Literature After Euclid

Literature After Euclid tells the story of the creative adaptation of geometry in Scotland during and after the long eighteenth century. Analyzing the work of Scottish literati, Matthew Wickman challenges how we perceive the Scottish Enlightenment and the modernist ethos that relegated "classical" Enlightenment to the dustbin of history.

Literature After Euclid
The Geometric Imagination in the Long Scottish Enlightenment

Matthew Wickman

2016 | 304 pages | Cloth $69.95
Literature
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Table of Contents

Introduction

PART I. THEOREM: SHAPES OF TIME
Chapter 1. Scotland's Age of Union: Toward an Elongated Eighteenth Century
Chapter 2. Scott's Shapes

PART II. SCHOLIUM: SCENES OF WRITING
Chapter 3. "Wild Geometry" and the Picturesque
Chapter 4. Burns After Reading, or On the Poetic Fold Between Shape and Number

PART III. LOCUS: MEASURING THE SCOTTISH ENLIGHTENMENT ACROSS HISTORY
Chapter 5. The Newtonian Turn/Turning from Newton: James Thomson's Poetic Calculus
Chapter 6. A Long and Shapely Eighteenth Century

Notes
Bibliography
Index


Excerpt [uncorrected, not for citation]

Introduction

Always visualize! Increasingly, this revision of Fredric Jameson's famous opening salvo in his 1981 study The Political Unconscious—"Always historicize!"—seems to be acquiring the status of an imperative in an age of big data, when traditional distinctions of canon and period seem ever less satisfying, ever more the product of historiographical accident. Visualization, the graphical display of information, accompanies a new method of historicist engagement: distant reading. As Franco Moretti puts it in his collection bearing that title, "The trouble with close reading," the method of much of the "new"—that is, old—historicism, "is that it necessarily depends on an extremely small canon. . . . [Y]ou invest so much in individual texts only if you think that very few of them really matter. Otherwise, it doesn't make sense." And in an era when digital archives make vast corpuses available online, a diminishing number of scholars, it seems, find close reading sensible. "Close reading is not only impractical as a means of gathering evidence in the digital library," Matthew Jockers argues, "but big data render it totally inappropriate as a method of studying literary history." In part, this is because the exponential increase in the amount of information at our disposal and the capacity to scale that information to sizes ranging from the virtually infinite to the infinitesimal will inexorably exert an influence on the kinds of historical questions we are able to pose. These are stories we must show as much as tell. And so, digital humanists make the case that scholars of literary history "have increasingly become involved in what is often referred to as the 'visual turn' . . . sometimes correlated with the 'spatial turn' that has favored mapping."

If we ask the question, as digital humanists often do, of how our tools for engaging the past reflect the tools of that past, then we may find ourselves considering "models of statistical expression, such as bar and pie charts, [that] came from the world of 18th century 'political arithmetic' and provided a rich and much developed legacy that extended the vocabulary of much older visual forms of diagrams, grids, and trees." Or, we may undertake a more elemental encounter with a discipline that underwrote many of these older models. I am speaking here of geometry, a mathematical practice in which visual display has traditionally been a matter of course. It is geometry that lured Moretti, who professed in his landmark 2005 book Graphs, Maps, Trees that the patterns of history revealed by distant reading provoked him. A "geometrical pattern is too orderly a shape to be the product of chance. It is the sign that something," some force of history, "is at work here—that something has made the pattern the way it is." This is, indeed, a compelling idea. But geometry is not a static or homogeneous discipline, however much we may associate it with ideal objects. Modern geometry comes in a multitude of varieties—differential, projective, non-Euclidean, and more. Even classical geometry bears a history; its triangles, circles, and squares contain crevices of human complexity that may not always appear at first glance. In the eighteenth century, for example, the earlier half of the period on which Moretti turns sustained attention, geometry was in some circles (excuse the pun) a fraught philosophical exercise whose controversies spilled into exercises in literary form. In some cases, these are the very forms Moretti analyzes through distant reading, though without probing the wrinkles that introduce alternative meanings into those forms—nuances that only the supplementation of one (historical) geometry onto another (heuristic) one reveals.

This book explores at closer view those shapes that, today, we idealize from a "distance"; that is, it examines the interface between literature and geometry in a place—Scotland—and during an extended moment—a (very) long eighteenth century (extending into the nineteenth and even the twentieth centuries)—when certain mathematico-philosophical paradigms came under increasing pressure without yet yielding to entirely new formations. To the extent that these older models informed the humanities, as we will see they did, this book might thus be said to discuss a kind of "crisis in the humanities" some two centuries prior to its irruption in the modern university. But what most interests me are the creative forms, literary and conceptual, that this crisis spawned. In examining them, I make no pretension that this is a book of mathematics; instead, I analyze literary experiments in what Arkady Plotnitsky calls "mathematical thinking" as the recrudescence of mathematical ideas in areas of culture that are not formally mathematical. The literature I analyze, for example, may not have directly intervened in mathematical debates during the (long) Scottish Enlightenment, but it creatively adopted and distorted mathematical ideas—or, as I will call them, figures of thought.

