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

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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 themost wellknown correlation between the two. Yet the epistemological surety Browningfinds 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 allcan have no more’ (Donne 2008: ll. 2324. This edition used throughout). Compared toBrowning, Donne appears a quantitative sceptic: a basic principle of number and multitudetells him that once a quantity is exhausted, ‘no more’ can be added. John Carey remarks ofDonne’s anxiety over measurement: ‘These are conflicts we stumble into once we try toquantify 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, thesuggestion that quantifying love is natural seems to overlook the mathematical and poeticdiscourses in which these poets participate when they presume, refuse, or worry over whatit means to ‘count the ways’. In other words, to what extent is Carey’s ‘inclination toquantify love’ a product of cultural experience?

[2] While criticism since the midtwentieth century has explored Donne’s relation to earlymodern scientific developments (Williams 1935; Coffin 1957; Empson 1957), more specificattention to the relationship of Donne’s work to mathematical developments in his timeneeds to be developed. This essay offers an assessment of how developments inmathematical symbolic language—specifically, Robert Recorde’s contribution to novelnotational figures—in midsixteenth century England may have influenced Donne’s poetics.While Carey concludes that ‘[Donne] seems to have regarded mathematics as, at best, acuriosity’, and that, ‘like most Elizabethans, Donne had virtually no interest in usingnumbers for the purpose of serious computation’ (1981: 12829), 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 inwhich Donne could explicitly rely on counting to articulate love and loss, with the formertallying time passed since a lover’s absence, and the latter, operating within a neoPythagorean 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. 2930), A.J. Smith notes that Donne is calculating the sum of thegendered 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 theerotic 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 lovepoetry reveals the striking frequency with which his poetics make use of quantitativelanguage. Thirtyfour of the fiftyfour ‘Songs and Sonnets’ contain some reference tonumber, such as ‘one’, ‘two’, ‘a hundred’, or ‘thrice’. Donne is even more preoccupied withrelationships between ‘all’ and ‘nothing’: he refers to ‘all’, ‘nothing’ or ‘none’ in thirtysix ofthe fiftyfour poems. Overall, fiftytwo 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 ofmathematics, as Carey observes, but his language is especially computative. As defined byAristotle, ‘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 sensein which numbers have a certain quality’ (1020b34). Quantitative language, in mydefinition, consists of verbal expressions of numerical degrees and spatial or temporalmagnitudes, in contrast to verbal expressions of kinds or essences.

[4] What does it mean for a poet to have numbers on his mind in turnofthecentury earlymodern England? In one sense, as Margaret Ferguson observes, it simply means being apoet: ‘As a verbal practice marked both by a concern for “measure” (as in syllable or linecounting) and by a tendency toward “license” (as in rulebreaking 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 narrativeswhich chart a dramatic shift from medieval structures of knowledge to scientific modernityoccurring in the fifteenth, sixteenth and seventeenth centuries (Daston 1991; Dear 1995;Crosby 1997), but also an assessment of both the numerological traditions and particularmathematical developments in England which contributed toward defining early moderns’relationships to numbers. My focus here lies in what purchase Donne gains in his poetics byrelying so frequently on quantitative language as a mode of articulation, insofar as suchlanguage alludes to a developing symbolic mathematical language that, in the seventeenthcentury, would assume epistemological claims that the English vernacular could not. AsPaula Blank observes, in addition to ‘mimetic theories of poetry’ and ‘ones that assimilateverbal art to the visual arts or to visual representation more generally’, ‘sixteenthcenturypoets […] additionally thought of their writing as an instrument of measure, one thatproceeded quantitatively rather than qualitatively, deciding relations rather than depicting“nature”’ (2006: 41). In this view of poetry, questions of numerological correlations betweenpoetic structures and the order of the cosmos become secondary to questions of taxonomy.Symbolic mathematics and the language of words constituted two developing, relatedsemiotic systems at the time, with shifting epistemological claims to the world and varyingcapacities for representing the realms of experience. Donne’s predilection for quantificationhighlights both the sympathies and disjunctions between these developing systems.

