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On History, Chaos, and Carlyle.

What the ... sciences are discovering today ... literature has always known. (Roland Barthes, "Science Versus Literature") (1)

In his Philosophical Essay on Probabilities (1812), Pierre-Simon Laplace sets out one of the most frequently cited views of a deterministic universe and a formulaic history. According to Laplace, history might be known by one "vast intelligence" and analyzed in terms of a single formula. He writes thatwe ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it--an intelligence sufficiently vast to submit these data to analysis--it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes. (2)

Clearly, this is a Newtonian view of the universe and time; as James Gleick notes, "Laplace [was] the eighteenth-century philosopher-mathematician who caught the Newtonian fever like no one else." (3) Still, Laplace's essay is only one extreme example of a rather common, Newtonian notion of the universe predicated on determinism and, therefore, predictability. For scientists like Laplace, one implies the other; because the universe is deterministic, the future can be extrapolated from a minute study of the past and the present: "the revolution in scientific thought that culminated in Newton," writes Ian Stewart,
  led to a vision of the universe as some gigantic mechanism,
   functioning "like clockwork" ... In such a vision, a machine is
   above all predictable.... An engineer who knows the specifications
   of the machine, and its state at any one moment, can in
   principle work out exactly what it will do for all time. (4)


The "vast intelligence" dreamt of by Laplace, which knows "all the forces by which nature is animated" and can predict the whole universe's future from the past, is, then, that of a superengineer or superphysicist.

It is also that of a historian-cum-prophet. Strangely enough, in Laplace's clockwork universe, his omniscient engineer-physicist is also, by definition, both historian and prophet for whom "the future, as the past, ... [is] present before ... [his/her] eyes." If this seems a rather peculiar intellectual melange to a twentieth-first-century reader, Laplace is actually gesturing towards an overwhelmingly important trend in Enlightenment and post-Enlightenment thought in which history, prophecy, and science were often rigorously combined or casually mixed up. Their combination is particularly apparent, for example, in some of the most influential nineteenth-century theorizations of history, including those of G. W. F. Hegel, Thomas Macaulay, Auguste Comte, J. S. Mill, Alexis de Tocqueville, G. H. Lewes, Herbert Spencer, and even Karl Marx. As John Schad remarks, "to a quite unprecedented extent, mathematical terms and principles were applied [in the nineteenth century] not just to the physical world but the whole life of man. Witness, in historiography, the efforts of Ranke, Comte and Taine both to study the past for 'statistical patterns' and to formulate thereby 'laws of history'" (5)--and, of course, many of these thinkers extrapolated from their deterministic "laws of history" future history: Comte, Hegel, and Marx are obvious examples in this respect.

If, though, many of these historians-cum-prophets and their predictions have proved rather fallible in retrospect, perhaps what Laplace is really looking forward to are the vast, infallible intelligences of modern computers. Computers can obviously command and analyze both individual formulae and the massive amounts of data to which Laplace refers, and on which so many nineteenth-century writers come to rely. Indeed, Gleick suggests that "the fathers of modern computing always had Laplace in mind" (14), and some of these fathers are not so historically distant to Laplace as might first appear. Most famous is Charles Babbage and the Difference and the Analytical Engines he designed in the 1820s and 1830s. Babbage proposed the Analytical Engine in 1834, and it was designated by his accomplice, Ada Lovelace, "a thinking ... [and] reasoning machine"; as Doron Swade puts it, "what we now take to be a computer is ... a general-purpose machine capable of being programmed by the user. And the Analytical Engine pretty well fits the bill." (6) At this point, Babbage declared, "the whole of arithmetic now appeared within the grasp of mechanism" (qtd. in Swade, Cogwheel, 91).

By grasping "the whole of arithmetic," Babbage's Engines seem to represent, at least potentially, Laplace's vast, all-seeing intellect, which can know all forces at once. Accordingly, Babbage's Engines also hold out the tantalizing promise of total predictability that, for Laplace, necessarily goes along with such omniscience. Since their future operation is predetermined by programming, predictability is in the very nature of computers, and this was certainly the case with Babbage's Analytical Engine, which was meant to be programmed with punched cards; as Swade remarks, Babbage fully appreciated "the exacting causality of machines and the uncompromising determinism of their design." (7)

