chaos theory literary theory

Modern Language Studies

Chaos Theory, Control Theory, and Literary Theory or: A Story of Three ButterfliesAuthor(s): Patrick BradyReviewed work(s):Source: Modern Language Studies, Vol. 20, No. 4, Literature and Science (Autumn, 1990), pp.65-79Published by: Modern Language StudiesStable URL: http://www.jstor.org/stable/3195061 .Accessed: 03/02/2013 06:20

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Chaos Theory, Control Theory, and Literary Theory or: A Story of Three Butterflies

Patrick Brady

"The true revolutionaries are those researchers who are engaged in fields where the mathematical models do not work so well, or maybe do not exist at all, and who are using the ideas of chaos to explain things that standard science cannot."

-Robert Pool, in Science, vol. 245 (7 July 1989) Chaos theory is about (dis-)order, a mode or degree of (dis-)

organization: it is about how or how much things are, or are not, organized-not about what is thus organized (let alone why). Control theory is about why-about the drive to order, to organize. Central to both theories is the issue of predictability. Chaos theory seeks to measure and describe; control theory seeks to derive and explain. In other words, chaos theory is phenotypical, while control theory is genotypical. Chaos theory, then, like structuralism, is a mode of formalism,' dealing less with content than with formal arrangement; as a result, it lends itself naturally to investigation in a variety of different disciplines, as structuralism did. Like structuralism, it holds out the prospect of renewing and radicalizing a whole spectrum of fields of research. Control theory likewise suggests ways of correcting and moving beyond certain positions adopted by Freud, Derrida, and others.

The aim of the present essay is to indicate the basic principles of chaos theory and control theory and then to verify their applicability and usefulness to the humanities, particularly literary theory and criticism,2 which have been languishing since structuralism degenerated into deconstructionism, and the history and philosophy of culture.3

In the early 1960s, several men carried out innovative research that led to chaos theory. One was Ren6 Thom, who developed a new branch of topology he called "catastrophe theory," which was devoted to the description and analysis, and ultimately the prediction, of processes which are abrupt or discontinuous. "The behaviour of continuous processes can be understood by using calculus, invented by Isaac Newton and Gottfried Leibniz three hundred years ago. But there has never been an equally effective form of mathematics for explaining and predicting the occurrence of discontinuous phenomena."4 Catastrophe theory was hailed as "an 'intellectual revolution' in mathematics-the most important development since calculus."5

A major feature of catastrophy theory is the use of "pictures": "What Rene Thom has done is to prove that, despite the almost limitless number of discontinuous phenomena that can exist in all branches of science, there are only a certain number of different 'pictures' or elementary catastrophes that actually occur."6

In 1977 I adumbrated the application of Thom's new perspective to the problem of reconciling Michel Foucault's epistemes, which are static, with history, which is dynamic. Thom's work suggested that the

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cultural-historical ruptures or coupures postulated by Foucault were not really "arbitrary" but merely extremely complex.'

Other scholars working along similar lines in the early 1960s included the mathematicians Edward Lorenz, Benoit Mandelbrot, and Stephen Smale, whose research is referred to not as "catastrophe theory" but as "chaos theory"--widely publicized by James Gleick's volume entitled Chaos: Making a New Science.8 This volume makes no mention of catastrophe theory, nor of Rene Thom nor his disciples Christopher Zeeman and Alexander Woodcock. Nor does it mention any of the participants in the Stanford symposium on "disorder theory" (1981)--not even Ilya Prigogine, although this Nobel Prize winner in chemistry is a leading contributor to chaos theory, even if not one of the aforementioned pioneers.9

For some, chaos "offers a way of seeing order and pattern where formerly only the random, the erratic, the unpredictable-in short, the chaotic-had been observed,""' as in the ordered pattern produced by random throwing of a die;" for others, it emphasizes that behind hidden order there exists a state of disorder, as in the pathological orderliness of certain emotionally disturbed families.'2 Joe Ford espouses the dictionary definition of "chaos," as "a state of things in which chance is supreme";'3 this looks suspiciously like "unconstrained randomness," which is precisely what chaos is not for other chaos specialists. If both views are right, the message seems to be that appearances of order or disorder often conceal their contrary; as Douglas Hofstadter puts it, "it turns out 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."'4 Such a spiral of order/disorder/order is formally reminiscent (especially if it is conceived of as open-ended) of the structures within structures posited by Levi-Strauss and Piaget.15 Chaos theorists' apparent contradictions (hidden order versus hidden disorder; predictability versus unpredictability) may result from their concentrating on different phases or aspects of the topic-like several blind scholars feeling different parts of an elephant.

A further problem arises from the following: we may sometimes have the impression that we perceive reality as totally disordered, but actually our faculties of perception are such that they impose order on reality in the course of perceiving it.16 Consequently, an impression of disorder may merely reflect some sort of overload of those faculties of perception; and the degree of order actually present independently of our perception remains problematic, unknowable.

Just as catastrophe theory was hailed as revolutionary--the most important development since calculus-chaos theory is claimed to be as radical a break-through as relativity theory and quantum mechanics, all three being revisions of Newtonian physics: "Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predictability."'7

Chaos theory has affected not only mathematics but also such sciences as physics, meteorology, astronomy, and chemistry, plus disciplines like medicine and economics.'8 66


I Chaos Theory and the Sciences, "Hard" and "Soft" Henri Poincar6 "was the first to understand the possibility of chaos

[and] unpredictability" (G1.46). He noted the intermittent character of the energy picture of a shaken fluid; this intermittence would now be termed "fractal" (G1.123). Poincar6 also enunciated in Science and Method an early formulation of profound significance: "It may happen that small differences in the initial conditions produce very great ones in the final phenomena. ... Prediction becomes impossible .. ." (G1.321). This (hyper-)sensitive dependence on initial conditions has now become known as the Butterfly Effect.