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

No mathematical treatise entirely avoids the connective tissue of verbal languageto link mathematical symbolic expressions, to comment on the process ofdevelopment of arguments, and so on. All our applications of mathematics, inthe context of which most of our present commonly used mathematics evolvedhistorically—in the natural sciences, engineering and design, commerce andcomputing—require verbal language to link mathematical tools to specific realworld things and events. (2002)

Lemke’s understanding of the relation between mathematical and verbal languages isinformed by a theoretical framework drawn from C.S. Peirce and pragmatism (Buchler1955; Houser and Kloesel 1992; Halliday 1978; Hodge and Kress 1988; Lemke1995). [1]Despite his observation of the ‘link’ which verbal language provides formathematical expressions, Lemke’s primary focus is on how mathematics functions as anindependent semiotic system, capable of producing meaning which verbal language cannot.My own approach diverges from the theoretical investments of pragmatism but usesLemke’s observation as a frame for considering economies between mathematical andverbal 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 increasedcultural 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 tohistoricize relations between the two languages. Specifically, it allows us to study hownotational developments in mathematics—on the order of syntax and symbols—aremanaged, or framed, through what Lemke calls ‘verbal language’, or, in the present essay, Ideem the English vernacular.

[6] Building from the seminal work on the history of mathematical notation by FlorianCajori, Lemke observes, ‘In most mathematical writing before modern times, symbolicexpressions were rare; they were integrated into the running verbal text, and they wereclearly meant to be read out in words as part of complete sentences that also includedordinary words’ (2002). Despite this longstanding historical relation between words andmathematical symbols, Jacob Klein, in a remarkable study of the algebraic innovations fromthe mathematicians Simon Stevin and François Viète, argues that a new conception ofnumber emerges in the early modern period, in which ‘the fundamental ontological scienceof the ancients is replaced by a symbolic discipline whose ontological presuppositions areleft unclarified’ (1968: 184). In other words, mathematics began to develop into a coherent,autonomous semiotic system, as disciplinary practice shifted from classical questions of theontological status of numbers (arithmos) toward semiotic considerations on notation (Klein1968; Rotman 1987; Hodgkin 2005). My intention here is to interrogate one example of theformulation of mathematics as an autonomous symbolic discipline in sixteenthcenturyEngland, in order to then consider how the poetic text relies repeatedly on the ‘connectivetissue 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 maytake half us men’ (ll. 2526), he is using the vernacular to articulate an equation linked tomathematical symbolic expressions. What does it mean when a poetic text, like ‘ThePrimrose’, relies on verbal language to facilitate such a relation to mathematical semioticfields?

[7] One can pose this question, I think, while keeping in mind, as Keith Thomas does in hisseminal essay on numeracy in England, ‘the importance of numbers in religious symbolismand allegory or of numerology in poetry and philosophical speculation’ (1987: 124). In ‘ThePrimrose’, for example, Donne is quite clearly appealing to symbolic numerical values as hecalculates relations between men and women, such that they equal ten. Robin Robbinsobserves 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 earlymodern 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 inDonne’s numbers, as studied by midtolate twentiethcentury numerological criticism(Fowler 1964, 1970, 1971; Patrides 1958; Heninger, Jr. 1974; Røstvig 1994), we may stillconsider to what extent his poetics engage features of a quantitative numeration derivedfrom the developing symbolic mathematics.

[8] With respect to developments in mathematics during the Renaissance, England was wellbehind the Continent. As Cajori observes, “Up to the seventeenth century, mathematics wascultivated but little in Great Britain. During the sixteenth century, she brought forth nomathematician comparable with Viète, Stifel, or Tartaglia’ (1991: 146). Thomas confirmsEngland’s rather slow start, noting, ‘Arabic figures had come relatively late to England; itwas only between the midsixteenth and midseventeenth centuries that they establishedthemselves in most forms of accountkeeping’ (1987:120). Furthermore, because of thisdelay, ‘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 ofEuclid, Robert Recorde emerged as a key figure in sixteenthcentury 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’splace in the early history of mathematical development in England. Notably, they do notassociate his value with theoretical contributions: ‘Recorde himself made no claim that hewas pushing forward the frontiers of mathematics. He was, rather, a communicator ofmathematical ideas who sought to explore ways in which to make mathematical knowledgeand skills available to a wide population’ (2012: 1). Recorde’s achievements lay in thesemiotic realm, specifically, in his dual emphases on the vernacular and symbolic notation.Recorde exemplified what Richard Mankiewitz identifies as ‘the tendency to write in thelocal vernacular in preference to Latin,’ a practice which ‘made mathematical textbooksaccessible to a wider public’ (2000: 70). During his lifetime, Recorde published fivemathematical 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 writtenin English:

