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Issue 6 (2014) - Numbers

Donne, by Number: Quantification and Love in ‘Songs and Sonnets’

James Beaver

[1] What does counting have to do with love? Elizabeth Barrett Browning’s ‘Sonnet LXIII’, which opens, ‘How do I love thee? Let me count the ways’ (2007: l.1), offers perhaps the most well-known correlation between the two. Yet the epistemological surety Browning finds in quantifying love is no given for a love poet. In ‘Love’s All (Lovers’ Infiniteness)’, John Donne, for example, refuses Browning’s inclination to count, worrying over what, exactly, a sum total would mean for his love: ‘Yet I would not have all yet, / He that hath all can have no more’ (Donne 2008: ll. 23-24. This edition used throughout). Compared to Browning, Donne appears a quantitative sceptic: a basic principle of number and multitude tells him that once a quantity is exhausted, ‘no more’ can be added. John Carey remarks of Donne’s anxiety over measurement: ‘These are conflicts we stumble into once we try to quantify emotions—yet wanting them quantified is the most natural thing in the world’ (1981: 126). Although we might empathise with Carey’s assertion on a personal level, the suggestion that quantifying love is natural seems to overlook the mathematical and poetic discourses in which these poets participate when they presume, refuse, or worry over what it means to ‘count the ways’. In other words, to what extent is Carey’s ‘inclination to quantify love’ a product of cultural experience?

[2] While criticism since the mid-twentieth century has explored Donne’s relation to early modern scientific developments (Williams 1935; Coffin 1957; Empson 1957), more specific attention to the relationship of Donne’s work to mathematical developments in his time needs to be developed. This essay offers an assessment of how developments in mathematical symbolic language — specifically, Robert Recorde’s contribution to novel notational figures — in mid-sixteenth century England may have influenced Donne’s poetics. While Carey concludes that ‘[Donne] seems to have regarded mathematics as, at best, a curiosity’, and that, ‘like most Elizabethans, Donne had virtually no interest in using numbers for the purpose of serious computation’ (1981: 128-29), Donne’s poetry suggests, alternatively, a sustained investment in quantitative language as a mode of articulation. Poems like ‘The Computation’ and ‘The Primrose’ serve as obvious examples of ways in which Donne could explicitly rely on counting to articulate love and loss, with the former tallying time passed since a lover’s absence, and the latter, operating within a neo-Pythagorean numerology to calculate an equation by which men and women add together. In that poem’s closing lines, ‘Numbers are odd, or even, and they fall / First into this, five, women may take us all’ (ll. 29-30), A.J. Smith notes that Donne is calculating the sum of the gendered numbers ‘2’ (for female) and ‘3’ (for male) to equal the five petals of the primrose (1996: 396). Such abstract number games, in the end, are used to represent lovers’ experience, whether the physical absence of a partner for a lengthy period of time or the erotic suggestiveness of a world in which, hypothetically speaking, ‘women may take us all’ (l. 30).

[3] Even more compelling than these specific examples, a brief survey of Donne’s love poetry reveals the striking frequency with which his poetics make use of quantitative language. Thirty-four of the fifty-four ‘Songs and Sonnets’ contain some reference to number, such as ‘one’, ‘two’, ‘a hundred’, or ‘thrice’. Donne is even more preoccupied with relationships between ‘all’ and ‘nothing’: he refers to ‘all’, ‘nothing’ or ‘none’ in thirty-six of the fifty-four poems. Overall, fifty-two poems contain some type of quantitative language, whether a number, ‘all’ or ‘nothing’, or less specific quantitative references like ‘increase’ and ‘proportion’. The sheer volume of such references hints that Donne has a vested interest in quantitative thought as a means of representation. He may not be a ‘serious’ student of mathematics, as Carey observes, but his language is especially computative. As defined by Aristotle, ‘quantum’ is concerned with that which is ‘numerable’ or ‘measureable’ (1020a10), and, as Paula Blank observes (2006: 41), it can be viewed in contrast to ‘quality,’ which, for Aristotle, refers both to ‘the differentia of the essence’ (1020a33) and ‘the sense in which numbers have a certain quality’ (1020b3-4). Quantitative language, in my definition, consists of verbal expressions of numerical degrees and spatial or temporal magnitudes, in contrast to verbal expressions of kinds or essences.

[4] What does it mean for a poet to have numbers on his mind in turn-of-the-century early modern England? In one sense, as Margaret Ferguson observes, it simply means being a poet: ‘As a verbal practice marked both by a concern for “measure” (as in syllable or line counting) and by a tendency toward “license” (as in rule-breaking and a love for excess), poetry enacts and reflects on many meanings of “numbers”’ (2013: 78). In another sense, though, this question requires not only our awareness of the broader critical narratives which chart a dramatic shift from medieval structures of knowledge to scientific modernity occurring in the fifteenth, sixteenth and seventeenth centuries (Daston 1991; Dear 1995; Crosby 1997), but also an assessment of both the numerological traditions and particular mathematical developments in England which contributed toward defining early moderns’ relationships to numbers. My focus here lies in what purchase Donne gains in his poetics by relying so frequently on quantitative language as a mode of articulation, insofar as such language alludes to a developing symbolic mathematical language that, in the seventeenth century, would assume epistemological claims that the English vernacular could not. As Paula Blank observes, in addition to ‘mimetic theories of poetry’ and ‘ones that assimilate verbal art to the visual arts or to visual representation more generally’, ‘sixteenth-century poets […] additionally thought of their writing as an instrument of measure, one that proceeded quantitatively rather than qualitatively, deciding relations rather than depicting “nature”’ (2006: 41). In this view of poetry, questions of numerological correlations between poetic structures and the order of the cosmos become secondary to questions of taxonomy. Symbolic mathematics and the language of words constituted two developing, related semiotic systems at the time, with shifting epistemological claims to the world and varying capacities for representing the realms of experience. Donne’s predilection for quantification highlights both the sympathies and disjunctions between these developing systems.

