Martin Rosenberg:

Chess RHIZOME:
Mapping Metaphor Theory onto Hypertext Theory

Introduction:

This approach to the study of metaphor in science may add a level of rigor to concerns over the value of investigations into scientific knowledge and practices by those outside the sciences proper, by forcing scientists to recognize the need to take the role of metaphor much more seriously. Recent debates over the cultural studies of science have brought to the foreground the problem of metaphor in scientific discourse. This problem manifests itself in particular through a series of recent challenges to the ways in which cultural theorists of science attempt to construct correspondences between the laws governing physics and human cognition and laws governing the behavior of human beings and their institutions. Paul Gross and Norman Levitt, Alan Sokal and Alain Bricmont and others disparaging such interdisciplinary inquiry have scorned such constructions. In an e-mail message to me last February, the mathematician Norman Levitt states that he sees no middle ground between the construction of is and is not in representing, for example, the relationship between the behavior of atoms and the behavior of thoughts. He takes exception to such theorizing. He does so even though such a correspondence has been suggested by both Jacques Derrida, the philosopher and literary theorist, in an essay entitled "White Mythology," and by Henri Poincaré, the last great renaissance mathematician of the modern era, in an essay on scientific creativity entitled "Mathematical Discovery."  

In her recent (September, 1998) essay in Physics Today, Mara Beller demonstrates convincingly that physicists themselves have indulged themselves in much the same way. She analyzes the pervasiveness of the construction of such correspondences between physical and cultural processes by such eminent physicists as Max Born, Niels Bohr, Werner Heisenberg, Wolfgang Pauli, John Wheeler and others, observing:    

Like the deconstructionist Jacques Derrida, whom Steven Weinberg attacked in his 1996 New York Review of Books article on Sokal's hoax, Bohr was notorious for the obscurity of his writing. Yet physicists relate to Derrida's and Bohr's obscurities in fundamentally different ways: to Derrida's with contempt, to Bohr's with awe.

Questions about the poetics of culture raised by Giambattista Vico and Friedrich Nietzsche, and more recently by Jacques Derrida and Hayden White, have become linked methodologically to the work on metaphor within the field of the philosophy of science. The issue of metaphor in science isn't simply subsumed by the question of competing concepts of reality: as objectively there;   as simply the construction of a model registering a scientist's observations. Metaphor becomes the ground upon which these competing concepts of reality struggle.  

Since my current book project Fables of Self-Organization: The Cultural Work of Complexity in the Avant-Garde confronts this problem directly, I thought it might be useful to perform what in the field of physics is called a "thought experiment," in order to model how certain kinds of tropes become implicated in certain scientific epistemologies and not others. I wondered whether it might be possible to model how certain kinds of tropes drift across disciplinary boundaries and perform certain kinds of cultural work. I wondered whether it might be possible to make visible the ways in which metaphors might become symptoms for basic questions concerning the nature of reality through the lenses of a range of disciplines.  

Hypertext environments seem ideal for these kind of "thought experiments." Furthermore, there might be a certain kind of "irony" that becomes possible, when, as I have written about elsewhere, the very kinds of tropical speculations over the nature of hypertextual space and time have led, in turn, to similar kinds of debates over the role of metaphor. So, keeping in mind the metaphor of the möbius strip, what I would like to do in the actual presentation is to demonstrate Chess RHIZOME. I would then like to use the occasion of this demonstration to foreground the additional theoretical problem created by representing structures and processes of thought in hypertext using tropes derived from the sciences, by modeling hypertextually the problematic role of metaphor in interdisciplinary science studies itself.  

Epicurus's Hooked Atoms: Poincaré's extended Metaphor

during a period of apparent repose, but of unconscious work, some of them are detached from the wall and set in motion. They plough through space in all directions...like the gaseous molecules in the kinetic theory of gases. Their mutual collisions may then produce new combinations. (Science and Method 61).

Moreover, he seems to ascribe to these entropic thought-swarms the capacity to self-organize in a way that would make the return of those atom-thoughts to their original positions on the walls impossible. These swarms may indeed overwhelm their containing structures, may even require the reorganization of the sedentary structures of the walls themselves. We can see how easily it would be to slide these terms over to the activity that becomes possible in a hypertext system marked by familiar conceptual walls. Because of the highly contingent nature of hypertextual structures, and the aleatory nature of its linking icons as sign-functions, we might imagine new ways of organizing information that might run counter to disciplinary rigidity.  

What follows, then, is an investigation of what these mazy rhizomatic formations might look like, as they become possible in a netherworld between hypertextual models of already existing disciplines. Chess RHIZOMEmarks one such envisioning. I hope that it will hint at specific ways for interdisciplinary inquiry into science, philosophy and the arts which is exemplified, in fact, by Poincaré's essay. Perhaps by modeling non-logical, non-sedentary conceptual realms that form contingently among or beneath disciplines through the medium of hypertext, it will become possible to identify as well certain formal properties of conceptual behavior that are both applicable and repeatable: that is, translatable to a variety of interdisciplinary investigations. Notice also, my claim that such an effect might be created even with the most basic elements of hypertext programming languages.  

