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Issue 6 (2014) - Numbers

Sexual and Poetic Figuration and the New Mathematics in Shakespeare’s Sonnets

Stephen Deng

[1] Shakespeare famously apologizes in the prologue to Henry V for the inability of his play to ‘cram / Within this wooden O the very casques / That did affright the air at Agincourt’ (1996: Henry V, Prologue, 12-14), calling attention to a key problem in accurately representing the drama of history, especially in terms of the sheer magnitude of an event, the specific figures involved. In this admission about the inadequacy of staging, the playwright invokes an unusual relation between literary and quantitative representation hinging on a ‘crooked figure’ common to both commercial theater and the new mathematics based on Hindu-Arabic numbers and positional notation:

O, pardon! since a crooked figure may
Attest in little place a million,
And let us, ciphers to this great accompt,
On your imaginary forces work.
[………………………………..]
Piece out our imperfections with your thoughts;
Into a thousand parts divide one man,
And make imaginary puissance.
(1996: Henry V, Prologue. 15-25)

The shape of the ‘wooden O’ and the ultimate emptiness of theatrical representation call to mind for Shakespeare the peculiar ability of another nothing, the Hindu-Arabic cipher or ‘0’, a placeholder that could magically multiply any number by ten just by its appropriate placement, part of the new mathematics that was gradually becoming accepted in early modern England. Only a handful of these ciphers, requiring but ‘little place’ in notation, can quickly turn one figure into a million. The actors in this formulation become ciphers that combine with the audience’s imagination — implicitly compared to non-zero numbers — in order to recreate the accurate scale at Agincourt. However, in the Prologue’s subsequent reformulation, it is the actors themselves who are the non-zeros combining with the ciphers of the audience’s imagination. He asks the audience to imaginatively divide any given figure on stage ‘into a thousand parts’ so that a few bodies can authentically represent the great battle at Agincourt by tacking the ciphers of the audience’s imaginations on to each figure on stage. [1] But regardless of whether the cipher in this operation is the actor or the audience’s imagination, Shakespeare conceives of the two assuming properties similar to the magic of zero, in being able to represent large magnitudes within a small space and thus produce a more convincing depiction of historical reality.

[2] This particular attempt at conjuring history through dramatic and quantitative representation intimates a relationship between literary and mathematical representation more broadly. First, since enumeration is a practice of counting objects, numbers tend to materialize implicitly what is otherwise immaterial, an ability that calls to mind the world-making capacity of literary representation, like the poet king Richard II employing his ‘still-breeding thoughts’ to ‘people this little world’ of his cell at Pomfret Castle (1996. Richard II, 5.5.8-9). And yet, rules within the system introduce the possibility of dematerialization, such as in the operation of subtraction or multiplication by zero: what is something can quickly become nothing. Such transformations are indicative of an imaginative capacity that enumeration makes possible: it allows one to count abstractly even in the absence of specific corresponding material objects.[2]  Moreover, because it constitutes a self-contained system, there is always the possibility for number to be abstracted from that which it is purported to count. This latter property raises the question of whether enumeration of material objects is akin to the substitutive effects of literary tropes. Note, for example, that the prologue asks the audience to ‘cram / Within this wooden O the very casques’, the soldiers’ helmets, as synecdochal, or perhaps metonymic, figures for the soldiers themselves, much like contemporary military references to ‘boots on the ground’. Is the abstraction of number in the representation of history any more reductive and dehumanizing than the abstraction of associating individual soldiers with their common headwear or footwear? With both enumeration and trope, and perhaps for any mathematical or literary figuration, the lack of personal and individual detail leaves such depictions of historical reality insufficient at best. The problem is most pronounced in cases such as this: the figuration of people and especially representations of complex identities.

