In a well-known passage from the 1822 novel Annals of the Parish, John Galt’s first-person narrator, the Reverend Micah Balwhidder, composes a paradoxical sentence in which he describes a world eluding his grasp, and thus at some level comprehends a situation he claims not to understand. Rehearsing his reflections of the year 1808, he tells us that his fictitious community of Dalmailing in rural western Scotland has already felt the steep costs of “the American war” as well as “the present just and necessary contest” with France (Annals 179); what is more, with the building of a new cotton-mill and the establishment of a new town which houses this mill, he and his parishioners have engaged “so much with concerns of trade, that [they have] become a part of the great web of commercial reciprocities, and [feel] in [their] corner and extremity every touch or stir that [is] made on any part of the texture” (180). Such webs, of course, are ubiquitous in the modern world; they hypostatize the complexity of global systems in which no community is fully autonomous because each is part of a vast network, every corner bearing on some other. What is more, the pulsations to this network are so numerous and rapid, deriving from so many butterflies batting their proverbial wings, that nobody can fully account for it.

The puzzle emerges when we attempt to reckon with that for which we professedly cannot account. Even if it were possible for us to number the filaments of the “great web” to which Balwhidder refers, there is, as Arjun Appadurai reminds us, “an inherent temporal lag between the processes of [what we call] globalization and our efforts to contain them conceptually” (Appadurai 4). Balwhidder’s wisdom here, such as it is, consists in knowing that he knows nothing and documenting his own comparative blur: “As I come towards the events of these latter days, I am surprised to find myself not at all so distinct in my recollection of them, as in those of the first of my ministry” (Annals 183). Indeed, his purpose in writing is to capture this sense of acceleration: he wishes “to testify to posterity anent [or about] the great changes that have happened in [his] day and generation—a period which all the best informed writers say, has not had its match in the history of the world since the beginning of time” (183). This remark seems to belong to Galt as much as to Balwhidder, for it evokes not only a group of influential Scottish Enlightenment literati, particularly the stadial theorists descending intellectually from Adam Smith (whose work culminates, of course, with the great treatise on “commercial reciprocities,” The Wealth of Nations) to Dugald Stewart (who coins the phrase “conjectural history”), but also Galt’s contemporary Walter Scott, who in his popular historical fiction was attempting to lend these changes narrative form. In his famous “Postscript, which should have been a Preface” in Waverley (1814), Scott asserts that “[t]here is no European nation which, within the course of half a century, or little more, has undergone so complete a change as th[e] kingdom of Scotland” (Scott 340) referring specifically to the deterioration of the clan system, “the abolition of the heritable jurisdictions of the Lowland nobility and barons,” the “total eradication of the Jacobite party,” and the “gradual influx of wealth, and extension of commerce, [which] have since united to render the present people of Scotland a class of beings as different from their grandfathers, as the existing English are from those of Queen Elizabeth’s time” (340). Invoking a logic of uneven development, Scott attributes more than two centuries of change to a scant two generations—a mere sixty years—in Scotland, particularly the Highlands.

And yet, unlike Balwhidder, Scott purports to be able to grasp these developments in their complexity if only because “the change, though steadily and rapidly progressive, has, nevertheless, been gradual” (Scott 340). At one level, Balwhidder concurs: “The regular course of nature is calm and orderly, and tempests and troubles are but lapses from the accustomed sobriety with which Providence works out the destined end of all things” (Galt 71), or the narrative closure which Waverley, for example, seems to provide. Hence, while Balwhidder registers “the great concern” he and his parish “all began to take in the American rebellion” in the year 1775, he also recognizes that “throughout the better half of the year” the parish had “but little molestation of any sort” (71). The complexity for Balwhidder consists not so much in the rate of change as in the virtually incalculable range of factors motivating it. One can document the beginning and end of the war, but the qualitative difference in the region’s genius loci was something else. “[S]aving the building of the cotton-mill and the beginning of Cayenneville” around it, “nothing more memorable happened in” the year 1788; “still, it was nevertheless a year of a great activity. The minds of men were excited to new enterprises; a new genius, as it were, had descended upon the earth, and there was an erect and outlooking spirit abroad that was not to be satisfied with the taciturn regularity of ancient affairs” (118). Hence, Balwhidder feels he can only relate the “consequences” rather than the causes of this brave new world (180).