[5] As J.L. Lemke says of the relation between the semiotic systems of mathematics and verbal language:

No mathematical treatise entirely avoids the connective tissue of verbal language to link mathematical symbolic expressions, to comment on the process of development of arguments, and so on. All our applications of mathematics, in the context of which most of our present commonly used mathematics evolved historically — in the natural sciences, engineering and design, commerce and computing — require verbal language to link mathematical tools to specific real-world things and events. (2002)

Lemke’s understanding of the relation between mathematical and verbal languages is informed by a theoretical framework drawn from C.S. Peirce and pragmatism (Buchler 1955; Houser and Kloesel 1992; Halliday 1978; Hodge and Kress 1988; Lemke 1995).[1] Despite his observation of the ‘link’ which verbal language provides for mathematical expressions, Lemke’s primary focus is on how mathematics functions as an independent semiotic system, capable of producing meaning which verbal language cannot. My own approach diverges from the theoretical investments of pragmatism but uses Lemke’s observation as a frame for considering economies between mathematical and verbal languages in a period when distinct boundaries between the two systems were not yet well defined. Although a range of valuable work has studied the effects of the increased cultural reliance upon quantification in the early modern period (Crosby 1997; Reiss 1997; Poovey 1998), the ‘link’ between ‘the connective tissue of verbal language’ and ‘mathematical symbolic expressions’ opens a particularly valuable critical space to historicize relations between the two languages. Specifically, it allows us to study how notational developments in mathematics — on the order of syntax and symbols — are managed, or framed, through what Lemke calls ‘verbal language’, or, in the present essay, I deem the English vernacular.

[6] Building from the seminal work on the history of mathematical notation by Florian Cajori, Lemke observes, ‘In most mathematical writing before modern times, symbolic expressions were rare; they were integrated into the running verbal text, and they were clearly meant to be read out in words as part of complete sentences that also included ordinary words’ (2002). Despite this long-standing historical relation between words and mathematical symbols, Jacob Klein, in a remarkable study of the algebraic innovations from the mathematicians Simon Stevin and François Viète, argues that a new conception of number emerges in the early modern period, in which ‘the fundamental ontological science of the ancients is replaced by a symbolic discipline whose ontological presuppositions are left unclarified’ (1968: 184). In other words, mathematics began to develop into a coherent, autonomous semiotic system, as disciplinary practice shifted from classical questions of the ontological status of numbers (arithmos) toward semiotic considerations on notation (Klein 1968; Rotman 1987; Hodgkin 2005). My intention here is to interrogate one example of the formulation of mathematics as an autonomous symbolic discipline in sixteenth-century England, in order to then consider how the poetic text relies repeatedly on the ‘connective tissue of verbal language’ to allude to symbolic mathematical expressions. When Donne, in ‘The Primrose,’ concludes, ‘if half ten / Belong unto each woman, then / Each woman may take half us men’ (ll. 25-26), he is using the vernacular to articulate an equation linked to mathematical symbolic expressions. What does it mean when a poetic text, like ‘The Primrose’, relies on verbal language to facilitate such a relation to mathematical semiotic fields?

[7] One can pose this question, I think, while keeping in mind, as Keith Thomas does in his seminal essay on numeracy in England, ‘the importance of numbers in religious symbolism and allegory or of numerology in poetry and philosophical speculation’ (1987: 124). In ‘The Primrose’, for example, Donne is quite clearly appealing to symbolic numerical values as he calculates relations between men and women, such that they equal ten. Robin Robbins observes that ten is a ‘triangular number, 1 + 2 + 3 + 4, symbolic of holiness and perfection’ (Donne 2008: 237). As Thomas notes of number in the period, ‘At all levels of society, number remained as much a language of quality as of quantity’ (1987: 124). As an early modern test case, Donne, no doubt, makes use of both dimensions of number in his poetics. And yet, while acknowledging the qualitative—the symbolic or allegorical—dimensions in Donne’s numbers, as studied by mid-to-late twentieth-century numerological criticism (Fowler 1964, 1970, 1971; Patrides 1958; Heninger, Jr. 1974; Røstvig 1994), we may still consider to what extent his poetics engage features of a quantitative numeration derived from the developing symbolic mathematics.

[8] With respect to developments in mathematics during the Renaissance, England was well behind the Continent. As Cajori observes, “Up to the seventeenth century, mathematics was cultivated but little in Great Britain. During the sixteenth century, she brought forth no mathematician comparable with Viète, Stifel, or Tartaglia’ (1991: 146). Thomas confirms England’s rather slow start, noting, ‘Arabic figures had come relatively late to England; it was only between the mid-sixteenth and mid-seventeenth centuries that they established themselves in most forms of account-keeping’ (1987:120). Furthermore, because of this delay, ‘Arabic figures had to be explained to those who found them strange and unfamiliar’ (Thomas 1987: 120). Along with John Dee, who provided the first English translation of Euclid, Robert Recorde emerged as a key figure in sixteenth-century English mathematics, publishing the first arithmetic, algebraic and geometric books in English.

[9] Gareth Roberts and Fenny Smith have recently emphasised the significance of Recorde’s place in the early history of mathematical development in England. Notably, they do not associate his value with theoretical contributions: ‘Recorde himself made no claim that he was pushing forward the frontiers of mathematics. He was, rather, a communicator of mathematical ideas who sought to explore ways in which to make mathematical knowledge and skills available to a wide population’ (2012: 1). Recorde’s achievements lay in the semiotic realm, specifically, in his dual emphases on the vernacular and symbolic notation. Recorde exemplified what Richard Mankiewitz identifies as ‘the tendency to write in the local vernacular in preference to Latin,’ a practice which ‘made mathematical textbooks accessible to a wider public’ (2000: 70). During his lifetime, Recorde published five mathematical texts, all in English.