[3] And yet numeric representation and the mathematical properties that accompany it allow Shakespeare, especially in his sonnets, to think in a sustained manner through the complexity of identity and the potential for imaginative enumeration, the possibility of creation through number.  In this article I will argue that, in early sonnets, Shakespeare alludes to the multiplicative power of the cipher as a placeholder in his expressions of desire for the propagation of beauty embodied in the ‘fair youth’.[3] Sonnet 6 in particular exploits this mathematical property to conceive generations of beautiful offspring from this solitary source of beauty, a calculus that assumes the very possibility of multiplying identities and therefore a rigid correspondence between father and child, leaving the mother a mere ‘nothing’ within the sexual operation. Moreover, like the prologue to Henry V, sonnet 20 extends this procreative power of zero to the imaginative realm, positing the potential for various ‘no things’ to produce multiple versions of the fair youth through means other than human reproduction, and once again calling attention to the possibility of ‘identity’ as multiple. But Shakespeare also introduces a more destructive power of zero within the context of the ‘dark lady’ sonnets, a dark side of the cipher that carried cultural resonance, not only because of distrust about the numerical magic associated with Arabic practices (Parker 2013: 223-26; Kaplan 1999: 102),  but also from the recurrent sexual associations with the cipher as a woman’s procreative ‘nothing’, combining with and at times threatening the unity or identity of her male partner. While the cipher could multiply other figures surrounding it, in other forms of combination, like multiplication and division with the cipher, it has the capacity to subsume other figures into itself. Later sonnets also consider potential paradoxes that emerge when different conceptions of number clash, especially between the new mathematics of the medieval and early modern periods and classical mathematics of Greece and Rome (Raman 2008: 168; Wilson-Lee 2013: 460-64).  In sonnets such as 135 and 136, Shakespeare introduces a classical conception of unity, which treated one as a non-number (and therefore comparable in kind to the relatively new figure of the cipher) and denied the possibility of fractions or ‘broken numbers’, only to counteract these principles with more modern conceptions of ‘one’ as both a countable unit critical to maintaining accurate accounts and as a divisible unit belying its status as the principle of all number. The convergence of these two systems gives rise to multiple, contradictory outcomes for ‘will’ in the sonnets, who either maintains himself as a unified entity, becomes fragmented as merely part of a larger whole, or becomes entirely subsumed or rewritten by association with the feminized cipher. In all of these instances, Shakespeare assumes an intimate connection between the figurations of number and person in order to assess the very notion of ‘identity’, and the article will conclude with an exploration of this term, that was emerging at the time within discourses on mathematics as well as with respect to the ‘identity’ of an individual. However, Shakespeare also recognizes the possibility of conflict that arises between these two discourses over the question of whether ‘identity’ is singular or multiple.

The new mathematics

[4] In his sonnets Shakespeare revisits the seeming paradox, exemplified in his prologue to Henry V, of the cipher being at once empty in itself but multiplicative in combination with other figures. The cipher was a key component of the Hindu-Arabic number system, which was imported, or perhaps re-imported, into late medieval Europe from the east (Kaplan 1999: 11-12, 17). Starting in the eleventh century, translations of the great Arab mathematician Al-Khwarizmi’s Arithmetic — by the Englishman Robert of Chester, who studied mathematics in Spain, and the Spanish Jew John of Seville — began to circulate in the Latin world, introducing the new method of reckoning to a scholarly audience (Menninger 1969: 411). This became the basis of what I am calling the new mathematics in medieval and early modern Europe in contrast to classical mathematics of Greece and Rome, which did not employ a notion of zero or any place-based system of notation, a concept I discuss further below. It was especially the advocacy of Leonardo of Pisa (1180-1250) — better known in the mathematics world by his designation as the son of Bonaccio, ‘Fibonacci’ — that made its practice more acceptable within the business community. Leonardo had learned arithmetic under the tutelage of an Arab master in the Pisan colony of Bugia, in present day Algeria. Believing this system to be superior to that of Roman numerals, he promoted its use in his 1202 manuscript, which he called Liber abaci, ‘the book of the abacus’, despite the text’s introduction of a system eliminating the need for an abacus (Swetz 1987: 11-12).

[5] Although Leonardo had important influence on the business community, it took several generations for the foreign system to become conventional in Europe, partly from xenophobic distrust due to its association with Arabic culture, partly from concern about fraud since it was easier to falsify the new numbers (which of course overlaps with the first reason), and partly from general confusion about the method in a time before printing. Fraud concerns appear to be the main purpose for a 1299 edict in Florence forbidding bankers from using the numbers, and for a requirement in 1348 at the University of Padua that booksellers have their prices marked ‘“non per cifras, sed per literas clara” (not by figures [or more accurately “ciphers”, a term used for all numbers], but by clear letters, i.e. in Roman numerals)’ (Pullan 1968: 34). Such suspicion would forestall widespread adoption of the system for several hundred years. Although references to the numerals appear in various medieval manuscripts, Roman numerals and tally marks continued in general use in Italy until the late fifteenth or early sixteenth century (Jaffe 1999: 33). Similarly, in England, there are various early allusions to zero — for example in 1399 William Langland refers to a ‘sifre…in awgrym, That noteth a place, and no thing availith’ — but most people persisted in using counter-boards and Roman numerals (Pullan 1968: 34). Even in Shakespeare’s day, account books such as those of Philip Henslowe recorded transactions using Roman numerals despite the fact that at the time ‘algorism’ had become more accepted and more useful to the business community. Information about the new computational methods had also become more widespread by this period. During the sixteenth century nearly a thousand arithmetic primers were published, including Robert Recorde’s influential The Ground of Artes, published in 1543, to explain the new mathematics to a broad audience of practitioners (Jaffe 1999: 34).

