by Alan Sokal
Differential Topology
This section contains the article’s second major piece of authoritative nonsense, namely Lacan’s text on psychoanalytic topology (which we analyse in Chapter 2). The articles applying Lacanian topology to film criticism and the psychoanalysis of AIDS are, sadly, real. Knot theory does indeed have beautiful applications in contemporary physics – as Witten and others have shown – but this has nothing to do with Lacan.
The last paragraph plays on the postmodern fondness for ‘multidimensionality’ and ‘nonlinearity’ by inventing a nonexistent field: ‘multidimensional (nonlinear) logic’.
Manifold Theory
The quote from Irigaray is discussed in Chapter 5. The parody again suggests that ‘conventional’ science has an aversion to anything that is ‘multidimensional’; but the truth is that all interesting manifolds are multidimensional.114 Manifolds with boundary are a classic subject of differential geometry.
Note 73 is deliberately exaggerated, though we are sympathetic to the idea that economic and political power struggles strongly affect how science is translated into technology and for whose benefit. Cryptography does indeed have military (as well as commercial) applications and has in recent years become increasingly based on number theory. However, number theory has fascinated mathematicians since antiquity, and until recently it had very few ‘practical’ applications of any kind: it was the branch of pure mathematics par excellence. The reference to Hardy was dangerous: in this very accessible autobiography, he prides himself on working in mathematical fields that have no applications. (There is an additional irony in this reference. Writing in 1941, Hardy listed two branches of science that, in his view, will never have military applications: number theory and Einstein’s relativity. Futurology is a risky enterprise, indeed!)
Towards a Liberatory Science
This section combines gross confusions about science with exceedingly sloppy thinking about philosophy and politics. Nevertheless, it also contains some ideas – on the link between scientists and the military, on ideological bias in science, on the pedagogy of science – with which we partly agree, at least when these ideas are formulated more carefully. We do not want the parody to provoke unqualified derision toward these ideas, and we refer the reader to the Epilogue for our real views on some of them.
This section begins by claiming that ‘postmodern’ science has freed itself from objective truth. But, whatever opinions scientists may have on chaos or quantum mechanics, they clearly do not consider themselves ‘liberated’ from the goal of objectivity; were that the case, they would simply have ceased to do science. Nevertheless, a whole book would be needed to disentangle the confusions concerning chaos, quantum physics and self-organization that underlie this sort of idea; see Chapter 7 for a brief analysis.
Having freed science from the goal of objectivity, the article then proposes to politicize science in the worst sense, judging scientific theories not by their correspondence to reality but by their compatibility with one’s ideological preconceptions. The quote from Kelly Oliver, which makes this politicization explicit, raises the perennial problem of selfrefutation: how can one know whether or not a theory is ‘strategic’, except by asking whether it is truly, objectively efficacious in promoting one’s declared political goals? The problems of truth and objectivity cannot be evaded so easily. Similarly, Markley’s claim (‘“Reality”, finally is a historical construct’, note 76) is both philosophically confused and politically pernicious: it opens the door to the worst nationalist and religious-fundamentalist excesses, as Hobsbawm eloquently demonstrates (p. 195).
Here are, finally, some glaring absurdities in this section:
Markley (p. 222) puts complex number theory – which, in fact, goes back at least to the early nineteenth century and belongs to mathematics, not physics – in the same bag as quantum mechanics, chaos theory and the now-largely-defunct hadron bootstrap theory.
He has probably confused it with the recent, and very speculative, theories on complexity. Note 86 is an ironic joke at his expense.
Many of the 11,000 graduate students working in solid-state physics would be pleasantly surprised to learn that they will all find jobs in their subfield (p. 225).
The word ‘Radon’ in the title of Schwartz’s book (note 104) is the name of a mathematician. The book deals with pure mathematics and has nothing to do with nuclear energy.
The axiom of equality (note 105) says that two sets are equal if and only if they have the same elements. To link this axiom with nineteenth-century liberalism amounts to writing cultural history on the basis of verbal coincidences. Ditto for the relation between the axiom of choice115 and the movement for abortion rights. Cohen has indeed shown that neither the axiom of choice nor its negation can be deduced from the other axioms of set theory; but this mathematical result has no political implications whatsoever.
Finally, all the bibliographic entries are rigorously exact, apart from a nod at former French minister of culture Jacques Toubon, who tried to impose the use of French in scientific conferences sponsored by the French government (see Kontsevitch 1994), and at Catalan nationalism (see Smolin 1992).
APPENDIX C
TRANSGRESSING THE BOUNDARIES: AN AFTERWORD*
Les grandes personnes sont décidément bien bizarres, se dit le petit prince.
(Antoine de Saint Exupéry, Le Petit Prince)
Alas, the truth is out: my article, “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity”, which appeared in the spring/summer 1996 issue of the cultural-studies journal Social Text, is a parody. Clearly I owe the editors and readers of Social Text, as well as the wider intellectual community, a non-parodic explanation of my motives and my true views.1 One of my goals here is to make a small contribution toward a dialogue on the Left between humanists and natural scientists – “two cultures” which, contrary to some optimistic pronouncements (mostly by the former group), are probably farther apart in mentality than at any time in the past fifty years.
