Essence is infinity as the supersession of all distinctions, the pure movement of axial rotation, its self-repose being an absolutely restless infinity.
—G. W. F. Hegel, Phenomenology of Spirit, 1807
Everything is similar if you’re willing to look that far out of focus. I’d watch that. Then you’ll find that black is white. Look for differences! You’re looking for similarities again. That way lies mind rot.
—Marvin Minsky, The Media Lab, 1987
IN RECENT YEARS, CHAOS theory—that new science of nonlinear dynamic systems—has captured the popular imagination. Its computer-graphic representations appeal not only to mathematicians and natural scientists but also to visual artists and a broad segment of the lay public. Its widespread allure, I believe, seems closely related to its figuration of new, uniquely electronic modes of “being-in-the-world,” and to its particular responsiveness to the crises of contemporary life that have given rise to the consciousness often associated with the “cultural logic of postmodernism.”1 But chaos theory’s fans have tended to ignore certain crucial elements of its practice. First, the sciences of chaos are yet another historically specific manifestation of the logic that informs post-Modern cultural production—a logic based on paradox, recursivity, multiplicity, a simultaneous fetishizing and trivializing of difference, and a consequent homogenization of populations that are actually heterogeneous into a totalized “mass” culture. Second, advancing notions of “chaos,” “difference,” “nonlinearity,” and “dynamical systems,” while paradoxically constructing and mapping an ordered, homogeneous, deterministic, and esthetically harmonious “computer world” that denies the existential value of difference, chaos theory has little to do with the specificity of human embodiment and historical situation. And third, chaos theory and its computer modeling of idealized virtual worlds are an attempt to resolve the vertigo of a dizzying electronic culture in which earlier systems of spatial, temporal, and bodily orientation no longer seem adequate.
These three propositions about chaos theory and its visual models arise from the belief that life in post-Modern societies is both philosophically “Enframed” (to use a Heideggerian term2) and quite literally “main-framed” by electronic technology in general and computers in particular. We must acknowledge that the “interface” between humans and computers—involving activities of electronic representation, signification, and simulation—constitutes a new ontological mode of “being-in-the-world,” new fields of experience, and new models and meanings of both “world” and “being.” In a general discussion of electronic media, cultural theorist Bill Nichols tells us, “The micro-electronic chip draws us into a realm, a design for living, that fosters a fetishised relationship with the simulation as a new reality all its own based on the capacity to control, within the domain of the simulation, what had once eluded control beyond it.”3 Libidinally driven by the desire for control, this fetishized relationship with simulation is nowhere more visible than in the computer-graphic models of “reality” subsumed under the ordering principles of what is paradoxically called “chaos theory.”
Chaos theory stands both as a privileged, if problematic, conceptual metaphor for post-Modern electronic culture and as a lived reality within it. As Nichols points out, “Conceptual metaphors take on tangible embodiment through discursive practices and institutional apparatuses. Such practices give a metaphor historical weight and ideological power.”4 Thus it is not surprising that the practices and apparatuses that “tangibly” embody chaos theory currently enjoy the intensely vested interest of both scientists and the lay public alike. What begs further exploration is the “ontological relevance”5 of such popularity at this historical moment. What kind of “being-in-the-world” does chaos theory construct through its accommodation of infinite randomness within a deterministic system? What kind of spatiality, temporality, and embodiment are formulated by its computer-graphic discourses? What kind of subjectivity is posited by its models, and also by its romantic rhetoric of lone “misfits of science” finally achieving communion and community across disciplinary borders?6 And finally, just what is the cultural significance of a discourse that shows and tells us that “an eerie type of chaos can lurk just behind a facade of order—and yet, deep inside the chaos lurks an even eerier type of order”?7
First, some definitions of chaos are in order. (The pun here is certainly intended.) Since the rhetoric of chaos theory is central not only to its construction but also to our understanding of its metaphoric appeal, it is illuminating to cull these definitions from both the popular and the scientific literature that together celebrate this new field of study (and herald it in suggestive book titles). “Over the last decade,” the jacket of James Gleick’s Chaos: Making a New Science tells us, for example,
physicists, biologists, astronomers and economists have created a new way of understanding the growth of complexity in nature. This new science...offers a way of seeing order and pattern where formerly only the random, the erratic, the unpredictable—in short, the chaotic—had been observed . . . .The science of chaos cuts across traditional scientific disciplines, tying together unrelated kinds of wildness and irregularity: from the turbulence of weather to the complicated rhythms of the human heart, from the design of snowflakes to the whorls of windswept desert sands. Highly mathematical in origin, chaos nonetheless is a science of the everyday world, addressing questions that every child has wondered about: how clouds form, how smoke rises, how water eddies in a stream.
One notes in this description not only a paradoxical use of the term “chaos” to nominate “a way of seeing pattern and order,” but also a poetic celebration of the breakdown of boundaries that “discipline” orders of scientific enterprise, of the transformation of the abstractly mathematical and complex into the concretely natural and simple, and of childlike wonder at the world.