This returns us to the puzzle to which we refer above, Balwhidder’s comprehension of incomprehension (the fact that he knows nothing, the Socratic basis of wisdom). “[T]he best-informed writers” claim that the “great changes that have happened in [Balwhidder’s] day and generation . . . ha[ve] not had [their] match in the history of the world since the beginning of time” (183). If this is literally true, then no account, stadial or otherwise, could fully explain it since such an account would speak only to stages of the world in process of perpetual antiquation. But if the claim of these “best-informed writers” is an exaggeration, then it simply indicates the delusional state of Enlightenment theorists who are unable to explain the world of which they are part. In other words, the world is either too complex to lend itself to a definitive analysis, or else the world might avail itself to the right model but we are simply ill-equipped to formulate it. I know that I know nothing either because the world is unknowable or else because I myself happen to be incapable of such knowledge.

Galt’s “great web of commercial reciprocities,” making “felt in [his] corner and extremity [of Scotland] every touch or stir that was made on any part of the [global] texture” is thus an index of the changes occurring in Balwhidder’s parish and also a self-consciously confounding rebus that defies its own solution (180). In mathematical terms, it comprises something like the problematic set of all sets made famous by Bertrand Russell in 1910—a paradox that undermined an early variant of set theory and, with it, certain ideas pertaining to the foundation of mathematics. Russell’s paradox presents a set defined as a set of all sets that are not members of themselves. If such a set does not contain itself, it contradicts its own definition; if it does contain itself, it violates its own condition (see Link 1-6). In like measure, Balwhidder’s web “contains” the world, including the Enlightenment theorists who supposedly explicate that world to us (inasmuch as they are part of it), without containing its own explanation. To that extent, Galt’s “great web,” his set of all sets, cannot count itself among its own elements. For that matter, this web does not even apply to the bulk of Galt’s narrative, describing merely one annum among others, one multiple among others. Most of these individual chapters possess a very different tone: “the most memorable thing that befell among my people [in 1763] was the burning of the lint-mill” (23); 1777 “may well be called the year of the heavy heart, for we had sad tidings of the lads that went away as soldiers to America” (80); 1783 “was another Sabbath year of my ministry. It has left me nothing to record, but a silent increase of prosperity in the parish. I myself had now in the bank more than a thousand pounds, and everything was thriving around” (102). Hence, in Galt’s Annals, the set of all sets is not only illogical in excluding a portion of itself but it is also part of a narrative that is larger than itself, and thus is something other than what it purports to be. The stickiest web in the Annals is the fact that this web “is” only on condition that it also “is not.”

