The Lorenz
or
Butterfly
Atrractor
Jo Alyson Parker
Spiraling down "the Gutter of Time": 
Tristram Shandy and the Strange Attractor of Death 

Disorder is never anything but a different order than we expect. --Jean Guitton (Favre 155) Some of the most evocative images in Tristram Shandy are graphical--the black page, yawning like an open grave, that follows the announcement of Yorick's death; the "flourish" Trim makes with his stick to represent an unmarried man's freedom; the five lines, interrupted by zigzags and curlicues, that Tristram tells us represent the narrative movement of the first five volumes; the marbled page, "motley emblem of my work" (226); and so forth. With the significant exception of the black page, all of these images are dynamical, and we might conceive that, had Laurence Sterne had access to the graphical representations of contemporary dynamical systems theory (popularly generalized as chaos theory), he might have included an image of a chaotic, or strange, attractor as an appropriate visual representation of the text. Although here we can show only a two-dimensional representation of it (see figure), on the computer screen the strange attractor evolves in the multi-dimensionality of state- space, as trajectories at times diverge and at times almost converge, but never intersect, attracted to the unstable attracting point or points that they can never attain. Tristram Shandy is analogous to a chaotic dynamical system, a bounded arena of infinite possibility. The text is a deliberate reaction to the linear narratives of its time, which move predictably to a steady state where their action ceases. In the following essay, I explore the strong similarities between the narrative trajectory of Tristram Shandy, hovering over the powerful, but unattainable attracting points of sex and death, and the infinitely evolving trajectory of the strange attractor, which maps a certain type of chaotic dynamical system. In examining Tristram through the lens of chaos theory, I do not want to suggest that Sterne had some sort of incipient understanding of this quintessentially postmodern science; indeed, Sterne and his contemporaries would have understood chaos as an absence of order, rather than the disorderly order or deterministic chaos that it has come to mean in our current scientific paradigm. Nor do I want to propose the strange attractor as an all-purpose model for narrative dynamics, a new formalism that can be applied to any and all texts no matter what the historical and social circumstances out of which they arise. What I do want to do is examine the appropriateness of the strange attractor--specifically the Lorenz or butterfly attractor--for modeling the narrative dynamics of a text like Tristram. I want to suggest, too, that the narrative dynamics of Tristram are very much a response to the era in which Sterne lived--a deliberate resistance to the determinism of Newtonian science to which the great linear narratives of the mid-eighteenth century conform. Although Sterne lacks the means for articulating a science of chaos, his text foregrounds the "order out of chaos" and bounded randomness that Newtonian science occludes. It thus provides an alternative means for narrating experience--complex, dynamic, non- linear. Newtonian or classical science is predicated upon notions of predictability and causality--"a clockwork view of the universe" (Hunt xvii) whereby we can accurately predict the future state of a system and retrodict its past state. In the late eighteenth century, the French mathematician Pierre Simon de Laplace envisioned "an intelligence that recognizes all forces of nature and the elements that compose it," for whom "nothing would be uncertain" (Favre 146). Significantly, in order for the notion of an ultimately predictable natural world to prevail, scientists operating under the Newtonian paradigm focused on problems whose solutions could be predicted with a fair amount of accuracy and ignored those that defied predictability, a situation that Stephen Kellert terms "linear prejudice" (143). This "linear prejudice" is fundamental to eighteenth-century novels, which move forward with deterministic inevitability to their culminations in marriage or death. For example, Tom Jones, a paradigm eighteenth-century novel, starts with Jones's birth, moves forward along fairly predictable lines, and ends with both his marriage and death--the death of the imprudent Jonesian self. Granted, such texts are rife with digressions and interpolations, but these can be regarded as "transient perturbations" or pockets of chaos that are smoothed out or dampened by the dominance of the overall linear tendency. Although we cannot predict precisely where the narrative will take us next, we know that, in Roland Barthes's terms, the "hermeneutic sentence" (S/Z 84) upon which it is predicated will be answered. Although his focus is not the linear narrative per se, Barthes implies that narrative and deterministic thinking go hand-in-hand: Everything suggests, indeed, that the mainspring of narrative is precisely the confusion of consecution and consequence, what comes after being read in narrative as what is caused by; in which case narrative would be a systematic application of the logical fallacy denounced by Scholasticism in the formula post hoc