Simply put, chaos is a field of study founded on the discovery that three or more simple linear equations, repeatedly fed into a computer, produce dynamic nonlinear behavior that becomes increasingly complex, erratic, and random. Structures of extraordinary complexity unfold from the repetition of simple given rules—implying that from completely determinate systems emerge unpredictable and chaotic results. In The Beauty of Fractals: Images of Complex Dynamical Systems (a volume that is at once a mathematical treatise and a popular coffee-table picture book), H.-O. Peitgen and P. H. Richter describe the mathematical paradox that generates their fascinating computer images: “Causality holds at every single instant, but it does not carry over a sequence of branchings. Sooner or later the initial knowledge of the system becomes irrelevant.”8 Gleick puts it more colloquially: “Nonlinearity means that the act of playing the game has a way of changing the rules.”9
Studying a wide “range of phenomena exhibiting a sensitive dependence on initial conditions,” including “weather patterns, some neurological and cardiac activity, the stock market,”10 measles outbreaks, astronomical orbits, and even potential international crises involving the possibility of nuclear war,11 scientists across a range of disciplines describe chaos as “a kind of order without periodicity,” or an “apparently random recurrent behavior in a simple deterministic (clockwork-like) system.”12 The paradox in these definitions is amplified in two others. Joseph Ford, physicist and (as Gleick puts it) “self-proclaimed evangelist of chaos,” defines chaos theory as “dynamics freed at last from the shackles of order and predictability . . . .Systems liberated to randomly explore their every dynamical possibility . . . .Exciting variety, richness of choice, a cornucopia of opportunity.”13 But opposing this “Free at last! Free at last!” celebration is mathematician John Hubbard, who dislikes the very term “chaos” because it implies randomness. “To him,” Gleick says,“ . . . simple processes in nature could produce magnificent edifices of complexity without randomness. In nonlinearity and feedback lay all the necessary tools for encoding and then unfolding structures as rich as the human brain.”14
Thus, as Clifford Pickover suggests in Computers, Pattern, Chaos and Beauty: Graphics from an Unseen World (a mathematical guidebook for laypersons who want to play with chaos in the privacy of their own homes), “Although chaos often seems totally ‘random’ and unpredictable, it actually obeys strict mathematical rules that derive from equations that can be formulated and studied.”15 The behavior of these mathematical models when transformed into computer graphics has led scientists to conclude that a complex new geometry underlies the randomness of natural forms. Scott Bukatman captures the simultaneously contained and vertiginous recursivity of this new geometry: “The line traced by a coastline, for example, exhibits an identical complexity at all magnifications. The natural order is not composed of pristine Euclidean forms of trapezoid and ellipse, it is a corpus of intricate and infinite fragmentation. . . . Dimensions are discovered which actually lie between the dimensions of human experience: fractal dimensions.”16
The new geometry of chaos has a set of mathematical motifs that refer both to the dynamics of nonlinear iterative systems and to their visible representations in computer graphics. Four are of particular relevance here, not only because together they seem emblematic of the cultural logic of post-Modernity, but also because they are the dominant motifs of chaos—and the ones that most fascinate the public.
The first is the Butterfly Effect. Discovered through electronic computation and named by Massachusetts Institute of Technology meteorologist Edward Lorenz, it describes the process by which tiny instabilities and imprecisions in the finite description of initial conditions (in this case the weather) have vast and unpredictable consequences over time—hence the impossibility of long-range weather prediction. Mathematically modeled, this movement from order to randomness is nonetheless contained, patterned, and represented in computer graphics. Images of the finite structure of the infinity of chaos resemble two butterfly wings. The shapes suggest the source of the motif’s name, but it is possible that Lorenz also remembered science-fiction writer Ray Bradbury’s short story “A Sound of Thunder”—an appropriate allegory for the process Lorenz’s image describes. Bradbury’s 1954 story concerns a recreational time traveler to the primordial past who partially steps off the path prescribed for his group of tourists. This very small action seems to result only in the death of a butterfly—until he returns to his own time, when he finds that the butterfly’s death, magnified by the passage of aeons, has so altered the substance of his culture that he cannot even read street signs. In sum, the patterns of the Butterfly Effect dramatize how “minute changes in the input of a nonlinear system canlead to large differences in the output.”17
A second motif central to chaos theory is the Strange Attractor, another model that figures the transformation of regular, ordered trajectories of behavior into chaos while at the same time it contains their randomness in finite forms. Like several magnets set close enough together to compete in attracting iron filings, Strange Attractors exert a pull that creates unpredictable “turbulence.” As Peitgen and Richter put it, “We can think of centers—attractors—which compete for influence on the plane: an initial point . . . is driven by the process to one center or another, or it is on the boundary and cannot decide.”18 Nonetheless, these centers of multiple influence finally, and finitely. shape regions and boundaries within which the random and chaotic cannot escape into the uncontainable disorder that for chaos theory must be unnameable and unspeakable.