Poincare's disciple George Birkhoff had among his students at M.I.T. a certain Edward Lorenz. Working on weather prediction in 1961, Lorenz accidentally rediscovered the Butterfly Effect; and because a slight variation in the weather pattern could produce a great distortion (non-linearity, chaos), he concluded that long-range forecasting was impossible. It is arguable, however, that the Butterfly Effect does not- cannot-prove that long-range forecasting is doomed, merely that it cannot be carried out in the present state of our technology, and therefore it is, for all practical purposes, (as good as) "impossible."'9 In any case, Lorenz then went further: in his weather model, rather than mere randomness he saw "a fine geometrical structure, order masquerading as randomness" (G1.22). Lorenz devised a water-wheel whose rotations, when mapped, "traced a strange, distinctive shape, a kind of double spiral in three dimensions, like a butterfly with its two wings. The shape signaled pure disorder, since no point or pattern of points ever recurred. Yet it also signaled a new kind of order" (G1.30). This type of graphic represents an "attractor," and this particular one, which we may call the Butterfly Attractor, is representative of a new category of attractor known as "strange attractors," which is specifically associated with chaos theory.

Benoit Mandelbrot studied several years of cotton price data, which had been presumed to move in a manner that was random and unpredictable in the short term, orderly in the long term. However, he discovered that price movements for daily changes and those for monthly changes matched perfectly: they produced curves that were symmetrical from scale to scale. As Gleick reports, "the degree of variation has remained constant over a tumultuous sixty-year period that saw two World Wars and a depression. Within the most disorderly reams of data lived an unexpected kind of order" (G1.86). Such an irregular phenomenon or datum that remained constant from scale to scale Mandelbrot called a "fractal." His studies of irregular patterns in natural processes (cotton prices, river floods) revealed a fractal or self-similar quality.

Poincare in 1892 disproved Newton's clockwork conception of the universe, based on calculus, with everything knowable and predictable, and opened the way to chaos-complexity, uncertainty, non-linearity (last-straw effect), unpredictability (i.e., not predictable by Newton's calculus). Contemporary astronomy builds on his intuitions. Thus many bodies of the solar system have chaotic orbits, according to M.I.T. astronomer Jack Wisdom. A more particular application of chaos in astronomy: Jupiter's Great Red Spot defied analysis and comprehension

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until, in the early 1980s, Philip Marcus created a model based on computer-generated images, which he assembled into an animated movie. This movie turned out to produce the appearance of an oval very similar to the Great Red Spot-an island of relative stability in the midst of chaotic turmoil. In chemistry, chaos theory is represented by such phenomena as the oscillations of the Belousov-Zhabotinski reaction20 and by the dissipative structures of Ilya Prigogine.21

From a structuralist point of view, the human brain and that projection of its functioning that we term the mind are prisoners of their own structure (or physiological organization), so that random activity is impossible. This introduces a significant distinction between sciences such as those we have just glanced at (physics, meteorology, astronomy, chemistry) and disciplines whose object is the human body (medicine) and human behavior either in general (psychology) or in particular circumstances (economics), the arts being of course allied to the latter.

In the human body, specialists have looked at several organs: 1. the lungs: order is normal, disorder is pathological (e.g. caused by cocaine); 2. the brain: order is abnormal, pathological (e.g. caused by cocaine or epilepsy); 3. the pituitary gland: order is abnormal, pathological (e.g. caused by cancer in pituitary cells); 4. the heart: here we have opinions that appear to contradict each other.

A group at Cedar Sinai Medical Center asserts (as repeated in Nova) that in the heart order is normal, disorder (e.g. fibrillation) is pathological (e.g. caused by cocaine), and chaos can be fatal because the heart is a rhythmic, periodic organ. On the other hand, Ary Gold- berger declares that, despite common assumptions that the healthy heart beats as regularly as a metronome, careful study shows that there is considerable variation in the time that passes between heartbeats in healthy people. By contrast, heart rhythm often becomes extremely periodic or regular just before certain types of heart attack: "The route to sudden cardiac arrest is marked in many instances by ... the loss of healthy fractal behavior and healthy chaos. By looking at these beat-to- beat fluctuations ... one may be able to anticipate sudden death before it occurs." In other words, chaos results from the loss of that desynchronization (apparent [i.e., constrained] randomness) of motor units that helps avoid tremors.22

Perhaps we may conclude that chaos theory looks beyond superficial, apparent order (Paul Rapp) to hidden, real disorder (Ary Goldberger), but then attempts to determine the principles of organization behind that disorder.

In the domain of psychology, we find Freudian and neo-Freudian psychoanalysis, with its concentration on the individual and neglect of relationships between individuals, less immediately relevant than transactional analysis (Eric Berne) and group behavior theory (Murray Bowen), which deal primarily with interpersonal dynamics. Apparent behavioral order may be pathological, and conceal emotional disorder (disturbance, instability). Such pathologically orderly behavior may reflect a hidden agenda, or-at an even deeper level-be unconsciously scripted; these are modes of "constrained randomness."