ergo propter hoc.... ("Structural Analysis" 266) Linear prejudice reaches its apotheosis in the great "autobiographical" novels of the nineteenth century, whose action begins with the self's fall into linear time and ends with the "death" of the narrated self into the narrating self, whereupon all seemingly casual events are gathered up into the overarching causal pattern and the narrating self "writes" from the temporal state of the narrating instance. Granted, Tristram Shandy is bound, like all autobiographies, by two definitive events, Tristram's birth and the death of the narrated self. It begins, in fact, with a beginning par excellence, describing not simply the birth, but what appears to be the actual conception of the protagonist. Tristram the narrator congratulates himself for the feat: "right glad I am, that I have begun the history of myself in the way I have done; and that I am able to go on tracing every thing in it, as Horace says, ab Ovo" (7). Tristram aims to reach the point where the narrated self becomes the narrating self: "whipp'd and driven to the last pinch, at the worst I shall have one day the start of my pen" (286). But the words preceding this statement indicate that the aim will never be realized: "I shall never overtake myself' (286). Tristram cannot, ultimately, discover the initial conditions that gave rise to his narrative trajectory or achieve narrative "death," except, of course, in the sense that the text does and must physically come to an end. Rather than being primarily linear, the narrative trajectory spirals round, jumping between two unstable attracting points that determine the "strange-attractor" structure of the text. Before examining the text's narrative structure, I want briefly to explain how a strange attractor features in dynamical systems theory. An attractor is simply what its name suggests: "what the behavior of a system settles down to, or is attracted to" (Crutchfield 50). We map the behavior of a dynamical system along the Cartesian coordinates of what is called state space, wherein each point represents one possible unique configuration of the system. The figure that is thereby generated is a representation of the dynamical system's evolution numerically. If the trajectory of the dynamical system assumes a repeating pattern in state space, then we say it has reached the attractor. For example, when mapping the behavior of a pendulum, we end up with a trajectory that spirals inward to a fixed point, the figure thus representing the pendulum's attraction to a final state of stasis. When mapping the behavior of a frictionless pendulum, we end up with a periodic orbit, the figure thus representing the pendulum's attraction to a particular set of repeating coordinates. Systems such as pendulums exhibit classically deterministic behavior; no matter how we vary the initial conditions within the basin of attraction, the trajectory will always fall onto the same attractor. Certain types of dynamical systems--such as a dripping faucet, a water wheel, or the weather--are chaotic in our contemporary sense of the term, and when we represent their evolution in state space we often end up with a strange attractor. With a dripping faucet, we know that drops will fall and that their mass and rate of speed in falling will lie within certain boundaries, as Robert Shaw's germinal study demonstrated. We cannot, however, solve the equations that would enable precise predictions of when, where, and how the drops will fall. When we map the system's behavior in state space, as computer simulation has enabled us to do, we find that the orbit tends to hover around certain coordinates within a basin of attraction, but we cannot predict exactly when the orbit will move closer or further away from those coordinates. In the case of a Lorenz or butterfly attractor (a particular subset of strange attractors), the orbit jumps between two attracting points, and we cannot predict when the jump will occur. We can conceive of the strange attractor in terms of "bounded randomness," as Thomas Weissert describes: "Because the trajectory on the attractor resides within a three-dimensional Cartesian space, the signifying point can trace out a path within the bounded region that never crosses itself, never repeats itself exactly, and never comes to rest on any one single point" (122). A system that gives rise to a strange attractor has an infinite amount of local variations within fixed global limits--thus, deterministic chaos or disorderly order. One important feature of the strange attractor is that, as the trajectory moves through state space, the "memory" of initial conditions is lost as new information replaces it. Because the finite bounds of the strange attractor must encompass exponentially diverging orbits (a potentially infinite process), a stretching and folding operation takes place, analogous to the stretching and folding that occurs as we knead bread-dough. If we put a drop of food coloring in the dough and then perform several iterations of the kneading process, we are unable to locate the original drop, although we can now see the streaks of color diffused throughout. In essence, beyond a certain point in time, one cannot retrodict a prior state of the system. Reframing my earlier discussion in terms of attractors, I would argue