[10] In The Pathway to Knowledg [sic] Containing the First Principles of Geometry (1551), he explains in his dedicatory epistle to Edward VI his civic aspirations for a treatise written in English:

And I truste (as I desire) that a great numbre of gentlemen, especially about the courte, whiche vnderstand not the latin tong, or els for the hardnesse of the mater could not away with other mens writyng, will fall in trade with this easie forme of teachyng in their vulgar tong, and so employe some of their tyme in honest studie, whiche were wont to bestowe most part of their time in triflyng pastime. (1551: sig. B3v)

Here, Recorde’s appeal to his sovereign invokes the humanist argument that knowledge of the classics would yield more effective servants of the state. If Recorde’s justification for the vernacular followed this long-standing humanist argument, his emphasis on symbolic mathematical notations, with respect to Arabic numerals, was a bit more novel. His best-known work, The Whetstone of Witte (1557), contains the first recorded use of  (=) for the equals sign in mathematical notation, in both England as well as the Continent (Mankiewitz 2000: 71). In the same text, Recorde uses the now-familiar modern notation of the addition (+) and subtraction (-) symbols for the first time in an English text. Recorde’s pedagogical contribution to symbolic mathematics reflects his aim to communicate its practices and principles to a broader English public.

[11] Of a particularly complex, detailed section on algebra in Whetstone, Ulrich Reich says the following on Recorde’s approach:

In retrospect we witness in this section part of the detail of the laborious process as mathematicians struggled over several centuries to get to grips with equations and their solutions, their efforts often frustrated and encumbered by unwieldy symbolism. Recorde visibly strives to improve the processes, by introducing enabling symbolism, by dismissing the ‘idle bablying’ of overelaboration, and by diligently searching for simplifications. (2012: 113)

If Latin was a linguistic barrier to certain English gentlemen’s ability to learn mathematics, so was this ‘unwieldy symbolism.’ The (=) symbol arises out of Recorde’s drive for notational simplicity: ‘And to auoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke vse, a pair of paralleles, or Gemowe [twin] lines of one lengthe, thus: ===== bicause noe. 2. thynges can be moare equalle’ (1557: sig. Ff2r). Like mathematicians before him, Recorde recognizes that symbolic mathematical notation becomes necessary as calculations become more frequent and complex. He could be called a notational pragmatist, in this sense, and, as such, he is well aware of the needs of his English readership, who may be unfamiliar not only with Latin, but with Arabic numerology and the basic syntax of mathematical operations. His ‘[twin] lines of one lengthe, thus: =====’ invokes a direct visual appeal to the reader, ‘bicause noe. 2. thynges can be moare equalle’.

[12] Recorde’s work as a communicator of mathematics means he spends considerable effort educating his audience on how to read the new semiotic system before it. This requires a basic hermeneutic skill set that acknowledges the fundamental disparity between the semiotic fields of symbolic mathematics and the vernacular. In a dialogue at the opening of the 1582 edition of The Grounde of Artes Teaching the Perfect VVorke and Practise of Arithmetike (originally published in 1543), the Master explains to his Scholar the relationship between (numerical) value and (signifying) figure (i.e., ‘6,’ ‘2,’ ‘8’), emphasizing both the link between numbers when they are connected together as well as the disjunction between numbers and words:

MAYSTER [sic]: Nowe then take héede, these certaine valewes euerye figure representeth, when it is alone written withoute other Fygures ioyned to him. And also when it is in the firste place, though manye other doe followe: as for example: This figure 9 is ix. standing now alone.

SCHOLER [sic]: Howe? is he alone and standeth in the middle of so many letters?

MAISTER [sic]: The letters are none of hys fellowes. For if you were in Fraunce in the middle of a M. Frenche men, if there were no English man with you, you woulde recken your selfe to be alone.

SCHOLER [sic]: So it is. Then 9 without more figures of Arithmetike, betokeneth ix, whatsoeuer other letters be aboute it. (1582: sig. D1r-D1v)

In this exchange, the Master delineates the fundamentals of numeration: value, figure, and place. Recorde is aware that the novice in mathematics needs to understand the value of a figure which ‘is alone written withoute other Fygures ioyned’ (i.e., ‘the figure 9 is [in value] ix.’) with respect to the vernacular. The Scholar is initially baffled by the disjunction between numerical figure and alphabetical letters: ‘Howe?’ he asks of the value of 9, ‘Is he alone and standeth in the middle of so many letters?’ The Master answers in a way we might expect from the author who justifies his use of the vernacular for the good of the English state: ‘The letters are none of hys fellowes,’ he says, just as an Englishman, surrounded by a thousand Frenchmen in France, ‘recken[s]’ [sic] himself alone. Recorde’s attention to this basic differentiation indicates that before he can expound on the syntax of symbolic mathematics, he must first clarify that there is a different syntax — or language — available to the student in mathematical signification, and, furthermore, that numerical figures and vernacular figures form separate sets of communities, as distinct, or so Recorde would have it, as national identities.

[13] Let us briefly pause to examine two features of the relationship Recorde establishes between mathematical language and the English vernacular. On the one hand, the substitution of the (=) symbol arises both from a pragmatic aim to ‘auoide the tediouse repetition of these woordes: is equalle to’ and because Recorde often uses the symbol in his own work. On the other hand, when it comes to the basic principles of numeration and the vernacular, a distinct boundary is posited. ‘Howe is he [the 9] alone and standeth in the middle of so many letters?’ the Scholar asks, only to hear the Master present a rule which emphasises starkly divisions in national identities: ‘The letters are none of hys fellowes’ (1583: sig. D1v). The division is, of course, ideologically charged, as Recorde plays upon the reader’s sense of his own Englishness as a discrete cultural category precisely at the moment he urges the reader to ‘recken’, or count: if you can understand how an Englishman ‘recken[s]’ [sic] himself alone in the middle of a thousand Frenchman, you can recognize the isolation of this symbol from words surrounding it. If, as Lemke notes, ‘No mathematical treatise entirely avoids the connective tissue of verbal language to link mathematical symbolic expressions’ (2002), we can observe here how economies between this connective tissue alter depending on what is at stake.

