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Issue 6 (2014) - Numbers

Epilogue — Writing in the Aftermath: Digital Humanities, c. 1600?[1]

Carla Mazzio

The little matter of distinguishing one, two and three—in a word, number and calculation:  do not all the arts and sciences necessarily partake of them?

— Plato, The Republic

The bureaucratization of knowledge is above all an infinite excrescence of numbering.

— Alain Badiou, Number and Numbers

[1] ‘Without words, there is no possibility of reckoning of Numbers,’ wrote Thomas Hobbes in his Leviathan, ‘much less of Magnitudes, of Swiftnesse, of Force, and other things, the reckonings whereof are necessary to the being, or well-being of man-kind’ (Hobbes 1651:14). Such a seemingly simple insight into the relationship between verbal expression and numerical computation is worth remembering at this point in history, particularly given the accumulated rise of symbolic notation, computer coding, and algorithms for the navigation of big data in the 21st century — when numbers and mathematical symbolism seem to have taken on lives of their own. Before the divide between the ‘two cultures’ of science and the humanities, facilitated by the development of disciplinary and professional specialization as well as shifting cultural conceptions of knowledge, truth and meaning, numbers and words were understood to have a great deal more in common than they do today.  Indeed, whereas Hobbes insisted that ‘the use of words in registring our thoughts, is nothing so evident as in Numbring’ (14), the equation seems in some ways to have reversed. The use of various forms of numbering in registering our thoughts — even or perhaps especially as humanities scholars involved in various arts and practices of words — may well evince, consciously or unconsciously, the power of numbering at work in our words and world today. We need only allude to the power of quantitative assessment over practices of scholarly evaluation and production in the UK (and increasingly America) to suggest the extent to which numbers have come to matter in the lives of departments, institutions, and scholars focused, in various ways, on the arts and practices of language and mediation across the humanities.  The extent to which numbers have come to matter, that is, cannot be underestimated in the critical turn to understand numbers in material as well as historical terms.

[2] If this volume is any indication, not to mention the collective bibliography that it represents, ‘numbers’ have become newly charged as signs, symptoms, and forces to be reckoned with. Indeed, given the ‘numerical turn’ in early modern studies in recent years, we might wonder exactly where, when, how, and why numbers became so charged and, by the same token, exactly what numbers have been charged with.[2] The epigraph above from the contemporary philosopher Alain Badiou, claiming that ‘the bureaucratization of knowledge is above all an infinite excrescence of numbering,’ may well resonate with those now confronted with numerical models of assessment across the humanities and social sciences (Badiou 2008:2). But this is just part of a much larger and more philosophical charge that Badiou has made against the ‘despotism of number’ over all aspects of knowledge acquisition and production across the arts and sciences, not to mention the mental habits of everyday life (4). Number as ‘today’s fetish,’ he writes, conceals more serious problems at stake in accessing substantial modes of thought and being (Badiou 2007: 26). Thinking about numbers in relationship to forms of counting is for Badiou a form of not thinking at all. He thus aims to turn to a pre-modern ‘ontology of number’ to counteract epistemologies of number integral to methodologies as well as institutional and cultural forces across the humanities, social sciences and sciences; integral to the numerical organization of lives, minds, and souls in forms of quotidian life, and thus the reduction of the human to numbers that count or do not count. [3]

[3] For Badiou, as for other thinkers for whom numbers used for purposes of counting have become inseparable from large-scale social transformations or re-constellations, approaches to number can often lead to very large generalizations. There is something about numbers today that almost seems to call out for a return to large-scale thinking, be it a return to longue durée historiography (if with attention to issues of socio-economic inequality) recently advocated by historians Jo Guldi and David Armitage or the shift to “distance reading” through graphs, maps and trees, posited by literary scholar Franco Moretti (Guldi and Armitage 2014; Moretti 2007, 2013). Many readers in fact drawn to this Special Issue, Numbers in Early Modern Writing, may well come equipped with various large scale narratives about the power of numbers as newly important vehicles of social and epistemological transformation in the early modern period. For longstanding debates about the rise of capitalism, rationalism, empiricism, objectivity, probability, ‘modernity,’ or governmental, bio-political regimes all clearly involve questions that centre around the status and power of number, calculation, and the work of writing, or discourse more broadly, in the world.