Moreover, Babbage also used the completed section of the Difference Engine no. 1 to demonstrate the "uncompromising determinism" of the world beyond it; as Swade points out, by drawing an analogy between the way in which his Difference Engine functioned and the workings of nature, Babbage sought to demonstrate that "miracles in nature are not violations of natural law but ... programmed discontinuities" so that "God was a programmer" (qtd. in Swade, "It Will Not," 46). If only by analogy, Babbage's machines also had the potential to reveal truths about the world beyond them and to comprehend and simulate--perhaps even predict--"miracles in nature." In this respect, Babbage yet again looks forward to twentieth-century computing and its preoccupation with second-guessing nature; as Gleick writes, "the history of computing and the history of forecasting were intermingled ever since John von Neumann designed his first machines at the Institute for Advanced Study in Princeton, New Jersey, in the 1950s. Von Neumann recognized that weather modelling could be an ideal task for a computer." (8)

If all this seems like Laplace's dream becoming a reality, the point that "weather modelling" has forcibly demonstrated in recent years is that the "miracles of nature" to which Babbage refers remain inexplicable miracles even--or especially--when simulated on computers. To put this another way, at the very moment when Laplace's dream seems to come true--at the very moment when the development of modern computing apparently promises total, deterministic predictability--it is actually disintegrating once and for all. This can be demonstrated by a frequently cited story from the 1960s about Edward Lorenz, a meterologist-cummathematician, who, as Gleick writes, "had boiled weather down to the barest skeleton" in a computer simulation, hoping to discover the key to weather patterns and, therefore, forecasting
  one day in the winter of 1961, wanting to examine one sequence
   [of weather] at greater length, Lorenz took a shortcut. Instead of
   starting the whole run over, he started midway through. To give
   the machine its initial conditions, he typed the numbers straight
   from the earlier printout....

     This new run should have exactly duplicated the old.... Yet
   ... Lorenz saw his weather diverging so rapidly from the pattern
   of the last run that, within just a few [simulated] months, all
   resemblance had disappeared ...

     The problem lay in the numbers he had typed. In the computer's
   memory, six decimal places were stored.... Lorenz had
   entered ... [a] shorter, rounded-off number, ... assuming that
   the difference ... was inconsequential.

     It was a reasonable assumption.... Lorenz's Royal McBee
   [computer] ... used a purely deterministic series of equations.
   Given a particular starting point, the weather would unfold
   exactly the same way each time. [So, theoretically,] given a
   slightly different starting point, the weather should unfold in a
   slightly different way.... A small numerical error was like a
   small puff of wind.... Yet in Lorenz's particular system of
   equations, small errors proved catastrophic (16-17, italics added).


This was, of course, one of the primary demonstrations of what has since become known in chaos theory as the Butterfly Effect or, more technically, "sensitive dependence on initial conditions," whereby, as Gordon Slethaug writes, "similar ... systems [are] ... never ... wholly identical and ... the results of ... small initial changes may be radically different" within these systems. Hence, "an extremely minor ... act [might] cause ... disruptions of a huge magnitude.... Lorenz suggests that a butterfly flapping its wings in Brazil may set off minor perturbations ... that are afterwards magnified, creating tornadoes ... in Texas." (9)

Consequently, Gleick says that Lorenz "decided that long-range weather forecasting must be doomed." (10) What Lorenz's simulation showed above all was that determinism does not necessarily imply predictability. Laplace and so many other nineteenth-century physicists, historians, sociologists, and philosophers assumed that the determinism of a Newtonian universe implied predictability; however, Lorenz's early work marked a decisive break between determinism and predictability. In this respect, it is important to note that Lorenz did use a "purely deterministic system of equations" in his computer simulation, but that these equations were so sensitive to initial conditions that minute differences in the initial variables resulted in vastly different outputs. Lorenz's equations are deterministic, but are so complex, so sensitive to initial conditions as to be entirely unpredictable--and, by analogy, the same can be said about the weather system they simulate. Since such apparently minor causes as "a butterfly" might become magnified into a tornado, there are clearly an infinite number of initial conditions to take into account, and even modern computers cannot handle infinite amounts of data: "to know a single state of the global weather system," writes Lorenz, "we must ... know the value of each variable at every point. Since there are plainly an infinite number of points in the atmosphere, the system ... [has] an infinite number of variables." (11)