Like the genre it is meant to satirize – myriad exemplars of which can be found in my reference list – my article is a mélange of truths, half-truths, quarter-truths, falsehoods, non sequiturs, and syntactically correct sentences that have no meaning whatsoever. (Sadly, there are only a handful of the latter: I tried hard to produce them, but I found that, save for rare bursts of inspiration, I just didn’t have the knack.) I also employed some other strategies that are well-established (albeit sometimes inadvertently) in the genre: appeals to authority in lieu of logic; speculative theories passed off as established science; strained and even absurd analogies; rhetoric that sounds good but whose meaning is ambiguous; and confusion between the technical and everyday senses of English words.2 (N.B. All works cited in my article are real, and all quotations are rigorously accurate; none are invented.)
But why did I do it? I confess that I’m an unabashed Old Leftist who never quite understood how deconstruction was supposed to help the working class. And I’m a stodgy old scientist who believes, naively, that there exists an external world, that there exist objective truths about that world, and that my job is to discover some of them. (If science were merely a negotiation of social conventions about what is agreed to be “true”, why would I bother devoting a large fraction of my all-too-short life to it? I don’t aspire to be the Emily Post of quantum field theory.3)
But my main concern isn’t to defend science from the barbarian hordes of lit crit (we’ll survive just fine, thank you). Rather, my concern is explicitly political: to combat a currently fashionable postmodernist/poststructuralist/social-constructivist discourse – and more generally a penchant for subjectivism – which is, I believe, inimical to the values and future of the Left.4 Alan Ryan said it well:
It is, for instance, pretty suicidal for embattled minorities to embrace Michel Foucault, let alone Jacques Derrida. The minority view was always that power could be undermined by truth ... Once you read Foucault as sa
ying that truth is simply an effect of power, you’ve had it. ... But American departments of literature, history and sociology contain large numbers of self-described leftists who have confused radical doubts about objectivity with political radicalism, and are in a mess.5
Likewise, Eric Hobsbawm has decried
the rise of “postmodernist” intellectual fashions in Western universities, particularly in departments of literature and anthropology, which imply that all “facts” claiming objective existence are simply intellectual constructions. In short, that there is no clear difference between fact and fiction. But there is, and for historians, even for the most militantly antipositivist ones among us, the ability to distinguish between the two is absolutely fundamental.6
(Hobsbawm goes on to show how rigourous historical work can refute the fictions propounded by reactionary nationalists in India, Israel, the Balkans and elsewhere.) And finally Stanislav Andreski:
So long as authority inspires awe, confusion and absurdity enhance conservative tendencies in society. Firstly, because clear and logical thinking leads to a cumulation of knowledge (of which the progress of the natural sciences provides the best example) and the advance of knowledge sooner or later undermines the traditional order. Confused thinking, on the other hand, leads nowhere in particular and can be indulged indefinitely without producing any impact upon the world.7
As an example of “confused thinking”, I would like to consider a chapter from Harding (1991) entitled “Why ‘Physics’ Is a Bad Model for Physics”. I select this example both because of Harding’s prestige in certain (but by no means all) feminist circles, and because her essay is (unlike much of this genre) very clearly written. Harding wishes to answer the question, “Are feminist criticisms of Western thought relevant to the natural sciences?” She does so by raising, and then rebutting, six “false beliefs” about the nature of science. Some of her rebuttals are perfectly well-taken; but they don’t prove anything like what she claims they do. That is because she conflates five quite distinct issues:
1 Ontology. What objects exist in the world? What statements about these objects are true?
2 Epistemology. How can human beings obtain knowledge of truths about the world? How can they assess the reliability of that knowledge?
3 Sociology of knowledge. To what extent are the truths known (or knowable) by humans in any given society influenced (or determined) by social, economic, political, cultural and ideological factors? Same question for the false statements erroneously believed to be true.
4 Individual ethics. What types of research ought a scientist (or technologist) to undertake (or refuse to undertake)?
5 Social ethics. What types of research ought society to encourage, subsidize or publicly fund (or alternatively to discourage, tax or forbid)?
These questions are obviously related – e.g. if there are no objective truths about the world, then there isn’t much point in asking how one can know those (nonexistent) truths – but they are conceptually distinct.