Chess as Metaphor, Model and Allegory:

Furthermore, chess models (just as the calculus does) the culture of control over the contingent possibilities for cause and effect. It does so by freezing events into a series of still frames (more like a single cinematic image out of a series than a tableau). These frames become mulled over by the players seeking to manipulate the game toward their preferred sequence of cause and effect which will lead to victory at some future point. At each moment during the course of a game, time stops, leaving a silent range of possible futures in response to possible moves plotted schematically in the minds of the players. Chess players are capable of prodigious feats of memory, feats that even mathematicians would envy, as Poincaré also states in his essay "Mathematical Discovery."  

It allegorizes, through the rules and consequences of attrition warfare, the historical conceit that civilization (Spengler's The West) finds itself mechanically dissipating inevitably toward cultural equilibrium, the thermodynamic endgame of heat death for closed systems natural and cultural, and the end of the game for both Kings, no matter who "wins."  

By offering these metaphors, models and allegories, the game of chess seems to the carry the considerable cultural baggage of two major assumptions in physics. First, the laws governing the dynamics of the game are symetrical with respect to time and space, and remain simple as well as immutable (no other game, like GO, can exist simultaneously). Second, its pieces form collectively a kind of machinery, and behave in a manner that is analogous to a closed thermodynamic system like a heat engine gradually approaching equilibrium. Control -- the mapping and enactment of causal relationships -- has its horizon of helplessness in the face of the contingencies of history, no matter what allegories we construct to mediate the uncertainty that we feel because of that helplessness. Chess, therefore, involves a grand narrative generated by the culture of control over the contingencies of duration. This narrative is premised upon the ability of the rules of the game to reduce the contingencies inherent in the history of this closed system onto the striations of projected futures that are precisely mappable, but which also remain forever threatened by the endgame of systems death. Here we can now address the relationship between metaphor and epistemology in the knowledge systems we construct for ourselves.  

Chess as a Theory-Constitutive Metaphor:

Thomas Kuhn has challenged Boyd on this point by questioning whether "successive scientific theories provide successively clear approximations to nature." This forces Pylyshyn to comment ironically on the phenomenon of scientists referring to "literal" and "figurative" metaphors. Pylyshyn goes on to single out, in the tradition of Poincaré and Bergson, the reification of geometry in western science as an example of how metaphors can become literal simply by the ways in which scientists render the grounding assumptions for that metaphor invisible to themselves. James Bono reviews this issue by emphasizing, for the cultural studies of science, the Viconian and neo-Nietzschean traditions in the human sciences which foreground the irreducibility of metaphor. This link between literary theory, rhetoric and the philosophy of science should add a level of rigor to recent debates concerning the value of such investigations of scientific practices by those outside the sciences proper.  

I would just like to add one more complication, by demonstrating that Boyd's notion of the Theory Constitutive Metaphor remains valuable because of its problematic status. Reading Boyd carefully, we find the TCM as unstable, hovering between two contradictory uses that we might use to explore the cultural work of chess:    

1. As constitutive of the assumptions of the domain from which it is derived.  

2. As a portal opening up new potential domains.  

When I stated earlier that the chessboard tropes visually and by analogy the assumption of an underlying Platonic timeless "Being" beneath the causal chain of violent events, I was making visible a certain fundamental epistemological assumption at work in the hard as well as human sciences. This assumption, deconstructed recently by the work of Ilya Prigogine and a student of Gilles Deleuze, Isabelle Stengers, views time as a function that is reversible, so that all complex phenomena can be explained by simple immutable laws that can map the chains of causality with precision because all events can be reduced to a geometrical grid. According to Prigogine and Stengers, of course, there is another fundamental assumption that makes no such claims and in fact argues that time is both irreversible and irreducible to a geometric grid. So the value of chess, as a theory constitutive metaphor, lies in its capacity to reveal its naïve or ironic appropriation.  

Richard Feynman uses chess to describe the simple laws governing the reversible and symmetrical nature of particle interactions in quantum electrodynamics in terms of the 1st Law of Thermodynamics (The Conservation of Energy and Matter). Ferdinand de Saussure uses chess to describe the laws govering the synchronic perspective of speech acts in structural linguistics. Claude Shannon uses a chess playing computer to foreground the laws of the computational paradigm of artificial intelligence. For these thinkers we might say that there is a certain naïvety in accepting without question the reversible perspective, and that this acceptance cuts across disciplinary boundaries in a way that becomes visible precisely because of their shared uncritical acceptance of the capacity of the chess metaphor to cut the world "at its joints."  

Duchamp explores the mapping of events to control the future trajectory of the chess system in his chess treatise on the Endgame Opposition et les cases conjugées sont reconciliées. He does so by isolating the condition in which the contingent and irreversible conditions of error creep into an otherwise over-determined ritual to avoid defeat by delaying the end of the endgame as long as possible. Yet you cannot win using the treatise; you can only avoid defeat. Wittgenstein uses chess ironically in "The Rejection of Logical Atomism" to underscore the inadequacy of any system of rules to explain communicative acts without taking into account the fact that these acts occur not in a silent timeless system but in the irreversible time of the world. Both Deleuze and Guattari, and Thomas Pynchon highlight the biases of top-down superimpositions onto the contingencies of the world by reference to chess, and explore the tropical implications of other games and other rules, such as Go, to open up a portal to new forms of thought. These two thinkers employ chess ironically as a theory-constitutive metaphor for two purposes: to subvert the fundamental assumptions about time, causality and certainty implied; and, to seek parallel tropical models (such as Go) for other, competing assumptions concerning the role of time in physical, cultural and cognitive processes as well.  

Conclusion: The Rhizomatic Behavior of Metaphors and the Role of Irony:

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