The third motif is the Julia set, a mathematical equation and a visible model of the boundary irregularities that result from nonlinear iterations. The “running” of Julia sets leads to the computer-graphic generation of endless tendrils and sea horse-like curls that represent the morphology of chaos and the boundaries where order and disorder entwine. “If we wander along the border” of these forms, “we notice a gradual metamorphosis. . . . At any given place, the motif is taken through an infinite number of variations.”19 Along with their esthetic appeal, models of Julia sets impress upon us the infinite irregularity and fragmentation of boundaries, the infinite differences that can emerge from a regulative sameness. Yet, as Peitgen and Richter go on to note, “The qualitative similarity of the forms is amazing,” and they further stress a constraint on all this difference: “There is one constant in the diversity of motifs in this morphology of Julia sets: the Mandelbrot set itself, which appears again and again in different sizes but always in the same form.”20
The Mandelbrot set, this fourth and most well-known motif of chaos theory, Gleick characterizes as “a way of seeing infinity.”21 Named for mathematician Benoit Mandelbrot, it stands as “a kind of public emblem for chaos, appearing on the glossy covers of conference brochures and engineering quarterlies, forming the centerpiece of an exhibit of computer art” that Peitgen and others took on the international circuit in the mid 1980s to introduce Mandelbrot’s “geometry of nature” to the general public.22 It is the recurrent structure of the Mandelbrot set that controls the Julia set’s infinite differences, appearing there constantly, at any magnification, to reveal sameness and order in chaos and to indicate a regulative geometry. The basic units of Mandelbrot’s model are “fractals” (for the “fractional dimensions” between integers), which mark and simulate irregular natural phenomena such as coastlines and landscapes, revealing that all of these boundaries become longer the finer the scale on which they are measured, and thus that “infinitely many paths lie in a finite space.”23 The result of Mandelbrot’s modeling of this natural irregularity, however, is his simultaneous modeling of its recursive self-similarity—that is, its euclidean symmetry across scale. Computer-graphic play with his equations generates not only gorgeously intricate designs but also self-similar patterns that repeat themselves over any scale, making it impossible to determine size by pattern. In essence, by this construction, the world “looks” the same at any magnification. Recuperating the specificity of infinite differences—repudiating chaos itself (as we used to think of it)—the Mandelbrot set dissolves the concept of origins and ends in an infinitely regressive and recursive display of self-similarity and order. Thus totalized within the “main frame” of the computer screen, the existential notion “frame” becomes meaningless in this modeling of the “natural” world—as do the relative values of “position” and “situation.” Describing fractal maps as representing “a kind of terminal vision,” Bukatman notes, “The scale of human perception and experience, already altered and augmented by telescope and microscope, no longer operates as an anchor for spatial exploration at all.”24
Indeed, perhaps the peculiar fascination of the images computer-generated by these mathematical motifs is a result of their uncoupling of human perception from the anchor of human scale, and from the spatial orientation that emerges out of the value-laden projection of a living corporeal subject into humanly habitable space. Scientists, artists, and the general public alike are compelled by the computer-graphic imagery of chaos. In its refusal to accommodate human bodily orientation they may find a strange liberation from the demands of humanly lived space and time, a dizzying yet exhilarating transcendence not only of physical ground but also of moral gravity.25
The most popular of the images are abstract color models of empirical scientific experiment and mathematical play—particularly the fractal designs inscribed by the Julia and Mandelbrot sets. These often evoke the mundane beauty of paisley prints, with their curved teardrop shapes, irregular tendrils, and intricate network of boundary relations among forms. Insofar as such images are usually presented multiply, however, through inserts or in varying levels of magnification that show a recursive and prospectively infinite self-similarity across scale, their beauty becomes peculiarly vertiginous and ecstatic—with this last word used not only in its current meanings but also in the original Greek sense of ekstasis: “a being put out of its place, distraction, astonishment, trance.”26 Bukatman has aptly described computer space, or “cyberspace,” as “terminal”—that is, as a paraspace, constituted at the computer, and as an absolute space, a space to end space as we humanly know and inhabit it. Yet he also suggests that terminal space, despite its apparently entropic and static qualities (“its vectored perfection, its spaceless space, its scaleless scale and its timeless time”), is nonetheless dynamic. His description might well account for the intense attention that abstract fractal images have generated: “The operative modality is not the absence of motion or circulation, but rather their passage beyond the threshold of human sense.”27 It is hardly surprising, then, that this kind of imagery should become almost mantric in its absolute presence, its totalizing containment of everything but no one, its “trajectory of implosion.”28
Recursive algorithms are also used, of course, to produce both “representational” simulations of “real” phenomena and imaginary landscapes and objects that bear uncanny likeness to their comparable “real world” counterparts. Whether images of a forest of trees or of the extraterrestrial mountainscape in A Vacation on Mars (one of Pickover’s simulations), of convoluted spiral seashells or of impossible forms given the perspectival treatment of realism, these simulations also have the characteristics of terminal space.29 The pictures always seem somehow hermetic—both literally and esthetically drained of atmosphere.30 They represent three-dimensional sites and objects in a superficially convincing way, they get the light, shadow, and texture of things uncannily “right,” but there is still something “wrong” with them. Almost all of these images, even most of the attempts at natural landscapes, look both impossibly real and really impossible. Despite or because of their detail and complexity, they lack existential vagueness, and seem, in their insistent exactitude and uncanny clarity, somehow schematic. Indeed these images might best be compared to photographs taken in outer space, where there is no atmosphere to soften the human gaze, and where human bodies can only survive with special suits and prostheses. Actually, these images are generated from outer space. They are real pictures, not of any humanly habitable scene, but rather of what science fiction writer William Gibson has called the “infinite datascape.”31 Their uncanny quality, I suggest, derives from the fascinating contradiction between their insistent existential cues and reference points and their refusal of human and embodied presence. Phenomenologically, these pictures are experienced as representations of “a fantastic realm within fractal dimensions, finally yielding an extended, but valid, reconception of the ‘real.’” 32