To explain what these figures are and what they might mean, let me resort to the familiar historicist device of the anecdote. Sometime around 1789 or 1790, when she was in her late twenties, Joanna Baillie assigned herself a peculiar task:

I heard a friend of ours, a mathematician, talking one day about squaring the circle as a discovery which had been often attempted but never found out[.] . . . I very simply set my wits to find it out. . . . "But surely" thought I "it will be found in Euclid," so I borrowed from my friend Miss Fordyce, now Lady Bentham, an old copy of Euclid. . . . I went through it by myself as well as I could, though in no very plodding way, being only intent on this one purpose. . . . But my disappointment & mortification may easily be guessed, when on arriving at the apendix of the book . . . I found my own discovery . . . proved in a different manner. "So I have mistaken what is meant by squaring the circle" said I bitterly to myself, and thus ended my mathematical pursuits. I had by this time written Basil & De Monfort and very soon consoled myself for such a wild goose chace.
Baillie's experience—in some ways repeating an idyll from her childhood when, "without any teacher, [she went] through a good part of Euclid for her own amusement"—seems familiar, even a little self-reflexive. Not only did she turn to the arts, specifically the theater, as a failed mathematician (the lot of many a student of literature), but the problem she addressed possessed an evocatively literary aspect. Contrary to her claims, the riddle of how to construct a square with the same area as a given circle using only ruler and compass had not already been solved (indeed, it would be proven insoluble later in the nineteenth century), but the equation of dissimilar properties—square is circle, this is that—corresponds with the structure of metaphor, the archetypal poetic trope. For Baillie, to square the circle was to craft the ultimate metaphor, to make romance a reality, to bring fancy to fruition.

But failing in mathematics—that is, in a "literary" aspect of geometry—she turned to literature—or to a "geometric" dimension of drama. I say this not because Baillie's Plays of the Passions, as she later called them and for which she is best known, are overtly mathematical but rather because they reveal the workings of a "methodical mind" that remained evocatively Euclidean. Baillie was fascinated, for instance, by idealized constructs or by what Plato called the geometric "knowledge of the eternally existent." In her "Introductory Discourse" to her published Series of Plays (1798), she professed her desire to distill the perfect shapes, as it were, of natural passions from the "decoration and ornament, all [the inflated] loftiness and refinement" of orotund poetry. Her early play De Monfort presents a kind of Platonic abstraction in the character of Lady Jane de Monfort, "[s]o stately and so graceful [in] her form" that other characters "shr[i]nk at first in awe." But Lady Janes are not ubiquitous presences in Baillie's Plays of the Passions; indeed, she tempered such archetypes with a dramatist's taste for mixed forms. The propensity to have "all tragic characters drawn very good or very bad . . . arises from a nobleness in our nature; but the general prevalence of [such designs] would be the bane of all useful and natural delineation of character." Hence, Michael Gamer observes, Baillie's theater "demonstrate[s] a doubleness of perspective" between the ideal shapes of the fancy and the contingent forms they take in everyday life. It's a case not of squared circles, two idealized constructs, but of conflicting dramatic imperatives.

Baillie's example speaks to the larger subject of this book, which concerns the relationship between literature and mathematics, especially geometry, in Scotland's long eighteenth century. I make the case for a kind of disjunctive union between these disciplines that causes them not so much (or not only) to inform or reflect as to supplement and provoke one another. In the chapters that follow, for example, historical fiction will be seen to evoke and disfigure calculus, and poems enacting the formation and breakdown of community will conjure the specter of irrational numbers. But to what effect, we might ask? How might the indication of a mathematical unconscious in these texts—or, more simply, a balky and bedimmed, though conscientious, engagement of mathematical ideas in them—expand the scope of implication of these texts and possibly reconfigure literary form and history? And how might the transmediation from one (mathematical) context to another (a literary one) expand our vision not only of what literary texts are but also of what they do—of how they intervene in knowledge creation?

While I focus primarily on some key literary exhibits from the early eighteenth through early nineteenth centuries (essentially, from poems by James Thomson to novels by Walter Scott), the backdrop for my study is the wider quarter-millennium between the analytic geometry of René Descartes and the self-conscious appeal to non-Euclidean geometry in the work of the European avant-garde. As different as the seventeenth and twentieth centuries are from one another, they represent historical bookends of an era in which mathematicians sought in various ways to circumvent the perceived limitations of classical geometry. For Descartes and his followers, this meant creating a coordinate system that affixed numerical or algebraic values to, for example, a given point along a plane, making it easier to calculate values; for avant-garde artists, it meant incorporating postclassical theories about the shape of the universe and the nature of reality into the visual and narrative arts, changing ideas about the nature of truth and the realm of the possible. The geometric thinking of Scottish Enlightenment literati—and I refer principally here to poets, novelists, and philosophers—falls literally and figuratively, I argue, between these two positions. Arriving two-plus generations after Descartes and a full century or more prior to, say, Marcel Duchamp, Scottish writers of the long eighteenth century, outwardly eschewing Cartesian innovation, often employed the language and constructs of classical geometry to creative ends that were neither evocatively Euclidean nor manifestly non-Euclidean. I call it a culture of late Euclideanism, a phrase that means little in mathematical-historical terms but indicates the deployment of a language of classically conceived nature to strange new ends. The book's title, Literature After Euclid, highlights the ambiguity of a literature imagined, at once, in the manner of and as a successor to Euclidean norms.