It was narrative puzzles like these that seemed to Galt to limit the authority of Scott’s Waverley novels. I mention Scott here because what Ian Duncan calls Scott’s shadow loomed large for Galt (see Duncan 215-20). He even refused to call Annals of the Parish a novel, referring to it instead as a “theoretical history,” as “a kind of treatise on the history of society,” and as a “fable.” Balwhidder’s fictitious parish of Dalmailing was meant to be metonymic of a much larger global sphere—a sphere which it nevertheless could not or would not name, not entirely. Galt imagined the Annals, P. H. Scott remarks, “not [as the] history of an actual place, but of an imaginary one which could nevertheless be taken as typical of a whole society” (P. H. Scott 32). This for Galt is what differentiated Balwhidder from many of Scott’s narrators and Dalmailing from, say, the Bradwardine estate in Waverley. The latter serves as the site of a union between the novel’s English protagonist and a Scottish heiress of modest means and thus exemplifies a symbolic merger of nations. In Waverley, national culture is the effect of narrative closure, the product of a classical equation in which 1 + 1 = 1: Edward Waverley plus Rose—two characters—equals one estate; England plus Scotland—two nations—equals one Britain. Galt, however, complicates this equation by adding narrative elements that, in great webs of narrative reciprocities, never wholly resolve themselves into one. For example, Balwhidder marries, but his wife dies; he marries again, and she dies again; he marries a third time, but with little thematic consequence. (He fixes upon a widow, “the relic of a Professor in the University of Glasgow.” At a table where she and Balwhidder are seated together, a friend puts the wing of a hen on both their plates and quips that “there have been greater miracles than these two wings flying together” [Galt 141-42]. After the marriage, little more is said of her. Hence, in the Annals, Balwhidder’s relationships—1 + 1 + 1—equal some fragmentary and un-Waverley-like multiple.) Meanwhile, Balwhidder’s narrative imbricates diverse rhetorical forms (memoir, sentimental tableau, theoretical history) without establishing an overarching representational logic. This includes the record’s ostensible form of the annal, since its serial presentation of time derives from Balwhidder’s ex post facto recollections and mostly takes the form of picaresque episodes. (The table of contents reveals as much. Between the years of 1772 and 1775, for example, we read about “[t]he detection of Mr. Heckletext’s guilt,” and that “Lord Eglesham comes down to the castle,” and about “[t]he murder of Jean Glaikit,” and that “Captain Macadam provides a house and an annuity for old Mrs. Malcolm” [xxi].)

What is the sum of all this pointed confusion? Katie Trumpener observes, acutely, that the failures of Galt’s texts to resolve their various narrative strands enable them “to recapture the thickness and jaggedness of lived history,” imparting a sense of progress as uneven and of national culture (or any principle of social cohesion, of collective closure, of meaning) as existentially uncertain (Trumpener 152). However, and as the problematic set of all sets indicates, precisely because Galt’s narratives speak to the complexities of experience, they also negate such experience by pulling the rug out from underneath its definition. That is, because “great webs” are figures of their own unraveling, “lived history” loses its threads in labyrinths of signification, in mazes of figures—or in what readers traditionally identify as Galt’s distinctive brand of irony. We have no experience of “commercial reciprocity” not only because its reticulum is too sublimely vast to comprehend, but also because its very existence is a mirage. What Balwhidder actually sees is not the “web” he imagines, but rather a change of ownership in the cotton mill, the formation of a Savings Bank, and a financially-motivated depression and murder-suicide of one of the mill’s overseers. The “web” is thus a figure that lends meaning to experience without consigning itself to that experience, especially not of the “jagged, lived” variety. The idea of the web, in fact, delivers us from experience by granting us a virtual vantage point outside it. In Galt’s narrative, then, experience, especially of prototypical Romantic solitude, involves not the writer’s refuge in nature (in which Balwhidder exhibits little interest) but rather the ruination of networks of meaning. In the Annals, we, like Balwhidder, experience we know not what: webs are sets are metaphors are narratives . . . are nothing.

Alain Badiou, who has thought rigorously about such paradoxes, explains them historically as a product of the confusion inscribed into the concept of number—a concept dense with ontological implications. The ancient Greeks identified being with whole numbers: anything that could be said to exist was essentially one thing. The “collapse of the Greek thinking of number” during the long eighteenth century (or longer: from the sixteenth through the nineteenth centuries) “proceeds from three fundamental causes,” Badiou argues (Number 7). I lack the space here to provide elaborate contexts for these causes, but we can at least review them briefly. The first concerns “the problem of the infinite,” which emerged with the invention of the calculus in the late seventeenth century (7). Devised to compute rates of change in phenomena ranging from the motion of the planets to the rise and fall of markets, the practice of calculus well into the nineteenth century employed series of numerical fragments to which one might assign limits (the point at which a fraction might be said to become too small to signify) without ever resolving these series into anything “whole.” Evocative of Zeno’s paradox of Achilles and the tortoise (in which Achilles approaches the tortoise without being able, numerically, to overtake it, dividing the distance by a half, then a fourth, then an eighth . . . ), fractions grew smaller—and denominators grew larger—without reaching a logical end. This raised philosophical questions about the status of infinity and also the viability of those calculations blithely ignoring the subversive implications of fragmentation or the spectacle of numerical ruin. The second problem concerned not the infinite but the inverse “ontological stopping point of number” in the void, or zero. The void came to denote both an absence of substantive being but also the means by which the former was measured; without designating anything in particular, it brought attention (as an empty unit, a pure placeholder) to the system in which substantive things acquired quantitative designation. Hence, anything that “was” only counted on the basis of things that “were not”—a metaphysical puzzle (7-8). The third problem proceeded simply from the erosion of belief in the idea of unified being—the growing conviction, from the sixteenth through the nineteenth centuries, of the irreducible complexity of the world, prompting intellectuals to seek a new basis on which to order experience. Georg Cantor’s set theory provided just such a basis, Badiou says, at the end of the nineteenth century, but this makes the long eighteenth century a period of ontological incoherence, of mathematical figures lacking a proper conceptual ground. Romantic-era numbers, even statistics and simple arithmetic, were effectively tropological constructs. Two plus two equaled a red, red rose.

