by Alan Sokal
As Irigaray anticipated, an important question in all of these theories is: Can the boundary be transgressed (crossed), and if so, what happens then? Technically this is known as the problem of “boundary conditions”. At a purely mathematical level, the most salient aspect of boundary conditions is the great diversity of possibilities: for example, “free b.c.” (no obstacle to crossing), “reflecting b.c.” (specular reflection as in a mirror), “periodic b.c.” (re-entrance in another part of the manifold), and “antiperiodic b.c.” (re-entrance with 180° twist). The question posed by physicists is: Of all these conceivable boundary conditions, which ones actually occur in the representation of quantum gravity? Or perhaps, do all of them occur simultaneously and on an equal footing, as suggested by the complementarity principle?74
At this point my summary of developments in physics must stop, for the simple reason that the answers to these questions – if indeed they have univocal answers – are not yet known. In the remainder of this essay, I propose to take as my starting point those features of the theory of quantum gravity which are relatively well established (at least by the standards of conventional science), and attempt to draw out their philosophical and political implications.
Transgressing the Boundaries: Towards a Liberatory Science
Over the past two decades there has been extensive discussion among critical theorists with regard to the characteristics of modernist versus postmodernist culture; and in recent years these dialogues have begun to devote detailed attention to the specific problems posed by the natural sciences.75 In particular, Madsen and Madsen have recently given a very clear summary of the characteristics of modernist versus postmodernist science. They posit two criteria for a postmodern science:
A simple criterion for science to qualify as postmodern is that it be free from any dependence on the concept of objective truth. By this criterion, for example, the complementarity interpretation of quantum physics due to Niels Bohr and the Copenhagen school is seen as postmodernist.76
Clearly, quantum gravity is in this respect an archetypal postmodernist science. Secondly,
The other concept which can be taken as being fundamental to postmodern science is that of essentiality. Postmodern scientific theories are constructed from those theoretical elements which are essential for the consistency and utility of the theory.77
Thus, quantities or objects which are in principle unobservable – such as space-time points, exact particle positions, or quarks and gluons – ought not to be introduced into the theory.78 While much of modern physics is excluded by this criterion, quantum gravity again qualifies: in the passage from classical general relativity to the quantized theory, space-time points (and indeed the space-time manifold itself) have disappeared from the theory.
However, these criteria, admirable as they are, are insufficient for a liberatory postmodern science: they liberate human beings from the tyranny of “absolute truth” and “objective reality”, but not necessarily from the tyranny of other human beings. In Andrew Ross’ words, we need a science “that will be publicly answerable and of some service to progressive interests.”79 From a feminist standpoint, Kelly Oliver makes a similar argument:
... in order to be revolutionary, feminist theory cannot claim to describe what exists, or, “natural facts.” Rather, feminist theories should be political tools, strategies for overcoming oppression in specific concrete situations. The goal, then, of feminist theory, should be to develop strategic theories – not true theories, not false theories, but strategic theories.80
How, then, is this to be done?
In what follows, I would like to discuss the outlines of a liberatory postmodern science on two levels: first, with regard to general themes and attitudes; and second, with regard to political goals and strategies.
One characteristic of the emerging postmodern science is its stress on nonlinearity and discontinuity: this is evident, for example, in chaos theory and the theory of phase transitions as well as in quantum gravity.81 At the same time, feminist thinkers have pointed out the need for an adequate analysis of fluidity, in particular turbulent fluidity.82 These two themes are not as contradictory as it might at first appear: turbulence connects with strong nonlinearity, and smoothness/fluidity is sometimes associated with discontinuity (e.g. in catastrophe theory);83 so a synthesis is by no means out of the question.
