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Aesthetics and the Two Cultures:
Why Art and Science Should Be Allowed to Go Their Separate Ways James Elkins

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convinced that science has much to do with painting—or with art in general. This makes its relationship to aesthetics problematic insofar as people in the arts can have a very different sense of aesthetics from those working in scientific disciplines. From this point of view, any claim that there is an aesthetic understanding shared by art and science—a dimension that might be “rediscovered”—becomes especially problematic. Several times I have started and abandoned a book project with the title The Drunken Conversation of Science and Painting. The title is meant to conjure a comedy of errors and misunderstandings, and the drunkenness is to imply that the two sides have some infatuation with one another, which compels them to keep talking without really connecting or making too much sense. If there is any rediscovery of aesthetics in the discourses of science or art, it doesn’t seem to be enacted in recognizable ways. There is, in fact, an intermittent conversation about aesthetics going on between art and science—it takes the form of colloquia, sessions in conferences, scattered scholarly papers, and occasional books—but I would claim it’s a “drunken conversation” involving more or less drastic mutual misunderstandings of basic terms. I have elaborated this at length in an essay reprinted in Art History versus Aesthetics, so I won’t repeat it here.1 What I am aiming at here is a heuristic introduction to the possibility that art and science are disconnected because they do not share some crucial common terms, especially regarding aesthetics.
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There is what I will call a standard art–science narrative about the points of intersection between science and art. That narrative stresses the empiricism of the early Renaissance, the geometrization of vision in the fifteenth century, the nineteenth-century infatuation with color theories, and the twentieth-century exploration of computer-assisted painting. If science is taken in a more capacious sense, then painting can be said to have come close to science many times. There have been full histories written around the standard narrative, from Ernst Gombrich’s surveys of naturalism to John Gage’s studies of color theory and Martin Kemp’s books and his columns in Nature. But there are reasons to say that the standard narrative is not wholly convincing. The first argument in the Drunken Conversation of Science and Art was to have been that even though the main points of the standard narrative are true, they capture very little of what makes art significant for the majority of viewers. A second argument would be that the standard narrative overestimates the scientific content of the links that it finds. Art history’s disenchantment with science is inversely proportionate to the enchantment of some scientists with what they perceive as deep consonances between art and science. Those arguments should take place within aesthetics, because they turn on the idea that science and art share central values such as simplicity, elegance, harmony, and beauty. That argument, which I think should be called the aesthetic argument about science, can be found for example in Subrahmanyan Chandrasekhar’s book Truth and Beauty: Aesthetics and Motivations in Science, and in various popular treatments of the “art of science.”2 I’d like to register my dissatisfaction with the standard art-science narrative and the aesthetic argument about science. The bulk of this essay is a review of three case studies: art historical writing about linear perspective, the “science” in Georges Seurat’s La Grande Jatte; and the appearance of fractal geometry in some contemporary art. In each case I argue that science doesn’t appear in the art, or in the art history, and that by implication an aesthetic discourse can’t bridge them. I end with some comments on the curious fact that few art historians care very much about science. It is fair to say that interest in the theme of science and art is small within art history. Conversely, scientists who write about the science of art are sometimes happily oblivious of the low quality of the art they investigate. When I suggested to Sidney Perkowitz,

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author of an article called “Science and Art Are Closer Than You Think,” that most interesting art has little to do with science, he pointed me to his book Empire of Light: A History of Discovery in Science and Art—but few of the artists in it are taken seriously by critics, museums, or art historians. (He cites, for example, Kelly Houle, Mark Dagley, and Dale Eldred.3) I would like to come to a better understanding of why my colleagues who are interested in art-science connections and technologically informed art tend to be avoided by the plurality of the discipline and why digital painting and graphical (as opposed to political or contextual) Internet art is still an anathema to the serious art world. Of course the unpopularity of a subject has no bearing on its truth, but the lack of talk between the sides is significant for the intellectual life of the university as a whole.