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

Here, Recorde’s appeal to his sovereign invokes the humanist argument that knowledge ofthe classics would yield more effective servants of the state. If Recorde’s justification for thevernacular followed this longstanding humanist argument, his emphasis on symbolicmathematical notations, with respect to Arabic numerals, was a bit more novel. His bestknown work, The Whetstone of Witte (1557), contains the first recorded use of (=) for theequals sign in mathematical notation, in both England as well as the Continent (Mankiewitz2000: 71). In the same text, Recorde uses the nowfamiliar modern notation of the addition(+) and subtraction () symbols for the first time in an English text. Recorde’s pedagogicalcontribution to symbolic mathematics reflects his aim to communicate its practices andprinciples to a broader English public.

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

In retrospect we witness in this section part of the detail of the laborious processas mathematicians struggled over several centuries to get to grips with equationsand their solutions, their efforts often frustrated and encumbered by unwieldysymbolism. Recorde visibly strives to improve the processes, by introducingenabling symbolism, by dismissing the ‘idle bablying’ of overelaboration, and bydiligently 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 fornotational 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 onelengthe, thus: ===== bicause noe. 2. thynges can be moare equalle’ (1557: sig. Ff2r). Likemathematicians before him, Recorde recognizes that symbolic mathematical notation



becomes necessary as calculations become more frequent and complex. He could be called anotational pragmatist, in this sense, and, as such, he is well aware of the needs of hisEnglish readership, who may be unfamiliar not only with Latin, but with Arabic numerologyand 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 moareequalle’.

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

MAYSTER [sic]: Nowe then take héede, these certaine valewes euerye figurerepresenteth, 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 forexample: This figure 9 is ix. standing now alone.

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

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

SCHOLER [sic]: So it is. Then 9 without more figures of Arithmetike, betokenethix, whatsoeuer other letters be aboute it. (1582: sig. D1rD1v)

In this exchange, the Master delineates the fundamentals of numeration: value, figure, andplace. Recorde is aware that the novice in mathematics needs to understand the value of afigure 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 disjunctionbetween numerical figure and alphabetical letters: ‘Howe?’ he asks of the value of 9, ‘Is healone and standeth in the middle of so many letters?’ The Master answers in a way we mightexpect from the author who justifies his use of the vernacular for the good of the Englishstate: ‘The letters are none of hys fellowes,’ he says, just as an Englishman, surrounded by athousand Frenchmen in France, ‘recken[s]’ [sic] himself alone. Recorde’s attention to thisbasic differentiation indicates that before he can expound on the syntax of symbolicmathematics, he must first clarify that there is a different syntax—or language—available tothe student in mathematical signification, and, furthermore, that numerical figures andvernacular figures form separate sets of communities, as distinct, or so Recorde would haveit, as national identities.

[13] Let us briefly pause to examine two features of the relationship Recorde establishesbetween mathematical language and the English vernacular. On the one hand, thesubstitution of the (=) symbol arises both from a pragmatic aim to ‘auoide the tediouserepetition of these woordes: is equalle to’ and because Recorde often uses the symbol in hisown work. On the other hand, when it comes to the basic principles of numeration and thevernacular, a distinct boundary is posited. ‘Howe is he [the 9] alone and standeth in themiddle 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 thereader’s sense of his own Englishness as a discrete cultural category precisely at themoment 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 theisolation of this symbol from words surrounding it. If, as Lemke notes, ‘No mathematicaltreatise entirely avoids the connective tissue of verbal language to link mathematicalsymbolic expressions’ (2002), we can observe here how economies between this connectivetissue alter depending on what is at stake.