that in the linear (auto)biographical novel, the birth of the protagonist initiates a (narrative) trajectory that is attracted to the fixedpoint of the protagonist's death, whether symbolic or real. Unlike that in linear narratives, however, the narrative trajectory of Tristram Shandy never comes to rest but hovers between two unstable attracting points. Although the novel spins off only a finite number of narrative starts, it gives us a sense of infinite potentiality by insistently flaunting their open-endedness. It works against our being able to retrodict a prior or predict a future state of the system. In Tristram Shandy, Sterne emphasizes the impossibility of pinpointing what we might call, with tongue only slightly in cheek, "the initial conditions" that would account for Tristram's subsequent history and the course of the narrative trajectory. In the first place, we are given reason to suspect that the interrupted intercourse of the Shandys may not actually be the moment of conception--that Tristram may, in fact, be illegitimate, as Homer Brown points out (730). Significantly, legitimation itself is a potent signifier of deterministic causality, demonstrating a clear connection to an origin and guaranteeing a (patri)lineal outcome. Whether Tristram is indeed illegitimate is indeterminate, indeterminable. Sterne avoids the clarification that would shed light on prior events. And even if Tristram's poor homunculus were brought into being during the ill-fated coupling, Tristram himself discovers that he must go further back than the conception to account for himself. But when he does, he confronts a tangle of rapidly proliferating choices: "To sum up all; there are archives at every stage to be look'd into, and rolls, records, documents, and endless genealogies, which justice ever and anon calls him [a man] back to stay the reading of:--In short, there is no end of it..." (37). Tristram does not actually supply us with these "endless genealogies, " but we are encouraged to picture a multiplicity of narrative strands moving backward. For Tristram, as well as the reader, initial information is replaced with new information, and he cannot locate a fixed origin that would account for who and what he is. Nor can Tristram or ourselves predict the future course of his narrative trajectory. Whereas within a classical dynamical system, events can be predicted, within a chaotic dynamical system, events are unpredictable beyond a certain point in time. In Tristram Shandy, there are certain discrete linear sequences, generally fully contained within one of the brief chapters--Dr. Slop's reading of Ernulphus's curse; the hot chestnut falling into the "hiatus in Phutatorious's breeches" (321), followed by the unfortunate result; Toby's and Trim's march from the bottom of the avenue to Widow Wadman's door; and so forth. Without such proairetic sequences, the text would be incomprehensible. But the sequences I have mentioned are part of longer sequences, and these rarely, if ever, proceed linearly. Although in his edition of Tristram Shandy James Work points out that "the leading overt actions of the story...are arranged within each sequence in perfect chronological order" (xviii), these sequences are still in process when we have reached the end of the text, and there are endless possibilities for the text to revisit these areas of its "state space." We may make a global prediction about Tristram's future--that he would eventually reach the point where he sets out to write his Life (a situation that never actually occurs in the text)--but we cannot make any sort of prediction about where the narrative trajectory will be by the time we turn the page. Certainly, it might be argued that there is a predictable aspect to the text. We are not surprised that, when Toby discerns "the transverse zigzaggery" of Walter's approach to his coat-pocket (160-61), he will be reminded of the battle of Namur, or that, when he hears that Dr. Slop is in the kitchen making a bridge, he thinks of his destroyed drawbridge. We expect Walter to come up with quirky arguments on estoteric subjects, and we expect our narrator to give the most innocent of subjects a risque turn. But predictability of character is not the same as predictability of sequence. And even if that sequence of episodes is structured so as to represent the path followed by the mind as it associates ideas, the path does not unroll linearly, inevitably. The mind skews temporal order, connects like with unlike. Mental "events" have causes, to be sure, but, as in a chaotic dynamical system, it is indeterminable which and how many causes lead to a particular effect and which and how many effects derive from a particular cause. Indeed, the text serves as an implicit demonstration of the fact that linear causality is an inadequate model for the complex workings of the mind, reminding us that the great explanative "narrative" put forward under the Newtonian paradigm leaves the human element out of the equation. The text is insistently non-linear. In the fifth chapter of the first volume, Tristram is born, and we are given an exact date, as if to suggest that we will be proceeding according to a strict chronological order. But thereafter, Tristram goes "backwards" to provide us with the history of the midwife, gives us the