Therefore, like Baillie's tale of a dashed geometric fantasy, the story I am telling is only elliptically mathematical. It concerns less the history of mathematics in eighteenth-century Scotland—a history recounted elsewhere by George Davie, Richard Olson, Helena M. Pycior, Alex D. D. Craik, Niccolò Guicciardini, and others—than an analysis of how mathematics inflects or even revises our understanding of the literary and intellectual history of the Scottish Enlightenment. At the same time, it also takes up ways in which Enlightenment writers drew upon mathematical ideas as fuel for literary flights of fancy. And while this study will anchor itself in the long eighteenth century, it will occasionally extend its analysis into the later nineteenth and twentieth centuries before circling back (in post-Euclidean fashion) to its historical point of origin. Call it the study of a long, looping eighteenth century.

Such recursions have become an important part of Scottish literary history. This is largely because the latter's evolution as a discipline has involved both the shadowing and occasional subversion of grand narratives that help explain other branches of English literature. Today, for example, the Scottish Enlightenment, popularly recognized for its broad influence on later modernity, is seen by many scholars as contemporaneous with a Romantic movement that, in traditional "English," supposedly succeeds it. Scottish modernism, meanwhile, when it is identified as such at all, represents less a violent break from the "classical" past than the reformulated perpetuation of deep Scottish traditions. I will discuss these dynamics in greater detail in later chapters; the point worth underscoring here is simply that Scottish literary history has tended to downplay or even deny the types of constitutive ruptures that help explain some of the prominent categories—"enlightenment," "romanticism," and "modernism"—we use to organize literary history in other national or even international traditions. In Scotland's case, it is especially difficult to say when one period leaves off and another begins, and connections between them often wind around themselves, fashioning strange and sometimes contorted designs from the imagined flow of time.

One could analyze such puzzles without reference to mathematics, but the latter brings powerful and provocative elements to it. This is especially the case relative to literature and the arts, where mathematics explains but then skews or even collapses period distinctions on a grand scale. Take, for example, one of modernism's credos that new conceptions of non-Euclidean space, mathematically conceived during the nineteenth century, transformed cultural consciousness. Max Weber, Henri Lefebvre, Anthony Giddens, and other social theorists, reprising the credos of modernism, say that modernity involves a widespread "ability to critically estrange or reflexively engage the contemporary arrangement of the world." Such zones of discrepancy, they contend, heighten our sense of difference from the past: "The spatial practices of modernity . . . create the conditions of possibility for practicing, conceiving, and living temporality and history in new ways." Modernity's novelty, the idea of history made "new," consists of an ethos of spatiotemporal rearrangement, a reconfiguration of the traditional dimensions of experience. Such experience takes perhaps its most iconic aesthetic form in Cubist painting and stream-of-consciousness narrative. And yet, these latter forms operate on principles of recursion, with the presumed sweep of the eye across a canvas or the movement of a narrative from one episode to the next doubling back on itself (as angles onto an object converge with each other or as the train of a story's associations or a character's thoughts collapses distant moments or locales). Paradoxically, then, it is the muddle of nominal distinctions, the circling of viewpoints around themselves, that announces an aesthetic departure from traditional habits of representation: the "space" of the artwork declares its modernity by challenging the idea of straightforward succession on which it is predicated.

In the arts, then, mathematical concepts thus accentuate and challenge revisionist histories, undercutting the very presumptions of progress (from one period to another) on which, for example, a certain narrative of modernism is founded. And so, what are we to make of the fact that Scottish mathematics of the eighteenth century traditionally carries the association—even the stigma—of an entrenched, antimodern classicism? The seventeenth and nineteenth centuries are remembered as more innovative centuries in mathematical history—the seventeenth for analytic geometry and the geometric calculus, for instance, and the nineteenth for a variety of non-Euclidean geometries. During the eighteenth century, Scotland's signal contribution to mathematics was in traditional, Euclidean geometry, most evidently in the internationally esteemed work of Colin Maclaurin, Matthew Stewart, and Robert Simson. Simson especially is noteworthy for the half-century duration of his career as professor of mathematics at the University of Glasgow (1711-61) and for the massive influence he exerted over other scholars in that field, including Maclaurin and Stewart. But the sheer force of this influence and the insistence of all three on retaining and even, in Simson's case, "restoring" Euclidean geometry tend to obscure the role Scots played in experimenting within (and often at or across the limits of) Euclid. The richest illustration here may belong to Thomas Reid, best known as the founder of Common Sense philosophy, who devised a dynamic thought experiment that expressly involves non-Euclidean space. Reid's example, which I discuss below and then take up again in later chapters, is especially important to this book, for his innovation in a work of philosophy speaks to the degree to which mathematics permeated Scottish thought and culture during the long eighteenth century.

