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.
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.
Those who seek extrascientific messages in what they think they understand about modern physics are digging dry wells. In my view, with two large exceptions, the results of research in physics (as opposed, say, to psychology) have no legitimate implications whatever for culture or politics or philosophy. (I am not talking here about the technological applications of physics, which of course do have a huge effect on our culture, or about its use as metaphor, but about the direct logical implications of purely scientific discoveries themselves.) The discoveries of physics may become relevant to philosophy and culture when we learn the origin of the universe or the final laws of nature, but not for the present.
The first of my exceptions to this statement is jurisdictional: discoveries in science sometimes reveal that topics like matter, space, and time, which had been thought to be proper subjects for philosophical argument, actually belong in the province of ordinary science. The other, more important exception to my statement is the profound cultural effect of the discovery, going back to the work of Newton, that nature is strictly governed by impersonal mathematical laws. Of course, it still remains for us to get the laws right, and to understand their range of validity; but as far as culture or philosophy is concerned the difference between Newton’s and Einstein’s theories of gravitation or between classical and quantum mechanics is immaterial.
I don’t mean to say that this part of Sokal’s satire was unjustified. His targets often take positions that seem to me (and I gather to Sokal) to make no sense if there is an objective reality. To put it simply, if scientists are talking about something real, then what they say is either true or false. If it is true, then how can it depend on the social environment of the scientist? If it is false, how can it help to liberate us? The choice of scientific question and the method of approach may depend on all sorts of extrascientific influences, but the correct answer when we find it is what it is because that is the way the world is. Nevertheless, it does no good to satirize views that your opponent denies holding.
I have run into the same sort of stumbling block myself. In an early draft of my book Dreams of a Final Theory,17 I criticized the feminist philosopher of science, Sandra Harding (a contributor to Social Text), for taking a relativist position that denied the objective character of physical laws. In evidence I quoted her as calling modern science (and especially physics) “not only sexist but also racist, classist, and culturally coercive,” and arguing that “physics and chemistry, mathematics and logic, bear the fingerprint of their distinctive cultural creators no less than do anthropology and history.”18 It seemed to me that this statement could make sense only to a relativist. What is the good of claiming that the conclusions of scientific research should be friendlier to multicultural or feminist concerns if these conclusions are to be an accurate account of objective reality? I sent a draft of this section to Harding, who pointed out to me various places in her writing where she had explicitly denied taking a relativist position. I took the easy way out; I dropped the accusation of relativism, and left it to the reader to judge the implications of her remarks.
When I was an undergraduate at Cornell I heard a lecture by a professor of philosophy (probably Max Black) who explained that whenever anyone asked him whether something was real, he always gave the same answer. The answer was “Yes.” The tooth fairy is real, the laws of physics are real, the rules of baseball are real, and the rocks in the fields are real. But they are real in different ways. What I mean when I say that the laws of physics are real is that they are real in pretty much the same sense (whatever that is) as the rocks in the fields, and not in the same sense (as implied by Fish19 ) as the rules of baseball. We did not create the laws of physics or the rocks in the field, and we sometimes unhappily find that we have been wrong about them, as when we stub our toe on an unnoticed rock, or when we find we have made a mistake (as most physicists have) about some physical law. But the languages in which we describe rocks or in which we state physical laws are certainly created socially, so I am making an implicit assumption (which in everyday life we all make about rocks) that our statements about the laws of physics are in a one-to-one correspondence with aspects of objective reality. To put it another way, if we ever discover intelligent creatures on some distant planet and translate their scientific works, we will find that we and they have discovered the same laws.
There is another complication here, which is that none of the laws of physics known today (with the possible exception of the general principles of quantum mechanics) are exactly and universally valid. Nevertheless, many of them have settled down to a final form, valid in certain known circumstances. The equations of electricity and magnetism that are today known as Maxwell’s equations are not the equations originally written down by Maxwell; they are equations that physicists settled on after decades of subsequent work by other physicists, notably the English scientist Oliver Heaviside. They are understood today to be an approximation that is valid in a limited context (that of weak, slowly-varying electric and magnetic fields), but in this form and in this limited context they have survived for a century and may be expected to survive indefinitely. This is the sort of law of physics that I think corresponds to something as real as anything else we know. On this point, scientists like Sokal and myself are apparently in clear disagreement with some of those whom Sokal satirizes. The objective nature of scientific knowledge has been denied by Andrew Ross20 and Bruno Latour21 and (as I understand them) by the influential philosophers Richard Rorty and the late Thomas Kuhn,22 but it is taken for granted by most natural scientists.
I have come to think that the laws of physics are real because my experience with the laws of physics does not seem to me to be very different in any fundamental way from my experience with rocks. For those who have not lived with the laws of physics, I can offer the obvious argument that the laws of physics as we know them work, and there is no other known way of looking at nature that works in anything like the same sense.
Interesting quotes from Weinberg:
Quantum mechanics provides a good example of the need to maintain this separation between physics and other forms of culture. Quantum mechanics has been variously cited as giving support to mysticism, or free will, or the decline of quantitative rationality. Now, I would agree that anyone is entitled to draw any inspiration they can from quantum mechanics, or from anything else. This is what I meant when I wrote that I had nothing to say against the use of science as metaphor. But there is a difference between inspiration and implication, and in talking of the “telling cultural implications” of quantum mechanics, Professor Levine may be confusing the two. There is simply no way that any cultural consequences can be implied by quantum mechanics. It is true that quantum mechanics does “apply always and everywhere,” but what applies is not a proverb about diverse points of view but a precise mathematical formalism, which among other things tells us that the difference between the predictions of quantum mechanics and pre-quantum classical mechanics, which is so important for the behavior of atoms, becomes negligible at the scale of human affairs.