Crucial to both chaos theory and its imagery, of course, are the computers that make these visible models of what are, after all, mathematical equations and calculations. It follows that chaos theorists would adopt a reverent attitude to the new technology. Peitgen and Richter’s rhetoric is telling: “Computers—generally suspected of impressing total order and discipline on every facet of life—have made possible this better understanding of harmony and chaos.”“ The computer ”can present us with imaginary worlds, put us into artificial landscapes, and cause us to forget the real world. But used with some reflection, it can also help us lift the veil on nature’s secrets."34 Thus emerges an apotheosis of the electronic machine.
NOW WHAT OF THE relevance of these mathematical motifs and computer-generated models of chaos to the “cultural logic” of post-Modernism? Post-Modern culture is electronic culture, and the dependence of chaos theory upon electronic mediation is obvious. Slightly less so is its literally microelectronic “design for living,” which, as Nichols argues, promotes a fetishized relationship with simulation as constituting a virtual or parallel world capable of being controlled in ways impossible outside “the domain of the simulation.”35 The world modeled by chaos theory is constructed through computer graphics and electronic calculation, and is constituted as a total, contained, flattened, uninhabitable, absolute space—a “hyperspace” that Heidegger might have envisioned as a space of absolution, “a space in which the peculiar mystery will be revealed by which technology brings about the deprivation of meaning.”36 Why a deprivation of meaning? As philosopher Michael Heim suggests, “Through calculation, the ‘world’ becomes in principle a set of totally manageable resource materials for the exercise of the human will. By placing everything before the human will, world ceases to be truly ‘world’ in the existential sense of an appealing context of involvements that call the human forth into creative and responsive acts of living. Heidegger coins a name for this all-encompassing presentation of everything as manageable: ‘the Enframing.’”37 In post-Modern culture as in chaos theory, the computer enframes the world by making it absolutely available and manageable. What emerges is not merely a computer-graphic image but a philosophical picture of a “world” deprived of meaning. That is, it makes no existential sense.
What Heidegger deplored, Jean Baudrillard celebrates. The computer has muted our sense of existential uncertainty with a “private ‘telematics.’” “Each person sees himself at the controls of a hypothetical machine, isolated in a position of perfect and remote sovereignty, at an infinite distance from his universe of origin.”38 It is not surprising, then, that amid all the rhetoric about chaos theory’s modeling of the “real” and the “natural” world, one finds telling admissions of how absolute its sovereignty is, and how its virtual spaces and hermetic landscapes do make their calculating creators put aside the real world. Peitgen and Richter mention, somewhat offhandedly, that fractal representation is of “processes which are, of course, simplified idealizations of reality.”39 Elsewhere they note, “We have to admit that some things about the pictures are not natural. The infinite microscopic depth to which the self-similarity seems to reach is a mathematical construct that does not exist in the real world . . . . Therefore, the process. . . is not a proper description of the real world. But we did not assert that it was!”40 And yet the appeal of chaos theory is its modeling of a lie, its construction of a totally available world in which management, order, and enframing control the natural and the random even as they assert them. Certainly the scientific enterprise has always sought such control and management—but before the emergence of contemporary electronic culture, as Fredric Jameson notes, there never was such “a new and historically original penetration and colonization” of both “Nature and the Unconscious.”41
This article permits no more than a catalogue of certain primary themes and esthetic features that many cultural critics see as characteristic of post-Modern representation and that apply equally aptly to the models of chaos theory. I have already discussed the depthlessness and absoluteness of a “hyperspace” that has no orientational center and no gravitational pull on the human subject.42 Movement across this space is seen as superficial, and as aimlessly fulfilling plural, random, and nonlinear trajectories. Enframed as a discrete and terminal totality, hyperspace absorbs time, is apocalyptically and esthetically the “end” of time—and of narrative. Both all margin and all center, hyperspace disperses and decenters our attention equivalently across its surfaces and yet simultaneously concentrates and implodes our attention within its boundaries. It tends to conflate scale as well as to flatten depth; megastructures and microchips look the same. And finally, as Jameson points out, hyperspace is “radically anti-anthropomorphic” and “incompatible with the representation of the body.”43
Temporal features of post-Modern representation indicate an absorption of time by absolute space. This absolution of time, this freeing of time from its existential obligations, is not only the end of the existential world in an eschatological sense but also the End of History.44 Thus post-Modern temporality —terminal time—is itself absolute and is enacted as a “series of pure and unrelated presents.”45 Yet this temporality is not static; it is just not going anywhere. Filled with curious things, it is dynamized as the reproduction and recycling of singular events. Nonlinear, for it no longer plots the causal relations and trajectories of narrative, post-Modern temporality is primarily reflexive and recursive.
