Chaos as Orderly Disorder: Shifting Ground in Contemporary Literature and Science N. Katherine Hayles IMAGINE THAT YOU are in the bowels of a computer, and a sequence of ones and zeros floats by. Without knowing anything about the program, you have no way of knowing whether you have just seen a portion of the Manhattan telephone dlrectory, the number 1,456, or "To be or not to be." At this level all information, whether G del's Theorem or Hamlet's soliloquy, exists in the same form. Carry the fantasy a step further and imagine that the computer itself, along with you, could also be specified by sequences of ones and zeros. We are now close to the world of Edward Fredkin, who asserts "the basic stuff that everything is made of is information.''l A professor at MIT who works at the intersection of physics and computer science, Fredkin believes that the fundamental structure of both matter and energy can be reduced to flows of information. To Fredkin the world is quite literally a text, a physical embodiment of informational markers. There was a time when Fredkin's views would have seemed extreme. But no longer. Across a wide spectrum of disciplines, information is emerging as a synthesizing concept that changes how we see the world. Technological developments have undoubtedly played crucial roles in bringing an information perspective into being, as have the social and economic interdependencies that have made instantaneous communication around the globe a necessity.2 In keeping with my focus on chaos, I should like to concentrate on a transformation within the information perspective itself. It occurred when information ceased to be thought of as inherently structured and became associated with randomness. Given the forces already at work within the culture that privileged information, this shift authorized a reevaluation of chaos. From this revisioning of chaos derive implications not yet fully understood, although it is already clear that they will be important in literary study and in many other fields. The identification of information with randomness can be dated precisely. It occurred in 1948, when Claude Shannon published a theory of information in two articles that have since become classics.Shannon defined information through an equation that looked very much like Boltzmann's equation for entropy.3 In contrast to Leon Brillouin, who used Maxwell's Demon to argue that information and entropy are opposites, Shannon used information and entropy as interchangeable terms. As early as 1877, Boltzmann had interpreted entropy as a statistical measure of disorder. By equating information with entropy, Shannon intimated that disorder could be seen in positive terms as the presence of information, rather than simply as the absence of order. Ironically, having raised this possibility, Shannon refused to explore its implications. He regarded such larger philosophical concerns as a waste of time. In fact, when other scientists began to see in his work possibilities for applications to other disciplines, he went into print to caution them that information theory properly applied only to a very restricted, technical domain.4 With thirty years' hindsight it is possible to see that Shannon's view of information was revolutionary, because it enabled a new view of chaos to emerge.Shannon's theory was appropriated by chaos theorists to redefine chaos as maximum information. From this appropriation has emerged a perspective that sees chaos not as an absence or a lack, but as the source of all that is new in the world. As with many ideas that seem new, this one is very old. In Paradise Lost, for example, God creates the world not from nothing but from primordial chaos. For Milton as for Shannon, chaos is not order's opposite but its precursor. What is new is the idea's rigorous quantitative expression and its centrality to research programs in nonlinear dynamics, irreversible thermodynamics, meteorology, epidemiology, and fractal geometry, among others. Known as the science of chaos, this interdisciplinary research has revealed a terrain between order and disorder. Chaos in the sense it is used in this research denotes complex systems that operate according to deterministic laws, and yet that behave unpredictably. Complex systems are configured so as to bring minute uncertainties in initial conditions quickly up to macroscopic expression: in the parlance of chaos theory, this is known as "extreme sensitivity to initial conditions." Although their behavior quickly becomes unpredictable, complex systems nevertheless become chaotic in predictable ways. Combining qualities that classical mechanics considered antithetical, chaos can be assimilated neither into order nor disorder. It names a new territory, designates previously unrec- ognized interactions, and relies upon different assumptions. Conditioned by classical modes of thought, we may wonder if any but the rarest of systems fulfills these criteria. In fact the orderly disorder of chaos is all around us, from cream swirling in coffee to the rise and fall of the Nile River, from global weather patterns to outbreaks of measles epidemics. In fact, so extensive are chaotic systems that they dwarf the ordered systems which science has traditionally regarded as norms for the universe. James Gleick, in his recent book on chaos, recalls Stanislaw Ulam's comment that to characterize chaos theory as "nonlinear science" is like calling zoology "the study of non-elephant animals." To see how chaos theory embodies new kinds of assumptions about complex systems, consider the work of Mitchell Feigenbaum, a physicist at Cornell University. In a review article in Los Alamos Science, Feigenbaum approaches chaos through the closely related concept of randomness.6 He asks us to consider in what way a number generated by a computer can be random. He points out that a computer-based random number generator can easily be constructed by creating a program that does "nothing more than shift the decimal point in a rational number whose repeating block is suitably long" (4). Numbers generated by this method are so lacking in pattern that they