dedication, which should indeed be "outside" the text proper (if there can be such a thing), recounts Yorick's history, and then jumps "ahead" to Yorick's death, which account is followed by the black pages, negatively imaging the white pages that customarily follow the end of a text. I need hardly add that each of these sequences is itself riddled with interpolations and temporal jumps. In the ninth volume, chapters 18 and 19 follow chapter 25, and their proper" place is filled by white pages, falsely representing the climax(the text's, Toby's) that cannot occur. In one volume, we may be traipsing around Europe with Tristram the narrator, the narrating instance itself evolving in time; in the next, we may be privy to the emotional modulations of Toby in love. We have no way of knowing when the trajectory will jump to another part of the attractor basin. It is no surprise that the unstable attracting points between which the narrative trajectory of Tristram Shandy jumps are death and sex-the former the great unknowable and the latter the great unmentionable. Powerful draws for Sterne and his culture, they concurrently, continually attract and repel the narrative trajectory. Sterne--that womanizing clergyman racked with consumption--is fascinated by the generative act he must not explicitly describe and the definitive act that he cannot. Of relevance here is Peter Brooks's description of narrative as "the thrust of a desire that never can quite speak its name--never can quite come to the point--but that insists on speaking over and over again its movement toward that name" (61). According to the constraints under which Sterne works, the attracting points of sex and death can be represented only through structural deferral and figural displacement. Although, by jumping between these two attracting points, the narrative trajectory of Tristram Shandy is like that of a Lorenz attractor, there is a significant difference. A rigid global predictability governs the trajectory of the Lorenz attractor, for it jumps between attracting points in a strictly alternating sequence. The text's narrative trajectory, however, does not so much alternate between sex and death as move toward, then away from climaxes. The attracting points are, in fact, integrally related, for each marks the culmination of an apparently linear sequence--life or love. When Slawkenbergius gives his critical disquisition on the movement of plot toward its culmination, he may as well be speaking of sexual, as well as narrative climax (an appropriate ambiguity, considering that the story he tells has to do with the Strasburgers feverish desire to satisfy themselves by touching Diego's huge "nose"): "The Epistasis, wherein the action is more fully entered upon and heightened, till it arrives at its state or height called the Catastasis . . .or the ripening of the incidents for their bursting forth in the fifth act" (266). Interestingly, the Strasburgers situation is anticlimactic, for Diego never returns to satisfy them. And, though the Strasburgers anticlimax is the climax of Slawkenbergius's story, we too are left unsatisfied, never finding out if the "nose" itself is real. We never, in fact, get to the thing itself, for, as we all know, despite Tristram's asseverations that "by that word I mean a Nose, and nothing more, or less" (218), a nose does not mean a nose, any more than sausages mean sausages and buttonholes mean buttonholes. Slawkenbergius's tale epitomizes Sterne's procedure of structural deferral and figural displacement. We should bear in mind that the strange attractor is both spatial configuration and temporal continuum; the entanglement of figurative displacement and temporal deferral creates the meaning structure that is Tristram Shandy. It is a given that, just as Tristram attempts to escape death through his wild zigzag across Europe, Tristram Shandy attempts to avoid its own "death" through its skewing of linear order, as Robert Alter and Murray Krieger have demonstrated. The text resists an ending that would be a result of its prior state and that would enable us to see an overarching causal pattern. The fact that Sterne's actual death left the text cut off in the middle of Toby's amours and the story of the Cock and Bull is beside the point, for the text in process is exactly what Sterne had been aiming at all along; in fact, we might even say that Sterne's actual death facilitated the text's avoidance of its own. We are in a state of endless deferral, and we notice that the closer any sequence comes to reaching a climax, the more interruptions and temporal leaps occur. Digressions indeed "are the life, the soul of reading," as Tristram exclaims, for they keep "the whole machine. . .a-going" (73)--keep the text from reaching its end. The narrative movement of Trim's "The Story of the king of Bohemia and his seven castles" replicates in miniature the overall narrative movement of the text itself. It is a felicitous instance of similarity-across-scale, a characteristic of dynamical systems whereby structural similarities occur at both global and local levels. Such scaling is often noted in fractal forms, wherein the lacy pattern we discern at one level replicates itself on smaller and smaller scales ad infinitum. Trim's story never gets beyond the title (set off in the text four