[4] The specific call by Hunt and Tomlin to explore numbers in writing over the course of this volume, however, opens up space for a different set of questions, not least by unhinging ‘numbers’ from those large conceptual categories so often associated with them, and thus from the often now reflexive ethical imperative to wrest particular kinds of authority from them. Numbers — in this volume and in scholarship to be produced in its wake — can thus roam as freely in the historical imagination as they did in early modern writing. For then, as now, numbers emerged in every genre of writing imaginable; from almanac to atlas, bible to budget, chronicle to cookbook, or diary, epic and fable to grimoire. They emerged in paratexts as well as texts in fascinating ways, with the capacity to disconcert and confuse as well as to orient and clarify the order of things.[4] The fact that numbers emerged in fundamental ways in texts concerned with the arts of language (logic, rhetoric, and grammar) as well as in those concerned with arts of calculation (arithmetic, geometry, music, and astronomy) has encouraged recent scholars to think more seriously and more locally about rhetorical dimensions of number and quantitative aspects of language in the early modern period.[5]  This movement alone, and the essays in this volume that develop upon it, seem to me to offer creative and intellectually far-reaching responses to the oft assumed antinomies between the power of numbers and vulnerability of humanistic inquiry in the present day.

[5] To take seriously the generic and taxonomic lability of early modern ‘numbers in writing’ opens up the possibility of rethinking contemporary models of generalization about — or based upon — numbers in scholarship, culture, and society. The recent impulse to turn or return to the distinctly material dimensions of numbers (as entities in and of themselves or as vehicles for the shaping of material worlds), moreover, can help to ground a more capacious understanding of the relationship between numbers, writing and the production of knowledge in both the present and the past. For if numbers were promiscuous in affiliation with genres of writing, modes of expression, and categories of knowledge, they were no less mobile in relationship to representational forms and material surfaces. They were of course inscribed or printed as Roman numerals, Hindu-Arabic numerals, words, marks, or dots among other forms. They could be found on clock-faces, tally-sticks, coins, dice, calendars, armillary spheres, gravestones and numerous other objects peopling the landscape of early modernity. Accordingly, like other kinds of text, numbers and numerical thinking alike often relied upon material technologies ranging from abacus, pen, and navigable book to scientific instruments within and beyond the book and page. Although numbers as symbols of quantity can often tend toward further abstraction, attending to the local conditions and the material surfaces upon which they existed or were imagined to exist (from parchment and erasable paper to canvas, stone, bone, wood, linoleum, metal, wax and sand) can help to draw attention to the inter-animation of media, materiality and modes of cognition across a range of disciplines.

[6] In the context of early modern incarnations of number, it is important to simply note that numerical modes of thinking often crossed the material/immaterial boundary in ways that energize many essays in this volume. Indeed, it is striking to note the extent to which numerical manipulation or mental calculation in this volume is understood to be embodied, be it through the logic of textbook arithmetic, the work of numbers in the art of fencing, or the sexual economies of zeros and ones in Shakespeare’s poetry. The attention to physical as well as semiotic dimensions of numbers across these essays attests, in part, to the power of material studies to bring even those seemingly abstract symbols of quantity down to earth, to the surfaces of pages, the tips of fingers, and into the play of minds and worlds compatible with recent approaches to embodied thought and extended cognition. To consider the history of numbers and writing in the present day is thus also to continue to complicate an ongoing history of oppositions between material and immaterial, concrete and abstract, mental and physical worlds through which numbers have come to mean.[6]

[7] Since the general subject of ‘numbers’ in the present day has the capacity to raise questions if not eyebrows about the making of credible or objective knowledge, the turn to exploring numbers in and as writing opens up timely questions about particular rhetorical ‘figures,’ as it were, that were and may continue to be integral to the making of fiction and the making of fact.[7] How, for example, might numbers have operated as vehicles of social as well as aesthetic power by conjuring illusions of material reality from a distance? Claims about the size of an army, the scale of one’s property, about a particular number of sheep or ducats can all serve as a means of ‘conjuring’ persons and things. The ways in which numbers can seem to make persons and things or actions materialize — a point emphasized by Stephen Deng in his exploration of numbers as part of the imaginative writer’s tool-kit as well as by James Beaver in his analysis of John Donne — offers an important counterbalance to distinctions often drawn between abstract number and material things, not to mention between the arts of number and the arts of language.

[8] While numbers could be mobilized, as Christopher Johnson has put it, ‘to give flesh to abstract ideas,’ the opposite was also often the case (2004: 74). The use of physical bodies to illustrate the logic of both numbers and letters in early mathematical textbooks is one case in point. Of course the practical orientation of many early vernacular mathematics led to necessary visual or rhetorical insertions of the practitioner or practitioners into the scene of calculation. But at the same time, the strategic verbal and visual representation of bodies, situations, and events in early mathematical texts of all kinds could conjure whole worlds of numerical engagement oriented toward individual and collective action.