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

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

This legacy includes an extensive mathematical vocabulary, largely based onborrowings from Latin and continental European languages, notably Italian,German and French. […] The legacy also extends to Recorde’s use of symbolismas part of a process of simplifying mathematical expressions: his use of the signof equality together with the signs for addition and subtraction for the first timein English, coupled with use of the cossic signs and signs indicating square andother roots borrowed from Scheubel, established an unprecedented style ofmathematical writing. (2012: 11617)



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

[16] England’s most famous mathematician of the early seventeenth century WilliamOughtred published Clavis Mathematicae (1631), a landmark mathematical treatise at thetime, and introduced the (X) symbol for multiplication, replacing the symbol of a cross(Smith 1958: 404405). According to Cajori, ‘[Oughtred] laid extraordinary emphasis uponthe use of mathematical symbols; altogether he used over 150 of them’ (1991: 157). LikeOughtred, John Wallis was an advocate of expanding the scope of mathematicalsymbolization, as Gordon Hull describes:

Thinkers such as Wallis, innovators in mathematical developments, expressedfewer or even no such worries about the scope of symbolization. Thinkers whostraightforwardly adhered to a premodern understanding of science tended todownplay 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 forefrontof mathematics in the English Renaissance. An increased complexity of computations wasaccompanied by a more nuanced language, as evident in the expansion of symbolicrepresentation to more complex ideas, such as infinity. In 1655, Wallis published DeSectionibus Conicis, the text widely credited with the first use of the lemniscate, the modernsymbol for infinity (∞) (Cajori 1928: 214; Maor 1991: 11). Wallis’s work, especially hisArithmetica 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 thecentury. Infinity, both as symbol and concept, reflected the increased level of sophisticationin symbolic mathematical language. It also, of course, had deep symbolic implications in therealms 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 figureeight on its side is an ancient symbol, ashadow 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 theanswer 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 becomingmore crucial to cultural articulation in the early modern landscape. As William Bouwsmasuccinctly puts it, ‘quantity now tended to be substituted for quality as the essentialprinciple of orientation’ (1980: 234). In other words, quantification afforded a means ofarticulation that extended beyond the mathematical. In a poem to the preface of ThomasHylles’s The Arte of Vulgar Arithmeticke (1600), an anonymous poet finds in numbersnothing less than the foundation of all language: ‘No state, no age, no man, nor child, buthere 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 ‘epistemologicalconfusion’ in the period (2004: 67) plays out, on at least one level, between the developingmathematical language of symbols and the language of words. Hylles’s poet’s tribute tonumber 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 significantto conceptions of poetry in the sixteenth and seventeenth centuries (2006; 2013). The OEDlists two entries from the end of the sixteenth century: E.K. glosses line 110 in the OctoberEclogue of The Shepheardes Calendar (1579) as, ‘The numbers rise so ful, and the versegroweth 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 lackpower to move / O sweet Maria, empress of my love, / These numbers will I tear, and writein prose’ (IV. 3. 5355). Such examples reflect the dual role ‘number’ played in the earlymodern 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, theOED dates the quantitative definition earlier than the metrical: ‘sum, total (early 12thcentury as numbre), grammatical number (13th cent)’ (‘number’, n.). Traced from theMiddle French, ‘number’ exhibits a tension still very much at play in the sixteenth andseventeenth centuries. Examining George Puttenham’s mathematicallyinflected treatmentof meter in The Art of English Poesie (1589), Blank contends that ‘his work is representativeof an early modern habit of confusing arithmos (for Puttenham, a variant of“arithmeticall”), rithmos, arithmetic, and the Latin ars metrica’ (2006: 42). Moreover, thisconfusion or tension in ‘number’ thrives precisely in the period in which symbolicmathematical 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 thefoundations of early modern thought. In his wide knowledge base, he was somewhat of ananomaly: a former aspiring courtier (‘Jack Donne’) who became an Anglican priest (‘Dr.Donne’), and, throughout, remained wellread in the most recent scientific andmathematical developments of his time. Herbert Grierson wrote that ‘no other poet in theseventeenth century known to me shows the same sensitiveness to the consequences of thenew discoveries of traveler, astronomer, physiologist and physician as Donne’ (1912: 189).Donne’s understanding of the implications of scientific and mathematical developments ofthe period underlies the quantitative references in his poetry, as he illuminates both theanxieties and paradoxes that the early modern period experienced with what Carla Mazzioidentifies as the ‘newly assertive regime of standard measurement’ (2004: 60). Donne foldsquantitative language effortlessly into his lovers’ experiences, suggesting its expansiverepresentational capabilities; and yet, he repeatedly interrogates what it means to ‘count theways’ of love: how quantification represents and orients experience, as well as how it fails todo just that. When the quantifiable enters Donne’s verse, it is always teetering under theinstabilities of hyperbole and competing forms of measurement. In this view, he figures asthe counterpart to Blank’s depiction of Shakespeare in the Sonnets, who, she contends,‘imagines unsettled, unstable, and uncertain relationships among the parts of his createdworks’ (2006: 43). Most of all, although he demonstrates an interest in what symbolicnumerology offers his accounts of love, Donne persistently refuses the expanded scope thequantifiable extends towards the regulation and systematization of experiences in space andtime: Donne’s lovers do not live on grids.