[14] Like mathematicians before him, Recorde can easily collapse words into a symbol to achieve linguistic elegance. In A History of Mathematics, Cajori demonstrates, by reviewing studies of medieval manuscripts, that the emergence of the (+) symbol for addition followed a similar operation: ‘the sign + comes from the Latin et, as it was cursively written in manuscripts just before the time of the invention of printing’ (1991: 140). Thus, a calculation of ‘5 et 7’, over a longe period of time, eventually became ‘5 + 7’. Here, then, the Latin literally collapses into symbol. Recorde explains his use of (+) and (-) in Whetstone as follows: ‘There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse’ (sig. S2v). Though the substitution of symbols for words may appeal to common sense, the tradition of notation in which Recorde engages in this moment is, in fact, fraught with tensions: specifically, tensions between words and symbols. As Cajori notes, the symbolic notation for addition and subtraction was also configured in letters which more directly corresponded to verbal counterparts: ‘In [Luca Pacioli’s] Summa de Arithmetica, Geometria, Proportioni et Proportionalità, the words ‘plus’ and ‘minus,’ in Italian piú and meno, are indicated by and ’ (1928: 107). These abbreviations spread across the Continent after their introduction, and ultimately rivalled, in representational capacity, the (+) and (-). ‘The + and –, and the and , were introduced in the latter part of the fifteenth century, about the same time,’ Cajori observes. ‘They competed with each other for more than a century, and and   finally lost out in the early part of the seventeenth century’ (1928: 236). The transition from the words ‘plus’ (più) and ‘minus’ (meno), to, respectively, the abbreviations and , and, then, in their eventual erasure and displacement from modern mathematical language, the (+) and (-) symbols, exhibits over the course of a long period of time a remarkable semiotic fluidity between the vernacular and mathematical symbolic language. It is the possibility afforded by this fluidity that allows Recorde to introduce, quite unremarkably, the substitution of (=) for equivalence.

[15] In this relatively early stage in the development of modern symbolic mathematical language in England, Recorde’s emphasis on notation is important. While not at the forefront of theoretical developments in mathematics, he does occupy a place at the forefront of the expansion of a symbolic mathematical language—in emphasising a consistent vocabulary and syntax apart from the vernacular, while simultaneously promoting the accessibility of mathematical texts in the English vernacular. Reich describes his legacy as follows:

This legacy includes an extensive mathematical vocabulary, largely based on borrowings from Latin and continental European languages, notably Italian, German and French. […] The legacy also extends to Recorde’s use of symbolism as part of a process of simplifying mathematical expressions: his use of the sign of equality together with the signs for addition and subtraction for the first time in English, coupled with use of the cossic signs and signs indicating square and other roots borrowed from Scheubel, established an unprecedented style of mathematical writing.   (2012: 116-17)

Recorde’s stress on ‘simplifying mathematical expressions’ to achieve a symbolic language that could simultaneously appeal to a broader English public and perform more complex operational functions is echoed by the more prominent English mathematicians who followed him, especially those in the first half of the seventeenth century.

[16] England’s most famous mathematician of the early seventeenth century William Oughtred published Clavis Mathematicae (1631), a landmark mathematical treatise at the time, and introduced the (X) symbol for multiplication, replacing the symbol of a cross (Smith 1958: 404-405). According to Cajori, ‘[Oughtred] laid extraordinary emphasis upon the use of mathematical symbols; altogether he used over 150 of them’ (1991: 157). Like Oughtred, John Wallis was an advocate of expanding the scope of mathematical symbolization, as Gordon Hull describes:

Thinkers such as Wallis, innovators in mathematical developments, expressed fewer or even no such worries about the scope of symbolization. Thinkers who straight-forwardly adhered to a premodern understanding of science tended to downplay the role of construction in knowledge acquisition. (2004: 121)

Such enthusiasm might be said to reflect an attitude held by many of those at the forefront of mathematics in the English Renaissance. An increased complexity of computations was accompanied by a more nuanced language, as evident in the expansion of symbolic representation to more complex ideas, such as infinity. In 1655, Wallis published De Sectionibus Conicis, the text widely credited with the first use of the lemniscate, the modern symbol for infinity (∞) (Cajori 1928: 214; Maor 1991: 11). Wallis’s work, especially his Arithmetica Infinitorum (1656) in which the lemniscate symbol appears again for infinity, is often considered a precursor for the development of calculus in the latter half of the century. Infinity, both as symbol and concept, reflected the increased level of sophistication in symbolic mathematical language. It also, of course, had deep symbolic implications in the realms of philosophy and theology, as Brian Rotman has demonstrated in wonderful detail (1987). The lemniscate, itself, channels symbolic traditions, both ancient and Christian. John Barrow observes, ‘The ribbon like figure-eight on its side is an ancient symbol, a shadow of the ancient ourobos symbol of the snake eating its tail’ (2008: 339). It also ‘provided the mysterious cross of St. Boniface in early Christian tradition’ (Barrow 2008: 339). Whether Wallis had either in mind is uncertain, but the difficulty in ascertaining the answer reflects Wallis’s unconcern with ‘the scope of symbolization’, as Hull phrases it (2004: 121). Rather than considering deeply the symbolic roots of the lemniscate, Wallis, like Recorde before him, was probably mostly concerned with introducing a functional, useful sign that could accommodate more difficult operations.