Figure 1. From Simon Stevin’s De Weehgdaet, Wisconstige Gedachtenissen (Leiden, 1608), Reproduced by Permission of the Huntington Library.

Figure 1. From Simon Stevin’s De Weehgdaet, Wisconstige Gedachtenissen (Leiden, 1608), Reproduced by Permission of the Huntington Library.

[9] The illustration from the Flemish Mathematician Simon Stevin’s De Weehgdaet (a text on weighing first published in 1586 and reprinted in his 1608 ‘Mathematical Memoirs’) is but a single example of the visually appealing and pedagogically useful depictions of bodies in action in sixteenth and early seventeenth-centuries vernacular texts [Figure 1]. Such forms of action and practice were not always, of course, textual—nor distinct from innovations in higher mathematics, as the case of Galileo, who was trained in engineering and military science, might suggest. But it remains notable that ‘the Everyman of early English practical mathematical literature’, as Kathryn James has recently put it, ‘is resolutely present on the battlefields, on ships, tramping the bounds of estates in the company of not always trusting or trustworthy tenants’ (2011: 6, italics added).[8] Whereas the issue of rank and status implicit in James’s description of bodies in action in English mathematical texts opens onto a well-known field of debate about relationships between artisans and aristocrats, for Ken Mondschein in this volume, it is the already idealized, elite body-in-motion of the fencer in sixteenth-century Italy that provided a ground for the placement (and thus transmission) of all manner of mathematical abstractions.

[10] Part of the larger question at stake here is how numbers may have been ‘conjured’ or made to matter as objects of social and epistemological value through various dimensions of writing and print. What kinds of authority, in other words, could numbers convey or disrupt? If numbers now have the power to convey authority in the establishment of fact or scale, numbers in early modernity in many ways depended upon a range of authorizing functions in order to matter. The close attention to the history of print and publication in considering the status of numbers on pages in essays by Tomlin and Hunt seems to me to further expand upon issues of authorship and authority. Tomlin’s demonstration of James Peele’s attempt to construct himself as an ‘author’ and to construct accountancy as part of a distinctly humanist publishing agenda by the King’s printer indexes the lability of early modern conditions of authority and authorship, not simply for readers but for writers and transmitters of technical knowledge. Hunt’s essay complicates authority of another kind: the authority of Michel Foucault in approaching — or generalizing about — tables in early modern books. Hunt not only exposes the immense amount of labour and typographic specialization that went into the printing of those ‘masses of numbers’ in numerical tables, but shows us how numerical units of information become detached from the mental processes that created them, in fact functioning as a kind of ‘cheat-sheet’ for those who wanted to avoid the often difficult labour of calculation. For Hunt, we need not all follow in the wake of Foucault and others who turn to the formal properties of textual or graphic culture (in this case the table) as indices of larger cultural models of thought. Some tables, like contemporary calculators, exist to eliminate rather than shape the process of thought.

[11] Numbers in Early Modern Writing thus seems to me to offer a kind of collective counter-response to some contemporary assumptions and large generalizations about numbers at work in relationship to both history and writing. In addition to the essays alluded to above, in those focused largely on numbers at play in poetic and dramatic literature, we see how productively imaginative fictions could draw upon the operational as well as symbolic and linguistic dimensions of arithmetic. We see this in the fascinating interplay of zeros and ones in relationship to issues of reproductive futurity and vulnerable masculinities in Shakespeare’s sonnets (Deng); in the quantitative dimensions of John Donne’s verse (Beaver); and in the quantitatively cast hyperbole in the revenge tradition, itself offering a model of exponential increase rather than an eye-for-eye equivalence of promised violence in relationship to an original crime (Dunne). So too, we have seen how rhetorical and logical modes can be understood to inform the composition of arithmetical knowledge, from the idea that the rhetorical category of dispositio (or arrangement) may be understood as an ordering principle of numbers in arithmetic to the attention that Robert Record pays to justifying numbers as integral to the art of speech itself (Wilde). And finally, we have seen how numbers could operate to embed messages in the form of codes that linked number-work with the very rhetoric of the ‘secret’ once linked with the occult (Ellison).[9] Throughout the essays, then, we see how deeply entwined the arts of rhetoric, grammar and logic were with worlds of numerical cognition in ways that nicely complicate, if often implicitly, large scale generalizations about numbers as vehicles of changing epistemes, mentalities, or epochs across time and space. At the same time, the fascination with the hyperbolic dimensions of number in several essays in this volume might be considered in light of the peculiar affinity between ‘number’ and overstatement, or between numbers and abstractions that can seem to unite otherwise incommensurable things, ideas, practices, and discourses. As John Dee (citing Giovanni Pico della Mirandola) put it in 1570, ‘By Numbers, a way is had, to the searchyng out, and vnderstandyng of euery thyng, hable to be knowen’ (sig j r-v).