Badiou’s solution to this problem involves a process of subtraction: we may ground numbers, and thus fashion a coherent concept of modern being and its appearance in worlds, on the basis of an ordering principle that is not itself an element of any set, or that subtracts itself from a pre-existing arrangement. This action makes up a “decision point” that prospectively takes the form of an “event,” representing the momentous rearrangement of a set or state of affairs. Badiou draws examples of such “points” or “events” from politics, science, art, and love. The individuals under Spartacus subtracted themselves from the hierarchy of Roman society and transformed the relationship between slaves and society (see Logics 51-52, 69-70); in Jean-Paul Sartre’s play Les Mains Sales, the character Hugo, enjoined by the Communist Party to kill a leader suspected of treachery, eventually subtracts himself from the party and assumes responsibility for his own actions (404-07). In terms of Romantic literature, and despite Scott’s reputation for ideological conservatism, one might say that the narrator of Waverley initiates a kind of event by subtracting himself from the chaos of experience (and from the “great web” of national and picaresque tales) and thus converts a welter of aleatory occurrences and character types into a legible ordering of history, a grand narrative of the etiology of modern Britain. This interpretation of Scott’s fiction would see it less as an apology of the status quo than as an active ordering principle—a “void,” as it were—availing history (and historical fiction) to a more radical set of possibilities (which is precisely how Scott was read by revolutionaries across Europe and beyond in the nineteenth and early twentieth centuries [see Pittock 187-210]). In this scenario, Scott would be to Galt what Cantor was to numbers.

Of course, this is not the historical narrative of Scottish Romanticism. Scott did not subtract himself from Galt; Galt, rather, responding to Scott, implicated Scott’s reader in webs of uncertainty, in riots of refractory mathematics—the erosion of ordering systems. This is the point Trumpener makes about Galt’s attention to the jaggedness of lived experience—so jagged, we said, that it confounds any unified conception of lived experience as heartily as it does a unitary idea of genre. In this respect, the closure Galt perceived in Scott’s Waverley novels was less the solution to an existential crisis than the product of an ill-conceived equation in which national being, or any existential form, is imagined as the sum of its history. For Galt, such sums never fully compute; no set is simply equal to itself.

This is not to say, however, that in undercutting subtraction Galt imagined no mathematical alternative—not that Galt, widely read but no mathematician, would have labeled it “mathematical.” In a brief 1833 narrative entitled “The Seamstress,” Galt presents a sketch of Miss Peggy Pingle, a woman who “had to make the needle her bread-winner” and who, after the death of her mother, became most notable for the mechanical regularity of her solitary existence (Galt, “Seamstress” 22). “Day after day was with Miss Pingle as the to-day is like the yesterday—twins could not more resemble each other,” Galt tells us. “The only irregularity in the pure flow and rill of her life, was from the lengthening and shortening of the days” (23). A nature unto herself, Miss Peggy nevertheless effectively stitched her own existence to that of the external world: “She could tell the character of the weather . . . by the dim, bright, or blazy aspect of the spark in her grate, that serve[s] to make the cold more sensible; and could read the omens which made her penurious candle oracular” (26). This capacity to “read” embers and flames also betokened supernatural realms beyond: through what the narrator calls her “pyrology,” Miss Peggy “could divine . . . that sailor[s’] wives, with close-drawn hoods, would restless walk the shore,” or that “cold-rife lovers would cuddle together,” or that “kechling [or cackling] gossips were with secret” (26).