[17] As the breadth of symbols expanded, mathematical relationships were also becoming more crucial to cultural articulation in the early modern landscape. As William Bouwsma succinctly puts it, ‘quantity now tended to be substituted for quality as the essential principle of orientation’ (1980: 234). In other words, quantification afforded a means of articulation that extended beyond the mathematical. In a poem to the preface of Thomas Hylles’s The Arte of Vulgar Arithmeticke (1600), an anonymous poet finds in numbers nothing less than the foundation of all language: ‘No state, no age, no man, nor child, but here may wisdome win / For numbers teach the parts of speech, where children first begin’ (1600: sig. C3v). In this celebration of number’s expressive capacities, we may well wonder: what of words?

[18] The tension arising in what Christopher Johnson identifies as the ‘epistemological confusion’ in the period (2004: 67) plays out, on at least one level, between the developing mathematical language of symbols and the language of words. Hylles’s poet’s tribute to number reveals in its very lines precisely this tension: the poet’s ‘number’ shares its etymology with the ‘number’ of ‘metrical periods or feet; lines, verses’ (OED, ‘number’, n. 17a). As Blank and Ferguson have studied, this sense of ‘number,’ now rare, was significant to conceptions of poetry in the sixteenth and seventeenth centuries (2006; 2013). The OED lists two entries from the end of the sixteenth century: E.K. glosses line 110 in the October Eclogue of The Shepheardes Calendar (1579) as, ‘The numbers rise so ful, and the verse groweth so big, that it seemeth he hath forgot the meanenesse of shepheards state and stile’; Shakespeare, too, in Love’s Labour’s Lost (1598), writes, ‘I fear these stubborn lines lack power to move / O sweet Maria, empress of my love, / These numbers will I tear, and write in prose’ (IV. 3. 53-55). Such examples reflect the dual role ‘number’ played in the early modern period. Its root, from the Latin numerus, meant ‘sum, total, numeral,’ but also ‘rhythm in words or music, grammatical number, metrical foot, (plural) metrical lines, musical strains’ (OED, ‘number’, n.). In the Old French and Middle French nombre, the OED dates the quantitative definition earlier than the metrical: ‘sum, total (early 12th century as numbre), grammatical number (13th cent)’ (‘number’, n.). Traced from the Middle French, ‘number’ exhibits a tension still very much at play in the sixteenth and seventeenth centuries.  Examining George Puttenham’s mathematically-inflected treatment of meter in The Art of English Poesie (1589), Blank contends that ‘his work is representative of an early modern habit of confusing arithmos (for Puttenham, a variant of “arithmeticall”), rithmos, arithmetic, and the Latin ars metrica’ (2006: 42). Moreover, this confusion or tension in ‘number’ thrives precisely in the period in which symbolic mathematical language takes shape. How does the ‘number’ of verse relate — or compete — with mathematical symbols?

[19] Writing at the turn of the century, John Donne was keenly aware of the tensions at the foundations of early modern thought. In his wide knowledge base, he was somewhat of an anomaly: a former aspiring courtier (‘Jack Donne’) who became an Anglican priest (‘Dr. Donne’), and, throughout, remained well-read in the most recent scientific and mathematical developments of his time. Herbert Grierson wrote that ‘no other poet in the seventeenth century known to me shows the same sensitiveness to the consequences of the new discoveries of traveler, astronomer, physiologist and physician as Donne’ (1912: 189). Donne’s understanding of the implications of scientific and mathematical developments of the period underlies the quantitative references in his poetry, as he illuminates both the anxieties and paradoxes that the early modern period experienced with what Carla Mazzio identifies as the ‘newly assertive regime of standard measurement’ (2004: 60). Donne folds quantitative language effortlessly into his lovers’ experiences, suggesting its expansive representational capabilities; and yet, he repeatedly interrogates what it means to ‘count the ways’ of love: how quantification represents and orients experience, as well as how it fails to do just that. When the quantifiable enters Donne’s verse, it is always teetering under the instabilities of hyperbole and competing forms of measurement. In this view, he figures as the counterpart to Blank’s depiction of Shakespeare in the Sonnets, who, she contends, ‘imagines unsettled, unstable, and uncertain relationships among the parts of his created works’ (2006: 43). Most of all, although he demonstrates an interest in what symbolic numerology offers his accounts of love, Donne persistently refuses the expanded scope the quantifiable extends towards the regulation and systematization of experiences in space and time: Donne’s lovers do not live on grids.

[20] In both ‘The First Anniversary’ and ‘The Triple Fool,’ to take examples of his probing of the disparities between quantification and experience, he sets quantitative language in relationship with emotion, specifically ‘grief’. In ‘The First Anniversary’ grief is that which is ‘without proportion’: ‘Since euen griefe it self, which now alone / Is left vs, is without proportion’ (ll. 307-8). In ‘The Triple Fool’ grief is unruly, that which the narrator proposes to tame in ‘numbers’: ‘Grief brought to numbers cannot be so fierce, / For, he tames it, that fetters it in verse’ (ll. 10-11). Just as proportion is lost in grief in ‘The First Anniversary’, so is there a hope to enclose grief in ‘numbers’ in ‘The Triple Fool’ — perhaps to regain proportion?

[21] These examples have two implications. First, in Donne’s poetics, quantitative language is made to engage the language around it. In ‘The Triple Fool’, Donne’s speaker sets ‘numbers’ beside ‘grief’ in a misguided attempt to impose order. This is critical: for Donne, ‘numbers’ do not exist in a vacuum, surrounded by symbols and signs, as in the mathematical equation, ‘9+13=22’, for instance. Donne’s ‘numbers’ are not separate from the terms that surround them; they must, as Recorde advises against, meet the other’s ‘fellowes’ (1583: sig. D1v). Like Recorde’s Frenchmen and Englishman, numbers and words exist uneasily side by side, but in Donne’s example, those ‘numbers’ are forced into conversation with the words that surround them—in this case, ‘grief.’ The result is a pairing of disparate modes of experience, orientations to the world that are incompatible with one another. ‘Numbers’ are removed from the isolation of mathematical language and made to engage with the resonances of an emotion, and they do so in the vernacular.