satisfy the most rigorous tests for randomness, yet the method that produces them is perfectly simple and deterministic. Technically, these numbers are called pseudo-random to indicate that they have been generated by a deterministic computer program. Feigenbaum's inspiration was to wonder whether other phenomena considered to be chaotic might also be pseudo-random, obeying deterministic programs just as pseud-random numbers do. This astonishing premise amounts to saying that chaos possesses a deep structure of order. One of the first indications that such a deep structure might in fact exist was Feigenbaum's discovery that systems which go from ordered to chaotic states follow a characteristic pattern of period doubling. Let us say, for example, that we are looking for a pattern in the behavior of an electrical oscillator. We notice the oscillator repeats its behavior after some time interval T. When the temperature is raised, the behavior of the oscillator becomes more erratic, and we now have to extend the time period to 2T to have a repeating pattern. When the temperature is raised yet again, the time required to observe a repeating pattern jumps to 4T, and so on. Eventually the time period will become so great that the oscillator has no repetitions in the time scale available for observation. At this point it is said to be chaotic. Period doubling is now recognized as a powerful generalization, describing the onset of chaos in everything from dripping faucets to Niagara Falls.7 At the time of his discovery, however, Feigenbaum was not thinking about physical systems. He was looking at the behavior of mathematical functions when they are iterated.To iterate a function means to use the output of one as the input for the next, each time performing the operation called for by the function. It is analogous to beginning at a certain place and doing a dance step; then starting from the new location each time, doing the dance step again and again. Iterating strongly nonlinear functions produces paths that have folds in them. So intricate are these folds that although the trajectories remain within a defined area, no two paths intersect or coincide. "This general mechanism," Feigenbaum comments, "gives a system highly sensitive upon its initial conditions and a truly statistical character: since very small differences in initial conditions are magnified quickly, unless the initial conditions are known to infinite precision, all known knowledge is eroded rapidly to future ignorance" (21). The startling aspect of Feigenbaum's work was his discovery that despite the different operations performed by different nonlinear functions--despite the different dance steps they used- -their iterated paths approached chaos at the same rate and showed the same characteristic patterns of period doubling. All that mattered was that the paths had folds of sufficient steepness. It may be hard for a nonscientist to appreciate the enormity of this discovery, but to a mathema- tician, sine waves are as different from quadratic equations as pirouettes are from bows to a ballet dancer. To find out that there is a way of looking at these functions that makes their operations seem not just similar but identical is analogous to discovering that there is a way of looking at Nureyev dancing and Donald Duck waddling that makes their performances into a universal constant applicable to anyone moving on that stage. What was this new way of looking? At the same time that the iterative process had the effect of overwhelming individual differences between functions, it also revealed a universality in how large-scale features related to small details. The shift in focus is from the particularities of a given function to the relation between different recursive levels in the iterative process. Imagine two paintings, each showing an open door through which is revealed another open door, through which is revealed another and another.... One way to think about the doors in these two paintings is to focus on the particularities of the repeated forms. Suppose the doors of the first painting are ornately carved rectangles, whereas the second painting shows doors that are unadorned arches. If we attend only to these shapes, the paintings might seem very different. But suppose we focus instead on the recursive repetition of doors in each painting and discover that in both paintings, the doors become smaller at a constant rate. Through this shift in focus, we have found a way of looking at the paintings that reveals their similarity to each other and to any other painting constructed in this way. The key is recursive symmetry. In physical systems, recursive symmetries permit fluctuations at the smallest level to be rapidly transmitted through the system. The symmetrical relationships between levels act like coupling mechanisms that allow tiny uncertainties to ripple through the system until they become macroscopic disturbances. Say, for example, that we are standing on a river bank, watching the water flow by. Most of the time small disturbances in the fluid path cancel each other out, so that the river flows smoothly between its banks. But when the right kind of symmetries are present, small disturbances are amplified until eddies and backwaters form. At these points turbulence sets in, and the flow patterns become extremely complex. Nevertheless, these complexities very often express themselves through recursive symmetries; large swirls of water have small swirls inside them, within which are smaller swirls.... The complex symmetries that are repeated across different levels of a complex system are crucial in understanding how the onset of chaos occurs. Chaos theory recognizes the importance of scale in a way that classical paradigms do not. In sharp contrast to the scale independence of Newtonian and Euclidean paradigms, chaos models are intrinsically and inevitably scale dependent. Fractal geometry is closely related to chaos theory, and it too emphasizes scaling symmetries across different levels. Benoit Mandelbrot, the inventor of this new geometry, coined the word fractal from the Latin adjective