Post-Modernism reformulates subjectivity as what Bukatman calls “terminal identity”: “a new subjectivity constituted at the computer station or television screen.”46 Dynamic, but no longer anchored in a space that admits the human body or living in a time that yields critical value from action, this new subjectivity seems part cyborg, part artificial intelligence, disembodied at the same time that it is prosthetically enhanced by electronic technology. Terminal identity thus defies and is denied bodily and moral gravity. As Jameson remarks, this “liberation. . . from the older anomie of the centered subject” transforms the grounded interest and care we think of as emotion into “intensities” that “are free-floating and impersonal, and tend to be dominated by a peculiar kind of euphoria.”47 Living absolutely, terminally, produces an “undescribable vividness, a materiality of perception properly overwhelming, which...dramatizes the power of the material—or better still, the literal Signifier in isolation,” and “bears a mysterious charge of affect.”48 High technology produces a technological high, a technological sublime. At the computer terminal, the special affect of centered subjectivity is literally displaced and displayed as the decentered subjectification of special effects.
In this context, the four mathematical motifs so central to chaos theory model not the “nature” they assert, but rather the “culture” of which they are a part. Together they narrate a cosmological allegory of the paradoxes, anxieties, and euphoria that inform post-Modern existence. Enframing chaos, the Butterfly Effect denies causality, coherence, and ultimately responsibility for the effects of action. It suggests that every infinitesimal difference makes such a difference that, in the end, we can never choose and control the outcome of our descriptions and our actions. Indeed, while some enthusiasts see this modeling as “an operational way to . . . reconcile free will with determinism,”49 it is also a modeling of terminal helplessness, an embrace of irresponsibility in a world already beyond control. “What do you do if all you can predict is unpredictableness?” a scientist asked recently at a chaos conference.50 The answer is that you do nothing—or anything.
Strange Attractors are also cultural models, serving to allegorize the paradox of post-Modernity’s simultaneous concentration and decentralization of power. They visualize competing pulls on the interest and attention of phenomena, the multiple influences provoking the object (here, the post-Modern subject) to unpredictable movement on erratic trajectories. These decentered and multiple influences, however, are ultimately totalizing—containing the behavior and defining the boundaries beyond which it cannot go.
Julia and Mandelbrot sets—always found together—dramatize the deceptive way in which post-Modern culture’s privileging of difference also trivializes it beyond value. For just as the Julia set celebrates infinite irregularity and difference, the Mandelbrot set asserts their self-similarity across scale. Differences thus become equivalent; they make no difference. They may attract our curiosity, but in the great or small scale of things their weight is virtually nil. Unless, of course, you have a human body rather than a terminal identity, and actually have to negotiate the irregularities of a coastline in a habitable world at a particular historical moment.
What all these models have in common, what gives them their peculiar “aura,” is, I have suggested, their appeal to our particular contemporary consciousness and their rejection of our investment in our bodies. We can “free-float” among their kinetic manipulations ungrounded, intense but uninvolved. Choice and history are no longer our responsibility. Displayed and displaced at the terminus of Being, at the end of time, we are in the realm of the technological sublime—an available, managed, and en framed world where total order grants us absolute disclosure and moral absolution. Responding to the loss of personal control and value in a world of incomprehensible complexity and random information, the mathematical models of chaos theory dramatize narrative strategies in which chaos is enframed by order—or seems equivalent to it. Finally, then, in its computer-graphic modeling and rhetorical “accounting” of the world, chaos theory is not about chaos at all.
