In May 1996 physicist Alan Sokal published an essay in the fashionable academic journalSocial Text. The essay quoted hip theorists like Jacques Lacan, Donna Haraway, and Gilles Deleuze. The prose was thick with the jargon of poststructuralism. And the point the essay tried to make was counterintuitive: gravity, Sokal argued, was a fiction that society had agreed upon, and science needed to be liberated from its ideological blinders.When Sokal revealed in the pages ofLingua Francathat he had written the article as a parody, the story hit the front page of theNew York Times. It set off a national debate still raging today: Are scholars in the humanities trapped in a jargon-ridden Wonderland? Are scientists deluded in thinking their work is objective? Are literature professors suffering from science envy? Was Sokal's joke funny? Was the Enlightenment such a bad thing after all? And isn't it a little bit true that the meaning of gravity is contingent upon your cultural perspective?Collected here for the first time are Sokal's original essay on "quantum gravity," his essay revealing the hoax, the newspaper articles that broke the story, and the angry op-eds, letters, and e-mail exchanges sparked by the hoax from intellectuals across the country, including Stanley Fish, George F. Will, Michael Berube, and Katha Pollitt. Also included are extended essays in which a wide range of scholars ponder the long-term lessons of the hoax.

Chapter One

ALAN SOKAL

Transgressing the Boundaries: Toward a Transformative

Hermeneutics of Quantum Gravity

Social Text, Spring-Summer 1996

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Transgressing disciplinary boundaries ... [is] a subversive undertaking since it is likely to violate the sanctuaries of accepted ways of perceiving. Among the most fortified boundaries have been those between the natural sciences and the humanities. --Valerie Greenberg, Transgressive Readings

The struggle for the transformation of ideology into critical science ... proceeds on the foundation that the critique of all presuppositions of science and ideology must be the only absolute principle of science.--Stanley Aronowitz, Science as Power

There are many natural scientists, and especially physicists, who continue to reject the notion that the disciplines concerned with social and cultural criticism can have anything to contribute, except perhaps peripherally, to their research. Still less are they receptive to the idea that the very foundations of their worldview must be revised or rebuilt in the light of such criticism. Rather, they cling to the dogma imposed by the long post-Enlightenment hegemony over the Western intellectual outlook, which can be summarized briefly as follows: that there exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole; that these properties are encoded in "eternal" physical laws; and that human beings can obtain reliable, albeit imperfect and tentative, knowledge of these laws by hewing to the "objective" procedures and epistemological strictures prescribed by the (so-called) scientific method.

    But deep conceptual shifts within twentieth-century science have undermined this Cartesian-Newtonian metaphysics (Heisenberg 1958; Bohr 1963); revisionist studies in the history and philosophy of science have cast further doubt on its credibility (Kuhn 1970; Feyerabend 1975; Latour 1987; Aronowitz 1988b; Bloor 1991); and, most recently, feminist and poststructuralist critiques have demystified the substantive content of mainstream Western scientific practice, revealing the ideology of domination concealed behind the facade of "objectivity" (Merchant 1980; Keller 1985; Harding 1986, 1991; Haraway 1989, 1991; Best 1991). It has thus become increasingly apparent that physical "reality" no less than social "reality" is at bottom a social and linguistic construct; that scientific "knowledge;' far from being objective, reflects and encodes the dominant ideologies and power relations of the culture that produced it; that the truth claims of science are inherently theory-laden and self-referential; and consequently, that the discourse of the scientific community, for all its undeniable value, cannot assert a privileged epistemological status with respect to counterhegemonic narratives emanating from dissident or marginalized communities. These themes can be traced, despite some differences of emphasis, in Aronowitz's analysis of the cultural fabric that produced quantum mechanics (1988b, esp. chaps. 9 and 12); in Ross's discussion of oppositional discourses in post-quantum science (1991, intro, and chap. 1); in Irigaray's and Hayles's exegeses of gender encoding in fluid mechanics (Irigaray 1985; Hayles 1992); and in Harding's comprehensive critique of the gender ideology underlying the natural sciences in general and physics in particular (1986, esp. chaps, 2 and 10; 1991, esp. chap. 4).