[20] In both ‘The First Anniversary’ and ‘The Triple Fool,’ to take examples of his probing ofthe disparities between quantification and experience, he sets quantitative language inrelationship 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 withoutproportion’ (ll. 3078). In ‘The Triple Fool’ grief is unruly, that which the narrator proposesto tame in ‘numbers’: ‘Grief brought to numbers cannot be so fierce, / For, he tames it, thatfetters it in verse’ (ll. 1011). 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 regainproportion?

[21] These examples have two implications. First, in Donne’s poetics, quantitative languageis 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 themathematical equation, ‘9+13=22’, for instance. Donne’s ‘numbers’ are not separate fromthe 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 wordsexist uneasily side by side, but in Donne’s example, those ‘numbers’ are forced intoconversation with the words that surround them—in this case, ‘grief.’ The result is a pairingof disparate modes of experience, orientations to the world that are incompatible with oneanother. ‘Numbers’ are removed from the isolation of mathematical language and made toengage 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 somethingwith our world and our ways of thinking: ‘numbers’ do not sit benignly beside ‘grief’—theywork upon it. Quantitative language becomes in ‘The Triple Fool’ a way of organizing ourworld that lays representational claims upon the nonmathematical. In this sense, Donne isquite aware that the discoveries in mathematics and sciences at the time have very realimplications on our everyday language and perceptions.

[23] For Donne quantitative language is ultimately a means of orientation. Even the nonmathematical can be defined based on its relationship to the mathematical: grief is simplythat which is ‘without proportion’. Yet, if the quantitative is such an active, pervasive meansof 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 laysclaims upon reality—as Galileo’s ‘language’ of God suggests.

[24] Donne recognizes how easily the distinction between mathematics as invention andmathematics as the ‘language’ of God can be blurred. In ‘The First Anniversary’, a tribute tohis patron Sir Robert Drury’s young daughter Elizabeth, who died in 1610, Donne takes theoccasion of Elizabeth Drury’s death to critique a way of seeing and interpreting nature thatis a product of developments in science. Ostensibly, this is a criticism of empiricists, butwhen 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 enforceMen to finde out so many Eccentrique parts,Such diuers downeright lines, such ouerthwarts,As disproportion that pure forme. (ll. 25157)