[6] The eventual adoption of the system occurred primarily because of its advantage for business purposes. In medieval Italian the Hindu-Arabic numerals are even referred to as ‘figura mercantesca’ (mercantile figures), pointing to their particular connection to business (Edler 1934: 121). Many proponents of the new mathematics claimed to be able to compute figures more quickly than those using counting-boards or abacuses and Roman numerals, which had been the most common method of counting in medieval Europe. In ‘The table of Verbes’ within his dictionary, John Palsgrave (1530: sig. [2]B6v) included as an example of ‘I reken’ the boast, ‘I shall reken it syxe tymes by aulgorisme or you can caste it ones by counters’. By the end of the seventeenth century, John Arbuthnot (1700: 27) could claim without apparent irony, ‘I believe it would go near to ruine the Trade of the Nation, were the easy practice of Arithmetick abolished: for example, were the Merchants and Tradesmen oblig’d to make use of no other than the Roman way of notation by Letters, instead of our present’. Pragmatism would eventually overcome xenophobia, convention and the initial confusion over the new methods, and even lead to European dependence on this foreign system.

[7] The greatest advantage to the system was in its positional notation for which the cipher played a critical role. Indeed, without the ability to represent an empty column, the system could not function because a practitioner would be unable to distinguish between numbers such as ‘12’ and ‘102’. In The Ground of Artes, Robert Recorde explains the importance of ‘ii. Valewes’ in the system, the values of individual figures and the values derived from their position in notation:

For the valewe is one thyng, and the figures are an other thynge, and that cometh partely by the dyuersite of fygures, but chefely of the places, whereby thei be sette… But here muste you marke that every figure hath .ii. valewes. One alwayes certayne, that it sygnifieth properly, which it hath of his forme. And the other vncertayne, whiche he taketh of his place. (1543: sig. A6v)

The ‘1’ in both ‘12’ and ‘102’ is of course the same and thus has the same value in itself — this is the first value described by Recorde. However, because of the zero placed between 1 and 2 in 102, the 1 in this case takes on a higher value from its position in the hundreds column rather than in the tens column. Zero is peculiar in that its individual value signifies nothing, and therefore in order to have any value at all it relies on the presence of other figures around it, which explains the Fool’s reference to Lear as ‘an O without a figure’ (1996: King Lear, I.4.191-92).[4] But despite its dependence on other figures, the zero’s positioning has the power to transform the positional value of all other numbers. In one of the first references to the ‘cipher’ in the English language (according to the OED), Thomas Usk notes that ‘Although a sipher in augrim have no might in signification of it selve, yet he yeveth power in signification to other’ (‘Cipher’ 2014). As I point out below, this codependency of zero and non-zero figures becomes an important quality for representing the procreative process in Shakespeare.

[8] Most importantly, the cipher tends to increase the value of other figures around it, as the anonymous Treviso Arithmetic (1478), the first printed arithmetic book, explains: ‘The tenth figure, O, is called cipher or “nulla”, i.e. the figure of nothing, since by itself it has no value, although when joined with others it increases their value’ (Swetz 1987: 41-42). As with the ‘12’ and ‘102’ example, placement of zeros increases the value of all figures to their left and therefore the value of the number overall. Robert Recorde explains how this continual process of placing zeros can quickly expand the figure:

[zeros] are of no valewe them selfe, but they serue to make vp nomber of places, and so maketh the figure folowynge them to be in a forther place, and therfore to signifie the more valewe, as in this example, 90 the cyphar is of no valewe, but yet he occupieth the fyrst place, and causeth 9 to be in the seconde place, and so to signifie .X . tymes 9 that is .XC. so [that] ii. cyphars thrusteth the fygure followyning them, into the .iii. place, & so forth. (1543: sig. B3v-B4r)

Every zero placed to the right of any given number will multiply the entire number by ten, quickly increasing its magnitude, like Shakespeare’s ‘ciphers’ in the prologue to Henry V, in only a ‘little place’ (1996: Henry V, Prologue, 16-17). With rapid increases in the scale of commerce and trade within early modern Europe, the advantage of such an efficient system of quantitative representation becomes clear.