These impossibly utopian models of recuperation might be poignant were they not frightening—given a totalizing agenda whose “political unconscious”51 speaks to both fascist yearnings and a dangerous relativism. What is poignant, however, is the ironically regressive narrative that chaos theory tells about its own emergence as a “new science.” This narrative is hardly post-Modern, or even Modern. Rather, it is Romantic. Leafing through the popular literature, noting the scientists’ self-description, we find stories of lonely, brooding heroes working on the margins of their discipline, like Heathcliff walking the moors: “a few freethinkers working alone, unable to explain where they are heading.”52 Eventually these “misfits of science” find one another. Having suffered the constraints of disciplinary specialization, they form a new specialty that fulfills a utopian desire for communion, or for wholeness, unity, and harmony. Then, while pursuing “objective” and “purely scientific” research, they rhetorically assert the unity of science and esthetics in a paean to nature and experience that evokes the sensibility of the Romantic poets. Chaos theory is called a “poetry of systems,” and Peitgen and Richter’s Beauty of Fractals begins, “Science and art: Two complementary ways of experiencing the natural world. . . . We have become accustomed to seeing them as opposite poles, yet don’t they depend on one another?”53 Also, while the scientific focus is presumably on chaos, subjective value is placed on harmony. An exhibit of fractal imagery was titled “Harmonie in Chaos and Kosmos.” And we are told of the images, “The chaotic component shown in the very fine structures does not overpower the whole work; there are large areas of order, sustained by regularity, and chaos and order appear to be joined in harmonious balance.”54
In accord with the romantic sensibility, nature is invoked. This is at a far remove from the esthetics of a mathematician like Bertrand Russell, who, in Mysticism and Logic, said, “Mathematics, rightly viewed, possess not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture.”55 Mandelbrot offers his “geometry of nature” as a response to mathematicians who “have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.”56 And despite the virtual space, hyperreality, and antianthropomorphism of computer modeling, one physicist tells us, “The revolution in chaos applies to the universe we see and touch, to objects at human scale. Everyday experience and real pictures of the world have become legitimate targets for inquiry.”57 Wonder also plays a large role in the narrative: wonder at the paradox that self-similarity and repetition lead to difference and unpredictability, that simplicity breeds complexity. And with wonder there is a romantic privileging of the intuitive and the irrational. Of an equation playing itself into “wondrous” design, Gleick reports that “the irrational fertilized the rational.”58 Wordsworthian poetry emerges: “When scientists saw what computers had to show, it seemed like a face they had been seeing everywhere, in the music of turbulent flows or in clouds scattered like veils across the sky. Nature was constrained. Disorder was channeled.”59
Despite this “channeling” of disorder, a belief in and reverence for the ineffability of the complex and dynamic is evident. (Again and again, the word “beyond” appears in the titles of presentations, exhibitions, and individual works of fractal imagery.) But the final triumph, the greatest joy, of these poets manqué is their ability to make the ineffable visible by means of the computer. Computer graphics enframe the invisible as not merely transcendent but absolutely transcendent. Aptly, a hallelujah chorus ends the narrative. “In a computer experiment,” one writer tells us, “data flowed like wine from a magic chalice.”60 And Peitgen and Richter sing out, “The mathematical and physical insights on which these pictures are based. . . will again revolutionize our scientific view of the universe. Our cathedral will be completely transformed; it will lose its gothic coolness and take on baroque features!”61
The rhetoric of chaos theory stands as an articulation both of the “free-floating,” valueless “intensities” that characterize the post-Modern, technological “sublime” experienced at the computer terminal, and of the romantic yearning for grounded value and “natural” affect denied to terminal identity. What is so compelling and “uncanny” about chaos theory’s enterprise is not only its hermetic vision of a world absolved of human existence, but also the “ghost in the machine”—the excluded human being and body. Thus this romantic discourse on the other side of the computer screen. Thus this attempt at a utopian “projection or transmission into the ‘infinite datascape’” of chaos’ models, into the “terminal space” that Bukatman notes has become “a legitimate part of human (or post-human) experience.”62 Disembodied at the computer terminal yet culturally en-framed by its technology, the ghost in the machine haunts this “new arena of human action and control through the practice of a new, fictional vision.”63