I suggest the following thought experiment. Suppose that physicists were to announce the discovery that, beneath the apparently quantum mechanical appearance of atoms, there lies a more fundamental substructure of fields and particles that behave according to the rules of plain old classical mechanics. Would Professor Levine find it necessary to rethink his views about culture or philosophy? If so, why? If not, then in what sense can these views be said to be implied by quantum mechanics?
I was glad to see that Professor Wise, an expert on late-nineteenth-century physics, finds no error in what I had to say about the history of science. Unfortunately he does find a great many errors in things that I did not say. I never said there were no physicists in the early twentieth century who found cultural or philosophical implications in relativity or quantum mechanics, only that in my view these inferences were not valid. I never said that the apparent subjectivism of quantum mechanics was “of no great historical significance,” only that I think we know better now. Just as anyone may get inspiration from scientific discoveries, scientists in their work may be inspired by virtually anything in their cultural background, but that does not make these cultural influences a permanent part of scientific theories. I never tried “to expunge all mystical physicists” as well as “creationists and other religious enthusiasts” from the history of science. I did say that I had never met a physicist who was a mystic, but my article had nothing to say about the frequency of other forms of religious belief among scientists, past or present.
I tried in my article to put my finger on precisely what divides me and many other scientists from cultural and historical relativists by saying that the issue is not the belief in objective reality itself, but the belief in the reality of the laws of nature. Professor Wise makes a good point that, in judging the reality of the laws of nature, the test is not just their validity, but also their lack of “multiplicity.” Indeed, as I wrote in my article, one of the things about laws of nature like Maxwell’s equations that convinces me of their objective reality is the absence of a multiplicity of valid laws governing the same phenomena, with different laws of nature for different cultures.
(To be precise, I don’t mean that there is no other valid way of looking at the electric and magnetic phenomena that Maxwell’s equations describe, because there are mathematically equivalent ways of rewriting Maxwell’s theory, and the theory itself can be replaced with a deeper theory, quantum electrodynamics, from which it can be derived. What I mean is that there is no valid alternative way of looking at the phenomena described by Maxwell’s equations that does not have Maxwell’s equations as a mathematical consequence.)
Whatever cultural influences went into the discovery of Maxwell’s equations and other laws of nature have been refined away, like slag from ore. Maxwell’s equations are now understood in the same way by everyone with a valid comprehension of electricity and magnetism. The cultural backgrounds of the scientists who discovered such theories have thus become irrelevant to the lessons that we should draw from the theories. Professor Wise and some others may be upset by such distinctions because they see them as a threat to their own “agenda,” which is to emphasize the connections between scientific discoveries and their cultural context; but that is just the way the world is.
I should perhaps have made more clear in my article that I have no quarrel with most historians, philosophers, and sociologists of science. I am a fan of the history of science, and in my recent books I have acknowledged debts to writings of numerous historians, philosophers, and sociologists of science.3 In contrast with Alan Sokal, who in perpetrating his hoax was mostly concerned about a breakdown of the alliance between science and the political left, my concern was more with the corruption of history and sociology by postmodern and constructivist ideologies. Contrary to what Professor Levine may think, my opposition to these views is not due to any worry about the effects they may have on the economic pinch hurting science. In years of lobbying for federal support of scientific programs, I never heard anything remotely postmodern or constructivist from a member of Congress.
Professor Levine and several others object to my criticism of Jacques Derrida, based as it seems to them on a single paragraph chosen by Sokal for mockery, which begins, “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.” When, in reading Sokal’s Social Text article, I first encountered this paragraph, I was bothered not so much by the obscurity of Derrida’s terms “center” and “game.” I was willing to suppose that these were terms of art, defined elsewhere by Derrida. What bothered me was his phrase “the Einsteinian constant,” which I had never met in my work as a physicist. True, there is something called Newton’s constant which appears in Einstein’s theory of gravitation, and I would not object if Derrida wanted to call it “the Einsteinian constant,” but this constant is just a number (0.00000006673 in conventional units), and I did not see how it could be the “center” of anything, much less the concept of a game.
So I turned for enlightenment to the talk by Derrida from which Sokal took this paragraph. In it, Derrida explains the word “center” as follows: “Nevertheless,… structure—or rather, the structurality of structure—although it has always been involved, has always been neutralized or reduced, and this by a process of giving it a center or referring it to a point of presence, a fixed origin.”6 This was not much help.
Lest the reader think that I am quoting out of context, or perhaps just being obtuse, I will point out that, in the discussion following Derrida’s lecture, the first question was by Jean Hyppolite, professor at the Collège de France, who, after having sat through Derrida’s talk, had to ask Derrida to explain what he meant by a “center.” The paragraph quoted by Sokal was Derrida’s answer. It was Hyppolite who introduced “the Einsteinian constant” into the discussion, but while poor Hyppolite was willing to admit that he did not understand what Derrida meant by a center, Derrida just started talking about the Einsteinian constant, without letting on that (as seems evident) he had no idea of what Hyppolite was talking about. It seems to me that Derrida in context is even worse than Derrida out of context.