In such an infinitely complex system, the masses of data analyzed by computer can never be quite enough, and accurate forecasting must be an infinitely receding horizon. Indeed, despite the hopes expressed for computer forecasting by von Neumann and others, what computers have achieved above all in this field is to bring attention to their own deficiency. By being able to process and analyze greater and greater masses of data, computers have demonstrated that, in terms of understanding and predicting complex systems like the weather, greater and greater masses of data still are always needed. In the latter half of the twentieth century, Brian Kaye writes,
  modern scientists became increasingly optimistic that they would
   achieve the highest levels of Laplacian determinism as they used
   their increasingly complex and massive computers.... However,
   the mountains of numbers churned out ... began to indicate
   that there were many physical systems which ... were so
   sensitive to initial conditions that any hope of predicting their
   future behaviour ... would remain forever an impractical
   dream. (12)


The dream has, though, always been open to question; the optimists' dream of Laplacian determinism and predictability has from its very inception been accompanied by pessimism and uncertainty. As soon as he has propounded the wish for a "vast intelligence," Laplace himself goes on to admit that such an intelligence "will always remain infinitely removed [from] ... the human race." (13) Hence his emphasis on probability theory for prediction; though his Philosophical Essay on Probabilities begins by setting out his ideal of a "vast intelligence" that knows and predicts everything with absolute certainty, the rest of the work proceeds to move away from this in favor of a much more uncertain mode of prediction based on probability theory.

Since Laplace's intelligence "will always remain infinitely removed [from] ... the human race," only probability theory and statistics--what Stewart calls the "practical arm of probability theory" (14)--can clumsily and inaccurately forecast the future. In point of fact, a few scientists were already coming to this conclusion in the later nineteenth century. At an 1873 meeting of the British Association for the Advancement of Science, for instance, James Clerk Maxwell proposed "to adopt the statistical method of dealing with large groups of molecules," because "the smallest portion of matter which we can subject to experiment consists of millions of molecules, none of which ever becomes individually sensible to us" (qtd. in Stewart, 51). Faced with the unknowable nature of individual molecules, Maxwell proposed to abandon the search for Laplacian certainty when attempting to understand and, indeed, predict the behavior of molecules: "[in applying] the statistical method ... to molecular science," he declared, "we meet with a new kind of regularity, the regularity of averages, which we can depend upon quite sufficiently for all practical purposes, but which can make no claim to ... absolute precision" (qtd. in Stewart, 52, italics added).

Despite Maxwell's claims, however, what the Lorenz story demonstrates above all is that, in many complex systems, "the regularity of averages" afforded by statistics is sometimes very far from being sufficient, particularly when used for the "practical purposes" of forecasting future behavior. Statistical prediction depends, as John Polkinghorne points out, on analyzing "bulk behavior ... from a coarse-grained averaging over contributions from many individual component states of motion," but, in a system like the weather which exhibits "sensitive dependence on initial conditions," such averaging necessarily becomes a very flawed means of prediction. (15) "Coarse-grained averaging" can hardly take into account minute causes such as butterfly wings, and is incapable, therefore, of predicting the resultant tornadoes in Texas.

If Lorenz's weather program proves this mathematically, many writers had pointed it out long before. Just as pessimism has always been the correlative of Laplacian optimism, skepticism about the efficacy of statistics has been around ever since they became so important to the social sciences in the early nineteenth century. The historian and social critic, Thomas Carlyle, for instance, directly challenges both the Laplacian view of the universe and the efficacy of statistics. In his novel, Sartor Resartus (1833-34), he condemns "Laplace's Book on the Stars" as a mere "Mechanism of the Heavens" unable to comprehend "the ... quite infinite depth ... of Nature." (16) Even more to the point, in his chapter on "Statistics" in his essay "Chartism" (1839), he asserts that "[statistical] tables are ... like the sieve of the Danaides; beautifully reticulated, orderly to look upon, but which will hold no conclusion ... [since] one circumstance left out may be the vital one on which all turned." (17) Carlyle, that is, emphasizes the vital importance of individual circumstances, something which is necessarily overlooked by the "coarse-grained averaging" demanded by statistics and probability theory. Well over a century before "chaos theory" brought such problems to consciousness in the scientific community, Carlyle understands the inadequacy of traditional statistics in dealing with systems that exhibit sensitive dependence on initial conditions, and where an individual circumstance might well be "the vital one on which all turned."