Reasons to Be Skeptical of the Aesthetic Argument about Science
There is an enormous uncollected literature of the uses of terms like “beauty,” “elegance,” “concision,” “harmony,” and “balance” among scientists. It is uncollected, probably, because it is usually nearly contextless. For example, the photographer Felice Frankel, interviewed the astrophysicist Jeff Hester about the famous Hubble image of the Eagle Nebula, which he helped produce. In the course of the interview Hester says, in passing, “interestingly, the beauty of the image is not happenstance. When people talk about ‘beauty,’ they are talking about the presence of pattern in the midst of complexity.” Frankel, the interviewer, doesn’t question this, and I think it is a common enough definition among scientists. But I have never heard it among art theorists, critics, or historians, except when the subject is Rudolf Arnheim (who had theories of pictorial symmetry that lend themselves to such conclusions).4 Concerning the aesthetic argument for an art-science link, Leo Steinberg’s attack on scientists’ uses of aesthetic terms in his essay “Art and Science: Should They Be Yoked?” is exemplary. He reports on his experience at a conference of scientists. They were congratulating one another on sharing crucial concepts with art, especially an “involvement with the specific materiality of things,” “the emotion of delight,” and “elegance in composition.”5 Steinberg says that art’s relation to materiality has lately

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grown somewhat intractable because of conceptual art, and he suggests that the new art demands philosophical thinking, like Arthur Danto’s. He doubts that artists are interested mainly in elegance or delight, and to prove it he cites incidents of attacks on paintings and sculpture that had recently been documented by David Freedberg, in Power of Images. Essentially Steinberg asks if throwing acid on a painting, or striking a sculpture with a hammer, are evidence of delight. It is a brilliant move, using Freedberg’s sources in such an outlandish way, and it is devastating to the sanguine and abstract notion that art is essentially “elegant.” Words from aesthetic discourse such as “beauty,” “elegance,” simplicity,” “harmony,” “delight,” and “pleasure” often recur in scientists’ writings about the supposed common ground with art. The terms have different histories: “Pleasure” in this sense certainly comes from Immanuel Kant, while “harmony” and “delight” could be traced back to Renaissance humanists such as Alberti, Leonardo, Filarete, and Pomponius Gauricus. But as they are deployed by contemporary scientists, I think words like “beauty” and “delight” owe more to notions of art that were current at the fin de siècle: They have the hazy idealistic feel of art criticism at the time of the symbolists, Wilde, Pater, and Stokes. Steinberg’s criticisms could be sharpened by demonstrating that scientists are applying a late romantic, premodern aesthetic to art in general and that Steinberg and Freedberg’s interests in distinctly non-Kantian reactions are s more in tune with modern and postmodern art. Steinberg ends on an indecisive note, wondering if the whole issue might be argued the other way. I am less undecided than him. I don’t often see the work that is done by calling an equation “elegant”: it is more an acknowledgment of its succinctness or its fruitfulness, or the way it compresses notations, than it is a purpose or even a quantifiable property. On the other hand—and here I completely agree with Steinberg—I seldom hear artists talking about how elegant, fruitful, or even beautiful their work is. Certainly those words would sound strange, or insufficient, in an art critic’s mouth. I don’t think that aesthetic concepts like beauty, delight, and elegance really are the workable bridges between art and science. Those words are too unfocused, too vague and ethereal, too well intentioned, emotionally pallid, sentimentally idealistic, formal, and slippery to yoke anything I recognize as science to anything I think of as art.

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Arguments against the Standard Art-Science Narrative
I’ll consider four possible arguments, in no particular order. 1. Saying, as I did, that the standard art-science narrative does not link science to much of art—that it hits the high points but leaves the vast majority of art untouched—does not amount to an argument that the standard narrative is wrong. But it means it can only explain part of art even in the centuries and cultures it includes. From a scientific viewpoint it does not matter if a theory explains only a little of a given subject, except that it will be abandoned if a different theory explains more of the subject—and that has not happened with the standard narrative. 2. It is the case that artists prominent in the standard narrative tend to be minor in art historical accounts. There is the seventeenth-century painter Ludovico Cigoli, who knew Galilei Galileo and painted the mountains of the moon; or the French painter Henri Valenciennes, who studied clouds with great accuracy; or the Dutch painter Gerard Ter Borch, known since his revival as a master of silks and satins; or the contemporary artist Vija Celmins, who paints stars and galaxies in the style of painterly abstraction. If you were to read only introductory chemistry and crystallography texts, it would seem that the minor artist M. C. Escher is one of the century’s most important innovators, but he remains absent from art historical textbooks. The canon of scientifically interesting artists is a strange one, a fact that should be bothersome because the values that make the art worth studying to begin with are at odds with the values that proceed from inquiries that search for scientific content. 3. It’s also true that in the twentieth century in particular, artists have been more interested in the applications of science in technology, new media, and engineering than in science itself. The conceptual apparatus of hypothesis and experiment hardly figures in art, while the technological apparatus of machinery, engineering, architecture, and scientific schemata have been ubiquitous since the “machine aesthetic” first came to the attention of the surrealists in the 1920s. -1— 0— +1— 4. What appears as science in modern art in particular is actually popularized science. Pablo Picasso learned a little about relativity from a high school teacher. Cubism cannot be explained well in terms of