In this passage, proportion is linked with human thought, which is then interrupted byobservation: ‘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 humanconcept, but one might argue that the ambiguity is precisely the point: the cosmologicalorder 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 ‘downeright lines’ that ‘disproportion that pure



forme’—‘disproportion’ deriving from a relationship between a way of seeing and natureitself. Importantly, both ‘pure forme’ and ‘disproportion’ are produced as ways of thinkingand seeing that blur human cognition and the natural world, invention and discovery. Withthe latter, though, we encounter a confused tangle of mathematical words, both numericaland geometric—‘many Eccentrique parts’ and ‘divers downeright lines’ that ‘men findeout’—which function as middlemen between the boundary of things natural and humanconstructions. The ambiguity here is more problematic than the ambiguity between humanthought and the cosmological order in the first example, because we have introduced theterms, 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 ofdevelopments in mathematics and science, things in nature exist within the humancognitive structures imposed upon them:

They haue empayld within a ZodiakeThe freeborne Sunne, and keepe twelue signes awakeTo 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. 2637)

Donne’s imagery of the ‘freeborne Sunne’’s losing battle with the ‘Zodiake’’s ‘twelue signes’,‘the Goat and Crabbe’, and ‘these Tropiques’ sets the dramatic tension between anepistemological order gonewrong and a natural world unable to escape the human eye. Thecognitive 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 symbolsand human perception, as observers rely upon ‘signs’ to ‘watch’. In the paradox at play forDonne, the world is disproportioned precisely when we attempt to confine it entirely withinthe 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 naturalworld. 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 waysin which the epistemological crisis—or, in Johnson’s terms, “confusion” (2004: 67)—residesin a tension of value at the level of competing languages. Straddling the boundary betweenthings natural and human constructions, mathematical ‘signs’ achieve a tremendouscapacity for explaining the world, and, in doing so, deprive verbal language of its owncapacity 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 FirstAnniversary’ reflects not only a loss in the natural world, but a loss in language as well. Inthe wake of recent scientific discoveries, the paths of all heavenly bodies are thrown off: ‘Alltheir proportion’s lame, it sinkes, it swels’ (l. 277). Proportion constitutes a relationshipbetween man and world. It is not only the heavenly bodies whose ‘proportion’s lame’, butour very relationship to them. In this sense, ‘proportion’, the word itself, has gone lame inlanguage. It is ‘lame’ precisely because its discursive value is constrained within theparameters of a scientific or mathematical taxonomy within which the natural world is alsocontained: ‘Man hath weau’d out a net, and this net throwne / Vpon the Heauens, and nowthey are his owne’ (ll. 279280). Is it possible that the proportion Donne considers here isthat of symbolic mathematics, represented in our modern nomenclature with (:)? Thoughthe 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 hislanguage, and yet distances this claim from the language of words, entrenching it insteadwithin symbols.

[28] It is no wonder, then, that for Donne, ‘beauties best, proportion, is dead’ (l. 307). Withthe 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 thingBe 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. 329336)

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

[29] The temptation to satisfy ‘good lookers on’ is, perhaps, unending. The compulsion tomeasure is difficult to resist. Once ‘Man hath weau’d out a net, and this net throwne / Vponthe Heavens, and now they are his owne’ (ll. 279280), what more was left but to describehow 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 hisown’. Though it is beyond the scope of this essay, one could argue, along a constructivistreading of mathematics, that the use of (∞) for the development of calculus that followeddid not require empirical verification, but, rather, agreement; that is, mathematicaldevelopments occurred not necessarily through discovery in the empirical or exploratorysenses, but rather by notational innovations, as symbols and syntaxes were graduallyaccepted or revised by the broader community of mathematicians.

[30] This emphasis on the primacy of mathematics made its way outside equations. It bledinto ways of thinking, and even intimate moments. Donne removes ‘numbers’ from thesymbolic field and places it in conversation with everyday language, in order to emphasizeits effect upon thought as well as its orientation of experience. Quantitative language, hesays, is doing something—with how we are thinking, how we are seeing, in short, how weare orienting ourselves in the world. And this comes at a cost, to perception and tolanguage. For all of his reliance upon quantitative language in his love lyrics, Donne’s mostmemorable moments are distinguished by his resistance to measurements of desires andemotions. In ‘Negative Love’, for example, he rejects measurement in favor of that ‘Whichcan 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. 323). This reticence toward measurement is reflected especially in Donne’s use ofquantitative language, which, while frequent, exhibits a deep scepticism over what countingwill 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 acknowledgesthe impossibilities of enumerating his lover’s parts in the Petrarchan fashion: ‘Ev’ry thy hairfor Love to work upon / Is much too much: some fitter must be sought’ (ll. 1920). The