One such system is history. In his essay "On History" (1830), Carlyle declares that "history ... lies at the root of all science," and his description of history's "Chaos of Being" (18) is quite remarkably prescient of the complex systems delineated by modern chaoticians like Lorenz. Certainly, Carlyle is writing in a very different historical and cultural framework, but there are points of connection between his theorization of history as a kind of chaos and the concept of chaos expounded in the twentieth century by Lorenz and others. For instance, Carlyle's conception of history is certainly sensitively dependent on initial conditions and, therefore, on individual circumstances. Since, for Carlyle, "the whole [of the universe] is a broad, deep Immensity, [in which] ... each atom is 'chained' and complected with all," each individual atom is necessarily of huge consequence, making it quite conceivable that one of the most "important personage[s] in man's history ... [was] the nameless boor who first hammered out for himself an iron spade" ("On History," 85, 83). This attitude towards history and the universe is explained further in Sartor Resartus, where Carlyle argues that "there is not a red Indian, hunting by Lake Winnipic, can quarrel with his squaw, but the whole world must smart for it: will not the price of beaver rise? It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the Universe" (186). On this definition of the universe, individuals and their actions are elevated to an importance denied them by other, contemporary theories of history; while Marx and others posit a historical determinism based on analyses of impersonal forces like class conflict and economics, Carlyle conceives a subversive view of the universe in which the individual frequently matters more than these impersonal forces. This is precisely what makes possible the belief in history-altering heroes--and, indeed, antiheroes--he expresses in almost all his works. In his essay "On History Again" (1833), he writes that
  the battle of Chalons, where Hunland met Rome, and the Earth
   was played for [and] ... the sweep of ... swords cut kingdoms in
   pieces ... hovers dim in the languid remembrance of a few; while
   the poor police-court Treachery of a wretched Iscariot, transacted
   in the wretched land of Palestine, ... for "thirty pieces of silver"
   ... lives clear in the heads, in the hearts of all men. (19)


If the "Chaos of Being" that is Carlylean history empowers "obscure" individuals like Christ and Judas Iscariot over and above the huge collective forces which met at Chalons, it also enacts the ambivalent role Carlyle assigns to democracy in his writing. The chaos of history is also that of democracy: in some of his later writings, Carlyle refers to democracy as "the voice of Chaos," (20) and declares that "certainly, by any ballot-box, Jesus Christ goes just as far as Judas Iscariot; and with reason, according to the ... Dismal Sciences of these days. Judas looks him in the face, ... slapping his breeches-pocket, in which is audible the cheerful jingle of thirty pieces of silver." (21) Evidently, Carlyle is castigating democracy here for equalizing Judas and Christ, yet in effect democracy only does the same thing as his chaotic history--it raises from obscurity to prominence figures who are, at best, ambivalent (anti) heroes like Judas, Oliver Cromwell, and Napoleon. Carlylean history is democratic in the sense that it frequently elevates to heroic status individuals who are, to say the least, morally dubious; as Eric Bentley notes, "Carlyle's hero [sometimes] wears a halo, but his name is Machiavelli." (22) Moreover, history elevates Judas Iscariots and Machiavellis in precisely the same way as democracy--by a "majority of votes" that decides who was a hero, and what was important: "it is [generally] settled by majority of votes," writes Carlyle, "that such and such a 'Crossing of the Rubicon,' an 'Impeachment of Strafford,' a 'Convocation of the Notables,' are epochs in the world's history," whether or not "the majority of votes was all wrong" ("On History," 84, italics added). Here, it becomes apparent that Carlyle's view of history and, by extension, democracy in the 1830s were informed by the fierce debates surrounding the first Parliamentary Reform Act of 1832 and the promise, or threat, of majority rule.