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relativity, and Picasso himself didn’t care: He used the bit of relativity he knew in a wilfully eccentric fashion. Popular science was a source for Odilon Redon, Max Ernst, René Magritte, Francis Picabia, and many others: But which artists made use of unpopularized science? The really exemplary scholarship of Linda Dalrymple Henderson shows this over and over: There is an intricate dialogue between modernism and science, but what appears as science is almost always popular science—or at least misunderstood, or reimagined science. The science in art, especially in the past two centuries, is simplified, misunderstood, or otherwise modified, and after a point it becomes counterintuitive to think of it as science at all. I take it as a starting point in this subject that science per se will not appear in art, because without the art it would only be science. The scientific content will therefore be embedded in a new matrix, one that will necessarily work against the scientific content as much as it enriches or otherwise alters it. At some point this should be troubling to people who study appearances of science in art, because it seems that what is being counted as scientific content is nothing more than remnants of scientific forms stripped of their content. Intentionally nonsensical uses of science are an exception, as in Marcel Duchamp’s inversions of scientific—but mainly technological—ideas. Many more artists take bits and pieces of science and put them together collage-fashion without attending to their original meanings. In sum: Western art has not obtained much of its meaning from science. To paraphrase T. J. Clark, science dines very poorly on the leavings of art.6 (He said it the other way around, but both are true.)

The Refraction of Perspective in Art History
I now turn to the less scientific and empirical aspects of this subject, and try to explain why art historians care so little for science, and I turn to the aesthetic argument. There are some large explanations available here, having to do with different educations, with the “two cultures,” as C. P. Snow defined them, and with the histories of disciplines. Some headway can be made by taking specific examples. I’ll consider two: the first has to do with the way that the mathematical discourse of linear perspective is deformed when it is imported into art history.

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Art historical texts that deal with perspective normally adopt one of two ways of working. Either they tend to be nontechnical and stress unquantitative qualities of the artworks or else they present themselves as technical papers, of interest to specialists in the history of perspective. Each subgenre has a typical methodology adapted to its public. In the first type, mathematical argument is avoided in favor of heuristic approaches couched in nontechnical language, normally peppered with perspective terms. Recent texts have taken perspective and its chief concepts in metaphoric and poetic senses, in part on the authority of the roots of perspective in ancient rhetoric; scholars have read symbolic, rhetorical, and expressive significance into mathematical terms such as “picture plane” and “axonometry.” There have been Lacanian and Husserlian readings of perspective and claims that epistemology itself is optimally modeled and to some extent prefigured in perspective. Perspective has been taken as a model of capitalism, of subjectivity, of the Kantian experience of space, and of the self-alienation of the philosophic subject. In the second type of writing, perspective’s terms are confined to nonallegorical meanings and the flow of the text itself may be interrupted by diagrams and formulas. The grafting of geometry onto humanist narrative can give such texts a consistent unresolved tension. In The Poetics of Perspective I conclude that perspective is an instance of the refraction between art history and a rigorous discourse it admires. Technical terms, dropped into what the classicist Wesley Trimpi calls “literary” writing (as opposed to “geometric” writing), have an unpolished, inharmonious relation to their surroundings.7 That contextlessness propels the terms, and the narratives that embed them, toward ever more unified, holistic connotations, and in extended texts individual terms such as “picture plane” can even become referents for “rigorous perspective” as a whole. Perspective thus enters art history not only as a loose, partly inconsistent collection of rhetorical redefinitions (as in Svetlana Alpers’s work) or as an ahistorical presence borrowed from mathematics, but also as a thing signified as a whole: Its individual meanings, proofs, injunctions, applications, technical procedures, specific history, and so forth—the range of its original meanings and uses—collapse into the flow of nontechnical, “literary” prose. When perspective terms act as an aggregate, they can buttress the persuasiveness of the text as a whole and create a certain scientific tone that can be used to underwrite broader conclusions—

