Shakespeare by Numbers: Mathematical Crisis in Troilus and Cressida

The current turn to the history of science and mathematics in early modern literary studies has opened the way for a range of arguments suggesting that Shakespeare’s use of specialized vocabularies represents a conscious and complex engagement with technical developments in his time and, further, that these engagements underpin many of the central emotional and ideological conflicts in the plays. One branch of this scholarship starts from the discursive, charting the manner in which these new vocabularies, especially actuarial and arithmetic innovations, provided fresh resources for articulating old power struggles while simultaneously reconfiguring these struggles by giving old words new meanings.

From a renewed interest in accounting as a site where the intellectual, social, and material met, recent studies of The Merchant of Venice have found new agency for Portia in her actuarial competence and fresh degradation of Shylock for his lack of it (Natasha Korda), as well as new foundations for considering legal conundrums in the abstract on the model of algebra (Shankar Raman); Raman also charts a path from actuarial accounts of time to ontological speculations in The Winter’s Tale.¹ Similarly, xenophobic resistance to Arabic numerals has been seen as infiltrating the language of Othello (Patricia Parker) and the analysis of legitimate heredity in Henry V (Eugene Ostashevsky).² A second branch of work, with which the present study might be classed, traces expressions of the (often traumatic) experience of paradigm shifts in early modern works including Shakespeare’s. In a seminal work on King Lear, Mary Thomas Crane has located the “ontological and epistemological chasm” of Lear’s madness in the rupture caused by atomism between “the nature of the material world” and “human embodied experience of its solidity and weight.”³

This essay uses a similar chasm in Troilus and Cressida as its leaping-off point and argues that Shakespeare’s interest in the sensorimotor disorientation caused by paradigm shifts can convincingly be located in mathematical (and more specifically geometric) ideas that provided him with potent metaphorical resources. Mathematical paradoxes in these plays trigger disorientation and provide a means to communicate this disorientation to the reader. So on the one hand, a series of extended metaphors blends the pragmatics of measurement with the abstractions of proportion, confoundingly embedding the infinite in the everyday. On the other, the ontological crises of Troilus (and other introspective princelings) are repeatedly likened to the contemplation of mathematical truths, truths that are vertiginous in being irrefutable, beyond the capacity of the imagination, and stubbornly resistant to moralization. Prominent but not alone among these tense mathematical paradoxes are Troilus’s “thing inseparate [that] / Divides more wider than the sky and earth” (5.2.155–56) and Hamlet’s nutshell that hems in “infinite space” (2.2.257).⁴ Shakespeare’s interest here seems to have been in these characteristics of mathematical truth, rather than in any of the particular techniques that were being studied and developed within the English mathematical community. However, the development of this interest may not have been happenstance and becomes clearer in the context of contemporary debates over the proper uses for mathematics and the opening in 1597 of Gresham College on Bishopsgate Street.

Gresham College was designed to provide free public lectures on (among other things) applicable mathematics for mariners and tradesmen; it was founded next to Shakespeare’s home of the late 1590s and stood on the main thoroughfare out of London to the Shoreditch theaters.⁵ Although Mordechai Feingold has convincingly argued against any actual dichotomy between a scientifically progressive, mercantile London and more conservative mathematical communities at the universities, it is nevertheless important that contemporary debates followed a Platonic precedent in opposing a mundane, practical mathematics and a refined, abstract one.⁶ Shakespeare’s use of mathematical metaphor in Troilus largely conforms to the terms of this debate, although its moments of crisis occur when dizzying perceptions of abstract mathematical truth are located in the everyday, unsettling the basic assumptions by which these characters had previously lived. As the philosopher Alain Badiou has repeatedly suggested, the confrontation in mathematics of a...