fractus (meaning "breakable") and fractional; it connotes both fractional dimensions and extreme complexity of form.8 The mathematics of fractional dimensions is complex, but the general idea is not hard to grasp. Whereas the familiar integer di- mensions of Cartesian space are entirely adequate to represent Euclidean shapes such as circles, triangles, and squares, they do not do justice to highly complex and irregular forms. The corrugations that mark the surfaces of these forms give them, in effect, an added fraction of a dimension.To show the importance of scale for fractal figures, Mandelbrot asks a question that looks as if it should have a straightforward, factual answer: How long is the coastline of Britain? (25-33). The question is more devious than it appears, because the answer is scale dependent. If we measure the coastline using a mile-long rule, we get a shorter answer than if we use a yardstick, for the mile rule cuts across irregularities that the yardstick measures around. If we use an inch rule the answer is still longer, because small pebbles are measured around; and if a micrometer is used, even irregularities within a single pebble count. In fact, Britain's coastline continues to grow without limit as the ruler scale decreases, at least down to molecular scales. Without specifying a ruler length, the question cannot be accurately answered. The example demonstrates why questions of scale are foregrounded in the new paradigms. In Euclidean geometry and Newtonian mechanics, the idea that one could get different answers when using different scales does not appear. It is not quite correct to say these older paradigms make global statements which are considered true for every level, because their globalizing approaches are so complete that the system is not conceived as having levels in any meaningful sense. In Euclidean geometry it does not matter whether an isoceles triangle is twice as large or two hundred times as large as another triangle of the same shape; whatever the scale, Euclidean geometry states that the three sides of similar triangles will be in the same proportion to each other. Fractal geometry does not challenge this assertion as such. Rather, it shifts the focus to complex irregular forms, for which scale appears as an important consideration, and movement between length scales becomes highly nontrivial. Similarly, Newtonian mechanics applies the same partial differential equations whether the object is a golf ball or a planet; in either case the masses move through time according to uniform laws of motion. But when the object has a complex internal structure consisting of distinct local levels, as is the case for a fluid in turbulent flow, length scale is critical because different portions of the fluid move at different speeds and with different kinds of motions. Under these conditions, Newtonian-based calculations are unmanageable for even a few points, and unthinkable for the thousands or millions it would take to model the system. The movement from scale-invariant models to scale-dependent paradigms has an obvious correspondence to the movement in critical theory away from totalizing theories. We must, however, be cautious in drawing inferences about what this correspondence means. What the new scientific paradigms cannot do, I think, is give us a transcendent perspective from which we can say other cultural developments are good or bad, true or false. In The Postmodern Condition, Lyotard argues that "paralogy" (an umbrella term under which he groups such diverse theories as fractal geometry, quantum mechanics, and G del's Theorem) provides corroborating evidence from within the physical sciences that will let us "wage a war on totality."9 This interpretation of the new scientific paradigms ignores the fact that they have not renounced globalization. Chaos theory, for example, simply achieves totalization in a different way, by focusing on recursive symmetries between levels rather than by following the motions of individual molecules. Chaos theory would not have attracted the attention has if it had simply confirmed what everyone already knew, that chaotic systems are disordered. No, what makes it noteworthy is the discovery that despite this disorder, universal structures can still be discerned. The thrust toward globalization is apparent in the name Feigenbaum chose for his discovery that chaotic systems can be described through universal constants: he calls it "Universality Theory." The belief that the science of chaos opposes globalizing theories is, then, a misapprehension about how these theories work. More fundamentally, Lyotard's claim that these paradigms can be used to wage a war against totality is wrongheaded because it confuses scientific theories with social programs. His apparent conviction that fractal geometry can combat totalitarianism is a modern version of social Darwinism. Such a belief ignores the ways in which scientific theories, like literary and cultural theories, are themselves social constructions.l0 Scientific paradigms do not exist in some ideal space above or beyond culture. They are part of their culture, which they both replicate and reinforce. In my view, the more productive ways to think about the relation of these paradigms to literary theory and literature start with the premise that they are social constructions and ask how their assumptions reinforce other assumptions in the culture. To begin probing these correspondences, consider how the new paradigms treat time.ll In Newtonian mechanics, objects moving through time are modeled as trajectories that can be broken into arbitrarily small intervals (this is essentially the basis for calculus). As the intervals approach zero, they are added together to get the trajectory as a whole. Underlying this method is the common-sense perception that movement through time can be equated with an object moving along some predictable path--for example, the parabolic arc of a baseball as it comes off the bat. However, if the moving shape is complex in the sense of being composed of multiple levels acting in different ways, the calculations very