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even if those conclusions aren’t really supported by the dazzling imported technical terms. The distance point, ground point, plane of projection, standpoint, measuring points, sociography, inverse perspective, reverse perspective, curvilinear perspectives, and the many rules for ellipses, ellipsoids, hyperbolae, and other exotic forms in perspective comprise a kind of homeless language that drifts, without adjudication, in the pages of art historical texts. The complexities of these transformations can give art historical texts on perspective a quality not often encountered in their perspectival originals: They can be effectively free of the possibility of clear refutation or confirmation. This is so because the technical glosses necessary to prepare their arguments for refutation or confirmation would be unwieldy. I cannot argue this fully here, because a demonstration would involve close readings of selected texts (e.g., Peter De Bolla’s Foucauldian analysis of the introductions to English perspective texts or Hubert Damisch’s Lacanian and Husserlian analysis of the città ideali paintings). What can be shown is that perspective in or as art history is disconnected from its geometric, mathematical, deductive original: It becomes, for better or worse, something new. Perspective is excerpted, the mathematics are removed, the actual constructions are deleted. “Perspective” in art history becomes incommensurate with its original.

The Grande Jatte Problem: What Is Science When It Is Immersed in Art?
Masaccio’s Trinità, as every textbook proclaims, is the first surviving painting in linear perspective. Does that mean, to draw the standard implication, that mathematics and painting were allied at that moment? Seurat’s La Grande Jatte was made with color theory in mind: But does that mean late nineteenth-century color theory and postimpressionism were linked? These aren’t straightforward questions, because on one level the answer is yes to both, but in another sense some violence is done to both color science and mathematics when they are said to be present in the paintings. It’s a longer argument than can be accommodated here; my example will be La Grande Jatte. Even after more than one hundred years, La Grande Jatte resists those who claim to see everything in it. The painting puts up formidable obstacles to any interpretation. To begin with, it is not always easy to

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know what Seurat knew: The most frequently cited sources for Seurat’s scientism are near-contemporaries Félix Fénéon and Paul Signac, and Seurat is not on record unambiguously agreeing with either one.8 In addition, Seurat was an uneven reader of science—some things he studied hard; others, off handedly, and there are examples of willful misunderstanding and selective reading. It is clear that he misunderstood a great deal, and some of the theorists he misunderstood were themselves mistaken.9 Assessing that kind of error involves studying twentieth-century color theory, which is itself a difficult subject. And aside from each of these problems, the painting itself seems unreliable, since its colors have faded unmeasurably and unevenly over time. Even so, these are only preliminary obstacles. They allow us to say—and this is the emerging consensus in recent scholarship—that Seurat was a poor scientist, confused even in comparison to the popular science writers of his day, so that La Grande Jatte is not, in this respect, “a definitive formulation of the technique, method, and theory of NeoImpressionism.”10 It may be true that Seurat’s “earnest convictions . . . provided both the justification and motivation for artistic projects more ambitious than he might otherwise have undertaken,” but that does not explain what the projects were.11 If pseudoscience was a catalyst to Seurat’s creation, what did it allow him to get on with? It needs to be said clearly that Seurat had no reason to paint any of the color effects he had been studying, because if they were accurate records of our subjective experience, they would be produced for us by any painting or natural scene. There is no reason to paint the world in dots in order to simulate the surfaces of the world, and there is no reason to paint simultaneous contrast, halos, iridescence or Mach bands, chiaroscuro, gradation, or any of the other phenomena since they would be reproduced in the act of perception. That is the fundamental stumbling block to calling Seurat “scientific,” and it is striking that Seurat himself copied a warning to this effect directly from Michel Eugenè Chevreul.12 Seurat read Chevreul fairly loosely, and it is at least possible that his interest in depicting simultaneous contrast was sparked by the fact that Chevreul had a large color illustration of it printed in his book.13 On the other hand Hermann von Helmholtz’s essay on painting and science, which Seurat apparently did not read, would have given him a reason to reproduce certain effects. When pigments cannot match the intensities of outdoor lighting, Helmholtz says, then painters might resort to subjective phenomena in