It is the post-1789 world of popular, democratic, and revolutionary movements that provides the generative, historical context for Carlyle's conception of history as a chaos made up of "the aggregate of all ... men's Lives" ("On History," 80, italics added). Despite his own reputation for authoritarianism and excessive hero-worship, Carlyle sets himself up against the traditional "Political Historian, once almost the sole cultivator of history ... [who] dwelt with disproportionate fondness in Senate-houses [and] ... Kings' Antechambers; forgetting, that far from such scenes,... a whole world of Existence ... was blossoming and fading" (87). Instead, Carlylean histories like The French Revolution (1837) attempt to encompass a "whole world of Existence"--and, if, in the final analysis, this world remains largely Eurocentric rather than truly worldwide, Carlyle does at least imply that the Chaos of Being emancipates and empowers even the obscure "red Indian, hunting by Lake Winnipic" in a way that must seem deeply subversive for any imperial or colonial status quo. Unlike the 1832 Reform Act, Carlyle's Chaos of Being enfranchises everyone, and, consciously or not, he thus aligns himself with the most radical elements of, for example, the Romantic movement or the Chartists. Even the creed of heroism and hero worship he develops more fully later can be seen to accord with this pattern, given the fact that most of Carlyle's heroes do not dwell in "Kings' Antechambers," but, as A. L. Le Quesne points out, are "meritocratic heroes," who "rise ... from obscurity." All Carlyle's heroes are, at least to begin with, "red Indian[s] hunting by Lake Winnipic." Indeed, Le Quesne goes further and argues that Carlyle's heroic ideals actually depend on revolutionary, or, at the very least, democratic chaos and social flux: "most of [Carlyle's] ... heroes ... rise to heroism from obscurity ... [so] a ... fluid society is likely to be best adapted for [them].... The great virtue of revolutions is that they provide this fluidity. They allow the true heroes of a society ... to rise to the top." (23)

What did not provide such fluidity, of course, was the very world which was shattered by the French Revolution and Napoleonic "heroism"--the world, that is, of the ancien regime and the Marquis de Laplace. If Carlyle's view of history is marked by and calls for a chaotic, revolutionary and democratic modernity, the fixity and determinism of Laplace's view of the universe is necessarily bound up with the rigid, hierarchical ordering of prerevolutionary France; after all, Laplace was an ardent and influential supporter of the restoration of the French monarchy in 1815, and Laplace's deterministic, mechanical system would seem to encode his support for a traditional, inflexible hierarchy. Obviously, the Newtonian-Laplacian notion of the universe as a "clockwork" mechanism bound together by universal gravity postulates fixity in all of its constituent parts, and, as Adam Phillips argues, "if the universe was rule-bound like a clock, regulated by discernible laws as Newton had shown, then the presiding question was whether the idea of laws of nature could be applied to human nature." (24) In Walter Houghton's words, "starting in the eighteenth century, a host of thinkers assumed a natural order in human society analogous to that which Newton had discovered in the physical world." (25) The "mechanical fixity" of Newton's universe is seen as analogous to a "natural order" or hierarchy in human society.

It is precisely this Newtonian-Laplacian linearity and fixity that Carlyle is castigating in "On History," when he attacks some historians for merely tracking "chains," or chainlets, of "causes and effects." He declares that "it is not in acted, as it is in written History," for, in the former case, "every single event is the offspring ... of all other events.... And this Chaos ... is what the historian will depict, and scientifically gauge ... by threading it with single lines of a few ells in length! ... Narrative is linear, Action is solid" ("On History," 84-85). Clearly, Carlyle's questioning of linearity here is subversive of any hierarchy, such as the ancien regime, which depends upon a myth of continuity and heredity.

Carlyle's questioning of linearity also implicitly undermines the kind of authority attributed in the eighteenth and nineteenth centuries to scientists and other intellectuals. Ian Wylie suggests that, for most thinkers of the eighteenth and nineteenth centuries, "Newton [had] ... [revealed] the universe ... [as] an ordered and rational economy in which things behaved the way they did because of a preestablished harmony that was comprehensible to ... a few individuals of genius, and could be communicated by these individuals to the rest of mankind." (26) This is the authoritarian subtext of eighteenth- and nineteenth-century notions of Newtonian-Laplacian order--that there are vast intelligences or "individuals of genius" who can observe and comprehend the natural order and who, therefore, have legitimate authority over others. The disordered, incomprehensible, and infinite nature of Carlyle's history and universe, however, makes the idea of a Laplacian, omniscient intelligence or genius simply inconceivable. Carlyle disavows the search for the "vast intelligence" that knows everything, declaring that
  mere earthly Historians should lower ... [their] pretensions,
   more suitable for Omniscience than for human science.... That
   class of cause-and-effect speculators, with whom ... all things in
   Heaven and Earth must be computed ... [should] have now
   wellnigh played their part in European culture, and ... be ...
   verging towards extinction. ("On History," 85-86)


For Carlyle, the human science of history can never approach the Omniscience of Laplace's vast intelligence or Babbage's ideal computer that can compute all causes and effects "in Heaven and Earth," because history is by nature "inexhaustible" and "infinite" (86-87). Instead, Carlyle substitutes a democratic, contingent notion of intelligence, whereby the historian or scientist is always subject to his/ her own historical and geographical context; as he writes, "all Universal History is [really] but a sort of Parish History; which the 'P. P. Clerk of this Parish,' ... puts together" (92).