Paul Watzlawick's work in psychological therapy is related to family behavior theory and transactional analysis-movements that are 68


concerned with unhealthily symbiotic relationships (e.g. between mother and child) that inhibit the development of emotional and psychological autonomy. Both family behavior theory and transactional analysis have been used in literary criticism over the last ten to fifteen years,23 and Watzlawick himself has made a psychological analysis of a literary text, namely the Albee play, "Who's Afraid of Virginia Woolf?"24

Disruption of order (when the latter is genuine, healthy, happy, serene) may also be pathological, reflecting an inabiltiy to cope with an "excessively" high bliss level: when the bliss tolerance level (BTL) is reached, our low self-esteem drives us to disrupt the blissful state. Moral license may well be an example of "testing the limits of permissibility," as children do, and serial killers, and certain television evangelists, who almost seem to want to be caught. In all such cases, those behaving this way may well be trying to provoke a punishment that will set limits to their freedom, because such limits are reassuring manifestations of order-and we all have a thirst for order.

Chaos theory may provide a key to sudden thoughts and intuitions, and to synthesis (right-hemisphere activities). Artists speak of their creativity as rising from a mental churning of "confusion, disorder and impurity" (sculptor George Segal) and of their "obsessive desire for reducing chaos and for finding beauty" (cellist Janos Starker) (my emphasis)." "Many writers, both male and female, use writing as a means of putting order into a disorderly world";26 is such "creation" a distortion, dissimulation, or deception?

According to Marilyn Yalom, women writers are subject to psychosis triggered by "the trauma of childbirth, motherhood and its entrapment and ways in which ability to procreate stirs memories of parents' deaths or creates fear of death of one's own child."27 Such women tend to view their writings as rivals or substitutes for children. "The core concerns of maternity and motherhood, the existential realities of aging and death, the crucial influence of mothers and fathers, and the perennial conflict between creation and procreation constitute the dominant chords in the fugue to madness.""28 The result is pathological emotional chaos.

From psychology, which deals with human behavior in general, we can move quite logically to economics, which deals with human conduct in specific circumstances.29 A leading chaos specialist in economics is William Brock, who declares: "Efficient market theory says returns are totally unforecastable. But my team has invented a test that shows there are patterns."'3

Another human (or social) science worth mentioning here is anthropology. The constrained randomness plotted by Lorenz in his "strange attractor" (the Butterfly Attractor)--randomness

within a limited (because fixed) space-is analogous to the territorial randomness of nomads like the Australian aborigines. Moreover, the aborigines don't believe in chance or random events: sickness is always caused deliberately by an enemy; weather changes only in response to rituals (man controls nature, as in New Age thinking).

II Chaos Theory: Definitions and Principles "Chaos" is, first, complexity, turbulence, discontinuous process;

second, it is disunity, fragmentation, and non-linearity; third, chaos is 69


constrained randomness, or relative uncertainty, and centrally engages the parameters of predictability and unpredictability. Chaos may be defined as low-level31 deterministic non-linear dynamics. Chaos theory casts doubt on (undermines) real randomness (total unpredictability) on the one hand and exact predictability on the other; it denies the possibility of unified order.32

Chaos theory manifests itself in the following features: (a) the carpet effect-chaotic processes can produce orderly patterns; (b) fractals--irregular shapes or number sequences that repeat themselves on varying scales (e.g. tree/branch/twig); (c) the butterfly effect-the fact that small causes can have great effects:

these exponential repercussions are based on (hyper-)sensitive dependence on initial conditions;33

(d) strange attractors-[computer graphics of] random behavior within set (i.e. system) boundaries.

III Chaos Theory and the Arts and Humanities A. literary analysis. When it comes to literature, some analogies

with the search for hidden order are of course obvious-perhaps too obvious. One example of this should suffice.

In 1966 I analysed Diderot's dialogue novel Le Neveu de Rameau-a robust, disorderly work that was generally considered to end in a stalemate or stand-off between the two speakers of the dialogue. When I broke the text down into levels of discourse, I discovered that one of these levels contained just four passages, similar in length and tone, that revealed a definite progress through the work and gave it, in spite of the superbly chaotic style, a clear and solid structure and a conclusion in which one side comes out as dominant and therefore successful.34 This order that governed the text had been concealed by a surface appearance of chaos.

However, while the analogy with chaos analysis is obvious, I knew nothing about chaos theory at the time, so the analysis owed nothing to that theory, and does not represent an application of it.

The non-linear character of chaotic phenomena recalls the distinction between tragedy, which is linear, and comedy, which is non- linear. The "non-linearity" of comedy is taken to be cyclical in essence, but after all, comedy, like history, never repeats itself exactly. Does this mean that the non-teleological quality of comedy justifies its assimilation to Edward Lorenz's Butterfly Attractor?35 I think not. The reason has to do with the difference between the Butterfly Attractor (what Gleick calls the "Lorenz Attractor") and the Butterfly Effect. The Butterfly Attractor represents a theoretically infinite irregular (unpredictable) line within finite set boundaries: in other words, random movement within con- straints-a definition of chaos. This, however, is not a definition of the non-linearity that characterizes chaos: "non-linearity" has to do with the "sensitive dependence on initial conditions," otherwise known as the Butterfly Effect.

What, then, is the relationship between the Butterfly Effect (disproportion between cause and effect) and the Butterfly Attractor (random movement within set boundaries)? While the two are quite 70


distinct, they both seem to deal with modes of the irregular, the unpredictable, the random. However, the Attractor emphasizes limits to the proliferation, while the Effect stresses proliferation that is virtually unlimited and therefore virtually unpredictable. They represent, re- spectively, two opposite faces of chaos theory: the optimistic (Butterfly Attractor) and the pessimistic (Butterfly Effect).