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order to remind viewers of the original conditions. But even if Seurat had seen that essay, it would not have any bearing on his project in La Grande Jatte, because the phenomena he studied are also effects of less intense illumination.14 Seurat’s “science” mixes empiricism and idealism in a manner that is at once specific and opaque to any single explanation: To adapt a phrase of Martin Kemp’s, it is neither science, pseudoscience, nonscience, nor nonsense. It is not entirely “specious in its theoretical formulation . . . applied with an indifference to any critical appraisal,” but neither is it “a definitive formulation of the technique, method, and theory of Neo-Impressionism.”15 The problem is initially a matter of finding out how Seurat conceived science, empiricism, logic, and self-consistency; but ultimately, the difficulty is finding any way to construct a responsible account of the picture. No matter which scientific theories we may decide to accept and which rules of application or irrelevancy we may adopt, the painting refuses to play along. La Grande Jatte is not an example of any theory, mistaken or otherwise. As we know from Seurat’s writings and from his friends, theory is what got his pictures started: He imagined theories as their underpinnings, their raisons d’être, and their necessary and sufficient explanations. But his imagining was flawed. Science and painting do not get along in the La Grande Jatte—they do not speak for one another, and they do not exemplify or signify one another. Their mutual disregard is uneven and sometimes—as in the “dots” that Joris-Karl Huysmans so brilliantly called “running fleas”—destructive. John Gage concluded that Seurat was indeed “scientific,” because of his “experimentalism,”16 and years before Robert Herbert had said the same thing. To Herbert, Seurat was scientific because he studied ephemeral phenomena of vision.17 “Science” in Herbert’s and Gage’s texts is an activity involving hypothesis, experiment, and falsification, and those are efficient and common characterizations of the scientific project. But two things stand in the way of enlisting Seurat’s painting as science, as thus defined. First it would have to be shown how La Grande Jatte is an instance of any experiment, or a consistent application of some coherent hypothesis. But then, even if La Grande Jatte embodies an experiment, it would have to be shown that the experiment had relevance to contemporary color science. To say his work is “experimentalist” is to say it borrows the idea of experiment from science, not that it is an example of a scientific

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experiment. It engages popular notions of science and translates them, unscientifically, into paint. There’s a certain anxiety here regarding painting’s inability to contain science. Why else should Seurat want to claim that his method demanded no manual skill? What else did he mean by saying his painting showed “the strictest application of scientific principles seen through a personality”? Why else might he have said that “they see poetry in what I have done. No, I apply my method and that is all there is to it”?18 To insist on the absence of affect is to protest too strongly and therefore to reveal an unease about the supposedly affectless “method.” “Painting” has to be done indirectly, by thinking only about “science,” but at the same time— and this is the “failure” of the painting and ultimately what makes it so interesting—science is ruined by painting, it cannot exist in painting, it dies in painting. Herbert supposes that this might have provided a kind of rationalist crutch—that the theory was a poorly built bridge from art to science. The painters wanted pure colors, Herbert proposes, and their theory helped them along with a bit of rationalism. It also helped the viewers, who could begin to read the canvases with the help of a theory.19 Alan Lee has echoed this in saying that the neo-impressionist movement needed to see itself as scientific in order to get underway.20 But there is more here than science, or theory, as springboard for invention: The science is woven into the work itself and into our experience of it. Science is stuck in La Grande Jatte like an insect in amber, preserved as the “flaw” that completes the work. I draw two conclusions from these examples. First, after a point—one that I think can hardly be defined—it ceases to make sense to refer to what happens in some artworks as science. The “science” becomes something weird, a dream or nightmare or collage or garbled mistranslation of science, but it isn’t science. The best way to understand what happens in a work like La Grande Jatte is to let the science go and think of its traces in the work as a kind of necessary fiction. Second, this is where art history comes in, because what matters is how Seurat and his contemporaries thought of what they were doing—how they came to believe that what they were doing was scientific or that it had “method.” It is profoundly unscientific to think in terms of groups of people, discourses, and conventions that lead people to believe certain things are true: But it is the only way to make contact with the reasons that La Grande Jatte or the Trinità are still central to what we think of as painting or art. Let me call this the

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Grande Jatte problem: To get at the science in art it is necessary to leave the science behind.