[22] The second implication of these examples is that quantitative language does something with our world and our ways of thinking: ‘numbers’ do not sit benignly beside ‘grief’ — they work upon it. Quantitative language becomes in ‘The Triple Fool’ a way of organizing our world that lays representational claims upon the non-mathematical. In this sense, Donne is quite aware that the discoveries in mathematics and sciences at the time have very real implications on our everyday language and perceptions.

[23] For Donne quantitative language is ultimately a means of orientation. Even the non-mathematical can be defined based on its relationship to the mathematical: grief is simply that which is ‘without proportion’. Yet, if the quantitative is such an active, pervasive means of orientation, from where does it derive its authority? As a language, or semiotic system, mathematics is invention, built upon notational innovations like Recorde’s (=), (+), and (-) symbols. In this sense, orientation derived from mathematical language is artificial. Yet, mathematics is also a means of interpreting the natural world. In this latter sense, it lays claims upon reality — as Galileo’s ‘language’ of God suggests.

[24] Donne recognizes how easily the distinction between mathematics as invention and mathematics as the ‘language’ of God can be blurred. In ‘The First Anniversary’, a tribute to his patron Sir Robert Drury’s young daughter Elizabeth, who died in 1610, Donne takes the occasion of Elizabeth Drury’s death to critique a way of seeing and interpreting nature that is a product of developments in science. Ostensibly, this is a criticism of empiricists, but when mathematics is taken for the language of empirical reality, it is implicated as well:

We thinke the heauens enioy their Sphericall,
Their round proportion embracing all.
But yet their various and perplexed course,
Obseru’d in diuers ages doth enforce
Men to finde out so many Eccentrique parts,
Such diuers downe-right lines, such ouerthwarts,
As disproportion that pure forme. (ll. 251-57)

In this passage, proportion is linked with human thought, which is then interrupted by observation: ‘We thinke’ the heavens to be ‘Sphericall’, and yet a more ‘perplexed course’ is ‘obseru’d’. Donne is not clear whether proportion is natural phenomenon or human concept, but one might argue that the ambiguity is precisely the point: the cosmological order and human thought are intricately connected in this epistemological framework. Human perception, though, disrupts the connection. Observations lead ‘men to finde out’ those ‘Eccentrique parts’ and ‘downe-right lines’ that ‘disproportion that pure forme’ — ‘disproportion’ deriving from a relationship between a way of seeing and nature itself. Importantly, both ‘pure forme’ and ‘disproportion’ are produced as ways of thinking and seeing that blur human cognition and the natural world, invention and discovery. With the latter, though, we encounter a confused tangle of mathematical words, both numerical and geometric — ‘many Eccentrique parts’ and ‘divers downe-right lines’ that ‘men finde out’ — which function as middlemen between the boundary of things natural and human constructions. The ambiguity here is more problematic than the ambiguity between human thought and the cosmological order in the first example, because we have introduced the terms, or vocabulary, of a different epistemological engagement with the natural world, while a question over that very framework remains: have we produced ‘Eccentrique parts’, or have they indeed been discovered, in nature?

[25] For Donne, the answer is hardly as clear as we might hope. In the wake of developments in mathematics and science, things in nature exist within the human cognitive structures imposed upon them:

They haue empayld within a Zodiake
The free-borne Sunne, and keepe twelue signes awake
To watch his steps; the Goat and Crabbe controule,
And fright him backe, who els to eyther Pole,
(Did not these Tropiques fetter him) might runne. (ll. 263-7)

Donne’s imagery of the ‘free-borne Sunne’’s losing battle with the ‘Zodiake’’s ‘twelue signes’, ‘the Goat and Crabbe’, and ‘these Tropiques’ sets the dramatic tension between an epistemological order gone-wrong and a natural world unable to escape the human eye. The cognitive structure has ‘empayld’, its astronomical ‘signes’ ‘watch’, ‘controule’, and ‘fetter’ the natural world. Number is integral and alive in this scenario: the ‘twelue signes awake / To watch his steps’ (emphasis mine). ‘Controule’ is realized through the union of symbols and human perception, as observers rely upon ‘signs’ to ‘watch’. In the paradox at play for Donne, the world is disproportioned precisely when we attempt to confine it entirely within the parameters of human cognition, of signs and perception.

[26] ‘The First Anniversary’ is as much about the threat to language as it is about the natural world. Donne knows that the way of seeing affects our understanding of reality, and, in turn, the relationship of words to that reality. His use of quantitative language highlights the ways in which the epistemological crisis — or, in Johnson’s terms, “confusion” (2004: 67) — resides in a tension of value at the level of competing languages. Straddling the boundary between things natural and human constructions, mathematical ‘signs’ achieve a tremendous capacity for explaining the world, and, in doing so, deprive verbal language of its own capacity for representing the order of that world. The lament in ‘The First Anniversary’ concerns, in this sense, a loss of meaning in words.

[27] Proportion is merely one linguistic casualty. His emphasis upon it in ‘The First Anniversary’ reflects not only a loss in the natural world, but a loss in language as well. In the wake of recent scientific discoveries, the paths of all heavenly bodies are thrown off: ‘All their proportion’s lame, it sinkes, it swels’ (l. 277). Proportion constitutes a relationship between man and world. It is not only the heavenly bodies whose ‘proportion’s lame’, but our very relationship to them. In this sense, ‘proportion’, the word itself, has gone lame in language. It is ‘lame’ precisely because its discursive value is constrained within the parameters of a scientific or mathematical taxonomy within which the natural world is also contained: ‘Man hath weau’d out a net, and this net throwne / Vpon the Heauens, and now they are his owne’ (ll. 279-280). Is it possible that the proportion Donne considers here is that of symbolic mathematics, represented in our modern nomenclature with (:)? Though the symbol had yet to be introduced, Donne anticipates the implications of the mathematician’s language on his own. The mathematician lays claim to ‘the Heauens’ in his language, and yet distances this claim from the language of words, entrenching it instead within symbols.