The Procreative Power of Zero

[9] This multiplicative capacity lends itself to representations of human procreation. The most explicit reference to this procreative power of zero within Shakespeare’s sonnets can be found in sonnet 6, which builds on the exhortatory message of the early sonnets for the propagation of beauty. This sonnet extends the financial language of its preceding sonnets by contrasting the ‘vse’ of one’s substance with ‘forbidden vsery’:

That vse is not forbidden vsery,
Which happies those that pay the willing lone;
That’s for thy selfe to breed an other thee,
Or ten times happier be it ten for one,
Ten times thy selfe were happier then thou art,
If ten of thine ten times refigur’d thee,
Then what could death doe if thou should’st depart,
Leauing thee liuing in posterity? (6. 5-12)

According to Aristotle, tokos, the Greek term for interest meaning ‘offspring’, signifies its status as unnatural breeding, which partially explains the connection Shakespeare makes between numbers and procreation. Usury continued to be denounced because of biblical prohibition despite a general acceptance in England of an interest rate of ten percent following the Usury Act of 1571 and the specific mention of ‘ten’ calls to mind for critics the accepted rate of interest in England at the time. For example, Natasha Korda relates the ‘legally tolerated’ rate of ten percent to the cipher, which ‘was associated with the calculation of interest and indebtedness; its power to increase or decrease by a factor of ten suggested the gains and losses of creditors and debtors, respectively’ (2009: 145; Hawkes 2001: 105; Herman 2000: 269-70).  As Stephen Booth points out, however, the ten-fold increase associated with the cipher would amount to a 1000 percent, not a 10 percent rate of interest (1997: 142). Therefore, while the sonnet evokes both usury, and the multiplication by ten associated with the cipher, the two are only indirectly related in terms of the general connection between finance and sexual reproduction.

[10] Most importantly, criticism relating the sonnets to usury has tended to subsume the new mathematics, which I believe should be a separate point of interest in the poems. Although there is no explicit reference to the cipher in sonnet 6, as in the prologue to Henry V, the specificity of ten children, who could themselves each produce another ten, clearly points to the cipher’s multiplicative power: placing a ‘0’ next to a ‘1’ produces ‘10’ children who would also be ‘ten times happier’ than the initial ‘1’ when they produce another ‘100’ children in total. Moreover, the notational placement of ones and zeros plays on the correspondence between numbers and gender that critics have noted in sonnet 20: ‘one thing’ or 1 = male; ‘nothing’ or 0 = female (Callaghan 2007: 75; Booth 1997: 164). The persistence and proliferation of beauty in the male youth requires his productive combination with a female. The youth would therefore be ‘refigur’d’ in being transformed from his initial ‘1’ into ‘100’ once his own ten children each produced ten more of their own, and despite his own subtraction from the equation upon death, he would be left ‘liuing in posterity’.

[11] Notice, however, that such procreative mathematics assumes continuity in identity between father and child: all children become mere ‘refigur’d’ versions of the father. Like the ‘casques’ at Agincourt in the prologue to Henry V, any sense of differentiation between people counted becomes erased by number and figurative representation. It was common to consider the offspring as close copies of the parent, with appearance an important indicator to prove one’s legitimacy. Nevertheless, we generally perceive clear demarcation in Shakespearean depictions of fathers and sons, differences that disappear in the procreative arithmetic he employs in sonnet 6. Identity moves from something individual and unique to something multiple and reproducible, but numbers alone in procreation clearly obfuscate some defining characteristics for the particular identities represented. Moreover, there is an assumption here that the woman is ‘nothing’ in the procreative process other than the ability to procreate. Like the cipher, she is valueless without any combination with the male’s ‘one’, and once she performs her part in procreation, her own identity becomes annihilated beyond the total number of ‘refigur’d’ versions of the father that she helps to create. Therefore the identity of both mother and child become subsumed into the identity of the father after such procreative arithmetic is employed.

