The singular focus of this book is the influence that sixteenth- and early seventeenth-century mathematical thinking exerted on the writing and production of popular drama between about 1587 and 1603. I concentrate upon six plays by five dramatists: Tamburlaine, Part 1 (1587) and Tamburlaine, Part 2 (1587) by Christopher Marlowe; Friar Bacon and Friar Bungay (1589) by Robert Greene; Old Fortunatus (1599) by Thomas Dekker; Hamlet (1600) by William Shakespeare; and The Tragedy of Hoffman (1603) by Henry Chettle. Each chapter attempts to analyse how the terms, concepts and implications of contemporary mathematics impacted upon these playsā vocabularies, forms and aesthetic and dramaturgical effects and affects.1 The six plays selected for analysis here are brought together by two simple factors: firstly, proximity, both chronological and institutional, and, secondly, a shared interest in and engagement with mathematical thinking. These two factors are not unlinked, for, as we shall see, mathematics was entering mass culture in the late Elizabethan period in a way that it had never done before. So, too, was dramatic art. Indeed, the period framed by the years 1587 and 1603 might be considered the first serious phase of early modern drama as a commercial phenomenon. As the citizens of society in these years grappled with the tenets of basic arithmetic, Euclidean geometry and complex algebra, so did they witness the rapid construction of public theatres, and the performances of the plays for which those theatres were designed. Mathematics may have had little need for dramatic art, but dramatic artāthe most eclectic of any mode of art in the periodāpicked up on the phenomenon of the rise and expansion of mathematical teaching, tools and methods, and utilised it to a variety of creative ends. That variety, even amongst a relatively small sample of texts from a relatively narrow chronological window, is the subject of this book.
The work of this introduction is threefold. Firstly, it will locate this book in its critical and scholarly context, providing a brief history of the technical and conceptual overlap between the mathematical and literary arts, and surveying and assessing contemporary scholarship pertaining to sixteenth- and early seventeenth-century mathematical culture, and its impact on literary creativity. Secondly, it will traverse the body of intellectual-historical information necessary to situate contextually the ensuing five chapters. This will comprise the bulk of this introduction, and is divided into four sub-sections. The first sub-section works towards a definition of mathematics in late Elizabethan England, whilst the latter three sub-sections attempt to locate mathematics in the spaces and institutions in which it was practised and taught: the universities, the city of London, and the printed book. In each of these latter three sub-sections, I endeavour to suggest and analyse points of transmission between those institutions and spaces, and the five dramatists who are this bookās prime focus. Thirdly and finally, this introduction will provide a summary of the chapters that are to follow it, in order to give a sense of the shape of the entire project. I hope, in the course of all this, that a number of this bookās conceptual and methodological decisions, habits and assumptions will be outlined, justified, and, indeed, where necessary, excused.
Mathematics and Literary Criticism
In the comic vision of Hades presented by Aristophanes in Frogs, Euripides challenges Aeschylus for his position in the āChair of Tragedyā (769).2 Before the official contest begins, Plutoās slave, who has already heard something of the impending matter, explains to Xanthias what he should expect to witness: āPoetic art will be weighed [ĻĻĪ±ĪøĪ¼Ī®ĻĪµĻĪ±Ī¹] in a balance [ĻĪ±Ī»Ī¬Ī½ĻĻ]ā, he proclaims, āand theyāll be bringing out rulers [ĪŗĪ±Ī½ĻĪ½Ī±Ļ], and measuring tapes for words [Ļį¼ ĻĪµĪ¹Ļ į¼Ļįæ¶Ī½], and folding frames [ĻĪ»Ī±ĪÆĻĪ¹Ī± Ī¾ĻĪ¼ĻĻĻ
ĪŗĻĪ±] [ā¦] and set squares [Ī“Ī¹Ī±Ī¼ĪĻĻĪæĻ
Ļ] and wedges [ĻĻįæĪ½Ī±Ļ]; because Euripides says heās going to examine the tragedies word for wordā (797ā802). His descriptive spoiler jars because the analytical tools he lists are not those of the linguistic arts but those of the quantitative sciences: how can Euripides apply the instruments of mathematics to the evaluation of tragic stage-plays? And yet, the slaveās words represent no mere comedic error or disciplinary mix-up, for as the battle between Aeschylus and Euripides reaches its climax, it becomes clear to Aeschylus that the only way for him to demonstrate his artistic superiority is in a strange act of measurement: āwhat Iād like to do is take [Euripides] to the scales [ĻĻĪ±ĪøĪ¼į½øĪ½]. Thatās the only real test of our poetry; the weight [Ī²Ī¬ĻĪæĻ] of our utterances will be the decisive proofā (1365ā67). In what follows, both poets speak lines of their most famous works into the āscale pansā (1378), and Dionysus declares whose words the scales deem heaviest, in an absurd literalisation of a common metaphor for the serious qualities of poetic writing. For all of Frogsā satire and parody, Aristophanesā play introduced a fascinating theoretical question to the Western canon: what might mathematics have to do with the production and reception of literary art?
This fundamental question underpins every aspect of this book, but my particular remit is, of course, much narrower. Indeed, it must be acknowledged now that the plays dealt with here are not entirely unique in their uptake of mathematical material, and that the early modern period, as Aristophanesā critical-creative text clearly evidences, was not the first to think about the relations of mathematics and literary art. This is partially a corollary of the universal nature of mathematics. Human beings, consciously or not, have always lived in mathematics as much as they have lived in language, and, as such, numbers exist almost anywhere one makes a concerted effort to look for them. But it is also because literary art in particular, as carefully formalised language, has always been attentive to matters of quantity, proportion and measure. The homologous condition of the mathematical and poetical arts has long been made clear by their shared terminology: ānumbersā are the base units not only of arithmetic, but of poetry also, the term acting as the traditional metonym for metrical feet, metre and verse more generally. This terminological confluence point began with the formation of the quantitative prosodies of classical languages, so that the Latin term numerus in relation to poetry can be found in Cicero, Quintilian and others.3 The term was carried into the Middle Ages by Augustine, and then transformed in the Renaissance into its vernacular forms: āthe numbers rise so ful, & the verse groweth so bigā, wrote Spenser in The Shepheardes Calender; āThese numbers will I tear, and write in proseā (4.3.52), exclaims Longueville in Shakespeareās Loveās Labourās Lost.4
George Puttenham began the second book of his The Arte of English Poesie, on āProportion Poeticalā, with the following sentence: āIt is said by such as professe the Mathematicall sciences, that all things stand by proportion, and that without it nothing could stand to be good or beautiful.ā5 If Puttenham had a particular mathematical source in mind, there is good reason to believe it could have been Henry Billingsleyās influential 1570 edition of Euclid, entitled The Elements of Geometrie of the Most Auncient Philosopher Euclide of Megara. In his introduction to Euclidās fifth book, Billingsley professed that āproportion and Analogie, or proportionalitie [ā¦] pertayneth not onely vnto lines, figures, and bodies in Geometry: but also vnto soundes & voyces, of which Musike entreatethā.6 Puttenham placed particular emphasis on āproportion, which holdeth of the Musicalā (as opposed to the āArithmeticallā or āGeometricallā) because, according to his belief, āPoesie is a skill to speake & write harmonically.ā7 In this, Puttenham differentiated himself from his frequent mentor, Aristotle. Although, in the fifth book of the Nicomachean Ethics , Aristotle considers arithmetical and geometrical proportionality in relation to various types of justice (as we shall see in Chap. 6), he says nothing of musical proportion in any context. In fact, in the Poetics , Aristotle makes clear...