Chaos theory, then, has profoundly altered the logic of the dominant scientific paradigms—or, as one psychiatrist and academic puts it, “What it . . . has changed in me is the way I think. I have lost sleep, lost grants, been accused of losing sanity, all driven by the absolute intuitive knowledge that this is the new way of looking at the universe!”64 This is chaos theory as the fictional vision of science: obsessional and totalizing. In a more local way, however, this new paradigm does have “real” and “human” applications. Paradoxically (given its computer-graphic exclusion of embodied being), many of the most practical have been in the areas of neurobiological disorders and heart disease. A neurobiologist tells us, “Everybody used to search for equilibrium, but now we understand that biological systems don’t go to equilibrium until they die and cease to exist.”65 And a cardiac specialist (who also calls himself a “fractologist”) says, “A healthy heart dances to fractal time.”66 Also, chaos theory has been heuristic outside the sciences, generating, inspiring, or confirming a new spatiotemporal esthetic in artistic practice. On the one hand it has influenced popular filmmaking, having informed and figured in such films as the “Star Wars” and “Star Trek” series. On the other, it has influenced more singular (and in some cases critical) artistic practice—as seen, for example, in last year’s exhibition “Strange Attractors: Signs of Chaos” at the New Museum, New York, which showcased the work of the Wooster Group, James Welling, Carter Hodgkin, and Bill Levine, among others.67 Considering the cultural implications of chaos theory’s impact on the arts, however, curator Laura Trippi is appropriately as cautious as she is celebratory: “If the new science offers a set of seeing-eye tools for transiting to an unimagined form of collective subjective experience, the question concerning technology remains one of who is absorbing whom.”68
As Martin Meisel notes, “Chaos appears in two modes: It can be imagined as a condition of unlimited plurality and diversity, or it can be imagined as a condition of extreme simplicity and undifferentiation to the point of sameness.”69 Chaos also appears in two experiential realms. One is the terminal space, the virtual reality, constructed at the computer screen by the absolute Being that is nobody; the other is the inhabited and invested space, the intentional reality, constructed in the phenomenological world by finite beings who are living bodies. Thus Trippi’s summary question—“the question concerning technology”—returns us to Heidegger and his critique of calculative thinking, of an en-framing that totalizes the world as available, manageable, absolutely enclosed and disclosed. Given that chaos theory is articulated in two modes and influences two realms of experience, and given that we are culturally immersed in both, it is vital that a dialectic of absorption—and incorporation—confront the confusions of our present “interface.” Happily, in fact if not in theory, it is impossible to contain totally the “unlimited plurality and diversity” of chaos in virtual computer-graphic space. Indeed the existential applications of chaos theory tell us what we already know but should never forget: there is no transcendence, no absolution here—outside the computer screen and in the world—where scale matters, where the body is.
Vivian Sobchack is Director of the Arts and a professor of film studies at the University of California, Santa Cruz. Her next book, The Address of the Eye: A Phenomenology of Film Experience, is to be published by Princeton University Press.
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NOTES
1. Although there are various and competing “versions” of post-Modernism, Fredric Jameson has usefully defined the term as characterizing not merely a set of esthetic features and/or hermeneutic strategies but the particular “cultural logic” that informs them. For Jameson’s initial articulation, see “Postmodernism, or the Cultural Logic of Late Capitalism,” New Left Review no. 146, London, July–August 1984, pp. 53–94.
2. Martin Heidegger, “The Question Concerning Technology,” Martin Heidegger: Basic Writings, ed. David F. Krell, New York: Harper & Row, 1977, p. 301.
3. Bill Nichols, “The Work of Culture in the Age of Cybernetic Systems,” Screen 29 no. I, London, Winter 1988, p. 33.
4. Ibid., p. 38.
5. This term is borrowed from Michael Heim, Electric Language, A Philosophical Study of Word Processing, New Haven and London: Yale University Press, 1987, p. 28: “By ontological relevance I mean the mode in which realities come to be conceived as publicly identifiable and intelligible. . . . The question of ontological relevance is not the same as sociological or psychosocial or anthropological questions about the way a specific group of empirically given persons have come to experience themselves and have come to think about themselves as they become accustomed to using a middle-class, electrical appliance. The philosophical question is instead the question about the way all contemporary contact with reality—including the -ologies of sociology, psychology, and anthropology—is affected by the new writing technology.”
6. Misfits of Science is actually the name of a 1986 science-fiction comedy film about the formation of community across disciplinary boundaries. Reading the plot synopsis clearly suggests contemporary allegory: “The ringleader of a group of individuals possessing unique abilities . . . rallies them together to combine their powers of mind control, cryogenics, electric energy, and size manipulation to save the world from a terrible neutron cannon developed by the government.”Mick Martin & Marsha Porter, Video Movie Guide 1988, New York: Ballantine Books, 1987, p. 1078.
7. Douglas Hofstadter, quoted on the book jacket of James Gleick, Chaos: Making a New Science, New York: Viking Penguin, 1987.
8. H.-O. Peitgen and P. H. Richter, The Beauty of Fractals: Images of Complex Dynamical Systems, Berlin and New York: Springer Verlag, 1986, p. 2.
9. Gleick, p. 24.
10. Clifford A. Pickover, Computers, Pattern, Chaos and Beauty: Graphics from an Unseen World, New York: St. Martin’s Press, 1990, p. 141.
11. Charles Petit, “The ‘Chaos Theory’ Shows a World as Unpredictable as Ever,” San Francisco Chronicle, 18 January 1989, p. A18.