[12] The slippery symbolic economy of ‘number’ and ‘numbers’ in the making of generalizations across distinct fields of thought, practice and locution has a powerful socio-economic correlative today. In Ted Porter’s formulation, ‘in intellectual exchange, as in properly economic transactions, numbers are the medium through which dissimilar desires, needs, and expectations are somehow made commensurable’ (Porter 1995: 86). The potential of ‘number’ to eliminate variability and complexity in language as well as in other conditions of material and mental life is one way to consider relationships between numbers and writing, not simply in the historical terms of the drive to create a universal language in the wake of the development and power of vernacular languages in the later seventeenth century but in terms of our own practices of thought, association, word choice and generalization as scholars interested in numbers and writing in both past and present. For what do we make of the powerful attention granted to the function, history and power of numbers represented by the largely early career scholars in this volume, particularly given the palpable presence of numbers at work across the humanities, involving the economics of scarcity, scale, and shifting cultural values? The answers to such a loaded question of course depend upon one’s approach to those numbers in writing. For me, the rise of the rhetoric of (as well as the various transformations constellated under) the ‘digital humanities’ may well be seen as a kind of unspoken dimension informing the work in this volume. Indeed, a close reader might note a trend across the essays that in fact departs from what Franco Moretti has termed ‘distance reading’ enabled by the massive digitization of texts that can now be sorted and assembled in ways that exceed the human capacity for textual comprehension. In contrast to the scale of textual meta-analysis enabled by the digital humanities, the essays in this volume arrive at generalizations through the careful examination of the numerical world of a single author or printer, within a single text, or across a delimited number of plays within a specific genre — all of which depend upon acute powers of close reading. This volume, that is, welcomes readers into a capacious understanding of ‘numbers’ but also into various forms of ‘large scale’ inquiry enabled by microscopic analysis in which details of history, texts and cultures come to matter as the texture of context becomes enlarged, more granulated. It is worth noting, in other words, the extent to which the essays within in effect counter a new economy of scale offered by digital manipulations that enable the kinds of ‘distance reading’ through graphs, maps and trees, aligning information in new ways to arrive at conclusions otherwise difficult to detect.

[13] Before making a further observation about the contribution constituted by this volume, here it is worth pointing out the problematic language of value so often aligned with vocabularies of measurement integral to scholarship: ‘big data’ can render other bases of analysis ‘small’, subjective or random. The ‘micro-history’ that once countered ‘macro-historical’, large-scale narratives can easily be rhetorically undermined as offering a form of knowledge that is limited in scale and thus in impact, as we have recently seen in the controversial The History Manifesto (Guldi and Armitage, 2014). Even the ‘close-reading’ that remains a staple of literary pedagogy and a continuing and essential ingredient of powerful writing and scholarship across the humanities can easily seem to imply, particularly in contradistinction to ‘distance-reading’, a lack of perspective or objectivity enabled by critical distance. Without buying into a logic in which size matters in the scope of analysis, argument, subject matter explored, it is worth remembering that ‘micro’ analysis and ‘close reading’ both involve processes of enlargement, magnification, a careful process of finding otherwise unobserved or underexplored networks of meaning within seemingly ‘small’ units of representation, be it in the form of image, text, sound or any other media form. Whether we invoke metaphors of microscopic, macroscopic or telescopic analysis, of close or of distance reading, we need to be fully aware of assumptions about the value of forms of thought and inquiry as delimited by models of measure, scope, scale, impact, or other forms of quantitative assessment.