On the one hand, this means that Carlylean history is inevitably limiting for the historian with pretensions to universality and omniscience. On the other hand, as has been seen, Carlyle's paradigm is also liberatory in that, though subject to his/her context or Parish, the individual is also working in a universe where "the casting of [a] pebble ... alters the centre of gravity of the Universe" and where "each atom is 'chained' and complected with all," (Sartor Resartus, 186) so the individual historian is not just a spectator but also actually affects and changes the universe she or he talks about. The individual historian, though bound to a seemingly insignificant Parish, will also have a universal effect on the history she or he talks about, presumably altering "the centre of gravity of the universe" if nothing else. In a "Chaos of Being," the Carlylean historian is the same as the Carlylean hero.

Various branches of late twentieth-century science and, particularly, chaos theory can be aligned with Carlyle's "Chaos of Being" in this respect. For a start, Carlylean historians (such as himself) and heroes (such as Cromwell and Napoleon) clearly undermine the utilitarian and statistical assumption of the primacy of the group over the individual, the large cause over the minute one. And, as has been seen, the Butterfly Effect is all about how apparently individual, minute circumstances are not necessarily less important than apparently large, collective causes. The privileging of large causes, so fundamental to Western science, fails to explain how certain natural systems function. Of the modern mathematician and pioneer of fractal geometry, Benoit Mandelbrot, Gleick remarks that, "instead of separating tiny changes from grand ones, [his work] ... bound them together." Gleick explains further:
  How big is it? How long does it last? These are [apparently] the
   most basic questions a scientist can ask.... They suggest ...
   [that] scale is important.... But the claim of fractal geometry
   is that, for some elements of nature, looking for a characteristic
   scale becomes a distraction. [For example, a] hurricane, by
   definition,... is a storm of a certain size. But the definition is
   imposed by people on nature. In reality, atmospheric scientists
   are realising that tumult in the air forms a continuum.... The
   ends of the continuum are of a piece with the middle. (27)


The mathematical and graphical depiction of the continuum comes in the form of the now well-known fractal pictures, the constitution of which usually consists of infinite self-similarity at all scales; Gleick explains that Mandelbrot's "irregular patterns in natural processes [all had] ... a quality of self-similarity. Above all, fractal meant self-similar. Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern" (103). As Mandelbrot himself writes of the phenomenon of Brownian motion, whereby particles suspended in liquids or gases move around in an apparently random manner,
  different parts of the trail of Brownian motion can never be
   precisely superposed on each other.... Nevertheless, the parts
   can be made to be superposable in a statistical sense. Nearly all
   the fractals in the present Essay are to some extent invariant
   under displacement ... [and] most ... are invariant under
   certain transformations of scale.... A fractal invariant under
   ordinary geometric similarity is called self-similar. (28)


Mandelbrot, it seems, envisages and partly realizes a different kind of statistics far removed from the nineteenth-century probability theory of Laplace or the statistical physics of Maxwell, where, in Polkinghorne's words, only "bulk behaviour ... from many individual component states of motion" can be taken into account. Mandelbrot conceives a statistics which can and does take into account what would seem to Laplace and Maxwell minute and insignificant. As Hugh Roberts points out, "true fractals do not permit any hierarchy of scales"; (29) Mandelbrot's fractals are based on a statistical science that, at least in theory, collapses the distinctions between the large and the small, between mass movements and supposedly individual randomness, demonstrating how the infinitely complex patterns and movements of the mass are strikingly self-similar to the equally infinitely complex patterns and movements of that which is relatively minute.

As if to justify his ambitious project, Mandelbrot repeatedly invokes previous writers, philosophers, and scientists. "It is good," he tell us, "to point out that self-similarity is an old idea," (30) and he goes on to appeal to Aristotle, Gottfried Leibniz, Immanuel Kant, Jonathan Swift, Georg Cantor, and even, oddly enough, Laplace. Given this illustrious prehistory of fractal geometry, it should hardly be surprising that Carlyle often seems to anticipate chaos theory and, in particular, Mandelbrot's work; after all, Carlyle studied mathematics at Edinburgh University.