quickly become unmanageable because they involve many coupled degrees of freedom. In the new paradigms, a shape is no longer conceived as a mass of points, but as the formulae used to generate and randomize the self similar forms that compose it. The new paradigms do not attempt to describe how each point within a shape moves. Rather, they focus on the transformation rules that govern the evolution of the shape's recursive symmetries through time. The advantage of this approach derives from the fact that in complex systems, very small changes in the initial conditions lead to very large changes in the final forms. By changing the iterative formulae only a little, complex forms can be made to move in very different ways.l2 Hence large-scale changes can be encoded with many fewer bits of information than would be required if each point within a complex form had to be advanced through time individually. Now consider how these views of time correlate with other kinds of cultural and social theories. Newton's conception of objects as masses of points is matched by Hobbes's conception of society as a group of autonomous individuals and by Adam Smith's conception of the economy as a collection of competing customers. Different as these theories are, they each assume that systems are constituted as groups of individual units which act in accord with general laws. They make the transition from the local site to the global system by applying general laws to masses of individual units. To make the system move through time, they add together the motions of individual units to arrive at a resultant. In contrast to these classical assumptions are those Foucault uses in his archaeologies. Foucault considers the individual not as an autonomous actor, but rather as a microcosm constituted by the tropes and organizing figures characteristic of the episteme. For Foucault, indi- viduals do not constitute culture; culture constitutes individuals. Moreover, at least in his early work, Foucault sees different cultural sites as manifesting the same principles of organization. Thus he argues that during the neoclassical period in Europe, the same organizing tropes appear in grammar, biology, political theory, and psychology.l3 My point here is not to validate Foucault's theory, but to show how the assumptions underlying his view of culture are isomorphic with the assumptions embodied in chaos theory. Both theories, although they are very different in many respects, embody a shift in focus away from the individual unit to structures that are replicated across many levels of a system. The correspondence suggests that the contemporary episteme is characterized by deep assumptions that have made the concept of an episteme thinkable. One criticism frequently made of Foucault's early approach is that it does not explain how changes take place through time (for purposes of this argument, assume that Foucault has characterized the periods accurately). How and why, Foucault's critics ask, did people stop be- lieving in similitude as an organizing trope and start believing in representation? The objection is not as straightforward as it appears, for what counts as a temporal explanation is fundamentally different in the new paradigms than it was in the old. The objection implies that a temporal explanation should place groups of autonomous actors along a time line and advance them according to laws or generalizations that explain why the actors behaved as they did. In the new paradigms, however, temporal explanation means something different. It implies understanding the structural principles that relate different sites by self-similarity, along with rules that state how these principles evolve over time. Foucault has achieved the first step in this kind of explanation by anatomizing the structural principles that underlie self-similar cultural forms. Although he has not given a full temporal explanation, he has nevertheless come much closer to it than his critics acknowledge, because they discount comparison of different kinds of self-similarities as the foundation on which temporal explanations are built.The correlation between the new scientific paradigms and Foucault's archaeologies suggests that an extremely wide-ranging cultural shift is in progress. It can perhaps best be characterized through the dialectics that the new paradigms have energized. The most important is the destabilization of the order/disorder opposition and the subsequent reevaluation of chaos as a presence rather than an absence--a presence, moreover, that is seen as more rewarding and fecund in its complexity than classical order. Closely related to the transvaluation of chaos is the energizing of the local/global dialectic. With the passages from one scale to another rendered problematic, the relation of local sites to global configurations becomes an important nexus for inquiry. Both the order/disorder and local/global dialectics are underlaid by a shift in focus from the individual unit to self-similar replication across the different levels of a system. When an opposition as central to Western thought as order/dlsorder is destabilized, it is no exaggeration to say that a major fault line has developed in the foundations of the culture. It would be strange indeed if there were not other theoretical enterprises that also work the fault line. Some of the most visible are within critical theory. Just as new concepts of chaos are changing how scientists think about informational systems, they are also affecting how literary critics write about texts. The major impetus for this revision has come from deconstruction, which Paul de Man sees as warning us that "nothing, whether deed, word, thought or text, ever happens in relation, positive or negative, to anything that precedes, follows or exists elsewhere, but only as a random event whose power . . . is due to the randomness of its occurrence.''l4 As the text is opened to an infinitude of readings and as meaning becomes indeterminate or disappears altogether, chaos apparently reigns supreme. In this extreme form, deconstruction seems to have gone beyond the premises that