The "third butterfly" of our title is one of which Eugene Chen Eoyang reminded me; I call it the Butterfly Perceiver. It is the butterfly a Chinese philosopher dreamed he was; when he awakened, he didn't know whether he was a philosopher who had dreamed he was a butterfly or a butterfly now dreaming he was a philosopher. This crucial problem of perception (see above) cannot continue to be ignored by chaos specialists.

The "chaos game" mentioned by Gleick (pp. 236-240) involves the chaotic (i.e. superficially random) quality usually associated with throwing dice or shuffling cards. Such processes have directly inspired certain literary works, whether thematically (as in a poem by Mallarme) or structurally (as in a novel by Marc Saporta). Let us first set the historical background to these works.

In French literature, a traditional determinism-sometimes Jansenist (Racine, Pr6vost), sometimes not (Diderot, Hugo, Zola)-was rejected at the outset of the twentieth century. Emile Zola, who dominated the literary scene in the late nineteench century, had stressed the determining role of heredity, varied not by individual uniqueness (let alone by free will) but only by diverse environmental conditions. How- ever, his contemporary, St6phane Mallarm6, thrust into the limelight in the eighteen-eighties by Verlaine (Pontes maudits) and Huysmans (A rebours), foreshadowed the new century in 1897 with his poem Un Coup de d&s jamais n'abolira le hasard. This theme of the relationship between dice-throwing and chance will be explored eighty years later by chaos theory (see below).

Some thirty years younger than Mallarme, Andr6 Gide and Marcel Proust virtually dismantled the traditional ideal model of psychological consistency. Gide preached moral and experiential flexibility or avail- ability (disponibilitd) and spontaneity (unpredictability); he also showed a character acting in a manner not only independent of Fate, Providence, and heredity but even independent of any motivation on his own part: this was the famous acte gratuit perpetrated by Lafcadio in Les Caves du Vatican, in which he pushed an unknown fellow-passenger from a moving train. Of course, unmotivated actions are impossible if we follow the reasoning of structuralism, since Man is not free: freedom is an illusion. Finally, the famous structure en abyme illustrated by Gide in Les Faux- Monnayeurs, in which Gide writes a novel called Les Faux Monnayeurs in which the novelist Edouard is writing a novel called Les Faux- Monnayeurs, is a good literary illustration of the concept of fractal, which as we have seen is an irregular shape that repeats itself on various scales.

Proust, in his vast novel A la recherche du temps perdu, provides several variations on various aspects of chaos theory. The opening passage reflects psychological confusion, or chaos.36 Not total, pure randomness, because within or behind this chaos there is a principle of

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order (unity in multiplicity, as Michel Serres puts it), namely the single unifying point of view of the narrator."7 The latter, however, like all first- person narration, is a tissue of statements that are all undecidable because they are stuck in the web of self-referentiality. The principle of unpredictability is also embodied in the father, who deliberately makes arbitrary decisions to inure his son to the unreliability of life (particularly interesting in association with his obsession with the weather, which Edward Lorenz, as we have seen, views as archetypally unpredictable). Moreover, in the name of a greater fidelity to life and reality, Proust portrayed characters inconsistently-appearing very different in differing circumstances, to the point that they hardly appeared to be the same characters at all (after carrying out this bewildering manoeuvre, Proust's narrator explains and justifies it in detail). The Butterfly Effect, with its tremendous effect produced by a relatively insignificant cause, is illustrated by the trivial but crucial incident of tasting that tea-cake (madeleine) soaked in tea which produces from his simple cup of tea the whole town of Combray with its gardens, and ultimately the entire huge novel.

At a later date, in an effort to go beyond even the "constrained randomness" of Julio Cortizar's novel Hopscotch, Marc Saporta created a novel entitled Composition No 1 that is printed entirely on separate cards which the reader shuffles to create his own "chaotic" novel.

Any confidence in human freedom was undermined by structuralism, and this return to scepticism was reinforced when chaos theory re-examined dice-throwing. The television special on chaos (Nova, 31st January 1987) began with a discussion of this apparently random activity-and a rather daunting discovery concerning it. Statistical analysis has shown that the results of dice-throwing are not genuinely random but merely chaotic-they are micro-indeterminate but macro-determinate. That is, there appears to be no pattern, but this appearance is false-a matter of scale: there is actually a highly ordered pattern to which the results of casting conform when sufficiently multiplied.

B. music, painting, architecture. The spontaneity of the Impres- sionists, who revolutionized painting and music a century ago and so opened the door to modem art, was viewed by their contemporaries as anarchistic and chaotic.38 This Impressionism was thematized as a program for the sister arts in Verlaine's Art po6tique.