[12] And yet this problem of subsumed identities does not prevent Shakespeare from exploring a more imaginative form of procreation in sonnet 20 based on a similar model. The final lines of the sonnet mention the ‘one thing’ and ‘nothing’ that have become a source of critical controversy, especially about Shakespeare’s (or the speaker’s) sexual proclivity (Callaghan 2007: 76):

And for a woman wert thou first created,
Till nature as she wrought thee fell a dotinge,
And by addition me of thee defeated,
By adding one thing to my purpose nothing.
But since she prickt thee out for womens pleasure,
Mine be thy loue and thy loues vse their treasure. (20. 9-14)

The main contention is over the interpretation of ‘nothing’. If we read the line to mean that the ‘one thing’ added to the youth by nature is of no purpose to the speaker (‘to my purpose nothing’), critics may interpret a rejection of homoerotic possibilities. On the other hand, if the ‘one thing’ added is a ‘nothing’, which could connote any orifice and thus not be gender-specific, one could read the final lines as an expression of homoerotic desire. Booth (1997: 165) suggests this double meaning in his citation of Martial’s epigram: ‘divisit natura marem: pars una puellis, / una viris genita est (Nature has divided the male: one part is made for girls, one for men)’. The first ‘thy love’ in the final line of sonnet 20 could then refer to the speaker’s ‘one thing’ (‘Mine’), and the second to the youth’s, the ‘vse’ of which would serve as ‘treasure’ for women.

[13] Therefore, while the final ‘vse’ of the youth for ‘womens pleasure’/‘treasure’ would indicate the combination of ‘1’ and ‘0’ as in sonnet 6, the allusion to the youth’s own ‘nothing’ suggests some other form of procreation represented in the poem, if not human reproduction. Despite the impossibility of human offspring from the relationship between two men, perhaps Shakespeare conceives of figurative offspring, maybe even the sonnets themselves, from this numerical magic of combining ones and zeros. The act of writing — the one thing that is the pen combined with the nothingness of the blank page — is of course central to the self-conscious creativity of the sonnets. Similarly, the centrality of writing to the new mathematics — and its key uses in accounting systems in order to keep track of material reality— suggests the possibility of materializing what is immaterial in other forms of representation. Multiplication in the new mathematics is, after all, mere figuration on a page. Indeed, it is the emptying out of the material in accounting — moving from elaborate verbal descriptions that identify particular things to abstract number — which allows for the multiplicity of representation. John Dee (1570: sig. []4v) notes this unusual status of ‘Things Mathematical’ as in between ‘material’ and ‘immaterial’ within his preface to Euclid: ‘For, these, beyng (in a maner) middle, betwene thinges supernaturall and naturall: are not so absolute and excellent, as thinges supernatural: Nor yet so base and grosse, as things naturall: But are thinges immateriall: and neuerthelesse, by materiall things hable somewhat to be signified’.[5] Thus despite the speaker and youth’s incapacity for human reproduction, methods of quantitative representation would lead Shakespeare to conceptions of other forms of abstracted procreation, which would be able to replicate the beauty of the young man even if not in human form.

[14] However, the procreative female who would serve to immortalize the young man (at the same time that her own identity would be subsumed) contrasts with the destructive sexuality of the ‘dark lady’ in later sonnets, a destructive capacity that is in line with other properties of the cipher. Even the productivity of the female zero could arouse negative connotations (Traub 2000: 443; Daileader 1998: 135). For example, in Cymbeline, Posthumus, upon being asked by Iachimo whether he wants to hear more about Innogen’s purported infidelity, tells him to ‘Spare your arithmetic, never count the turns. / Once, and a million!’ (1996: II.4.142-3). The ignominy of one illicit sexual act assumes an equivalency to a million with the multiplicative power of the female cipher, a crucial factor in the ‘arithmetic’ that Posthumus attempts to avoid. And in Middleton and Rowley’s The Changeling, De Flores contemplates in an aside the burgeoning relationship between Alsemero and Beatrice, imagining that one adulterous affair would quickly multiply to others (and hoping to be included among those numbers):

                                                                          if a woman
Fly from one point, from him she makes a husband,
She spreads and mounts then, like arithmetic,
One, ten, a hundred, a thousand, ten thousand –
Proves in time sutler to an army royal.                                                                                              (1990: II. 2. 60-64)

Such instances show that the multiplicative power of the cipher in the context of gender could be employed for other numbers (lovers, sexual acts, diseases, etc.) besides progeny. Once a number becomes abstracted from what it originally counts or accounts for, it can be attached to any other countable entities instead. So the potential for replication extends even across multiple categories of objects.