make science possible. Yet Geoffrey Hartman, confronted with the tangled, contaminated, displaced, deceptive" text of Derrida's Glas, speculates that deconstruction is opposed to more traditional, humanistic readings because it is more scientific. "The result for our time of deconstruction in general and Glas in particular] may be a factional split between simplifying types of reading that call themselves humanistic and indefinitizing kinds that call themselves scientific," Hartman writes.l5 He is correct, perhaps in a sense he did not intend, in linking deconstruction's "indefinitizing" strategies with science. Deconstruction shares with chaos theory the desire to breach the boundaries of classical systems by opening them to a new kind of analysis in which information is created rather than conserved. Delighting in the increased complexity that results from this "scientific" process, both discourses invert traditional priorities: chaos is deemed more fecund than order, uncertainty is privileged above predictability, and fragmentation is seen as the reality that arbitrary definitions of closure would deny. The vertigo characteristic of deconstruction appears when we realize that texts, far from being ordered sets of words bounded by book covers, are reservoirs of chaos. Derrida initiates us into this moment through his concept of iteration. Any word, he argues, acquires a slightly different meaning each time it appears in a new context. Moreover, the boundary between text and context is not fixed. Infinite contexts invade and permeate the text, regardless of chronology or authorial intention. For example, Hamlet influences how we read Rosencrantz and Guildenstern Are Dead; but Rosencrantz and Guildenst rn Are Dead also influences how we read Hamlet. The permeation of any text by an indefinite and potentially infinite number of intertexts implies that meaning is always already indeterminate. Because all texts are necessarily constructed through iteration (that is, through the incremental repetition of words in slightly displaced contexts), indeterminacy inheres in writing's very essence. We can see iteration at work in the dense, highly repetitive analysis of Rousseau that occupies the last half of Derrida's Of Grammatology. Rousseau is well suited to Derrida's deconstructive project because his thought is expressed through a series of hierarchical dualities: nature/ culture, animal/human, speech/writing. For Rousseau, the first term of each of these dualities is privileged. The second term is belated contaminated, a fall from the "pure" first term. His announced aim is to correct modern decadence by returning to the originary first term, rejecting culture for nature, writing for speech, and so on. Through a rigorous reading of Rousseau's texts, Derrida shows that this attempt at purification is fundamentally misguided because the idea of origin is an illusion. The demonstration concentrates on the supplement, a word that Rousseau uses in the Confessions as a euphemism for masturbation.16 Sex is natural, good, healthy; but since he is tormented by fear of women and venereal disease, Rousseau continually finds it necessary to resort to the supplement. Derrida shows that a similar dialectic emerges with each set of Rousseau's dualities. Rousseau denounces writing but does so by writing texts; he embraces nature but finds that its deficiencies necessitate the education he advocates in Emile, and so forth. To supplement something implies that the original is already full and self-sufficient, in contrast to the sup- plementary material, which comes after and is superfluous. Yet in each case the first term, nature for example, is "naturally" deficient, making the supplement indispensable. In what sense then is the supplement more "unnatural" than nature? Through this implicit contradiction, Derrida shows that the supplement is in fact what allows the privileged term to be constituted. The originary precedence of the privileged term is revealed as an illusion, a myth or longing for origin rather than an origin as such. According to Derrida, every text will have a concept that functions as the supplement does in Rousseau. The supplement (or its analogue) is, Derrida argues, a kind of fold in the text whose indeterminacy is revealed through repetition. In his view such a fold is necessarily present, because there must always be some means by which the text can constitute the differences that enable it to postulate meaning. The fold can be thought of as a way to create the illusion of origin. Once in place, all subsequent differences are declared to derive from the originary difference marked by the fold. When the text is "unfolded," this stratagem is revealed and the regulated exchanges between the alleged origin and subsequent differences that enable the text to operate will appear. It is precisely this "unfoldlng" that iteration accomplishes. In Derrida's hands, repeating Rousseau's language with incremental differences becomes a way to unfold and make visible the inherent contradictions upon which the text's dialectic is based. This iterative procedure produces the undecidables that radically destabilize meaning. "It [is] certainly a production," Derrida writes, "because I do not simply repeat what Rousseau thought of [the supplement]. The concept of the supplement is a sort of blind spot in Rousseau's text . . . [The production of undecidables] is contained in the transformation of the language [that the text] designates, in the regulated exchanges between Rousseau and history. We know that these exchanges only take place by way of the language and the text" ( 163-64). The goal of iteration is thus to make visible the lack of ground for the alleged originary difference, thus rendering all subsequent distinctions indeterminate. Derrida's deconstructive methodology is strikingly similar to the mathematical techniques of chaos theory. Recall that Feigenbaum attributed the universal element in chaotic systems to the fact that they were generated from iterative functions. He showed that for certain functions, individual differences in the equations are overwhelmed