In modern architecture criticism we find a similar attempt to relate chaos theory to deconstructivist architecture and to such post-modernist phenomena as deconstructionism. Thus we find Thomas Fisher asserting the existence of ties between "the deconstruction theories of literary critics, the chaos research of physicists, and the work of post-structuralist philosophers."39 He does this by stressing that deconstructivism reflects fragmentation and that deconstruction espouses the "idea that unity is impossible and that order is always undercut by that which it represses."40 Chaos is then seen as a similar undermining of order, by the repressed text. Such a repressed text might correspond to the hidden agenda or script studied by contemporary psychotherapists, as in transactional analysis (see above). Kurt Andersen, on the other hand, divorces deconstructivism from post-modernism, referring to "architecture's tired to- 72


and-fro between caricature modernism (the neurotic Rubik's Cubes of the deconstructivists) and caricature classicism (the pretty confections of the postmodernists)."41

C. period style. While it is tempting to see as "historically- conditioned" the twentieth-century conjunction between modem art and literature and chaos theory, the truth is more complex. Many of the central tendencies of modernism, which was born from late-19th-century Impressionism, are to be found in the rococo art and literature of the early eighteenth century. In the domain of rococo art (architecture, decoration, painting), we find fairly clear examples of the indeterminacy, fractals and strange attractors, and butterfly effects associated with chaos.

(a) carpet effect. The rococo represents apparent disorder (atheism, atechtonicity, etcetera) by comparison with Classical order, as reflected in the rococo's dispensing with the orders of columns on Classical facades. Indeterminacy is well illustrated by rocaille ornamentation, in the analysis of it provided by Nicholas Pevsner: "The forms in detail seem to be incessantly changing, splashing up and sinking back. What are they? Do they represent anything? Sometimes they look like shells, sometimes like froth, sometimes like gristle, sometimes like flames."42 Compare with this David Ruelle's description of strange attractors: "These systems of curves, these clouds of points suggest sometimes fireworks or galaxies, sometimes strange and disquieting vegetal proliferations."43 However, as with strange attractors, closer inspection reveals that the apparent disorder of rocaille and rococo is simply a more complex mode of order-non-linear, unpredictable but constrained in its spontaneity, studied in its negligence. Further still, this highly organized disorder may be viewed as papering over the fundamentally disorderly society that led to the French Revolution. In painting, a swirling, "chaotic" movement is one of Boucher's most characteristic contributions to the rococo.

(b) fractals. The rocaille constitutes, in fact, a fractal, in Mandel- brot's sense, to the extent that it is an irregular shape repeating itself on varying scales. The analogy is obvious. But is it meaningful or is it merely "metaphorical?" This is a problem that tormented people a great deal in the hey-day of structuralism, when there was similar concern about the validity of extrapolation from one field to another. The rocaille does signify beyond what it "represents" (e.g. in the way it is used-to dissimulate techtonicity, for example), but nowhere near as much as fractals do, because fractals are merely graphics of flows that animate other phenomena. Of course, what would be really new and intriguing would be to view the rocaille as a graphic representation of the amorphous social and psychological movements that characterized the rococo period and are reflected in its aesthetic. We should then turn a problem into a challenge and an opportunity.

(c) butterfly effect. The butterfly effect is represented in the rococo by such things as the tremendous role played (according to the great rococo specialist Fiske Kimball) by a mere marginal notation from Louis XIV to Mansart regarding the decoration of the apartments of the young Duchesse de Bourbon: "de l'enfance r6pandue partout." What of rococo literature?

(a) carpet effect. We find indeterminacy (unfinished, non- 73


teleological narratives), non-linearity (predominance of comedy in the theatre), spontaneity and unpredictability (the kiss-a whim or caprice- in Goethe's Die Laune des Verliebten44). The "constrained randomness of a chaotic system may be seen in the "studied negligence" of the rococo. The "repressed text" of deconstructionism (post-modernism) finds its counterpart in the existential anguish concealed beneath the rococo hedonism of Voltaire's Le Mondain: this "mask of pleasure" has as goal the "muting of pain." In plays like Le Jeu de ramour et du hasard (again the theme of chance) and She Stoops to Conquer, we see the experimental introduction of a perturbance of the social order (the Ancien Regime) that is pathologically rigid-as in Watzlawick's procedures producing rapid therapeutic change ("cure") of scripts. The inconsistency or incoherence (mdlange de tons) in a novel like La Vie de Marianne provide further illustrations of chaos.

(b) fractals. One example of a fractal is a chaotic or "strange" attractor, which is a state towards which a system tends. A strange attractor is stable, low-dimensional, non-periodic, and characterized by complicated geometry, unpredictable, chaotic movement, and apparent internal randomness. Since it has an infinitely long line within a finite area, its true dimension is fractional-hence a strange attractor is fractal. One example of strange attractor is the toying with the absurdity of class distinctions in Marivaux: the writer allows himself complete freedom, at least in appearance, but this is only possible because he accepts the boundaries set by the comic convention and the rococo social system.

(c) butterfly effect. Examples of butterfly effect may be seen in Marivaux's passage on rart de mettre un ruban (in La Vie de Marianne) and in Pope's The Rape of the Lock, where a trivial incident inspires a masterpiece which, in turn, inspires the whole of European poetry. This magnificent treatment of a trivial topic is directly contrary to the neo- Classicism of a writer like Montesquieu, for whom it is "comme de l'or que vous mettriez sur l'habit d'un mendiant."45

IV From Chaos to Control When we perceive order or disorder, we cannot know whether

what we perceive is real, "out there," as Rene Girard apparently believes, or exists only in the mind, as L6vi-Strauss tends to suggest. Do we need to introduce order into a genuinely disorderly external reality, or merely to develop and project a perception, a conviction, of order?

Moreover, is the thirst for order a biological or physiological given, stemming from the very structure of our instrument of perception (namely, the brain), as structuralism asserts, or is it a psychological acquisition, imposed on us by the trauma of birth and reinforced by the helplessness of the human infant?