Like many modern mathematicians, Carlyle is particularly concerned with the nature of infinity. For him, history is not only "of infinite depth behind us," but also "of infinite breadth around us" ("On History Again," 99). Just as Mandelbrot's fractal representations of various phenomena are infinitely detailed on microscopic and macroscopic scales, so Carlylean history is both infinitely huge and infinitely minute; Carlyle declares that "Time, like Space, is infinitely divisible; and an hour with its events, with its sensations and emotions, might be diffused to such expansion as should cover the whole field of memory, and push all else over the limits" (95). Carlylean history is, in modern terms, a kind of fractal; when he talks of an "ever-living, ever-working Chaos of Being, wherein shape after shape bodies itself forth from innumerable elements" in which "each atom is 'chained' and complected with all" ("On History," 85), the pictoral nature of his imagery might well suggest to a modern reader the infinitely complex patterns imagined by Mandelbrot and others. This could be said of all of the various images Carlyle uses in the two essays on history; at another point, for instance, he declares that "we might liken Universal History to a magic web; and consider with astonishment how ... the ever-growing fabric wove itself forward, out of that ravelled immeasurable mass of threads and thrums" ("On History Again," 98). In one peculiar passage, he writes that a religious historian might attempt to "pause over the mysterious vestiges of Him, whose path is in the great deep of Time, whom History indeed reveals, but only all History, and in Eternity, will clearly reveal" ("On History," 85). For the religious historian, that is, history is a fractal in a strict sense, since it is not only "Eternal" and infinite, but it is also infinitely self-similar on different scales: vestiges of the divine are similarly present at microscopic and macroscopic scales.

Carlyle repeatedly gropes towards a new language, a new mode of representation, a new kind of science in his conceptualization of history. Throughout the two essays on history, he uses a welter of pictoral metaphors to capture his vision of history--and, if all these images seem inadequate and are rejected one after another for something new, perhaps the metaphor he is really looking for has not yet been invented. Over and over again, his images seem to grope towards--but fail, of course, to reach--the modes of "scientifically gaug[ing]" and representing chaos that experimental mathematics and fractal geometry have now made conceivable. In the last image at the end of "On History Again," Carlyle attempts to plot his view of history in geometrical terms in a way that must at least bring to mind the ability of modern mathematics to represent complex systems pictorially--and that, by its emphasis on the infinite, comes close to being a kind of early fractal. "In shape," he writes, "we might mathematically name [history] ... Hyperbolic-Asymptotic; ever of infinite breadth around us; soon shrinking within narrow limits: ever narrowing more and more into the infinite depth behind us" (99).

Oddly enough, then, Carlyle's "Chaos of Being" does have a kind of geometric shape--chaos is also patterned--however strange and complex that pattern might seem to those contemporary, "Newtonian" historians who try to gauge the "Chaos of Being" with their linear "chains," or chainlets, of "causes and effects." John Clubbe notes that, "by the early nineteenth-century, the view of chaos as an unformed void began to be replaced by the view of chaos as an antagonist to order," (31) an attitude which is fundamental to the assumptions made by various historians and scientists in the nineteenth century. By contrast, Carlyle's view of history is very much a twentieth-century science in its ability to discern pattern within disorder, and vice versa; as Clubbe remarks, "the emerging science of chaos but gives a local habitation and a name to what Carlyle had intuitively grasped long before: that ... chaos serves as both a precursor and a seedbed of cosmos" (76). This, of course, is one of the fundamental points of Mandelbrot's fractal geometry and chaos theory in general: chaos and order, chaos and mathematics, chaos and pattern, pattern and randomness are not necessarily mutually exclusive categories, but, rather, each is often inscribed in the other. According to chaos theory, patterns exist within chaos, which exists within patterns, which exist within chaos and so on; as Clubbe notes, "Lorenz ... has found unpredictability in chaos, but he has also found pattern.... [and] Gleick explains how, within apparent chaos, nature reveals meaning and structure: 'the essence of the earth's beauty lies in disorder, ... a peculiarly patterned disorder'" (76). Likewise, Carlylean past and future history is at once a "Chaos of Being" and "definitely shaped, predetermined and inevitable" (80).

(1.) Roland Barthes, "Science Versus Literature," in Twentieth Century Literary Theory: A Reader, ed. K. M. Newton (Basingstoke: Macmillan, 1988), 144.