[28] It is no wonder, then, that for Donne, ‘beauties best, proportion, is dead’ (l. 307). With the death of proportion, comes the end to its meaning:

And that, not onely faults in inward parts,
Corruptions in our braines, or in our harts.
Poysoning the fountaines, whence our actions spring,
Endanger vs: but that if euery thing
Be not done fitly’nd in proportion,
To satisfie wise, and good lookers on,
(Since most men be such as most thinke they bee)
They’re lothsome too, by this Deformitee. (ll. 329-336)

‘Proportion’, here, means something quite different than the ‘round proportion embracing all’ earlier in the poem (l. 252). Deflated in value, it becomes ‘Deformitee’. Curiously, this ‘Deformitee’ arises from corruption within and corruption without. There is something wrong with our cognitive models — ‘corruptions in our braines’ —yet also with our way of seeing. This is a proportion borne of observation: ‘To satisfie wise, and good lookers on’. We do things in a proportion not necessarily in accordance with nature, but in accordance with the terms of convention. This is ‘proportion’ that is a product of convention, a term framed by and for ‘good lookers on.’

[29] The temptation to satisfy ‘good lookers on’ is, perhaps, unending. The compulsion to measure is difficult to resist. Once ‘Man hath weau’d out a net, and this net throwne / Vpon the Heavens, and now they are his owne’ (ll. 279-280), what more was left but to describe how this net is weaved, to build the language? Wallis introduces the symbol for infinity (∞) in 1651, in what we might perhaps deem a literal signification of ‘the Heavens […] are his own’. Though it is beyond the scope of this essay, one could argue, along a constructivist reading of mathematics, that the use of (∞) for the development of calculus that followed did not require empirical verification, but, rather, agreement; that is, mathematical developments occurred not necessarily through discovery in the empirical or exploratory senses, but rather by notational innovations, as symbols and syntaxes were gradually accepted or revised by the broader community of mathematicians.

[30] This emphasis on the primacy of mathematics made its way outside equations. It bled into ways of thinking, and even intimate moments. Donne removes ‘numbers’ from the symbolic field and places it in conversation with everyday language, in order to emphasize its effect upon thought as well as its orientation of experience. Quantitative language, he says, is doing something — with how we are thinking, how we are seeing, in short, how we are orienting ourselves in the world. And this comes at a cost, to perception and to language. For all of his reliance upon quantitative language in his love lyrics, Donne’s most memorable moments are distinguished by his resistance to measurements of desires and emotions. In ‘Negative Love’, for example, he rejects measurement in favor of that ‘Which can by no way be express’d’ (l. 11); the speaker of ‘The Relic’, too, refuses to measure, stating, ‘All measure and all language I should pass, / Should I tell what a miracle she was’ (ll. 32-3). This reticence toward measurement is reflected especially in Donne’s use of quantitative language, which, while frequent, exhibits a deep scepticism over what counting will achieve for his lovers. In the Neoplatonic musings of ‘Air and Angels’, for example, Donne allows ‘That [Love] assume thy body’ (l. 13), but, then, immediately acknowledges the impossibilities of enumerating his lover’s parts in the Petrarchan fashion: ‘Ev’ry thy hair for Love to work upon / Is much too much: some fitter must be sought’ (ll. 19-20). The indescribable is figured as the impossibility of enumerating a love which inheres neither ‘in nothing nor in things / Extreme and scatt’ring bright’ (ll. 21-22), an entity, that is, neither consisting of the null set nor the multitude. If Donne’s lover observes and counts, he says, he restrains love to a representational order with which it is inherently incompatible.

[31] The problem of enumerating love using the Petrarchan blazon is echoed in Donne’s concerns over tracking love through time. Again, although he does count love in time, he more often suggests that love obeys a time outside of the systemized quantification of temporality afforded by the clock. He states this thesis most directly in ‘The Sun Rising’: ‘Love, all alike, no season knows nor clime, / Nor hours, days, months, which are the rags of time’ (ll. 9-10). Because of the self-identity it possesses in the nature of its unity, love refuses a representational knowledge produced in ‘the rags of time’. At times, a love which does, and does not, belong in time is depicted within a single poem. ‘The Legacy’ observes, rather precisely, ‘an hour’ since the lovers parted (l. 3), while then claiming, more abstractly, that ‘lovers’ hours be fully eternity’ (l. 4). Similarly, ‘A Lecture upon the Shadow’ remarks upon the ‘three hours which we’ve spent / In walking here’ (ll. 3-4), even as Donne’s speaker goes on to suggest love resides in a different timescale altogether: ‘Love is a growing or full constant light, / And his first minute after noon is night’ (ll. 25-26). In the final lines of ‘A Fever’, Donne’s speaker trades in eternity for one hour: ‘For I had rather owner be / Of thee one hour than all else ever’ (ll. 27-8). The sexual, physical suggestiveness in this closing seems at odds with the timelessness Donne allows his lovers elsewhere. Yet, rather than contradicting, ‘Love, all alike, no season knows nor clime, / Nor hours, days, months, which are the rags of time’ (ll. 9-10), it is quite possible Donne is simply using this ‘one hour’ as another play on how ‘lovers’ hours be fully eternity’ (‘The Legacy’, l. 4). We expect timelessness; he offers an hour. It is in the hyperbole of this enumeration that lovers’ time inheres.