For example, Harding (citing Forman 1987) points out that American research in the 1940s and 50s on quantum electronics was motivated in large part by potential military applications. True enough. Now, quantum mechanics made possible solid-state physics, which in turn made possible quantum electronics (e.g. the transistor), which made possible nearly all of modern technology (e.g. the computer).8 And the computer has had applications that are beneficial to society (e.g. in allowing the postmodern cultural critic to produce her articles more efficiently) as well as applications that are harmful (e.g. in allowing the U.S. military to kill human beings more efficiently). This raises a host of social and individual ethical questions: Ought society to forbid (or discourage) certain applications of computers? Forbid (or discourage) research on computers per se? Forbid (or discourage) research on quantum electronics? On solid-state physics? On quantum mechanics? And likewise for individual scientists and technologists. (Clearly, an affirmative answer to these questions becomes harder to justify as one goes down the list; but I do not want to declare any of these questions a priori illegitimate.) Likewise, sociological questions arise, for example: To what extent is our (true) knowledge of computer science, quantum electronics, solid-state physics and quantum mechanics – and our lack of knowledge about other scientific subjects, e.g. the global climate – a result of public-policy choices favoring militarism? To what extent have the erroneous theories (if any) in computer science, quantum electronics, solid-state physics and quantum mechanics been the result (in whole or in part) of social, economic, political, cultural and ideological factors, in particular the culture of militarism?9 These are all serious questions, which deserve careful investigation adhering to the highest standards of scientific and historical evidence. But they have no effect whatsoever on the underlying scientific questions: whether atoms (and silicon crystals, transistors and computers) really do behave according to the laws of quantum mechanics (and solid-state physics, quantum electronics and computer science). The militaristic orientation of American science has quite simply no bearing whatsoever on the ontological question, and only under a wildly implausible scenario could it have any bearing on the epistemological question. (E.g. if the worldwide community of solid-state physicists, following what they believe to be the conventional standards of scientific evidence, were to hastily accept an erroneous theory of semiconductor behavior because of their enthusiasm for the breakthrough in military technology that this theory would make possible.)
Andrew Ross has drawn an analogy between the hierarchical taste cultures (high, middlebrow and popular) familiar to cultural critics, and the demarcation between science and pseudoscience.10 At a sociological level this is an incisive observation; but at an ontological and epistemological level it is simply mad. Ross seems to recognize this, because he immediately says:
I do not want to insist on a literal interpretation of this analogy ... A more exhaustive treatment would take account of the local, qualifying differences between the realm of cultural taste and that of science [!], but it would run up, finally, against the stand-off between the empiricist’s claim that non-context-dependent beliefs exist and that they can be true, and the culturalist’s claim that beliefs are only socially accepted as true.11
But such epistemological agnosticism simply won’t suffice, at least not for people who aspire to make social change. Deny that non-context-dependent assertions can be true, and you don’t just throw out quantum mechanics and molecular biology: you also throw out the Nazi gas chambers, the American enslavement of Africans, and the fact that today in New York it’s raining. Hobsbawm is right: facts do matter, and some facts (like the first two cited here) matter a great deal.
Still, Ross is correct that, at a sociological level, maintaining the demarcation line between science and pseudoscience serves – among other things – to maintain the social power of those who, whether or not they have formal scientific credentials, stand on science’s side of the line. (It has also served to increase the mean life expectancy in the United States from 47 years to 76 years in less than a century.12) Ross notes that
Cultural critics have, for some time now, been faced with the task of exposing similar vested institutional interests in the debates about class, gender, race, and sexual preference that touch upon the demarcations between taste cultures, and I see no ultimate reason for us to abandon our hard-earned skepticism when we confront science.13
Fair enough: scientists are in fact the first to advise skepticism in the face of other people’s (and one’s own) truth claims. But a sophomoric skepticism, a bland (or blind) agnosticism, won’t get you anywhere. Cultural critics, like historians or scientists, need an informed skepticism: one that can evaluate evidence and logic, and come to reasoned (albeit tentative) judgments based on that evidence and logic.
At this point Ross may object that I am rigging the power game in my own favor: how is he, a professor of American Studies, to compete with me, a physicist, in a discussion of quantum m
echanics?14 (Or even of nuclear power – a subject on which I have no expertise whatsoever.) But it is equally true that I would be unlikely to win a debate with a professional historian on the causes of World War I. Nevertheless, as an intelligent lay person with a modest knowledge of history, I am capable of evaluating the evidence and logic offered by competing historians, and of coming to some sort of reasoned (albeit tentative) judgment. (Without that ability, how could any thoughtful person justify being politically active?)
The trouble is that few non-scientists in our society feel this self-confidence when dealing with scientific matters. As C.P. Snow observed in his famous “Two Cultures” lecture 35 years ago:
A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you read a work of Shakespeare’s?
I now believe that if I had asked an even simpler question – such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, Can you read? – not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their neolithic ancestors would have had.15
A lot of the blame for this state of affairs rests, I think, with the scientists. The teaching of mathematics and science is often authoritarian16; and this is antithetical not only to the principles of radical/democratic pedagogy but to the principles of science itself. No wonder most Americans can’t distinguish between science and pseudoscience: their science teachers have never given them any rational grounds for doing so. (Ask an average undergraduate: Is matter composed of atoms? Yes. Why do you think so? The reader can fill in the response.) Is it then any surprise that 36 per cent of Americans believe in telepathy, and that 47 per cent believe in the creation account of Genesis?17