I am going to follow the latter line of reasoning, and argue that we feel threatened by our perception at birth of the chaotic character of our environment, which leaves us with a sort of "disorder neurosis" that leads to a compulsion to control (not unlike Adler's libido dominandi, except that the source is not libido but anxiety).

The determining effect of the birth trauma stems from the violent rejection of the infant by the mother's body, which thrusts it out from 74


the warm, dark, silent, liquid passivity of the nurturing womb through a passage of life-threatening compression and out into the cold, blinding, noisy, dry air and the necessity to breathe-such is the child's first experience of rejection, of Otherness, and of the environment outside the womb. In a word, this external reality is alien, hostile, incomprehensible, unpredictable, uncontrollable.

As Freud argues very plausibly, the infant feels threatened by the unpredictable and uncontrollable autonomy of the Mother, who comes and goes at will, abandoning him at her discretion to the threatening Otherness of his environment. The child attempts to inure itself to the pain of this abandonment by means of the therapeutic ritual of fort/da, or "hide and seek."

However, Freud claims that the child views its feces as a substitute for the penis, a detachable "part" of his own body that he/she can give as a gift in a kind of surrogate autocastration.

I suggest, on the contrary, that the feces represent not the penis (symbolizing sex) but an Other (symbolizing alienation): excretion, by showing the child that he or she can create an Other, has a twofold therapeutic function associated with the drive to control. Excretion involves both control of Self (through a mastery of the bodily function that helps us to diminish the threatening unpredictability of life) and control of Otherness (through the production or "creation" of a visible, concrete Other). This latter becomes part of the child's environment, but is non-threatening because created by the child him/herself. In fact, the experience of congestion/expulsion/relief makes excretion an analogue of the birth the infant has experienced, only now he/she is in control; and the feces, as product of the activity, represent the new-born infant. All of this contributes to the taming of the child's environment.

The idea of a Creator God is one which crystallizes in a transcendental symbol the therapeutic reassurance of producing a non- threatening external reality. For humans, of course, God is part of the reality that is external to them; but this is compensated by the "controll- ability" of God. God is controlled by our definition of God. If we define Him as terrible and vengeful, as in the Hebrew Old Testament, then He is predictable; if we define God as loving and forgiving, as in the New Testament, then again God is predictable. God may be omnipotent, but he is not free; our definitions tie His hands. Consequently, God does not function as unknowable and hence frighteningly uncontrollable, unpredictable.

The creative gesture of God is imitated by the creative artist, whether painter, composer, or writer. Unlike the literary critic or theorist, the creative writer is God-like in the arbitrary, gratuitous character of his activity: like God, he imagines and creates something out of nothing.

The notion of a Creator God may well have been inspired by the perception of the reproductive powers of Woman-and here it is well to recall that God was once a Woman. How deeply primitive people, who did not link their own role in intercourse to Woman's solitary role in childbirth many months later, was impressed by Woman's ability to reproduce-that is, in his eyes, to create Other Selves-has been demon- strated by Bruno Bettelheim, who traces the symbolic wounds of male

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initiation rites back to womb-envy.46 Artistic creation provided Man with an activity analogous to Woman's reproduction-but in the case of literature it became analogous only when the oral tradition was replced by written literature, which created an external object that was part of a non-threatening (because personally fabricated) environment.

The conception of ecriture as alienating and therefore suspect (Rousseau, Levi-Strauss) is taken even further by Derrida, who in 1972 appears to compare it with masturbation. However, while the pen, like the penis, may be seen as similarly instrumental, this assimilation scarcely supports the down-grading of kcriture, for it emphasizes the pen's need for a partner (paper): if pen without paper is like penis without vagina, that may surely be interpreted as throwing a more favorable light (in Derrida's own terms) on dcriture than on mere parole. If such biological analogies are desirable, surely more appropriate ones can be found; one is tempted, indeed, to propose a revalorizing conception of &criture, which unlike parole produces an externalized object that is concrete and visible, thus creating a satisfying feeling of Otherness relating to the creation of the universe by the Self. (This tames the feeling of menace normally associated with the Otherness of the universe around us.) This production of a visible object relates ecriture to certain biological functions of prime significance to the organism, namely excretion and female reproduction; on the social level, the corresponding function is the expulsion of the scapegoat. There are two categories of function in which the process of expulsion is preceded by congestion of the organism involved, and followed by relief and satisfaction. (Girard speaks in connection with scapegoating of unanimity of violence followed by unification of the community.) These two categories may be termed the category of the potential and ephemeral (ejaculation, menstruation, parole) and the category of the actual and permanent (excretion, childbirth, ecriture). The second category, then, would include all artistic creation productive of permanent "residue": however lucid and rational the actual process of creation, the drive to create (externalize, expel) art works is rationally inexplicable, except as an analogue of the drive to expel excreta, progeny, scapegoat. This perspective, of course, dis- tinguishes the dcriture of creative writing from other modes of dcriture (which have a rational and usually even a utilitarian basis), and thus may provide a clue to the elusive criterion of littdraritd. The arts, then, are related by this common drive to imitate the various movements of expulsion and to tame the irreparable Otherness of the universe by producing that universe oneself.

In When God Was a Woman, Merlin Stone demonstrates con- vincingly that the Hebrew story of the Garden of Eden was a propaganda instrument of male chauvinism;47 the drawing forth of Eve from the body of Adam then becomes a particularly vivid example of male womb-envy. This idea is interesting to the student of the phenomenon of artistic creation: the creative artist's imitation of the gesture of a Creator-God may well have evolved by analogy with the primitive artist's imitation of the more obvious act of Woman in producing new life.