If Galt’s “web” expresses what Badiou portrays as the paradox of numbers during the Romantic era, namely their status as tropes and hence their dissolution into figurality, his portrait of “eydency” spins a web (and builds a figure) of a different variety. I am speaking here of the practice of geometry, which retained its currency in Scotland as the principal mode of mathematical inquiry even amidst the disciplinary drift toward algebra across much of Europe (see Pycior 242-43). “The Seamstress” is hardly geometric in any literal sense, no more than Annals of the Parish is arithmetic or set-theoretical. However, the story shares with geometry a kind of metaphysical coordination of the rational and the sensible, the shapes of (Miss Peggy’s) thought with the structures of reality, “eydency” with the external world. In this respect, Galt’s “reminiscence” was broadly cultural as well as personal and fictive. John Keill, a Scot who was the first person to lecture on Isaac Newton’s work at the University of Oxford early in the eighteenth century, explained that the resistance to algebra shared by several of his contemporaries was motivated in large part by the conviction that “many Propositions, which appear conspicuous in [Euclid, are] knotty . . . and scarcely intelligible to Learners by [the] Algebraical Way of Demonstration.” This was because geometry shows “Evidence by the Contemplations of Figures,” as opposed to the “Symbols, Notes, or obscure Principles” one finds in algebra (Keill, “Preface,” no pagination). Algebraic innovations enabled greater dexterity in processing mounds of data, but they also exacerbated the ontological confusion to which Badiou refers by employing negative and irrational (read: un-whole) numbers. Geometry, meanwhile, partly circumvented such conundra by sketching proportional lines in the place of fractions or numbers with infinite and non-repeating decimal points, thus compensating visually for technical failures either of calculation or philosophy. For the Scottish Enlightenment literati to whom Balwhidder appeals, geometry represented the reconciliation of the world as we think it with the world as it appears to us. It also evoked a longer tradition of Scottish metaphysics as an intellectual inheritance predating the 1707 Union, such that geometry, like Scots, was a national language (see Davie 127-49). In Galt’s Scotland, geometry thus named the science that stitched together present and past, culture and nature; without resolving the quandaries of negative, irrational, and complex numbers that purportedly embroiled the Romantic period in an ontological muddle, geometry nevertheless lent these creaturely units eloquent expression in the form of shapes, figures, “eydent” sketches—a metaphorics of the eye.

The more precise relationships between literature and geometry during this period exceed the boundaries of this essay. Still, the divergence of Galt’s portrait of Miss Peggy from the ironic jumble of Balwhidder’s narrative indicates how, in the world of Scottish Romanticism, 1 and 1 may not always have equaled 1. More broadly, certain species of literary representation may not have reduced to any composite of numbers or (algebraic) variables; “quantities” and “magnitudes” were measured in more ways than Waverley could “count.” If this seems like common sense—since when are “rocks and stones and trees” reducible to ones and two and threes?—let us nevertheless not be naïve: as William St. Clair has shown in the statistics drawn from publishing and as Franco Moretti has sketched by way of graphs, maps, and trees, literature and mathematics remain segregated in much literary criticism only because of our failures to understand the affinities between those two cultures. And yet, in a special issue like this one on the concept of number in the Romantic period, Galt’s story prompts us to ask whether the most romantic numbers—the “illustrations” and sketches, the visions of “industry free from labour” (with its infinite divisions)—were even “numbers” at all, or were coincident with numerical logic. Indeed, Galt plays something of a Blake to Badiou’s Newton, reminding us that not every “being” that cuts the airy way is closed by the numerical associations of ontology.