Such provocative convergences between geometry and the humanities allow us to reimagine literary and intellectual history, both substantively and formally (that is, in terms of what-led-to-what and also of what history even "is" as a figure—a shape—of thought). But these encounters, I claim, could only happen in a society where geometry suffused popular consciousness, however much or little particular writers may have engaged or grasped it in its fine details. Geometry, in other words, was not only a rigorous discipline but also a cultural medium, a trope.

In his memorable 1962 study The Democratic Intellect, George Davie explains why this was the case in eighteenth-century Scotland, remarking that geometry constituted a centerpiece of a Scottish university curriculum that impacted numerous corners of Scottish society. The nation's disproportionately high number of universities (five, compared with only two in England) meant that a greater percentage of Scots received some advanced training. And yet, in most cases, this was not higher education as we know it today, consisting less of intensive specialization than of broad exposure to a variety of subjects. The unifying link between these subjects, Davie argues, was philosophy, or metaphysics, which inculcated what we would call critical thinking. Geometric reasoning, with its emphasis on precision and logical exposition, featured prominently there. But "[t]he national habit was to treat mathematics as a cultural subject, not as a technical one, and it was found generally that the best way to maintain the students' interest in the subject was to give courses in which . . . elementary mathematics was discussed with special reference to its philosophy and its history." In this regard, mathematics functioned "as one of the 'humanities.'" This is why a number of distinguished Scottish Enlightenment literati remembered today for their contributions to philosophy and the arts were also mathematicians, particularly geometers.

Examples here are plentiful and impressive. We might begin with Reid, who eventually published his most famous book, An Inquiry into the Human Mind on the Principles of Common Sense, in 1764 after assuming the professorship of moral philosophy vacated by Adam Smith at the University of Glasgow. However, Reid composed most of this work while holding a professorship at King's College, Aberdeen, where his lectures "ranged across Euclidean geometry, algebra, fluxions [or Newtonian calculus], applied mathematics, mechanics, astronomy, electricity, magnetism, hydrostatics, pneumatics, physical optics, catoptics and the theory of vision," many facets of which found their way into the Inquiry. We might consider also the case of Adam Ferguson, author of An Essay on the History of Civil Society (1767) and hailed as "the father of modern sociology." Ferguson was named professor of mathematics at the University of Edinburgh in 1785 after serving (from 1759) as professor of natural philosophy and then (from 1764) as professor of pneumatics and moral philosophy. His Essay does not take up mathematics directly, but the latter informs Ferguson's philosophy in subtle but substantive ways, as when Ferguson explains the course of civilization by formulating astronomical analogies that were themselves the province of applied mathematics ("Where states have stopped short in their progress . . . we may suspect, that however disposed to advance, they have found a limit, beyond which they could not proceed. . . . On this supposition, from being stationary, they may begin to relapse, and by a retrograde motion . . . arrive at a state of greater weakness"). Newton introduced the notion of limits in his fluxional calculus, which was a conceptual apparatus used to calculate rates of motion and change. To cite another example (to which we will return below), Dugald Stewart, the son of the geometer Matthew Stewart and eventually Ferguson's successor as the chair of moral philosophy, also lectured on mathematics at the University of Edinburgh. John Playfair, meanwhile, was professor of mathematics there until assuming the position of chair of natural philosophy.

The migration of Scottish philosophers into and out of mathematical chairs in Scottish universities illustrates Davie's point. Unsurprisingly, then, mathematics informed diverse areas of the curriculum. The poet James Thomson, for instance, was taught the moral-philosophical implications of Newtonian philosophy while a student at the University of Edinburgh from 1715 to 1719. After making his way to London to seek his fortune, he took up a position at Watt's Academy, a school that emphasized Newtonian science. Eventually, Newtonian thought and tropes would suffuse Thomson's influential poem The Seasons, as we will discuss in Chapter 5. Or consider the very different case of Robert Burns, who had no university education but was tutored in geometry as a boy and later received further training in applied geometry when he began working for the excise. Geometric tropes and riddles crop up throughout Burns's work, as we will see in Chapter 4. They do so as well in the work of James Macpherson (see Chapter 1) and Walter Scott (see Chapter 2). We have already discussed Joanna Baillie's familiarity with mathematics. And the list goes on, as one would expect in a nation where geometry functioned as a lingua franca, or as what Regina Hewitt would call a source of "symbolic interaction" among disciplines as well as people.