as iteration proceeds, so that even though the systems become chaotic, they do so in predictable or regulated ways. Derrida claims that his iterative methodology is similarly regulated, in the sense that its production of undecidables is not a capricious exercise but a rigorous exposition of the text's inherent indeterminacies. For both Derrida and Feigenbaum, iterative methodology is closely tied in with the concept of the fold. Feigenbaum showed that systems which make orderly transitions to chaos always have folds in their iterative paths. Within the complex regions created by these folds, orbits wander in unpredictable ways. Where does this unpredictability come from? Since the iterative formulae and computer programs that enact them are perfectly deterministic, it could only come from the initial conditions. Iteration produces chaos because it magnifies and brings into view these initial uncertainties. Similarly, Derrida attributes textual indeterminacy to the inherent inability of linguistic systems to create an origin. In Derrida, the fold marks the absence of an origin, just as the inability to specify initial conditions with infinite accuracy marks the onset of chaos for Feigenbaum. Thus nonlinear dynamics and deconstruction share not just a general attitude toward chaos, but specific methodologies and assumptions. There are, of course, also significant differences between them. Feigenbaum works with the exact definitions of mathematical formulae; Derrida is concerned with language, which is notoriously resistant to formalization. One measure of these differences is disagreement among deconstructionists and scientists on how extensive chaos is. For Derrida, textual chaos is always already in Rousseau and in every other text. By contrast, scientists acknowledge that ordered, predictable systems do exist, although they are not nearly as widespread as classical science had supposed. Feigenbaum, for example, takes as granted that only certain classes of iterative functions become chaotic. Moreover, he acknowledges that until very recently, virtually all sci- entific knowledge derived from the study of ordered systems (14-15). Where deconstructionists see an apocalyptic break with logocentrism, scientists are likely to think of their work as a continuation of what went before. To a deconstructionist, to say someone is a recuperator is a damning comment; for most scientists recuperation is not an issue, because they see their work as enhancing rather than discrediting traditional scientific paradigms. These differences are symptomatic of the different values the two disciplines place on chaos. For deconstructionists, chaos repudiates order; for scientists, chaos makes order possible These differences notwithstanding, Derridean deconstruction and nonlinear dynamics parallel each other in a number of ways. The new scientific paradigms challenge the primacy traditionally accorded to ordered systems; deconstructive theories expose the interrelation between traditional ideas of order and oppressive ideologies. The scientific theories show how deterministic physical systems become chaotic because initial conditions cannot be specified with infinite accuracy; deconstructive readings operate upon texts to reveal the indeterminacy that re-marks an absent origin. The scientific paradigms embody a shift of perspective away from the individual unit to recursive symmetries; deconstruction writes about the death of the subject and the replicating, self-similar processes that constitute individuals. The science of chaos reveals a territory that cannot be assimilated to either order or disorder; deconstruction detects a trace that cannot be assimilated to the binary oppositions it deconstructs. These correspondences are not accidental. They reflect what Christine Froula, in comparing deconstruction with quantum mechanics, has identified as a deepening crisis of representation in Western thought.l7 Froula suggests that common sources for quantum physics and Derridean deconstruction do exist. It may be that common sources also exist for chaos theory and deconstruction, most probably in information theory. However, I have chosen not to make an influence argument, because I believe that such arguments obscure the larger significance of the parallels outlined above. Let us suppose, for example, that I could identify a definitive source that would connect Derrida with chaos theory. This still would not explain why that source, among many possible ones, caught his attention. To explain this, I would have to postulate some prior source, for it must have sensitized him to the issues he found in the later source. But this prior source must also have had an earlier source to explain why it seemed significant.... If I attempt to trace an entire network of sources, then I have in effect moved from an influence to an argument about culture. In addition to the problem of infinite regress, influence arguments also suffer from a tendency to flatten the complexities of scientific inquiry. In practice, identifying an influence almost always means finding a scientific work that has influenced a literary text. The premise that influence flows from science to literature implicitly valorizes science as the source of truth to which literature responds. Such an approach ignores the ways in which scientific theories, no less than literary theories and literature, are social constructions that reflect the prevailing concerns of the culture. Science is not a monolithic"source," but a complex field of discursive and experimental activities that has its own dissonances, fault lines, and convergences. Let us agree, then, to leave the question of influence aside, and turn instead to the implications these isomorphisms have for literary study.In my view, the parallels between chaos theory and deconstruction signal more than the emergence of new paradigms. They point to a shift in the ground of representation itself, which is bound to have profound implications for literature.l8 In the space remaining, I sketch very quickly a few of the many possibilities for literary study by speculating on the