The Dangerous Cipher

[15] But in addition to being able to multiply various quantities, the cipher tends to subsume other numbers into itself, an operation that counters the procreative power of zero discussed earlier, which tends to leave the zero as ‘nothing’ other than its ability to multiply ones. According to the multiplicative property of zero, any number times zero produces zero, and according to the property of division, zero divided by any number maintains itself. Therefore, the cipher cannot be transformed by other figures in such operations. While some mathematicians following Aristotle insisted on the indivisibility of one since it is the principle of unity, the truly indivisible unit proved instead to be zero. This appropriative tendency emerges in sonnet 134 by the reference to the lady as a ‘vsurer’ who has claimed the youth and ‘mortgag’d’ the speaker to her ‘will’ (1-2). While once again the language of usury becomes prominent here (Korda 2009: 129),  the transformation in meanings of ‘will’ in this and the following two sonnets suggests that the source of her appropriative power is from the same ‘nothing’ that was a source of creative power in earlier sonnets.

[16] It is this promiscuity and sexual desirability of the lady that gives rise in sonnet 136 to concerns about the destruction of male identity. The ‘one’ will mentioned early in the sonnet eventually becomes a ‘nothing’ by the end, or merely the name ‘Will’:

Will, will fulfill the treasure of thy loue,
I fill it full with wils, and my will one,
In things of great receit with ease we prooue,
Among a number one is reckon’d none.
Then in the number let me passe vntold,
Though in thy stores account I one must be,
For nothing hold me so it please thee hold,
That nothing me, a some-thing sweet to thee.
Make but my name thy loue, and loue that still,
And then thou louest me for my name is Will.                                                                                (136. 5-14)

Valerie Traub (2000: 444) finds in the ‘phallic “one”’ of the first two lines of this passage a ‘fantastic desire to return to a state of undifferentiation: not the merger of infant with maternal body, but the cramming of the mistress’s womb with male bodies, and in so doing, eliminating all space for independent female desires’. It is significant that whereas in sonnet 135 ‘will’ assumes the connotation of both male and female sexual organs, in sonnet 136 the male ‘will’ predominates. However, Eve Kosofsky Sedgwick (1985: 38) observes that in the sonnet ‘the men, or their “wills”, seem to be reduced to the scale of homunculi, almost plankton, in a warm but unobservant sea’. Both readings, the male body as both dominant and insignificant, are in fact consistent with Shakespeare’s own mathematical inconsistency. The sonnet, especially the line ‘Among a number one is reckon’d none’, alludes to the classical principle that one is not a number but the principle of number, so that as Leonard Digges writes, ‘Number is the multitude of Unites sette together’ (1579: sig. B1r). The speaker therefore utilizes the status of one as a non-number in order to compare himself to another non-number, the cipher: ‘For nothing hold me so it please thee hold’. Natasha Korda (2009: 144) notes that while the reference to one as a non-number sets up the ‘gendered opposition between the male one and the female “nothing”’ as in sonnet 20, this very opposition ‘is destabilized […] by the female creditor’s “will” — construed as both the enormity of her wants and the spaciousness of the receptacle in which her sexual and monetary “treasure” (l. 5) is stored’. I would agree that this opposition becomes destabilized, but it does so primarily because of the arithmetic properties of the figures involved, especially the cipher in the equation which tends to subsume all other figures. While the speaker hopes that he will remain ‘some-thing sweet’ to the lady and even just ‘one’ in her ‘stores account’, the realization is that he has become a mere nothing within the context of another all-encompassing nothing. The statement would therefore suggest a collapsing of identity between the male one and female cipher as both are either ‘all one’ or ‘as good as none’ (Booth 1997: 469; Blank 2006: 143-44).