times, the last three with the inaccurate addition "continued") and the first incomplete sentence, and it ends up being displaced by Toby's history of gunpowder and Trim's history of his amours with the Fair Beguine, whose climax (literal and figurative) is interrupted by Toby's unwittingly periphrastic comment about what Trim must have done once his "passion rose to the highest pitch"--that is, clap the Beguine's hand to his lips and make a speech (375). When Toby later asks what became of the story, Trim replies, "We lost it, an' please your honour, somehow betwixt us" (381), and we may well feel that the story of Tristram has itself been lost. The fact that the narrating instance is itself subject to temporality ensures that the death of Tristram's narrated self can never occur. Tristram's precise dating of when he is writing indicates that his history advances as he writes--chronology here used to subvert "the clockwork hegemony" (Kellert 145) instigated by Newtonian science. And, of course, that situation leads to the famous Shandean paradox, whereby the loner Tristram is at his writing, the further he gets behind: I am this month one whole year older than I was this times twelve-month; and having got, as you perceive, almost into the middle of my fourth volume--and no farther than to my first day's life--'tis demonstrative that I have three hundred and sixty-four days more days of life to write just now, than when I first set out; so that instead of advancing, as a common writer, in my work with what I have been doing at it, I am just thrown so many volumes back.... It must follow, an' please your worships that the more I write, the more I shall have to write.... (286) For Tristram, writing does not move inevitably to its own cessation, but is endlessly generative as it is attracted to the climax it must never reach. The apparent impotence of the Shandy family is an appropriate figure for the climax-less text. The text, in fact, is climax-less in more than one sense. As in the story of Tristram's "conception" and that of the Fair Beguine, sexual climaxes themselves are temporally deferred. They are also figuratively displaced. Tristram Shandy speaks endlessly around sex, but never directly of it. As we move through the narrative, we acquire more and more means or talking about it by not talking about it, each iteration of a particular motif--such as noses and sausages enabling the strange-attractor structure to evolve in the state-space of the text. The narrative trajectory of Tristram Shandy challenges the linear prejudice of Sterne's age. But the commentary in the text itself also challenges the deterministic predictability of Newtonian science. Sterne makes a pseudo-solemn prediction of scientific progress achieving a sort of Laplacian vantage; the various branches of knowledge "have, for these two last centuries and more, gradually been creeping upwards towards that Akun of their perfections, from which, if we may form a conjecture from the advances of these last seven years, we cannot possibly be far off" (64). Significantly, the perfection of knowledge "will put an end to all kind of writings whatsoever" (64) an achievement against which Tristram Shandy directly, forcefully, testifies. In the person of Walter Shandy, Sterne mocks the progressive impetus of Newtonian science. Walter, the ultimate systematizer, attempts to weigh all the variables of situations to determine the future course of his offspring. The culmination of his systematizing is the TRISTRApoedia, which, as Tristram tell us, is intended "to form an INSTITUTE for the government of my childhood and adolescence" (372). But all of Walter's well-laid plans are overturned by little but crucial circumstances. Walter's scientific optimism is belied by his experience--the sensitive dependence on initial conditions wherein little causes, amplified by feedback, give birth to great and unpredictable effects. Indeed, Walter himself argues against the classical tendency to disregard small uncertainties in a system: In a word, he would say, error was error,--no matter where it fell,-whether in a fraction,--or a pound,-- 'twas alike fatal to truth, and she was kept down at the bottom of her well as inevitably by a mistake in the dust of a butterfly's wing,--as in the disk of the sun, the moon, and all the stars of heaven put together. (145) Although Walter has not quite articulated the "butterfly effect"-- described in the popular scenario wherein the flapping of a butterfly's wings can have drastic effects on the weather--the passage seems a suggestive anticipation of it. Error, so Walter Shandy would have it, "creeps in thro' the minute holes, and small crevices" (146), leading to catastrophic effects. Whereas the order and predictability of the linear narratives of his day complement the assumptions of Newtonian science, Tristram Shandy calls these assumptions into question. The text both thematizes deterministic chaos and enacts it. Sterne, in effect, gives us a chaotic text-globally determined, locally unpredictable. I began this essay with the warning that we must avoid using the strange-attractor structure as a new "dynamic" formalism upon which we map all narratives. Such a structure is a local phenomenon, discernible in certain texts as a response to particular culturo-socio-historical