This conception refines the theory of (artistic) creation I posited (as an alternative to Derrida's masturbation) in 1976. The series is now 76


conceived as follows: Child: 1. fear of Otherness (birth trauma; survival fear inspired by

autonomy/unpredictability of Mother) 2. desire to eliminate unpredictability of Other, through control 3. feces analogon (control of Self; control of Other); creation of

Other (NOT autocastration, as in Freud) Adult: 4. love-making analogon (control of Other), libido dominandi

5. creationism analogon (control of God-omnipotent, but benevolent, therefore predictable)

6. reproduction analogon (creation of Other), womb-envy: creation of Other Self (NOT masturbation, as in Derrida)

7. attempt at control of Otherness (external reality), art: magic simulacrum.

Conclusion.-The challenges posed by chaos theory and control theory are not of the same order. Control theory owes key elements to Otto Rank (the birth trauma) and Bettelheim and therefore owes much to Freudian theory, however much it may reject some aspects of the latter. The challenge is simply that of winning acceptance. Chaos theory, on the other hand, raises the question of extrapolation from one field to another, and the status of such extrapolation. It is easiest when reduced to fairly general principles, but more insightful when based on an imaginative use of analogies. One risks falling between the two stools of respectable banalities and over-adventurous use of the merest metaphors. The former are of little interest, so the challenge here is one of refining the analogies used so as to combine original insights with plausible comparisons. "Plausible," "acceptable"-again, of course, we find that the challenge ultimately comes down to winning acceptance.

In any case, a heightened sensitivity to chaos is evident in contemporary intellectual life,48 and may be expected to grow in the coming decade.

University of Tennessee

NOTES

1. On the radically formalist character of structuralism, cf. the following formulation: "Dans le reel comme en math6matiques, toute forme est un contenu pour celles qui l'englobent et tout contenu est une forme pour ceux qu'il contient" (Jean Piaget, quoted with approval by Claude L'vi-Strauss in L'Homme nu [Paris: Plon, 1971], p. 561). Cf. Marshall McLuhan's idea that "the medium is the message."

2. For a similar verification of the validity and value of structuralism, see P. Brady: Structuralist Perspectives in Criticism of Fiction (Bern: Lang, 1978).

3. Cf. P. Brady: "Immanence, Semiotics, and the 'New Contextualism': Theory and Illustration of a History and Philosophy of Culture," invited lecture, Harvard University, December 1976; modified version published as "Towards a Theory of the Rococo," The Comparatist, vol. IX (May 1985), pp. 4-17.

4. Charles Panati in Newsweek, 19th January 1976, p. 54. 5. Ibid. 6. Ibid.

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7. See my article "Period Style in the Light of Structuralism, Semiotics, and Catastrophe Theory," French Literature Series, vol. IV (1977), pp. 119-130.

8. New York: Viking Penguin, 1987. Other sources of the present essay include the television special (Nova, P.B.S. 31st January 1987).

9. Some catastrophe theorists (mathematicians) participated in the Stanford symposium. The only disorder specialist mentioned by Gleick as involved in chaos theory is the economist Kenneth Arrow-and then not in Gleick's volume but in his article in The New York Times, 22 November 1987 (Section 3: Business). Incidentally, the first chaos conference took place in 1977 (G1.183-184), four years before the Stanford conference on disorder.

10. See Gleick, op. cit., cover. 11. See the discussion of "the chaos game," ibid., pp. 236-240; also Nova. 12. See Paul Watzlawick in Paisley Livingston, ed.: Disorder and Order:

Proceedings of the Stanford International Symposium (September 14-16, 1981) (Saratoga, Ca.: Anma Libri, 1984), p. 63.

13. See Ford's letterhead. Jim Yorke, who apparently first used the term "chaos" in this sense (in the early 1970s), is upset that scientists are looking for order in chaos: see Robert Pool, in Science, vol. 245 (7 July 1989), p. 28.

14. Quoted in Gleick, op. cit. (inside front cover). 15. See above, note 1. 16. Maps in the brain model the world according to Michael Arbib: see his

In Search of the Person (Amherst: U. Mass. P., 1985), p. 36. Cf. "Perceptions are to a large degree creations, and memories are part of an ongoing process of imagination closely akin to literary creation" (John Roy: "Brain Theory and the Poetics of Consolation," Mosaic, vol. 21, nos. 2-3 [1988], p. 85). In this light, Yorke's objections (above, p. 4, note 4) seem naive.

17. Quoted, without attribution, in Gleick, p. 6. 18. On the crucial and ambiguous question of the validity and status of

extrapolation from one field to another, see above, epigraph, from Pool, art. cit.

19. Since the difference between short-range and long-range forecasting is merely one of degree, not of kind, it follows that if short-range forecasting is possible (as Lorenz agrees) then long-range forecasting must also be possible.

20. Pool, art. cit., p. 27. 21. See I. Prigogine and G. Nicolis: Self-organization in non-equilibrium

systems: From dissipative structures to order through fluctuations (N.Y.: Wiley, c. 1977). Also I. Prigogine and I. Stengers: Order out of chaos (N.Y.: Bantam, 1984), based on their La nouvelle alliance (Paris: Gallimard, 1979).

22. Cf. Ary Goldberger: "Nonlinear Dynamics, Fractals, Cardiac Physiology, and Sudden Death," in L. Rensing et alii: Temporal Disorder in Human Oscillatory Systems (N.Y.: Springer Verlag, 1987).