[14] The word ‘digital’ has of course carried a great deal of rhetorical and symbolic capital in recent years, particularly when paired with ‘humanities’, for the ‘addition of the high-powered adjective to the long-suffering noun’ can suggest to many, as Adam Kirsh has put it, ‘nothing less than an epoch in human history’ (2014). Generalizations about ‘digital’ technology no less than numbers themselves as constituent elements of humanistic practices, institutions and systems of organization are often hyperbolic, an overstatement of a case that we are just beginning to understand. What is so refreshing about this volume is that it represents a new generation of scholars working within historical and literary contexts to come to grips, in various ways, not with a ‘digital condition’ of early modernity or of the present moment, but with varied and often surprising conditions of digits, by which I index both senses of the term ‘digits’, alluding to numbers and fingers, symbols of quantity that might also lead us back to our own writing, reading, and working hands. Putting digits in the hands of new generations of students and scholars as objects and subjects of humanistic inquiry seems to me central to the necessary process of arriving at new generalizations and forms of understanding that confront — rather than enact — fears, fantasies, or displaced anxieties about agency encoded in a turn to numbers, to digits, as instruments of thought, perception, and social organization. If this volume represents a new understanding of the ‘digital humanities’, c.1600, this is but the beginning of a movement through which we may reckon with the place and power of numbers as they come to matter in the aftermath, as it were, of a powerful cultural awareness of numbers as central to our understanding of just what counts and what does not.

NOTES

[1] I would like to thank the editors of this volume, and also Heidi Brayman Hackel, Dympna Callaghan and Heather James for helpful comments on this afterword.[back to text]

[2] See especially Glimp and Warren(2004), xv-xxix.[back to text]

[3] The vivid image of numerical excrescence that conjures a deforming social and epistemological body with no end in sight indexes, if in small, how Badiou at once reveals and relies upon the power of numbers to infiltrate whole systems of thought. Although Badiou postulates a pre-modern ‘ontology of number’ as one way to escape or counter the tyranny of numbers as vehicles of counting, he seems to at times to be caught within the very prison-house of number that he at once describes and constitutes.[back to text]

[4] For an early seventeenth-century dialogue concerning the common confusion among students ‘almost ready to go to university’ about basic numbers within books (in both letters and numbers, Roman Numerals and Hindu-Arabic ‘figures’) see Brinsley (1613) 25-26.[back to text]

[5]  On the relationship between the arts of the trivium and arts of the quadrivium in early modern France and Italy, see especially Reiss (1997); on rhetorical categories of invention and disposition in relationship to algebra, see Cifoletti (2004), 132-153; on Humanist and aristocratic readers of early vernacular mathematical texts in England, see James (2011), 1-16, and for a seminal approach to the power of zero across a range of early modern forms of representation, see Rotman (1987). For a volume that deals with the ‘imbricated histories of numbers and letters’ in medieval and early modern culture, see Glimp and Warren (2004), xvi. Glimp and Warren, in turn, call attention to earlier scholarship on this ‘mutual imbrication’ that will be of particular interest to readers of this volume, by Clanchy (1979), in which we find ‘technologies of writing’ deployed by institutional administrators and poets alike and by Jed (1979), who examines ‘graphic habits’ shared by Florentine humanist and mercantile cultures.[back to text]

[6] For a range of approaches to inscription, materiality and mathematic and scientific texts, see Lenoir (1998) and Chemla (2004). As Lenoir puts it at the outset of ‘Inscription Practices and the Materiality of Communication’ in Inscribing Science, Metaphors of inscription and writing figure prominently in all levels of discourse in and about science. The description of nature as a book written in the language of mathematics has been a common trope since at least the time of Galileo, a metaphor supplemented in our own day by the characterization of DNA sequences as a code for the book of life, decipherable in terms of protein semantic units. An important recent direction in the fields of science and literature studies is to consider such descriptions as more than metaphoric, as revelatory of the process of the process of signification in science more generally’ (1).[back to text]

[7] On numbers and the emergence of the concept of the ‘fact’ from early modern English accounting practices and discourses, see Poovey (1998) and also Porter (1995).[back to text]

[8]On the promotion of vernacular mathematics through print technology and appeals to various models of practice, see Johnson (1991).[back to text]

[9] In contrast to mathematical textbooks of the seventeenth century that so often disavowed affiliations with the occult through the stress on ‘easy’, plain and practical instruction (Neal, 1999), books on cyphering, as Ellison observes, capitalized on the history of the secret within the tradition of the occult.[back to text]

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_____. 2008. Number and Numbers, trans. Robin Mackay (Cambridge: Polity Press)

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Dee, John. 1570. ‘Mathematicall Praeface’ to Euclid Elements of Geometrie…. (London)

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Johnson, Stephen. 1991. ‘Mathematical Practitioners and Instruments in Elizabethan England’, Annals of Science, 48, 331-344

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