But consistently with any language, which traffics in idioms, colloquialisms, figures of speech, and even slang, geometry took a variety of discursive and material forms in Enlightenment Scotland. Reid, for example, devised his thought experiment in non-Euclidean geometry not as a response to Euclid (the founder of the problematic parallel postulate), Galileo (the first person, according to Edmund Husserl, to "mathematize nature"), or Colin Maclaurin (Reid's teacher at Marischal College) but rather to David Hume. Hume's Treatise of Human Nature (1739-40), which purported "to introduce the experimental method of reasoning into moral subjects," asserted that all understanding, even geometric reasoning, finds its origin somewhere in our experience. On this basis, Hume had called into question the parallel postulate and, with it, the province of reason itself: "How can [a mathematician] prove to me . . . that two right lines cannot have one common segment? . . . [S]upposing these two lines to approach at the rate of an inch in twenty leagues, I perceive no absurdity in asserting, that upon their contact they become one." Geometry was not the object of Hume's critique, either, as much as an occasion for him to undercut pretensions to pure rationality, the supposed foundations of geometric reasoning. Reid's rejoinder took aim at Hume's reference by positing an apparently straight line traced around the surface of a sphere. If an observer were placed at the center of that sphere (and were nothing more than an instrument of vision, devoid of the sense of touch, for instance), she would not be able to recognize any curvature in the line. The "straight" streak across the sky would eventually simply appear, inexplicably, to rejoin itself. Reid's example purports to undercut Hume's notion that experience alone is adequate to the subversion of reason. His non-Euclidean experiment, predicated on the possibility of curved space, was born from the practical aim of justifying the quotidian, commonsense reliability of our rational faculties.

Notwithstanding the force of Reid's rebuttal, Hume's argument, which precariously perches human knowledge on "fictions of the understanding," would reemerge in the work of Walter Scott, whose historical novels employ such fictions in order to reconstruct plausible explanations for the course of human affairs. (I take up the creatively geometric qualities of these "fictions" in Chapter 2.) Equally influential on Scott was Dugald Stewart, who incorporated "the mathematical sciences" into his famous model of conjectural or theoretical history. Conjectural history accounts for the course of historical events beyond the reach of memory or historical record. Stewart formulated these ideas partly on the basis of an analogy with mathematics, discerning there "a better opportunity than in any other instance whatever, of comparing the natural advances of the mind with the actual succession of hypothetical systems." Mathematics, in other words, provided Stewart with a mode of reasoning and also with a series of examples of historical reconstruction that were the very essence of conjectural history. (His father, Matthew Stewart, in concert with Robert Simson, had vigorously attempted such reconstructions or "restorations" of supposedly lost portions of Euclid's oeuvre.) Hence, while Scott claimed, perhaps demurely, to be "an utter stranger to geometry," his fiction imported sophisticated (if residual) geometric paradigms into its representational structure and then, as we will see, dynamically reconfigured them in accordance with the demands of "history" as he envisioned it.

So, was Scott a geometer? No. But can geometry and its place in Scottish Enlightenment and Romantic culture enhance and in some ways revise our understanding of Scott's work? Yes, absolutely. And in pursuing a line of thinking that discloses the intersection of the humanities with so-called STEM fields (science, technology, engineering, and mathematics), this book supplements and enters into conversation with recent studies of the "long" Scottish eighteenth and nineteenth centuries that reveal Scottish literature's meaningful intersections with geography (Penny Fielding, Eric Gidal), geology (Adelene Buckland), and the sciences of man (Ian Duncan), to say nothing of books that divulge its relations to psychology (Juliet Shields, Evan Gottlieb) and media studies (Maureen McLane).

At a more general level, this book might be considered part of a modest but nevertheless noticeable "mathematical turn" in literary studies. Literary scholars from a variety of fields, interested in a wide range of subjects, are drawing upon mathematics as a way of reconfiguring periods, authors, texts—even the concepts of writing and history. This is true even (if not especially) for books that are by no means stricto sensu mathematical, like Moretti's Graphs, Maps, Trees or Wai Chee Dimock's Through Other Continents, which invokes fractals. But here, let me mention two other studies that address in a more rigorous fashion the integral relationship between mathematics and culture during the eighteenth and nineteenth centuries, for they touch upon a phenomenological difference between geometry and algebra that is important to my argument. In the first of these, Leon Chai traces the origins of the most universalizing schools of theory (for example, structuralism) to the Romantic era and accords special attention to the theoretical algebra of Évariste Galois. Around 1830, Galois had posed the question of "whether any equation . . . was solvable without [anybody] actually solving it." This was a hypothetical or theoretical query whose technicalities exceed the boundaries of our study here. More pertinent is what Chai perceives as the chief contribution of Galois's algebra to Romantic theory in "the spatial perspective" it accorded to problems: "What Galois offered Romantic theory, first of all, was a new way to look at concepts. Specifically, Galois theory attempted to describe concepts spatially," at least after a fashion, "in the notions of a field or group. . . . In particular, he saw how a spatial description of concepts might yield a new kind of insight into various problems or questions even if you didn't know exactly what elements were involved. Precisely because you lacked that knowledge, you focused on a simple question: whether they might collectively be said to form a set of some kind." As Chai sees it, these operations connected Galois's theory to other spatializing abstractions of the Romantic era, like Hegel's ideas concerning the stratified and dialectical arrangement of social phenomena and their stages of history. But as Alain Badiou has argued, the mathematical medium enabled Galois to address these questions of organization even more schematically, with dynamic consequences—theoretical and poetic—for thought.