indescribable is figured as the impossibility of enumerating a love which inheres neither ‘innothing nor in things / Extreme and scatt’ring bright’ (ll. 2122), an entity, that is, neitherconsisting 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’sconcerns over tracking love through time. Again, although he does count love in time, hemore often suggests that love obeys a time outside of the systemized quantification oftemporality 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 oftime’ (ll. 910). Because of the selfidentity it possesses in the nature of its unity, loverefuses a representational knowledge produced in ‘the rags of time’. At times, a love whichdoes, 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, moreabstractly, 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. 34), even asDonne’s speaker goes on to suggest love resides in a different timescale altogether: ‘Love is agrowing or full constant light, / And his first minute after noon is night’ (ll. 2526). In thefinal lines of ‘A Fever’, Donne’s speaker trades in eternity for one hour: ‘For I had ratherowner be / Of thee one hour than all else ever’ (ll. 278). The sexual, physical suggestivenessin 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. 910), 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). Weexpect 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 ‘throwingbeyond’) 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 helpfulfor 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 aplay on measurement, what does he ‘throw’ ‘beyond’? ‘Beyond’ what, exactly? ‘Throwingbeyond’, 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 praiseor 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 ultramodum’ (2007: 2767). 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 bothits conventionality and fallibility. And, ultimately, it serves as recognition of those aspects ofthe world and experience that cannot be brought under measurement in any conventionalsense, or, rather, which obey alternative orientations, representational schemes andtaxonomies altogether.

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



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. 16)

The hyperbole at work builds until the reader loses count—in fact, is overwhelmed byenumeration. Robbins comments on the sum: ‘By now the “years since yesterday” total2,400, implying that every hour has seemed like a hundred years’ (Donne 2008: 158). Thespeaker reflects on this protracted life of the lover in the final lines, ‘Yet call not this longlife, but think that I / Am by being dead immortal—can ghosts die?’ (ll. 910). Thesuggestion of immortality, as Robbins notes, is especially appropriate for the poem’s tenthline: ‘Ten is a circular number (all its powers, 102, 103, etc., beginning with itself), thussymbolising eternity’ (Donne 2008: 158). Donne’s hyperbolic addition here yields, then, anentirely 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 singularhuman experience, or it folds into symbolic, allegorical numerology, allusive of the veryontologies—modes of being—which Klein argues are no longer part of theoretical inquirywith the increased focus of mathematics as a semiotic discipline (1968: 184).

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

Our two souls therefore, which are oneThough I must go, endure not yetA breach, but an expansion,Like gold to aery thinness beat. (ll. 2124)

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 loversare not abstract ideas, not mathematical concepts, but physical things, incapable of suchreduction. Donne is wary of reducing the physical to the abstract—of removing these loversfrom a perhaps messy reality to ‘aery thinness’. He reconsiders: ‘If they be two, they are twoso / As stiff twin compasses be two’ (ll. 2526). This metaphor proves more satisfying,preserving the physical. Here, there is no abstruse reduction: two is two. But now, in thephysical form, each becomes an accompanying symbol of measurement: ‘twin compasses’.In transforming each, Donne is ostensibly taking back measurement from the ‘good lookerson’, 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 ofmeasurement, notably, parallels the restoration of proportion. ‘Thy firmness’, Donne says,‘makes my circle just.’

Brown University

Notes

[1]Lemke references these sources directly in his essay, and the central element of eachwork is developing Peirce’s conception of social semiotics. For further reading on thesemiotic perspective that Lemke draws upon, see especially C.S. Peirce, 1960. CollectedPapers of Charles Sanders Peirce, vols. 1 and 2 (Cambridge, MA: Belknap Press of HarvardUniversity). See also the selections ‘Logic Semiotic: The Theory of Signs’ and ‘The Nature ofMathematics’ (Buchler 1995: 98119, 135149). [back to text]

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

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