    Here my aim is to carry these deep analyses one step further, by taking account of recent developments in quantum gravity: the emerging branch of physics in which Heisenberg's quantum mechanics and Einstein's general relativity are at once synthesized and superseded. In quantum gravity, as we shall see, the space-time manifold ceases to exist as an objective physical reality; geometry becomes relational and contextual; and the foundational conceptual categories of prior science--among them, existence itself--become problematized and relativized. This conceptual revolution, I will argue, has profound implications for the content of a future postmodern and liberatory science.

    My approach will be as follows. First, I will review very briefly some of the philosophical and ideological issues raised by quantum mechanics and by classical general relativity. Next, I will sketch the outlines of the emerging theory of quantum gravity and discuss some of the conceptual issues it raises. Finally, I will comment on the cultural and political implications of these scientific developments. It should be emphasized that this essay is of necessity tentative and preliminary; I do not pretend to answer all the questions that I raise. My aim is, rather, to draw the attention of readers to these important developments in physical science and to sketch as best I can their philosophical and political implications. I have endeavored here to keep mathematics to a bare minimum; but I have taken care to provide references where interested readers can find all requisite details.

[1] Quantum Mechanics: Uncertainty, Complementarity,

Discontinuity, and Interconnectedness

It is not my intention to enter here into the extensive debate on the conceptual foundations of quantum mechanics. Suffice it to say that anyone who has seriously studied the equations of quantum mechanics will assent to Heisenberg's measured (pardon the pun) summary of his celebrated uncertainty principle :

We can no longer speak of the behaviour of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively ...

When we speak of the picture of nature in the exact science of our age, we do not mean a picture of nature so much as a picture of our relationships with nature .... Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man [ sic ] and nature. The scientific method of analysing, explaining and classifying has become conscious of its limitations, which arise out of the fact that by its intervention science alters and refashions the object of investigation. In other words, method and object can no longer be separated. (Heisenberg 1958, 28-29; emphasis in original)

    Along the same lines, Niels Bohr (1928; cited in Pais 1991, 314) wrote: "An independent reality in the ordinary physical sense can ... neither be ascribed to the phenomena nor to the agencies of observation." Stanley Aronowitz (1988b, 251-56) has convincingly traced this worldview to the crisis of liberal hegemony in Central Europe in the years prior and subsequent to World War I.

    A second important aspect of quantum mechanics is its principle of complementarity, or dialecticism. Is light a particle or a wave? Complementarity "is the realization that particle and wave behavior are mutually exclusive, yet that both are necessary for a complete description of all phenomena" (Pais 1991, 23). More generally, notes Heisenberg,

the different intuitive pictures which we use to describe atomic systems, although fully adequate for given experiments, are nevertheless mutually exclusive. Thus, for instance, the Bohr atom can be described as a small-scale planetary system, having a central atomic nucleus about which the external electrons revolve. For other experiments, however, it might be more convenient to imagine that the atomic nucleus is surrounded by a system of stationary waves whose frequency is characteristic of the radiation emanating from the atom. Finally, we can consider the atom chemically.... Each picture is legitimate when used in the right place, but the different pictures are contradictory and therefore we call them mutually complementary. (1958, 40-41)

    And once again Bohr (1934; cited in Jammer 1974, l02): "A complete elucidation of one and the same object may require diverse points of view which defy a unique description. Indeed, strictly speaking, the conscious analysis of any concept stands in a relation of exclusion to its immediate application." This foreshadowing of postmodernist epistemology is by no means coincidental. The profound connections between complementarity and deconstruction have recently been elucidated by Froula (1985) and Honner (1994), and, in great depth, by Plotnitsky (1994).

    A third aspect of quantum physics is discontinuity, or rupture: as Bohr (1928; cited in Jammer 1974, 90) explained, "[the] essence [of the quantum theory] may be expressed in the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories and symbolized by Planck's quantum of action" A half century later, the expression "quantum leap" has so entered our everyday vocabulary that we are likely to use it without any consciousness of its origins in physical theory.

    Finally, Bell's theorem and its recent generalizations show that an act of observation here and now can affect not only the object being observed--as Heisenberg told us--but also an object arbitrarily far away (say, on Andromeda galaxy). This phenomenon--which Einstein termed "spooky"--imposes a radical reevaluation of the traditional mechanistic concepts of space, object, and causality, and suggests an alternative worldview in which the universe is characterized by interconnectedness and (w)holism: what physicist David Bohm (1980) has called "implicate order." New Age interpretations of these insights from quantum physics have often gone overboard in unwarranted speculation, but the general soundness of the argument is undeniable. In Bohr's words, "Planck's discovery of the elementary quantum of action ... revealed a feature of wholeness inherent in atomic physics, going far beyond the ancient idea of the limited divisibility of matter" (Bohr 1963, 2; emphasis in original).