Chai's disclosure of the shared spatial dimensions of the new algebra with other Romantic-era formations leads us to Alice Jenkins's compelling work on the meaning of spatiality in early nineteenth-century Britain. Similarly to Chai, "[t]he kind of space discussed in [Jenkins's] book . . . is the immaterial, conceptual space . . . that allows us to perceive and compare distances, sizes, and locations." But here, it is geometry and not algebra that serves as the focal point, for "geometry carried profound significance for the early nineteenth century by representing space in its purest form." Geometry represented a theory (or even a metatheory) of space in everyday life. That said, it is precisely where such spatiality was not pure or not strictly theoretical—that is, where it breached the boundaries of geometry proper—that it operates most powerfully in Jenkins's book, informing such cultural phenomena as the rhetoric of landscape in gardening, painting, and Wordsworthian poetry as well as a host of innovations in the physical and social sciences. If Chai's point is that Galois delineates Romantic theory at its highest level, Jenkins reminds us that geometry informs the metaphorics of spatiality on which such theory was implicitly, even if only figuratively, predicated.

Jenkins's work is crucial to my own, for I too focus on the cultural inscriptions of "geometry." And I too am interested in the interface between literature and geometry, a zone of imagination defamiliarizing each discipline. As a literary scholar, I am most intrigued (like Moretti and Dimock) by the way geometry helps us reimagine literary form and history. Hence, while I draw necessarily from important work in mathematical history, geometry is most significant to my study when it ceases to be purely geometrical and becomes something figurative—metaphorically and, after a fashion, diagrammatically. I borrow here from the illuminating discussion by John Bender and Michael Marrinan of a "culture of diagram" in the eighteenth century. As they see it, the diagrams employed in the French Encyclopédie illustrated not only particular objects but also the mental processes whereby we arrive at understanding. Modeled after geometry, the "virtual space[s]" of these figurative objects made possible "an imagined, tactile manipulation of things"; encyclopedic diagrams functioned as a heuristic mode of representation connecting mind and world. And the encyclopedists were not unique: Domenico Bertolini Meli observes that "[d]espite the growth of algebra," which acquired tremendous significance both mathematically and philosophically during the seventeenth and eighteenth centuries, "the geometrical diagram was a key tool of investigation. Mathematicians from Galileo to Newton worked and reasoned with the help of geometrical figures." (And indeed, the philosophical tension between algebra and geometry is a recurrent subject in this book, with the debates over calculus a particularly fruitful locus of discussion.)

One of my book's contentions, if I may put it this way, is that geometry in eighteenth-century Scotland possessed a meta-diagrammatic quality. That is, in addition to providing thinkers with useful sketches of the pathways of thought, geometry functioned as a medium through which literati reasoned across disciplines. A discrete science, geometry also served then as a common language connecting disparate fields: mathematics and philosophy, the natural and moral sciences, history and literature. (So it was that Henry Home, Lord Kames imagined his voluminous Elements of Criticism [1762], an exemplary work in literary studies, after the virtually universal [and, in Scotland, widely disseminated] Elements of Euclid.) I discuss several such examples of geometrically mediated works of literature in this book. The book's aim, however, is not simply to catalog such examples and create a broad cross section of geometry's permeation of Scottish literary culture in the long eighteenth century but rather to attend to particular cases that reveal something at play in the workings of literary form. I take this approach for three reasons. First, the Scottish Enlightenment is widely seen as a key moment in the development of modern literature and literary studies, both relative to the elaboration of literary discourse as creative or fictive writing and to the institutionalization of English literature as a discipline. And geometry's presence in Scottish literary culture helps us better understand how that culture's exponents imagined literary form (even, in ways, as a kind of shape) and its place among the incipient disciplines. Second, the relationship between literature and geometry, as well as the latter's relation in Scottish universities to the metaphysical tradition, makes literature a compelling discursive site for the explication, expression, and revision of tradition and hence a powerful vehicle not only of metaphysics but also of historiography. But third, and reflecting now on the first two, geometry's relation to literary texts and culture also modifies how we understand such categories as literature and history and thus "literary history," which is why the enigmatic status of Scotland's long, looping eighteenth century—at once classical and romantic, enlightened and modern—becomes important not only to Scotland or even to literary history itself but also to how we tell the broader story of literature's emergent place in the world of the sciences and, more expansively, the modern disciplines.