(2.) Pierre-Simon Laplace, A Philosophical Essay on Probabilities, trans. Frederick William Truscott and Frederick Lincoln Emory (New York: Dover, 1995), 4.

(3.) James Gleick, Chaos: The Making of a New Science (London: Vintage, 1998), 14.

(4.) Ian Stewart, Does God Play Dice? The Mathematics of Chaos (Oxford: Basil Blackwell, 1989), 9, 12.

(5.) John Schad, The Reader in the Dickensian Mirrors: Some New Language (New York: St. Martin's P, 1992), 94.

(6.) Ada Lovelace, "Sketch of the Analytical Engine," in Literature and Science in the Nineteenth Century: An Anthology, ed. Laura Otis (Oxford: Oxford UP, 2002), 19; Doron Swade, The Cogwheel Brain: Charles Babbage and the Quest to Build the First Computer (London: Little Brown, 2000), 113. Further references to this latter work are cited parenthetically in the text.

(7.) Doron Swade, "'It Will Not Slice a Pineapple': Babbage, Miracles and Machines," in Cultural Babbage: Technology, Time and Invention, ed. Francis Spufford and Jenny Uglow (London: Faber and Faber, 1997), 47. Further references to this essay are cited parenthetically in the text.

(8.) Gleick, Chaos, 14.

(9.) Gordon E. Slethaug, Beautiful Chaos: Chaos Theory and Metachaotics in Recent American Fiction (Albany: State U of New York P, 2000), xxiii.

(10.) Gleick, Chaos, 17.

(11.) Edward N. Lorenz, The Essence of Chaos (Seattle: U of Washington P, 1993), 81.

(12.) Brian Kaye, Chaos and Complexity: Discovering the Surprising Patterns of Science and Technology (Weinheim: VCH Verlagsgesellschaft, 1993), 5.

(13.) Laplace, A Philosophical Essay, 4.

(14.) Stewart, Does God Play Dice?, 46.

(15.) John Polkinghorne, Quantum Theory: A Very Short Introduction (Oxford: Oxford UP, 2002), 6, italics added.

(16.) Thomas Carlyle, Sartor Resartus, ed. Kerry McSweeney and Peter Sabor (Oxford: Oxford UP, 1999), 195. Further references to this work are cited parenthetically in the text.

(17.) Thomas Carlyle, "Chartism," in English and Other Critical Essays (London: Dent, 1967), 170.

(18.) Thomas Carlyle, "On History," in English and Other Critical Essays, 80, 84, italics added. Further references to this work will be cited parenthetically in the text.

(19.) Thomas Carlyle, "On History Again," in English and Other Critical Essays, 97. Further references to this work will be cited parenthetically in the text.

(20.) Thomas Carlyle, Latter-Day Pamphlets, in The Works of Thomas Carlyle, 30 vols. (London: Chapman and Hall, 1898), 20:5, italics added.

(21.) Thomas Carlyle, "The Nigger Question," in English and Other Critical Essays, 316.

(22.) Eric Bentley, A Century of Hero-Worship (Boston: Beacon P, 1957), 71.

(23.) A. L. Le Quesne, Carlyle (Oxford: Oxford UP, 1982), 64-65.

(24.) Adam Phillips, introduction to A Philosophical Enquiry into the Origin of our Ideas of the Sublime and the Beautiful, by Edmund Burke, ed. Adam Phillips (Oxford: Oxford UP, 1990), xi.

(25.) Walter E. Houghton, The Victorian Frame of Mind, 1830-1870 (New Haven and London: Yale UP, 1957), 147, italics added.

(26.) Ian Wylie, "Romantic Responses to Science," in A Companion to Romanticism, ed. Duncan Wu (Oxford: Blackwells, 1999), 505.

(27.) Gleick, Chaos, 86, 107-08.

(28.) Benoit Mandelbrot, The Fractal Geometry of Nature (New York: W. H. Freeman, 1983), 18.

(29.) Hugh Roberts, Shelley and the Chaos of History: A New Politics of Poetry (Pennsylvania: Pennsylvania State UP, 1997), 276.

(30.) Mandelbrot, The Fractal Geometry of Nature, 19.

(31.) John Clubbe, "Carlyle's Subliminal Feminine: Maenadic Chaos in The French Revolution," Carlyle Studies Annual 16 (1996), 77.

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Date:Jun 22, 2004
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