significance of this shifting ground for reading individual texts, developing critical strategies, and postulating cultural theories. Reading Individual Texts The emergence of similar concerns across a wide variety of disciplines suggests that they run very deeply through the cultural matrix.There are many sites within the culture where one can read the inscription of these isomorphisms, including contemporary literature.For example, in Doris Lessing's The Golden Notebook, the concern with chaos is at once thematic, social, psychological, and specifically literary.l9 The fragmented form of the novel reflects the psychic fragmentation of the central character, Anna Wulf. Anna attempts to cope with her life by relegating its complexities to different note-books: a red notebook for her political experiences, black for her African experiences, blue for her personal life, yellow for the present.As each narrative becomes more unsettled--the British Communist party fragments over Stalin's atrocities, her lover abandons her, her best friend's child attempts suicide--Anna seeks desperately for someway to integrate the proliferating disorder into some kind of intelligible system. The crisis comes when she papers her apartment walls,as high as she can reach, with newspaper clippings about horrific events, rapes, murders, genocide, riots. Spending her days reading the clippings and putting up more, Anna is surrounded by chaos inside and out. From this nadir, she tries to rediscover herself as a writer, and the golden notebook--the narrative the novel turns into--comes into being. Central to Anna's emerging reorganization is her ability to recognize recursive symmetries among and between her different notebook narratives, while still validating their local variations. After she be-comes involved in a destructive relationship with a psychotic lover recognize the futility of her self-replicating assumptions. The final chapter repeats the text's opening lines but then develops in different directions. These almost-but-not-quite reflections suggest that chaos and order have come together in a union delicately balanced between schizophrenic disorder and sterile repetition. The Golden Notebook, then, is playing out in narrative form some of the same dialectical tensions that are embodied in the new paradigms. Of course I do not mean to imply by this that Lessing was influenced by chaos theory. Rather I am suggesting that the same forces within the culture that authorized chaos theory are inscribed within Lessing's narrative. Although I will not have time to discuss them here, other contemporary fictions where these inscriptions may be read include (to mention only a few) Calvino's If on a winter's night a traveler, DeLillo's White Noise, Robbe-Grillet's Jealousy, Coover's Pricksongs and Descants, Lem's Fiasco, and Robinson's Housekeeping. Developing Critical Strategies The emphasis on scale in the new paradigms speaks to a familiar phenomenon in literary studies the way a text may be perfectly coherent on one level, and yet on another level chaotic. For example, consider the scale-dependence of Derrida's deconstruction of Rousseau. Before Derrida there was widespread consensus about what Rousseau meant; yet the inversions that Derrida effects within Rousseau's text are virtually irrefutable. The new paradigms suggest these different views may be a function of the reader's critical distance from the text. From a certain distance the Confessions appears coherent; closer up (and Derrida's readings are typically very close), the ungrounded nature of the discourse appears. Closer still and the text becomes regulated again, as the systematic nature of the ungrounded oppositions appears; closer still, and it dissolves into the undecidability of the trace. The lingering assumption that propositions, if they are to be valid, must hold true for all critical distances from the text is challenged by the new paradigms. By revealing scale invariance as an assumption rather than a given, they help to bring into view similar assumptions within literary discourse. I can imagine a time when any statement about a text would have to be prefaced by an indication of the critical distances for which it holds true. Already under suspicion within the literary community, globalizing statements which purported to hold true for every level would be subjected to even more severe scrutiny than they now are. (The exception, of course, would be globalizing statements which took scale dependence as their subject.) One possibility for developing new critical strategies, then, is to attend to questions of scale and use them to think about how local sites are incorporated into textual systems. A second set of possibilities emerges from the redefined relation between order and chaos in the new paradigms. Here I shall mention the work of just one theorist to indicate very briefly how these ideas are being incorporated into literary discourse. William Paulson, in his study of information theory and literature, The Noise of Culture, argues that texts can be seen as self- organizing systems in Prigogine's sense.20 Paulson asks us to consider how we read a difficult poem. On a first reading there will be parts of the poem that do not seem to make sense--parts that we perceive as noise rather than information, disorder rather than order. Because we accept the poem as a functioning entity (that is, as a system), we reread it. Now our perceptions are different, for they have been slightly reorganized by the first reading. On the second reading, more elements are fit into what we begin to perceive as an emerging design. The point Paulson makes about this process is that it is because the system is initially perceived as disordered that a more complex kind of order can emerge. As the transvaluation of chaos becomes more extensive within the culture, there may well emerge still other kinds of theories that reenact this transvaluation in terms of reading and writing texts. Postulating Cultural Theories The new paradigms suggest that culture itself might be constituted as a complex system. Following this clue, we can think of the