[17] However, the reference to the ‘reckon’d’ one as none introduces a complication since it could mean either ‘consider’ or ‘count’. He acknowledges the fact that in her ‘stores account I one must be’. That is, despite its status as non-number, one must be reckoned/counted within the accounts — it is a component, indeed the basis, of the composite number that represents the sum (of lovers in the metaphor). This recognition is illuminated by the fact that ‘Among a number one is reckon’d none’ does not stand alone as a statement, but is preceded by ‘In things of great receit with ease we prooue […]’. The classical comprehension of the one’s role, the sonnet points out, is suggested (though not definitively proven) by the fact that one among many is essentially none. His desire, then, is not to be considered as ‘nothing’ but as close to nothing or as if he were nothing because the ‘one’ of his account is insignificant compared to the ‘number’ within which he would like to ‘passe vntold’. This is also the reason he can remain ‘some-thing sweet’ (perhaps with a pun on the ‘sum’ of all the lovers) despite his appeal to be ‘reckon’d’ or considered as nothing. Sonnet 136, therefore, puts pressure on the classical conception of one as a non-number by introducing the fact that in modern accounts, every ‘one’ matters in establishing a full record of transactions and calculations. All must eventually add up. It was for a similar reason that in 1585 the Flemish mathematician Simon Stevin insisted that one should be considered a number, rejecting the classical view of its special status (Ostashevsky 2004: 208).

Broken Numbers

[18] Sonnet 135 poses a similar challenge to its classical principles by introducing the concept of fractions, another key mathematical component which, by being considered as numbers, negated the idea that one is the basis of all numbers. In the Metaphysics, Aristotle had written that ‘to be one is to be indivisible…a unity is the principle of number’ (1966: 1052b16-22). Some mathematicians such as John Dee held on to this view in rejecting the new idea of fractions as numbers: ‘vulgar Practisers’ (from which he of course excludes himself) ‘extend [the] name [of Numbers] farder, then to Numbers, whose least part is an Vnit. For the common Logist, Reckenmaster, or Arithmeticien, in hys vsing of Numbers: of an Vnit, imagineth lesse partes: and calleth them Fractions’ (1570: sig. *2r). However, Shakespeare, in his prologue to Henry V, alludes to fractions when he asks the audience, ‘Into a thousand parts divide one man, / And make imaginary puissance’ (1997: 24-25). By linking this division of one actor to the multiplication of imagined soldiers on his insufficient stage, the playwright encourages his audience to ignore the classical indivisibility of one and to consider this act of division a conjuring of numbers.

[19] Whether the classical or more modern understanding of ‘one’ predominates will determine how we interpret sonnet 135:

Who euer hath her wish, thou hast thy Will,
And Will too boote, and Will in ouer-plus,
More then enough am I that vexe thee still,
To thy sweet will making addition thus.
Wilt thou whose will is large and spatious,
Not once vouchsafe to hide my will in thine,
Shall will in others seeme right gracious,
And in my will no faire acceptance shine:
The sea all water, yet receiues raine still,
And in aboundance addeth to his store,
So thou beeing rich in Will adde to thy Will,
One will of mine to make thy large Will more.
Let no vnkinde, no faire beseechers kill,
Thinke all but one, and me in that one Will.       (135. 1-14)

In addition to the play on his name and the general term for sexual desire (as in Twelfth Night’s subtitle ‘What You Will’), ‘will’ assumes particular references to both male and female sexual organs. In fact, the wordplay evokes the combination of the two, especially with the references to ‘adding’ (‘To thy sweet will making addition thus’) but at the same time leaves uncertain what quantity results from the sexual operation. In the middle of the sonnet, the speaker reiterates the claim that his own will would be an insignificant part of the ‘large and spatious’ will of the lady’s, a veritable drop in the ocean. And yet he first describes his own ‘Will in ouer-plus’, alluding not only to his excessive sexual desire but also to his own abundance of semen. His multitudinous seed thereby challenges his own described unity, the ‘One will of mine’ that he wishes to be added to her ‘spatious’ will. But even if he can restore unity through his one ‘will’ that will be added to ‘make thy large Will more’, he recognizes that his own unity represents only part of the larger collective. Once again he attempts unification by asking that she ‘Thinke all but one, and me in that one Will’. Still, the ability for him to remain unified in the end assumes the classical conception of one as indivisible. In that case, when he is ‘in that one Will’, he has completely appropriated not only her will but the will of all her other lovers (consider it me when you think of that one will). If, on the other hand, we permit the possibility of fractions and therefore a divisible one, then his being ‘in that one Will’ means that he is merely a part, and a small fraction of the whole at that.