Secondly, the postmodern sciences deconstruct and transcend the Cartesian metaphysical distinctions between humankind and Nature, observer and observed, Subject and Object. Already quantum mechanics, earlier in this century, shattered the ingenuous Newtonian faith in an objective, pre-linguistic world of material objects “out there”; no longer could we ask, as Heisenberg put it, whether “particles exist in space and time objectively”. But Heisenberg’s formulation still presupposes the objective existence of space and time as the neutral, unproblematic arena in which quantized particle-waves interact (albeit indeterministically); and it is precisely this would-be arena that quantum gravity problematizes. Just as quantum mechanics informs us that the position and momentum of a particle are brought into being only by the act of observation, so quantum gravity informs us that space and time themselves are contextual, their meaning defined only relative to the mode of observation.84
Thirdly, the postmodern sciences overthrow the static ontological categories and hierarchies characteristic of modernist science. In place of atomism and reductionism, the new sciences stress the dynamic web of relationships between the whole and the part; in place of fixed individual essences (e.g. Newtonian particles), they conceptualize interactions and flows (e.g. quantum fields). Intriguingly, these homologous features arise in numerous seemingly disparate areas of science, from quantum gravity to chaos theory to the biophysics of self-organizing systems. In this way, the postmodern sciences appear to be converging on a new epistemological paradigm, one that may be termed an ecological perspective, broadly understood as “recogniz[ing] the fundamental interdependence of all phenomena and the embeddedness of individuals and societies in the cyclical patterns of nature.”85
A fourth aspect of postmodern science is its self-conscious stress on symbolism and representation. As Robert Markley points out, the postmodern sciences are increasingly transgressing disciplinary boundaries, taking on characteristics that had heretofore been the province of the humanities:
Quantum physics, hadron bootstrap theory, complex number theory, and chaos theory share the basic assumption that reality cannot be described in linear terms, that nonlinear – and unsolvable – equations are the only means possible to describe a complex, chaotic, and non-deterministic reality. These postmodern theories are – significantly – all metacritical in the sense that they foreground themselves as metaphors rather than as “accurate” descriptions of reality. In terms that are more familiar to literary theorists than to theoretical physicists, we might say that these attempts by scientists to develop new strategies of description represent notes towards a theory of theories, of how representation – mathematical, experimental, and verbal – is inherently complex and problematizing, not a solution but part of the semiotics of investigating the universe.86, 87
From a different starting point, Aronowitz likewise suggests that a liberatory science may arise from interdisciplinary sharing of epistemologies:
... natural objects are also socially constructed. It is not a question of whether these natural objects, or, to be more precise, the objects of natural scientific knowledge, exist independently of the act of knowing. This question is answered by the assumption of “real” time as opposed to the presupposition, common among neo-Kantians, that time always has a referent, that temporality is therefore a relative, not an unconditioned, category. Surely, the earth evolved long before life on earth. The question is whether objects of natural scientific knowledge are constituted outside the social field. If this is possible, we can assume that science or art may develop procedures that effectively neutralize the effects emanating from the means
by which we produce knowledge/art. Performance art may be such an attempt.88
Finally, postmodern science provides a powerful refutation of the authoritarianism and elitism inherent in traditional science, as well as an empirical basis for a democratic approach to scientific work. For, as Bohr noted, “a complete elucidation of one and the same object may require diverse points of view which defy a unique description” – this is quite simply a fact about the world, much as the self-proclaimed empiricists of modernist science might prefer to deny it. In such a situation, how can a self-perpetuating secular priesthood of credentialed “scientists” purport to maintain a monopoly on the production of scientific knowledge? (Let me emphasize that I am in no way opposed to specialized scientific training; I object only when an elite caste seeks to impose its canon of “high science”, with the aim of excluding a priori alternative forms of scientific production by non-members.)89
The content and methodology of postmodern science thus provide powerful intellectual support for the progressive political project, understood in its broadest sense: the transgressing of boundaries, the breaking down of barriers, the radical democratization of all aspects of social, economic, political and cultural life.90 Conversely, one part of this project must involve the construction of a new and truly progressive science that can serve the needs of such a democratized society-to-be. As Markley observes, there seem to be two more-or-less mutually exclusive choices available to the progressive community:
On the one hand, politically progressive scientists can try to recuperate existing practices for moral values they uphold, arguing that their right-wing enemies are defacing nature and that they, the counter-movement, have access to the truth. [But] the state of the biosphere – air pollution, water pollution, disappearing rain forests, thousands of species on the verge of extinction, large areas of land burdened far beyond their carrying capacity, nuclear power plants, nuclear weapons, clearcuts where there used to be forests, starvation, malnutrition, disappearing wetlands, nonexistent grass lands, and a rash of environmentally caused diseases – suggests that the realist dream of scientific progress, of recapturing rather than revolutionizing existing methodologies and technologies, is, at worst, irrelevant to a political struggle that seeks something more than a reenactment of state socialism.91
The alternative is a profound reconception of science as well as politics:
[T]he dialogical move towards redefining systems, of seeing the world not only as an ecological whole but as a set of competing systems – a world held together by the tensions among various natural and human interests – offers the possibility of redefining what science is and what it does, of restructuring deterministic schemes of scientific education in favor of ongoing dialogues about how we intervene in our environment.92
It goes without saying that postmodernist science unequivocally favors the latter, deeper approach.
In addition to redefining the content of science, it is imperative to restructure and redefine the institutional loci in which scientific labor takes place – universities, government labs, and corporations – and reframe the reward system that pushes scientists to become, often against their own better instincts, the hired guns of capitalists and the military. As Aronowitz has noted, “One third of the 11,000 physics graduate students in the United States are in the single subfield of solid state physics, and all of them will be able to get jobs in that subfield.”93 By contrast, there are few jobs available in either quantum gravity or environmental physics.
But all this is only a first step: the fundamental goal of any emancipatory movement must be to demystify and democratize the production of scientific knowledge, to break down the artificial barriers that separate “scientists” from “the public”. Realistically, this task must start with the younger generation, through a profound reform of the educational system.94 The teaching of science and mathematics must be purged of its authoritarian and elitist characteristics,95 and the content of these subjects enriched by incorporating the insights of the feminist,96 queer,97 multiculturalist98 and ecological99 critiques.
Finally, the content of any science is profoundly constrained by the language within which its discourses are formulated; and mainstream Western physical science has, since Galileo, been formulated in the language of mathematics.100, 101 But whose mathematics? The question is a fundamental one, for, as Aronowitz has observed, “neither logic nor mathematics escapes the ‘contamination’ of the social.”102 And as feminist thinkers have repeatedly pointed out, in the present culture this contamination is overwhelmingly capitalist, patriarchal and militaristic: “mathematics is portrayed as a woman whose nature desires to be the conquered Other.”103, 104 Thus, a liberatory science cannot be complete without a profound revision of the canon of mathematics.105 As yet no such emancipatory mathematics exists, and we can only speculate upon its eventual content. We can see hints of it in the multidimensional and nonlinear logic of fuzzy systems theory;106 but this approach is still heavily marked by its origins in the crisis of late-capitalist production relations.107 Catastrophe theory,108 with its dialectical emphases on smoothness/discontinuity and metamorphosis/unfolding, will indubitably play a major role in the future mathematics; but much theoretical work remains to be done before this approach can become a concrete tool of progressive political praxis.109 Finally, chaos theory – which provides our deepest insights into the ubiquitous yet mysterious phenomenon of nonlinearity – will be central to all future mathematics. And yet, these images of the future mathematics must remain but the haziest glimmer: for, alongside these three young branches in the tree of science, there will arise new trunks and branches – entire new theoretical frameworks – of which we, with our present ideological blinders, cannot yet even conceive.
I wish to thank Giacomo Caracciolo, Lucía Fernández-Santoro, Lia Gutiérrez and Elizabeth Meiklejohn for enjoyable discussions which have contributed greatly to this article. Needless to say, these people should not be assumed to be in total agreement with the scientific and political views expressed here, nor are they responsible for any errors or obscurities which may inadvertently remain.