The book divides its study into three parts, each consisting of two chapters. The first part constitutes a theoretical overview of the subject, the second addresses iconic exhibits of the geometric imagination in Scottish culture, and the third probes the historical limits—the origins and aftermaths—of eccentric Euclideanism in Scottish Enlightenment culture. Chapter 1 sets forth what I call the late rather than non-Euclidean poetics of the Scottish Enlightenment, particularly as they pertain to literature and culture. I then turn in Chapter 2 to their illustration through a peculiar but telling manipulation of space in Walter Scott's second novel, Guy Mannering. There, at a key moment in the plot when the young protagonist returns from abroad to a Scottish estate that once belonged to his family but of whose origins he is oblivious, Scott enfolds a classical, Euclidean shape into a larger, non-Euclidean one. He does so as a self-reflexive literary rather than mathematical exercise, but the complex design of his narrative at this moment reveals Scott's sophisticated manner of navigating between "history" and "romance," the understanding and the imagination. The intersection of narrative and geometry in Scott's work proves to be uncanny, revealing how literature was capable not only of representing intellectual conflict but also of operating at the frontiers of available paradigms. This becomes especially important when we consider how critics have implicitly and in some cases expressly articulated a vision of Scott as an apologist for a modernity that operates on algebraic principles—that is, on a series of substitutions and displacements of a world reduced to a sequence of numbers. This chapter analyzes the differences between the geometric and algebraic interpretations of Scott, arguing that the geometric picture presented in Guy Mannering opens us to different formal and even ethical dimensions of Scott's work. Indeed, what critics have long recognized of Scott's novels, namely that their generic imbrication of fiction, history, and romance overdetermines Scott's narrower political convictions, intensifies when we reflect on the implications of the complex shapes embedded within them.

One way in which the subject of shape has long informed criticism of Scott is through the language and imagery of the picturesque, an aesthetic mode that influenced Scott and that has come to define the iconography of modern—and, seemingly, perpetually ancient—Scotland. In Chapter 3, I take up important ways in which theorists of the picturesque (and travel writers who adopted its conventions in the late eighteenth and early nineteenth centuries) effectively negotiated the limits of classical geometry in the scenic visual and verbal ways they arranged the Scottish landscape. Travelers did so partly by representing bizarre forms of nature that seemed opposed to the regular shapes of Euclid and partly by calling attention to the exigencies and inadequacies of traditional (Euclidean) perspective. The picturesque thus became a language of artistic abstraction that redounded upon and experimented with the geometric medium of its exposition. And while this describes picturesque aesthetics generally, its status as a late Euclidean scene of writing becomes especially representative of the interstitial status of late eighteenth- and early nineteenth-century Scottish culture, for which the categories of "Enlightenment" and "Romanticism" are notoriously labile.

One of the most distinctive figures associated with the Scottish landscape (albeit in its pastoral rather than Highland settings) is Robert Burns, whose status as national poet represents a fusion of place and people. His poetry, to which I turn in Chapter 4, also represents a merger of languages (English and Scots), forms (satire, description, elegy, epistle), eras (classical and modern), and national spaces (Scottish, British, and internationalist). But his work also negotiates relationships between the arts and sciences, as well as between classical and more expressly experimental forms of each. My aim in this chapter is to explain how this is so and, by extension, what Burns means to literary history. As we will see, Burns brings into relief the complex dynamics at play in key humanistic and literary concepts that were implicated in the logic of geometry, like Adam Smith's concept of sympathy (which fashioned individual and group psychology around a spatial relationship between subjects, objects, and "impartial spectators"). His poems "To a Louse" and "To a Mouse," for example, enact failures of sympathy and install beings characterized by their irreducible irrationality—an ontology of more and less than "one," the classical geometric idea of unity. For that matter, the very concept of a national poet, which is how Burns styled himself, rests on a border between a unified concept of the people and a fragmentation of that unit into a chaos of self-interested individuals—in effect, between a metaphysical idea of form and the dispersal of that ideal into a morass of modern numbers, which is precisely where some of the period's key philosophical debates involving geometry irrupted.

The conflict between form and number, we will see, comprises not only the intuitive nexus of the Burnsian legacy but also the more literal origins of calculus, whose practitioners derived in the place of whole numbers a malleable panoply of incremental units that made for more precise (albeit imaginary) systems of calculation. Having already discussed the historical and philosophical rudiments of the calculus in earlier chapters, I turn in Chapter 5 to a more rigorous examination of the conflict in Newton's fluxional calculus between its practical efficacy and its theoretical riddles and implications. Crucially, it was not only Scottish geometers who took up these conundrums and rushed to Newton's aid; so did poets like James Thomson. And it is Thomson's freighted poetic defense of Newton that I take up here. Thomson envisioned the Newtonian system as an imaginative poetics whose effects were both beneficial and mortifying to conventional poetry. In The Seasons, therefore, Thomson tacked a course between Newton and Milton that both accommodated and undercut the natural philosophy it purported to describe. As Thomson enacts it, to make like Newton is also to diverge from Newton; hence, in attempting to emulate Newton's calculus in explaining nature's universals, Thomson actually distorts and displaces it. The poem thus effectively foreshadows the twentieth century's "two cultures" debate between science and literature, speaking eloquently to an ambivalence toward the Newtonian project that permeated the Scottish Enlightenment, including in the work of some of Newton's most fervent defenders.

