implications, without the benefit of any intermediate reasoning. With a straight face, he leaps from Bohr’s observation that in quantum mechanics “a complete elucidation of one and the same object may require diverse points of view which defy a unique description” to the conclusion that “postmodern science” refutes “the authoritarianism and elitism inherent in traditional science.” He blithely points to catastrophe theory and chaos theory as the sort of mathematics that can lead to social and economic liberation. Sokal shows that people really do talk in this way by quoting work of others in the same vein, including applications of mathematical topology to psychiatry by Jacques Lacan and to film criticism by Jacques-Alain Miller.

I find it disturbing that the editors of Social Text thought it plausible that a sane working physicist would take the positions satirized in Sokal’s article. In their defense of the decision to publish it, the editors explain that they had judged that it was “the earnest attempt of a professional scientist to seek some kind of affirmation from postmodern philosophy for developments in his field.”8 In an introduction to the issue of Social Text in which Sokal’s article appears, one of the editors mentions that “many famous scientists, especially physicists, have been mystics.”9 There may be some working physicists who are mystics, though I have never met any, and I can’t imagine any serious physicist who holds views as bizarre as those that Sokal satirized. The gulf of misunderstanding between scientists and other intellectuals seems to be at least as wide as when C.P. Snow worried about it three decades ago.

  1. 1

    Alan D. Sokal, “Transgressing the Boundaries—Toward a Transformative Hermeneutics of Quantum Gravity,” Social Text (Spring/Summer 1996), pp. 217-252.

  2. 2

    Alan D. Sokal, “A Physicist Experiments with Cultural Studies,” Lingua Franca (May/June 1996), pp. 62-64.

  3. 3

    In an afterword, “Transgressing the Boundaries,” submitted to Social Text, Sokal explained that his goal was not so much to defend science as to defend the left from postmodernists, social constivists, and other trendy leftists.

  4. 4

    For instance, there is a linear relation between the number of calories in a cake and the amounts of each of the various ingredients: the graph of calories versus ounces of any one ingredient, holding the amounts of all the other ingredients fixed, is a straight line. In contrast, the relation between the diameter of a cake (of fixed height) and the amounts of its ingredients is not linear.

  5. 5

    Operations are said to be noncommuting if the result when you perform several of them depends on the order in which they are performed. For instance, rotating your body by, say, thirty degrees around the vertical axis and then rotating it by thirty degrees around the north-south direction leaves you in a different position than these operations would if they were carried out in the opposite order. Try it and see.

  6. 7

    Bruce Robbins and Andrew Ross, “Mystery Science Theater,” Lingua Franca (July/August 1996).

  7. 8

    Robbins and Ross, “Mystery Science Theater.”

  8. 9

    Andrew Ross, “Introduction,” Social Text (Spring/Summer 1996), pp. 1—13.

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