[20] While ‘will’ in these sonnets primarily bears connotations of sexual desire or the sexual organs, the potential for its unification, fragmentation or dissipation suggests that it extends more broadly to the notion of identity, especially because of the potential for puns on the poet’s own name: what effect does ‘will’, in its various sexual associations, have on ‘Will’? According to the OED, the mathematical meanings of ‘identity’ — for example, in Billingsley’s translation of Euclid, ‘Proportionalitie is a likenesse or an idemptitie of proportions’ — emerged in the late sixteenth century, around the same time as the meaning of ‘identity’ as ‘The sameness of a person or thing at all times or in all circumstances; the condition of being a single individual; the fact that a person or thing is itself and not something else; individuality, personality’ (‘Identity’ 2014). Note, however, that Billingsley’s ‘idemptitie’ in the context of ‘proportionalitie’ implies a comparison between two objects, so that even the notion of ‘identity’ in this context works against the potential of ‘identity’ as individuality or uniqueness. In the sonnets, Shakespeare employs such emergent and convergent conceptions — albeit by employing the term ‘will’ instead of the more modern ‘identity’ — to consider how the mathematics of sexuality might produce tension and contradiction in the establishment of male identity. Of course the identity under consideration is only the male identity, the phallic oneness that becomes either maintained (through propagation of future generations) or threatened by its interaction with the female cipher. The mathematics of gender identity in the sonnets clearly privilege the male at the expense of the female, as if the very possibility of ‘female identity’ is excluded.[6] Moreover, the female principle understood in mathematical terms can be understood only in relation to the male principle since in itself it remains, to quote Lear’s fool, merely ‘an O without a figure’: the female ‘O’ always serves as the dependent ‘other’ for the male ‘figure’ even as it has the capacity to affect the male.

[21] How exactly this ‘O’ affects the ‘figure’ becomes an important concern within the sonnets. The dangerous cipher of the later sonnets becomes an infinitely divisible and cooptive entity threatening the unified identity (i.e., the ‘oneness’) of the speaker (and the youth) even as he relies on it in the earlier sonnets to maintain, through its reproductive power, the beautiful identity of the ‘fair youth’, an identity in itself that proves potentially multiple. The later sonnets’ emphasis on classical mathematics, and especially classical conceptions of unity, would tend to encourage interpretations that find no potential fragmentation of identity, though it does leave open the possibility of comparison and relation between the cipher and the one as special ‘non-numerical’ figures. On the other hand, their inclusion of more modern conceptions of the function of one would encourage interpretations of fragmentation as well as resistance to the collapsing of binaries. Of course this very process of abstracting identity to number already entails a significant loss, if not absolute annihilation of identity. Once numbers are abstracted from what they count, those same numbers can be used to count various other entities (implying the potential for multiplicity even across various categories), and the original referent for the numbers may be forgotten. Part of the enumerative process is this ability to separate number from materiality. But the problem of identity in the sonnets also reminds us that numbers are not mere abstractions, that they have a cultural history with significance beyond the technological facilitation of more efficient counting and accounting, a history that often engages with material concerns such as those of commercial and political culture, and gender and sexuality.

Michigan State University

NOTES

[1] Ostashevsky (2004: 212) notes that this passage not only invokes the paradox of multiplying by dividing but also the ontological indivisibility of one as each part resulting from the division of each actor would still be considered one thing and not a fraction of a thing.[back to text]

[2] On the cipher as the limit of such ability to associate number with object see Rotman 1996: 13.[back to text]

[3] In all references to particular sonnets, I follow the numbering of the 1609 printing. All citations of sonnets are from Booth’s (1997) edition of Shakespeare’s Sonnets.[back to text]

[4] Jaffe (1999: 41) points out that ‘O’s status as somehow different from other numbers is emphasized in the new math primers by the fact that it is always described separately, set apart’. For more on Lear and the cipher, see Rotman 1987: 78-86.[back to text]

[5] The signature for the citation from John Dee is an unusual character showing a finger of a hand pointing to the right (called a “fist” or “manicule”). The only font I have found that can represent it is Wingdings 2. The Unicode for it I believe is U+1F449 (white right pointing backhand index), which wordpress does not support. More can be read on Wikipedia.[back to text]

[6] An interesting counter-example to this negation of female identity might be seen in Wilson-Lee’s (2013: 459-60) reading of Cressida’s fragmentation or fractioning in Troilus and Cressida. The very possibility of fractioning implies an original unity of identity.[back to text]

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