local as designating a site within a culture where the self-similarities characteristic of the system are reproduced. Conceived as images of each other, local and global are related as microcosm is to macrocosm, although each level also contains areas so complex that they are effectively chaotic. Movement between levels is easy or possible only when the symmetries align. At this point cultures are ripe for change, because they become extremely sensitive to microscopic perturbations. Such a view of the systemic behavior of a culture does not require that all configurations within it be self- similar. But when significant convergence does occur, the model predicts that small fluc- tuations will have large-scale effects. From the viewpoint of the cultural analyst, this model is attractive because it foregrounds self-similar replications, which are obviously easier to find and document than isolated instances. Moreover, because the system at this point is susceptible to dramatic and sudden changes, an exploration of the deep assumptions embodied in these configurations is likely to have significant explanatory power for ep- istemic shifts. The model gives us a way to understand how Foucault could be right in postulating a self-similar episteme for a given period, and still not commit us to saying that knowledge everywhere in this period was organized according to these tropes (because there are always random variations), nor to saying that culture always works like this. In other words, it gives us a way to say that the local and global sometimes reproduce each other so that universals appear to run through the system, and sometimes not. The model should be of especial interest to theorists working in the area of literature and science. One of the most problematic issues in the field at present--one that I have wrestled with repeatedly--is how to talk about isomorphic concepts between disciplines and yet do full justice to the distinct tonalities and values that these concepts have when they are embedded in different sites. The double gesture of recognizing global structures and yet valorizing local sites is in my view both necessary and inevitable. It speaks to postmodern culture; but beyond this, in a very real sense, it is postmodern culture. In conclusion, I wish to emphasize that I do not see the shifting ground explored in this essay as a uniform change throughout the culture. The accommodations, resistances, and convergences that occur between the scientific and literary paradigms indicate how fissured and multilayered the cultural response is to the transvaluation of chaos. Change arrives not as a monolithic unity, but as complex vortices of local turbulence. Not to see that the agitation is general is to miss the fact that there are significant changes in the underlying cultural currents; not to notice that the turbulence follows different dynamics at different sites is to miss the complexities that the new views of chaos both initiate and signify. NOTES 1. Edward Fredkin, quoted in Richard Wright, "The On-Off Universe," The Sciences (January-February 1985), 7. 2 The literature on these aspects of the information perspective is too extensive to cite here. Representative texts are Daniel Bell, The Coming of the Post-Industrial Society (New York, 1973), and Communication and Control in Society, ed. Klaus Drippendorff (New York, 1979). 3 Claude E. Shannon, "A Mathematical Theory of Communication," Bell System Technical Journal, 27 (1948), 379~23, 623-56. The papers are reprinted along with an interpretive commentary in Claude E. Shannon and Warren Weaver, The Mathematical Theory of Communication (Urbana, Ill., 1949). 4 Claude E. Shannon, "The Bandwagon," IEEE Transactions on Information Theory IT-2 (1956), 3. 5 James Gleick, Chaos: Making a New Science (New York, 1987), p. 68. 6 Mitchell Feigenbaum, "Universal Behavior in Nonlinear Systems," Los Alamos Science, 1 (1980), ~27; hereafter cited in text. 7 Robert Shaw, The Dripping Faucet as a Model Chaotic System (Santa Cruz, Calif., 1984). Niagara Falls would of course be an instance of turbulent flow; see, e.g., Kenneth Wilson, "The Renormalization Group and Critical Phenomena," Reviews of Modern Physics, 55 (1983), 583-600. 8 Benoit Mandelbrot, The Fractal Geometry of Nature (New York, 1983); hereafter cited in text. 9 Jean-Fran ois Lyotard, The Postmodern Condition: A Report on Knowledge, tr. Geoff Bennington and Brian Massumi (Minneapolis, 1984), p. 82. 10 In other sections of The Postmodern Condition Lyotard shows a keen awareness and sensitivity to the interrelations between culture and science. I suspect that Lyotard's valorization of these scientific paradigms as enemies of` totalitarianism derived from his desire to find a counterbalance to his foregoing argument (which in my view leads to quite other conclusions) and to close his book on an optimistic note. 1.l In this discussion I am indebted to lectures by Mitchell Feigenbaum and Benoit Mandelbrot at the Cornell University conference on "Analyzing the Inchoate," Ithaca N.Y., April 1987. 12 This procedure is discussed in M. F. Barnsley et al., "Solutions of an Inverse Problem f`or Fractals and Other Sets," Proceedings of the National Academy of Sciences, 83 (1986), 1975-77. 13 Michel Foucault, The Order of Things: An Archaeology of the Human Sciences (New York, 1970). 14 Paul de Man, "Shelley Disfigured," in Harold Bloom et al., Deconstruction and Criticism (New York, 1979), p. 69. 15 Geoffrey Hartman, "Monsieur Texte II: Epiphony in Echoland," Georgia Review 30 (1976), 183. 16 Jacques Derrida, Of Grammatology, tr. Gayatri Chakravorty Spivak (Baltimore 1976), pp. 141~4; hereafter cited in text. 17 Christine Froula, "Quantum Physics/Postmodern Metaphysics: The Nature of Jacques Derrida," Western Humanities Review, 39 (1985), pp. 287-313. 18 These implications are explored in depth in my book-in-progress, Chaos Bound: Orderly Disorder in Contemporary Literature and Science (forthcoming, 1989). 19 Doris Lessing, The Golden Notebook (New York, 1962). 20 William Paulson, The Noise of Culture: Literary Texts in a World of Information (Ithaca, 1988).