[2] Hermeneutics of Classical General Relativity

In the Newtonian mechanistic worldview, space and time are distinct and absolute. In Einstein's special theory of relativity (1905), the distinction between space and time dissolves: there is only a new unity, four-dimensional space-time, and the observer's perception of "space" and "time" depends on her state of motion. In Hermann Minkowski's famous words (1908): "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (translated in Lorentz et al . 1952, 75). Nevertheless, the underlying geometry of Minkowskian space-time remains absolute.

    It is in Einstein's general theory of relativity (1915) that the radical conceptual break occurs: the space-time geometry becomes contingent and dynamical, encoding in itself the gravitational field. Mathematically, Einstein breaks with the tradition dating back to Euclid (which is inflicted on high-school students even today!), and employs instead the non-Euclidean geometry developed by Riemann. Einstein's equations are highly nonlinear, which is why traditionally trained mathematicians find them so difficult to solve. Newton's gravitational theory corresponds to the crude (and conceptually misleading) truncation of Einstein's equations in which the non-linearity is simply ignored. Einstein's general relativity therefore subsumes all the putative successes of Newton's theory, while going beyond Newton to predict radically new phenomena that arise directly from the nonlinearity: the bending of starlight by the sun, the precession of the perihelion of Mercury, and the gravitational collapse of stars into black holes.

    General relativity is so weird that some of its consequences--deduced by impeccable mathematics, and increasingly confirmed by astrophysical observation--read like science fiction. Black holes are by now well known, and wormholes are beginning to make the charts. Perhaps less familiar is Gödel's construction of an Einstein space-time admitting closed timelike curves: that is, a universe in which it is possible to travel into one's own past !

    Thus, general relativity forces upon us radically new and counterintuitive notions of space, time, and causality; so it is not surprising that it has had a profound impact not only on the natural sciences but also on philosophy, literary criticism, and the human sciences. For example, in a celebrated symposium three decades ago on Les Langages critiques et les sciences de l'homme , Jean Hyppolite raised an incisive question about Jacques Derrida's theory of structure and sign in scientific discourse:

When I take, for example, the structure of certain algebraic constructions [ensembles], where is the center? Is the center the knowledge of general rules which, after a fashion, allow us to understand the interplay of the elements? Or is the center certain elements which enjoy a particular privilege within the ensemble? ... With Einstein, for example, we see the end of a kind of privilege of empiric evidence. And in that connection we see a constant appear, a constant which is a combination of space-time, which does not belong to any of the experimenters who live the experience, but which, in a way, dominates the whole construct; and this notion of the constant--is this the center?

Derrida's perceptive reply went to the heart of classical general relativity:

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.

    In mathematical terms, Derrida's observation relates to the invariance of the Einstein field equation Gµv = 87[Pi]GTµv under nonlinear space-time diffeomorphisms (self-mappings of the space-time manifold that are infinitely differentiable but not necessarily analytic). The key point is that this invariance group "acts transitively": this means that any space-time point, if it exists at all, can be transformed into any other. In this way the infinite-dimensional invariance group erodes the distinction between observer and observed; the [Pi] of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity; and the putative observer becomes fatally de-centered, disconnected from any epistemic link to a space-time point that can no longer be defined by geometry alone.

[3] Quantum Gravity: String, Weave, or Morphogenetic Field?

However, this interpretation, while adequate within classical general relativity, becomes incomplete within the emerging postmodern view of quantum gravity. When even the gravitational field--geometry incarnate--becomes a noncommuting (and hence nonlinear) operator, how can the classical interpretation of Gµv as a geometric entity be sustained? Now not only the observer, but the very concept of geometry, becomes relational and contextual.

    The synthesis of quantum theory and general relativity is thus the central unsolved problem of theoretical physics; no one today can predict with confidence what will be the language and ontology, much less the content, of this synthesis, when and if it comes. It is, nevertheless, useful to examine historically the metaphors and imagery that theoretical physicists have employed in their attempts to understand quantum gravity.

(Continues...)

Excerpted from The Sokal Hoax by . Copyright © 2000 by University of Nebraska Press. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.