23. See P. Brady: "Farms, Trees, and Bell-towers: The 'Hidden Meaning' of Triads in Proust's Recherche," Neophilologus, LXI, 3 (July 1977), pp. 371- 377; Marcel Proust (Boston: G. K. Hall, 1977), pp. 48-55, 83-91; "Scripting, Surrogate Mothers, Incest Taboo and Creativity: Zola's Twofold Self- betrayal in L'Oeuvre," Neophilologus, LXIX, 4 (October 1985), pp. 533- 538; "Womb-envy, Counterscript, and Subversion: From L'Oeuvre to Les Noeuds d'argile," L'Esprit Crdateur, XXV, 4 (Winter 1985), pp. 59-70.

24. P. Watzlawick et alii: The Pragmatics of Human Communication (New York: Norton, 1967).

25. David Maxfield: "Creative Minds," Texas, Houston Chronicle Magazine, 7 February 1988, pp. 4-5.

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26. Marilyn Yalom: Maternity, Mortality, and the Literature of Madness (Penn State U.P., 1989).

27. Beverly Beyette, reviewing Yalom in The New York Times. 28. Yalom, op. cit., quoted in Beyette, rev. cit. 29. Economists Richard Thaler of Cornell, Lawrence Summers of Harvard,

and Robert Schiller of Yale stress the role of psychological factors- irrational emotions, unfounded optimism or pessimism, contagious enthu- siasm or discouragement-in stock market performance. Cf. R. M. Hogarth and M. W. Reder, eds.: Rational Choice: The Contrast Between Economics and Psychology (Chicago: U.C.P., 1986). This volume details not only differences but common ground and mutual influence between these two disciplines.

30. Cf. his essay "Chaos and Complexity in Economic and Financial Science," in G. M. Furstenberg, ed.: Acting under Uncertainty: Multidisciplinary Conceptions (forthcoming).

31. "Low-level" or "low-dimension" here means: "involving relatively few variables, thus making prediction possible."

32. Chaos is related to aporia (undecidability) and entropy (decrease in, or degradation of, energy).

33. Such disproportion between cause and effect is a mode of nonlinearity. 34. "Structure and Sub-structure of Le Neveu de Rameau," L'Esprit Createur,

Spring 1968, pp. 34-41. Hidden order in Lettres persanes is referred to by Montesquieu as "une chaine secrete;" in Le Neveu it is described by Goethe as "une chaine d'acier qu'une guirlande d6robe a nos yeux."

35. See above, p. 7, and Gleick, op. cit., opposite p. 114. 36. His style has been characterized as chaotic: see G. Antoine: "Proust ou le

chaos metaphorique," Cahiers de lInstitut de Linguistique, X, 1-3 (1984), 17-25.

37. See P. Brady, op cit. (Marcel Proust), Ch. 1. 38. The new "orderliness without repetition" represented by strange attractors

like Lorenz's Butterfly Attractor (above, p. 7) was prefigured by Debussy's Impressionist goal of eliminating the repetition on which Classical music had been based.

39. Progressive Architecture, December 1988, p. 7. 40. Ibid., loc. cit. 41. Time, 20 March 1989, p. 75. See also Gleick, op. cit., pp. 116-117. Chaos

theory has inspired art exhibitions: "Strange Attractors: Signs of Chaos," New Museum of Contemporary Art, New York City, 13 September to 26 November 1989 and "Strange Attractors: The Spectacle of Chaos," Kaos Inc. Art Show, Chicago, same dates.

42. N. Pevsner: An Outline of European Architecture (London: Penguin, 4th ed. 1953), p. 195.

43. Gleick, op. cit., p. 153. 44. See P. Brady: "Rococo Style in European Theatre," in M. G. Badir and D.

J. Langdon, eds.: Eighteenth-Century Theatre: Aspects and Contexts (Edmonton, Alberta: U. of Alberta [Dept. of Romance Languages and Comparative Literature], 1986), pp. 53-73.

45. Montesquieu: Cahiers, 1716-1755 (Paris: Grasset, 1941), p. 70. 46. Symbolic Wounds (New York: Collier, 1962). 47. London: Harcourt Brace, 1978. 48. See for example the historian Gertrude Himmelfarb's resistance to the

suppression of contingency and unpredictability in Francis Fukuyama's influential essay "The End of History?" in The National Interest, Summer 1989, as reported by Richard Bernstein in The New York Times, 27 August 1989.

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Article Contentsp. 65p. 66p. 67p. 68p. 69p. 70p. 71p. 72p. 73p. 74p. 75p. 76p. 77p. 78p. 79

Issue Table of ContentsModern Language Studies, Vol. 20, No. 4, Literature and Science (Autumn, 1990), pp. 1-120Front Matter [pp. 1-32]Introduction: A Topography of What's New in the Study of Literature and Science [pp. 3-14]Literary Studies and the Sciences [pp. 15-31]Deconstruction, Quantum Uncertainty, and the Place of Literature [pp. 33-39]Eudoxical Discourse: A Post-Postmodern Model for the Relations between Science and Literature [pp. 40-64]Chaos Theory, Control Theory, and Literary Theory or: A Story of Three Butterflies [pp. 65-79]The Holographic Paradigm: A New Model for the Study of Literature and Science [pp. 80-89]The Trial in the Stone Quarry [pp. 90-102]Oliver Sacks: The Ecology of Writing Science [pp. 103-120]Back Matter

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