Readers will notice that, from Chapters 2 through 5, my argument unfolds through a backward chronology: beginning with Scott in the 1810s, I move to a consideration of the picturesque near the turn of the nineteenth century, then to Burnsian poems of the 1780s before jumping back a half-century to Thomson's poetry of the 1720s and 1730s (which was conceived during the era when Scottish Enlightenment geometry was beginning to arrive at its most forceful articulation). While each chapter cuts a broad historical swath (Chapter 4, for instance, brings Smith's moral philosophy from the 1750s and 1760s into contact with Burns's poems and then traces the logic of Burns's revisionist model of sympathy into nineteenth-century theories of topology that inform present-day practices in the [post]humanities), I proceed generally through a reverse chronological trajectory as a way of undertaking with literary readers unfamiliar with geometry a kind of journey into the heart of mathematical darkness—which is to say, into a set of ideas that has exerted a powerful but rarely recognized force on literary studies. Taking this path also enables me to clarify the relationship between geometry and its creative adaptation in later, more familiar (but now defamiliarized) literary and artistic contexts, not only in Burns and the picturesque and Scott but also in modernist works that reprised those earlier, innovative "forms."

Chapter 6 is the lone exception to this reverse chronological movement, taking stock of the long history of Scottish geometry by examining its recrudescence in later modernity. Beginning where Chapter 5 leaves off, with Thomson's poetry, it takes up the vestiges of Newtonian thought in Thomas Reid's Common Sense philosophy, then moves into Reid's legacy in Poe's 1848 cosmological essay Eureka before tracing the echoes of that legacy into the avant-garde. I show, for example, how Poe's essay became a key theoretical text for Charles Baudelaire and the Symbolists and how Walter Benjamin, drawing upon these various influences, adopted Poe's portraits of Newton and Johannes Kepler and brought them into his own work. I discuss Benjamin's well-known circuit of thought alongside Patrick Geddes's efforts to link modernist experimentation with Celtic traditions in his 1890s-era Scottish art journal, The Evergreen, and conclude by analyzing one of the key exhibits from the tradition of Scottish modernism that followed Geddes's line of thought, Hugh MacDiarmid's poem "On a Raised Beach." MacDiarmid's poem asserts the durability but also the radical quality of certain natural forms through time and thus represents a Scottish movement that drew, on one hand, upon national traditions and, on the other, upon a set of wider European ideas that had themselves been inflected by those same traditions—hence, upon developments that were both "new" and atavistic. MacDiarmid gazed at primordial Shetland rocks and beheld not only the cosmos and a set of cosmopolitan ideas but also the image of his own national inheritance refracted through those objects. This concluding chapter thus lights on the elliptical as well as the more overt presence of Scottish geometry in a late—an even later—Euclidean moment.

At its core, this is a book about the allure of form at an especially provocative and extended moment in literary history. I attend particularly to fortuitous instances of shape that reveal, first, how seemingly divergent disciplines intersect in works of literature and, second, how these convergences help us remap literary history. I am thinking less of Gaston Bachelard's evocative "poetics of space" than of the types of designs Moretti, for example, has taken to sketching as a way of illustrating—diagrammatically—the flow of time and its impact on genre. Increasingly evident in the humanities in the form of data visualizations, these shapes that so inspire digital humanists also appear occasionally in particular works—say, in the way a poem or narrative delineates (and implicitly spaces) its objects. But ultimately, I am less intrigued by the status of visual forms as data than I am by the effect of their appearance or by the supplement that shape adds to (literary) form. It conjures a unique intellectual constellation in the Scottish Enlightenment, beginning with David Gregory in the late seventeenth century and concluding with Scott in the early nineteenth, when the very idea of such figures arrives at an especially compelling degree of imaginative and self-reflexive exposition. This is a moment when literati dynamically explored the manifold possibilities and implications of forms, and their striking variants in the period's literature enable us to pose a set of simple but far-reaching questions, to wit: What would it mean to imagine a poem or any work of literature not only as a puzzle of signs (the [post]structuralist reflex) but also as a constellation of shapes—that is, to think of it not only by way of algebra, with its linguistic logic of symbolic substitution, but also through geometry, with its model of spatial relations? Indeed, what might it mean to conceive of a line of poetry? To answer these questions is to better grasp a world whose contours (as "visualizations") are increasingly familiar to us but whose history, in the work of an influential group of Scottish writers, risks perpetual obscurity.