12. Hao Bai-Lin and H. Bruce Stewart, quoted in Gleick, p. 306.
13. Joseph Ford, ibid.
14. Gleick, pp. 306–7. Italics mine.
15. Pickover, p. 141.
16. Scott Bukatman, “The Cybernetic (City) State: Terminal Space Becomes Phenomenal,” Journal of the Fantastic in the Arts 2 no. 2, Syracuse, Summer 1989, p. 55.
17. Pickover, p. 141.
18. Peitgen and Richter, p. 8.
19. Ibid., p. 17.
20. Ibid. Italics mine.
21. Gleick, p. 98.
22. Ibid., p. 221.
23. Ibid., p. 140.
24. Bukatman, p. 56.
25. I have made this point elsewhere in my work. See “Postfuturism,” chapter 4 in my Screening Space: The American Science Fiction Film, New York: Ungar, 1987, and “The Scene of the Screen: Towards a Phenomenology of Cinematic and Electronic Presence,” in Materialität der Kommunikation, ed. H. U. Gumbrecht and K. L. Pfeiffer, Frankfurt, Suhrkamp Verlag, 1988, pp. 416-28 (forthcoming in English in Post Script, Jacksonville, Fla.)
26. Webster’s New World Dictionary of the American Language, College Edition, New York: The World Publishing Company, 1966, p. 459.
27. Bukatman, p. 45.
28. Ibid.
29. See Pickover, the color plates and descriptive listings in appendix A, pp. 319–21.
30. Here it is worth emphasizing the Greek derivation and meanings of “hermetic”: “1. . . . of or derived from Hermes Trismegistus and his lore; hence, 2. magical; alchemical. 3. [from use in alchemy), completely sealed by fusion, soldering, etc. so as to keep air or gas from getting in or out; airtight.” Webster’s, p. 680.
31. William Gibson, Neuromancer, New York: Ace Books, 1984, p. 261.
32. Bukatman, p. 55.
33. Peitgen and Richter, p. 180.
34. Ibid., p. 3.
35. Nichols also distinguishes post-Modernism from the residual logics of realism and Modernism in relation to their economic modes, temporal foci, and subtexts. He links realism with entrepreneurial/industrial capitalism, with a temporal focus on reproducible instances, and with a subtext of possession. Modernism is informed by monopoly capitalism, by a temporal mode of ubiquitous occurrences, and by a subtext of mediation. Post-Modernism emerges with multinational capitalism, has a temporal mode focused on processes of absorption and feedback, and a subtext of control (p. 27).
36. Steve Rugare, “The Poetics of Real Estate,” Qualifying Essay, History of Consciousness Graduate Program, University of California, Santa Cruz, March 1988.
37. Heim, p. 80.
38. Jean Baudrillard, “The Ecstasy of Communication,” in Hal Foster, ed., The Anti-Aesthetic: Essays on Postmodern Culture, Port Townsend, Wash.: Bay Press, 1983, p. 128.
39. Peitgen and Richter, p. 5. Italics mine.
40. Ibid., p. 18.
41. Jameson, p. 78.
42. A fuller accounting of the characteristics of post-Modem space, lime, and subjectivity can be found not only in Jameson but also in chapter 4 of my Screening Space.
43. Jameson, p. 76.
44. I am indebted for this formulation to Rugare on the philosophical implications of monumental architecture.
45. Jameson, p. 72.
46. Bukatman, “Terminal Identity: Image and Subjectivity in Postmodern Science Fiction.” Unpublished manuscript.
47. Jameson, p. 64.
48. Ibid., p. 73.
49. Gleick, p. 251.
50. Alvin M. Saperstein, quoted in Petit.
51. The reference here is a concept central to Jameson’s The Political Unconscious: Narrative as a Socially Symbolic Act, Ithaca: Cornell University Press, 1981: the understanding that “there is nothing that is not social and historical—indeed, that everything is ‘in the last analysis’ political,” and that all cultural artifacts are constituted as “socially symbolic acts” (p. 20).
52. Gleick, p. 37.
53. Peitgen and Richter, p. 1.
54. Ibid., p. 179.
55. Bertrand Russell, quoted in Pickover, p. 173.
56. Peitgen and Richter, p. v.
57. Gleick, p. 6.
58. Ibid., p. 223.
59. Ibid., p. 152.
60. Ibid., p. 210.
61. Peitgen and Richter, p. 175.
62. Bukatman, p. 60.
63. Ibid. Italics mine.
64. Arnold Mandell, quoted in Laurie Garrett, “Life Is Chaos,” Newsday, 7 March 1989, p. III:1.
65. Walter Freeman, quoted in ibid.
66. Dr. Ary Goldberger, quoted in ibid.
67. Strange Attractors: Signs of Chaos, exhibition catalogue, New York: The New Museum of Contemporary Art, 1989. The catalogue also has some excellent commentary relevant to the issues explored above.
68. Laura Trippi, “Fractured Fairy Tales, Chaotic Regimes,” in ibid., n.p.
69. Martin Meisel, “Chaos Déjà-Vu,” in ibid., n.p.