Chaos Theory and Painting
An analogous argument can be made about fractal geometry and chaos theory, kinds of physics and mathematics that are strongly visual. The swirling, “paisley” patterns and “biomorphs” that are familiar on calendars, postcards, and computer screens are drawn by the computer in the same way that a parabola or a circle is drawn by a geometry student— except that the calculations necessary for detailed fractal forms are beyond human capacity. Most of the attention in the technical literature is focused on the properties of the equations or on their applications. But neither the scientists nor the mathematicians are free of artistic purpose, and they alter and enhance the bare mathematics in order to make their printouts into aesthetically pleasing pictures. That artistic overlay is significant for a number of reasons: The scientists who create the images tend to have an unsteady grounding in the history of art, and they draw on nascent and uncognized aesthetics to choose and arrange their images. Writers in the humanities therefore experience the new geometry at a double remove, because they see the forms without their mathematical meanings and with an overlay of colors and compositions that are not dictated by the equations. Despite the growing literature, neither side sees the other very clearly. There are two “strange attractors” (a fractal geometry expression) involved in this conversation: One, the seductive world of art, aligned, as it seems to those outside it, with culture, meaning, and a host of ghostly values including elegance and beauty. The other, the forbidding world of mathematical physics, empowered so it seems to those outside it, with a wondrous new way of understanding the world. As in the two cases of perspective and nineteenth-century color theory, science and art are enamored of one another, and, like lovers in a comedy, they imagine the object of their attention somewhat unrealistically. Within mathematics, there is no question of the importance of the new discoveries. The “new geometry” knows itself to be fundamental: “Euclid,” Benoit Mandelbrot announces in The Fractal Geometry of Nature, will be “used in this work to denote all of standard geometry.”21 Interestingly this new geometry also knows itself to be beautiful and thus

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deliberately invokes an aesthetic reflection upon its products as if they were art (though the nature and extent of that knowledge are open to question). Mandelbrot quotes an article in Science that makes a parallel between cubism, atonal music, and modern mathematics beginning with “Cantor’s set theory and Peano’s space-filling curves.” He sees a rococo phase in mathematics before the modern era, followed by a visual austerity.22 When it comes to art, he makes a poorly articulated and unconvincing historical and aesthetic reading of his own fractal inventions, according to which the extravagant, ebullient forms he has visualized are “minimalist art”—a most unlikely identification.23 There is also an unwillingness on Mandelbrot’s part to mix art and science: When computer printouts are to be judged aesthetically, he gives them self-parodistic titles such as the “Computer Bug as Artist, Opus 1,” thereby publishing aesthetic results as mistakes, “bugs” in programs. Part of the meaning of such titles resides in Mandelbrot’s mimicry of contemporary painting styles; “Opus 2” is like an angular Clifford Still or Franz Kline. He also thinks his polychromic computer printouts are “austere.”24 The reason is they have simple mathematics behind them, and so his misidentification with minimalism is an example of nonvisual thinking—what a mathematician would call “analytic” rather than “synthetic” reasoning.25 Meanwhile, mathematicians such as Hans-Otto Peitgen “wrap” fractal images around spheres, so their computers can generate “moons” and fantasy spacescapes that are less like the tongue-in-cheek graffiti of Kenny Scharf than they are like the serious kitsch of the fin de siècle. Computer palettes continue to be set in psychedelic, hokey, holographic, iridescent, heavy metal combinations. (Colors are not part of the mathematical properties of fractals. They are chosen at will by the programmers.) The aesthetic values of the mathematicians are circumscribed by the domain of fantasy, especially medieval revival and late twentieth-century primitivism, and their formal strategies devolve from unacknowledged sources in German romanticism. They are anything but postmodern, though the artists that admire the new geometry often are.26 The art world certainly has not done much better in understanding what the mathematicians are saying. Discourse is marked by misuse of mathematical terminology, a love of catchwords, and the construction of more or less tenuous metaphorical bridges between the concerns of the humanities and the claims of the new geometry. The lexicon of this scienza nuova rhymes with terms already given us by post-structuralism:

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chaos theory, chaotic dynamics, fractal, fractoid, fractal dimension, rupture, elementary catastrophe, laminar flow, turbulence, irregularity, imbalance, iteration, self-similarity, spikes, dwell bands, connected sets, and a host of eponymous attractors (Rössler’s, Lorenz’s, Ueda’s), all resonate with figures already at use in contemporary visual theory and literary criticism. For example, Slavoj Žižek’s Looking Awry describes a swirling, wreathlike strange attractor as an “ ‘anamorphotically’ disfigured circle.” This usage takes anamorphosis (as in his title) and the misspelled word “anamorphotically” (the usual form is “anamorphically”) from Jacques Lacan’s description of the gaze and brings them into a context in which they have no mathematical meaning. Anamorphosis has resonance with other passages in Looking Awry, but it is interesting that Žižek does not find it necessary to remark either on the meaning of the new spelling or on the absence of any projection in chaotic dynamics that might give the term mathematical sense. This particular kind of ruptured context is often accompanied by “risky” homologies (the word is Žiž$ek’s), and in this case he draws a parallel between the opposition of normal and strange attractors and “the opposition between the balance toward which the pleasure principle strives and the Freudian Thing embodying enjoyment.”27 Both neologisms and “risky” homologies function by eliding scientific context. Both the mathematicians and the artists are agreed on one point: Fractal geometry might somehow be applied to painting (or to film or computer graphics) because it models natural forms so well. But even that notion may not be as straightforward as first assumed. On the surface, it is easy to see why some artists and computer graphics experts are intrigued by the potential uses of fractals. It’s not just that the new geometry looks like everything in nature from frost ferns to silver trees. It’s that it looks so much like older styles of Western and non-Western painting. In one place, its forms are virtual duplicates for rococo frills and swags. Other equations recall rocaille, Ohrmuschelwerk (cartouches in the form of ears), arabesques, and even paisley. And there are echoes of the intentional asymmetries of Alexander Cozens and John Constable, and the “leaf beauty” of John Ruskin. The meteorologist E. N. Lorenz, who helped found chaotic dynamics by discovering the first “strange attractor” in a simplified model of atmospheric circulation, has recently become interested in these associations.28 I visited him once in his lab at MIT, and he

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showed me printouts of strange attractors (systems of differential equations) in which tangled lines within larger tangles reminded him of a bird in a thorn bush (he labeled his printouts that way)—but such forms also speak of painting and bear an uncanny resemblance to some Chinese painting such as Chu Ta’s many versions of Bird and Rock.29 The metaphoric range appears unlimited within the domain of represented and real organic and inorganic growth. This apparently unlimited applicability may then be contrasted to the near-absence of geometric rules in modern painting. Modern art had long ago “overthrown” linear perspective, which was the traditional theoretical geometric accompaniment of artists’ organic improvisations. Postmodernism has long since forgotten that act of forgetting, and for several decades, except in the specialized case of geometric abstraction, painting has been without its traditional geometric foundation. Since chaotic dynamics and fractals are the first theories that purport to account for those nonlinear phenomena that were once taken to be ungeometric and beyond the reach of Euclid, they have the potential to be far more decisive in painting than linear perspective with its patently artificial rules could ever hope to be. Potentially the new geometry could ground every organic, asymmetric, complex form in painting in a way analogous to the way linear perspective stands behind the infinite, the isotropic, the mechanical, and the architectonic. In such a scenario the relation between painters and their geometry would also change: Artists could no longer escape the heritage of geometry by turning to organic forms like landscapes, and, conversely, it would no longer be as clear what would constitute a use or even acceptance of the new geometry, since fractals would presumably remain impractical for drawing (except by computer). There will be no book titled Elementary Lessons in Fractal Drawing. Mark Tansey has done several paintings with fractal themes. In one, surveyors attempt to measure a wild coastline. Their instruments are no match for their subject, especially since it is itself a gigantic version of a Julia set, one of the derivatives of the Mandelbrot set, a fundamental fractal form. The rocks pun into fractal “sea horses,” forming a progression of nearly but not perfectly identical forms. The lowest sea horse, the one behind the female surveyor at the right, epitomizes the new mysteriousness by sporting an implacable sphinx’s face; and beneath her hand smaller sea horse sphinxes curl away into an undefinable infinity. This is a new way for geometry to be with painting: Instead of being “in perspective” or