Works Cited
Adams, Hunter Havelin III. 1990. African and African-American contributions to science and technology. In African-American Baseline Essays. Portland, Ore.: Multnomah School District 1J, Portland Public Schools.
Albert, David Z. 1992. Quantum Mechanics and Experience. Cambridge, Mass.: Harvard University Press.
Alexander, Stephanie B., I. David Berg and Richard L. Bishop. 1993. Geometric curvature bounds in Riemannian manifolds with boundary. Transactions of the American Mathematical Society 339: 703–716.
Althusser, Louis. 1969. Freud and Lacan. New Left Review 55: 48–65.
Althusser, Louis. 1993. Écrits sur la Psychanalyse: Freud et Lacan. Paris: Stock/IMEC.
Alvares, Claude. 1992. Science, Development and Violence: The Revolt against Modernity. Delhi: Oxford University Press.
Alvarez-Gaumé, Luís. 1985. Topology and anomalies. In Mathematics and Physics: Lectures on Recent Results, vol. 2, pp. 50–83, edited by L. Streit. Singapore: World Scientific.
Argyros, Alexander J. 1991. A Blessed Rage for Order: Deconstruction, Evolution, and Chaos. Ann Arbor: University of Michigan Press.
Arnol’d, Vladimir I. 1992. Catastrophe Theory. 3rd edn. Translated by G.S. Wassermann and R.K. Thomas. Berlin: Springer.
Aronowitz, Stanley. 1981. The Crisis in Historical Materialism: Class, Politics and Culture in Marxist Theory. New York: Praeger.
Aronowitz, Stanley. 1988a. The production of scientific knowledge: Science, ideology, and Marxism. In Marxism and the Interpretation of Culture, pp. 519–41, edited by Cary Nelson and Lawrence Grossberg. Urbana and Chicago: University of Illinois Press.
Aronowitz, Stanley. 1988b. Science as Power: Discourse and Ideology in Modern Society. Minneapolis: University of Minnesota Press.
Aronowitz, Stanley. 1994. The situation of the left in the United States. Socialist Rev
iew 23(3): 5–79.
Aronowitz, Stanley and Henry A. Giroux. 1991. Postmodern Education: Politics, Culture, and Social Criticism. Minneapolis: University of Minnesota Press.
Aronowitz, Stanley and Henry A. Giroux. 1993. Education Still Under Siege. Westport, Conn.: Bergin & Garvey.
Ashtekar, Abhay, Carlo Rovelli and Lee Smolin. 1992. Weaving a classical metric with quantum threads. Physical Review Letters 69: 237–40.
Aspect, Alain, Jean Dalibard and Gérard Roger. 1982. Experimental test of Bell’s inequalities using time-varying analyzers. Physical Review Letters 49: 1804–1807.
Assad, Maria L. 1993. Portrait of a nonlinear dynamical system: The discourse of Michel Serres. SubStance 71/72: 141–52.
Back, Kurt W. 1992. This business of topology. Journal of Social Issues 48(2): 51–66.
Bell, John S. 1987. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. New York: Cambridge University Press.
Berman, Morris. 1981. The Reenchantment of the World. Ithaca, N.Y.: Cornell University Press.
Best, Steven. 1991. Chaos and entropy: Metaphors in postmodern science and social theory. Science as Culture 2(2) (no. 11): 188–226.
Bloor, David. 1991. Knowledge and Social Imagery. 2nd edn. Chicago: University of Chicago Press.
Bohm, David. 1980. Wholeness and the Implicate Order. London: Routledge & Kegan Paul.
Bohr, Niels. 1958. Natural philosophy and human cultures. In Essays 1932–1957 on Atomic Physics and Human Knowledge (The Philosophical Writings of Niels Bohr, Volume II), pp. 23–31. New York: Wiley.