[32] Christopher Johnson contends that ‘hyperbole ([…] literally means a ‘throwing-beyond’) is Donne’s signature trope’ (2004: 75). In the etymology to which Johnson points, the question of measurement is underscored. Blank’s reading of Puttenham is again helpful for understanding the taxonomic register to tropes: ‘tropes that are based on identifications, such as metaphor, may thus be understood “mathematically” as well as visually: rather than “likenesses” they create “equalities”’ (2006: 42). When Donne engages in hyperbole as a play on measurement, what does he ‘throw’ ‘beyond’? ‘Beyond’ what, exactly?  ‘Throwing-beyond’, I want to argue, posits both a limit point and its transgression, and, in so doing, taxes the very notion of measurement. Puttenham names hyperbole ‘the Overreacher’ or ‘Loud Liar’, and admonishes its application for challenging measure: ‘For although a praise or other report may be allowed beyond credit, it may not be beyond all measure’ (2007: 276). Puttenham labels the first example he presents of the trope ‘ultra fidem and also ultra modum’ (2007: 276-7). Donne’s use of hyperbole, then, is at odds with that ‘net throwne / Upon the Heavens’ of ‘The First Anniversary’. In other words, his ‘measurement’ is not ‘throwne / Upon’, but rather stretches the net, calling our attention to it, emphasizing both its conventionality and fallibility. And, ultimately, it serves as recognition of those aspects of the world and experience that cannot be brought under measurement in any conventional sense, or, rather, which obey alternative orientations, representational schemes and taxonomies altogether.

[33] When he does use calculation or measurement, it is to emphasize the varying, and at times incompatible, orientations that quantification provides for lovers’ experiences. Just as he removes ‘numbers’ from the symbolic mathematical field in ‘The Triple Fool’, so he makes calculations outside of mathematical isolation. As Johnson says, ‘numbers and calculation are also used […] to give flesh to abstract ideas’ (2004: 75). In ‘The Computation’, calculation stretches days and years, a physical life ‘thrown-beyond’ its limits:

For my first twenty years, since yesterday,
I scarce believed thou couldst be gone away;
For forty more I fed on favours past,
And forty on hopes that thou wouldst they might last;
Tears drown’d one hundred, and sighs blew out two;
A thousand, I did neither think nor do […]  (ll. 1-6)

The hyperbole at work builds until the reader loses count — in fact, is overwhelmed by enumeration. Robbins comments on the sum: ‘By now the “years since yesterday” total 2,400, implying that every hour has seemed like a hundred years’ (Donne 2008: 158). The speaker reflects on this protracted life of the lover in the final lines, ‘Yet call not this long life, but think that I / Am by being dead immortal — can ghosts die?’ (ll. 9-10). The suggestion of immortality, as Robbins notes, is especially appropriate for the poem’s tenth line: ‘Ten is a circular number (all its powers, 102, 103, etc., beginning with itself), thus symbolising eternity’ (Donne 2008: 158). Donne’s hyperbolic addition here yields, then, an entirely different sense of temporal experience than we expect in the conventional lifespan. Number either becomes broken, as it overwhelms and surpasses any sense of a singular human experience, or it folds into symbolic, allegorical numerology, allusive of the very ontologies — modes of being — which Klein argues are no longer part of theoretical inquiry with the increased focus of mathematics as a semiotic discipline (1968: 184).

[34] ‘The Computation’, an explicit reference to mathematics, is a reflection on how one measures experience. The relationship between the abstract and material, so critical to Donne’s poetics, was, in his time, beginning to find expression in symbolic mathematical language. Mathematical concepts were made material in symbols, and these symbols, in turn, provided the framework for a language to discern reality. Of course, ‘The Computation’ is not only about measuring time, but also about measuring love. Love, like time, is both abstract and physical, drawing it dangerously close to the field of symbolic mathematical language. In acknowledgement of this, lovers must resist measurement, as Donne suggests in ‘A Valediction: Forbidding Mourning.’ Do not mourn, he says, less our love be exposed. The empiricists are at the doorstep, prepared to make measurements, even in this intimate space. They are the ‘good lookers on’, like those who stand over virtuous men as they die: ‘some of their sad friends do say, / “Now his breath goes,” and some say, “No”’ (ll. 3-4). But where to escape? As symbolic representation expands, how can the lovers avoid being absorbed by it?  Donne attempts to collapse the relationship of two into one, a favourite numerical trick of his early lyrics:

Our two souls therefore, which are one
Though I must go, endure not yet
A breach, but an expansion,
Like gold to aery thinness beat. (ll. 21-24)

This seems an acceptable solution: if all relationships can be absorbed by measurement, then remove relationship from representation. The problem, of course, is that these lovers are not abstract ideas, not mathematical concepts, but physical things, incapable of such reduction. Donne is wary of reducing the physical to the abstract — of removing these lovers from a perhaps messy reality to ‘aery thinness’. He reconsiders: ‘If they be two, they are two so / As stiff twin compasses be two’ (ll. 25-26). This metaphor proves more satisfying, preserving the physical. Here, there is no abstruse reduction: two is two. But now, in the physical form, each becomes an accompanying symbol of measurement: ‘twin compasses’. In transforming each, Donne is ostensibly taking back measurement from the ‘good lookers on’, and restoring it to the lovers, who are alone capable of estimating their relationship. The compass is an interesting choice here for Donne, because, like a mathematical symbol, it is a tool for measurement — abstract mathematics made physical. It is this restoration of measurement that Donne celebrates at the close of the poem. The restoration of measurement, notably, parallels the restoration of proportion. ‘Thy firmness’, Donne says, ‘makes my circle just.’

Brown University


[1]Lemke references these sources directly in his essay, and the central element of each work is developing Peirce’s conception of social semiotics. For further reading on the semiotic perspective that Lemke draws upon, see especially C.S. Peirce, 1960. Collected Papers of Charles Sanders Peirce, vols. 1 and 2 (Cambridge, MA: Belknap Press of Harvard University). See also the selections ‘Logic Semiotic: The Theory of Signs’ and ‘The Nature of Mathematics’ (Buchler 1995: 98-119, 135-149). [back to text]


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