circumstances. But I want to turn back on myself here and point toward a way in which dynamical systems theory can give us a means of articulating our complex experience of narrative form. In a recent issue of Lingua Franca, Steven Johnson argues against the analogy that a novel is a complex system: The greatest problem with literary chaotics may be that a work of literature is not a system at all, in the Santa Fe sense of the term--that is, a dynamic mix of agents interacting in real time. Novels, for example may be about complex systems (cities, economies, ecosystems, and so on), and they are certainly the products of complex systems (the neural nets of the human mind), but they themselves are language based, static, dictated from the outside. (50) Dynamical systems theory, however, gives us the means of reconciling the apparent dichotomy between a static form, subject to structuration, and our dynamic experience of the reading process in real time, of reconciling the apparent dichotomy between a closed, fixed, determinable "meaning" and the dissipation of all meaning into an infinite regress of indeterminism. I return once more to Tristram Shandy to illustrate my point. There is, after all, a global determinism governing the text. Rather than calling this determinism the text's teleology, which would imply a controlling consciousness, I would, borrowing the term from Favre et al., call it the text's teleonomy--that is, controlling factors that are directed to a certain end (xxiii). Sterne follows a certain plan as writer--to pen a Life of his hero--and whether that plan is an ad hoc one is beside the point. The events the narrator describes in the earlier volumes determine what he can say in the later ones; if he tells us at one point, for example, that the affair between Toby and Widow Wadman came to naught, he is not going to have them married in a later chapter. We must even contend with the historical determinant of Sterne's death, which kept him from finishing the text. In essence, we have a particular textual setup that is inviolable. Yet the global determinism of the text is subject to the local randomness of culturo-socio-historical changes that result in different ways of interpreting the text--including our epoch of postmodern science, which allows us to discuss it in terms of disorderly order. Our readings, as Stanley Fish reminds us, derive from the particular interpretative community out of which we operate, and chaos theory may give us a means for accounting for the entanglement of authorial intention and interpretative strategies whereby we make sense of a text. We can also speak in terms of the reading process itself being determined. Although Tristram Shandy may be non-linear in its approach to time, it is set up so that we read it linearly, from first page to last. Yet local violations of the linear determination of the text can take place; although we may sacrifice a certain amount of the sense, we can jump around, skip entire sections, return again and again to favorite passages, and wrench those passages out of context so that we can perform, in Barthes's terms, the "manhandling" of the text that constitutes "the work of the commentary" (S/Z 15). Sterne's sly directive at the outset of a new chapter that the inattentive reader "turn back" to the previous one "and read the whole chapter over again" (56)--a situation that would entrap us in a loop--and his withholding of the eighteenth and nineteenth chapters in volume nine point to his acknowledgment that the global determination of the linear reading process can be subverted by the local randomness of our idiosyncratic readings. In her introduction to the collection Chaos and Order, Katherine Hayles comments, "One way to understand the connection between literature and science is to see the science as a repository of tropes that can be used to illuminate literary texts" (20). But, as the essays in the collection end up demonstrating, science provides more than a repository of tropes. A shift in scientific thinking impacts upon the culture at large and is impacted by it. Just as chaos theory has prompted scientists to refocus on problems previously deemed insoluble, it may enable those of us in literary studies to refocus on problems of narrative structure and meaning, providing (as all theory does) a provisional solution to the questions we ask of texts. Through its exacerbation of disorderly order, Tristram Shandy may, in fact, serve as a sort of paradigm text for discussions of narrative form and chaos theory. In Viktor Shklovsky's famous formulation, it may indeed be "the most typical novel of world literature" (89), drawing through its strangeness our attention to the chaotic element inherent in narrative itself. As scientists have discovered, disorderly order is more common--and more meaningful--than classically deterministic order. Within the bounded "state space" of his text, Sterne playfully puts in motion a trajectory that promises to evolve infinitely as it bounces between the unstable attracting points of sex and death. Despite his attempt to "mend" himself, Sterne does not give us the straight line of the linear text; he understands only too well that is indeed "the line of GRAVITATION" (4775) that leads to the blank, black page which comes at the end of every Life.