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“in” some other geometry, the painting is “about” geometry. Renaissance painters used perspective, but they didn’t draw pictures of perspective. The new approach is self-reflexive, but it is also problematic, since it is not an application in the sense that fractals seem to promise. I do not mean to promote sobriety, or to say that there is some ideal form of responsible communication between these scientists and these artists. Instead, I would like to suggest that we consider the meanings and the potential of our writing on the subject rather than continuing as if the new forms could simply be “applied” to the world or “imported” into art, or as if any metallic enhancement of a computer graph would make an acceptable picture. Equally it is hard to know what is inappropriate. The relation of perspective, the outgoing geometric standard, to this new source of geometry is problematic and unresolved. It is possible that the mathematicians’ dependence on fantasy art and decadent popular illustration might be close to contemporary art in ways that we do not yet appreciate. Nor does it necessarily make sense to emend the humanists’ use of scientific terms for distant rhetorical purposes, since that custom is well attested in the history of Western thought. The art world imbibes its science with some abandon, and scientists sidle up to art without knowing quite what to say. The various mistranslations may be evidence that the exchange between geometry and painting has not yet run its course. In particular, I would like to read the metaphorization of mathematics by the humanities, and the rewriting of visual history in mathematical terms, as legacies of the unresolved— unresolvable—traditions of linear perspective.

Conclusions
The cognitive scientist Ellen Winner’s essay, “Art History Can Trade Insights with the Sciences,” is an example of the kind of perplexity with which scientists note art historians’ lack of interest in science.30 Winner says, plausibly, that the only reason the claims advanced by the physicist Charles Falco are known in art history is because he teamed up with David Hockney and was prominent at the N.Y.U. conference in December 2001, at which art history was under “attack.” At the beginning of her essay, Winner lists seven reasons why art historians reject Falco’s claims about the use of optical aids by Renaissance artists, beginning with “artists did not need to ‘cheat’ because they were highly trained in drawing

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from observation,” and so forth. She notes that four of the seven do not rule out optical devices. She does not comment on the seventh reason: “the lens hypothesis . . . is of no interest to art historians.” Toward the end of the essay, she notes that Falco and Hockney “did not speak of the meaning or beauty of a work, issues that engage humanists. But why didn’t art historians think it important to learn how an artist created that work?” No answer appears in her essay. It is a crucial question, however, for the abyssal misunderstandings between art and science. Part of the answer is that few art historians think that it is promising that “neuroscience is moving into the study of the arts,” so that magnetic resonance imaging allow scientists “to track how the brain processes works of art.” Another part of the answer is that historians relativize truth to its contexts. For example, Winner shows that if an art historian like David Galenson argues that Picasso’s Women of Avignon is his best work, that shows he is the product of a certain history of the reception of Picasso, one that he partly orchestrated. Other histories—which are available—would have given Galenson different starting points.31 Still another part of the answer is that art historians don’t talk in terms of evidence, hypothesis, and conclusions—not always (though certainly often) because they are not “trained” in it. This occurs for a more systemic reason: They belong to a different writing tradition, the one Wesley Trimpi calls “literary.” Winner is right to keep calling on art historians to pay attention to science; but she misunderstands the reasons why most art historians will not answer, no matter what their educational background. It does not need to be laid at the door of education, as C. P. Snow did: It depends on a deeper division in Western discourse. Three insuperable problems and the result is a lurching incoherent conversation: The one we have had for the last hundred years and which shows no signs of sobering up.

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