How to Read an Early Modern Map: Between the Particular and the General, the Material and the Abstract, Words and Mathematics
London Metropolitan University
Edwards, Jess. "How to Read an Early Modern Map: Between the Particular and the General, the Material and the Abstract, Words and Mathematics." Early Modern Literary Studies 9.1 (May, 2003): 6.1-58 <URL: http://purl.oclc.org/emls/09-1/edwamaps.html>.
...positivist historians have plenty to do when confronted with a previously unknown map. Besides establishing its date and authorship, they can analyze material form, method of drawing or reproduction, use of inks or paints, projection, linework, extent of generalization, choice of symbols, stylistic affinities, sources of information, method of survey, influence on other maps, archival history, distribution, and use. What can the non positivist scholar do except say, "Just as I thought: more glorification of state power" (Andrews 31-32)
Let me begin with a cartographic paradox. In one respect maps seem the most superficial and self-evident of texts. We expect most adults to be able to read a map, whether it was produced in the seventeenth century or yesterday. Cartography, we might presume, is a pretty universal mode of communication, and part of the textual common ground of modernity. Yet the forms and functions of the modern map are in reality multi-faceted. Maps may signify territorial "reality" or some utopian nowhere. They may refer to physical, or to cultural objects. They may be intended for the most pragmatic uses, for decoration, or simply to signify their own map-ness. And the list could be considerably extended. As a paradoxically protean cultural form, the map has always been the meeting point for a wide range of knowledges and cultural practices. No wonder, then, that it has become an important focus for the modern academy's drive towards interdisciplinary research, and for varying practices of interpretation.
Where conferences and journals dealing with the history of cartography might once have drawn an audience of specialist historians of art and science agreeing broadly in their respective methodologies, and dividing the territory of the map between them, recent debates have placed an assortment of disciplinary frames around cartography. These range from Peircian semiology, which explains generalised sets of cartographic forms in terms of a universal communicative function (the translation of spatial relationships) to an empiricist, archival cultural history, which explains an array of cartographic forms and functions in terms of the specific material circumstances of their production and consumption. Between these poles, scholars vary in their willingness to generalise about the map, and to treat it as a text which anyone beyond its original producers and immediate consumers might read. We might, in fact, say that recent scholarship on cartography mirrors cartography itself in its variation between local, or topographic focus, and aspirations to universal, cosmographic range.
The first half of this article will describe some of the forms the debate about the nature and interpretation of early modern maps has taken in recent years. I'm primarily concerned with the implications of a new, critical history of cartography for literary studies and so I won't be attempting to represent the full range of this broad interdisciplinary field. For the bigger picture from the perspective of specialist cartographic history itself readers are directed to the last decade or so of the journals Cartographica and Imago Mundi, where positions such as those caricatured above by J. H. Andrews have been defined and defended with a new critical self-awareness. Even within my selective, literary emphasis I'll be sampling recent work to indicate trends, rather than attempting a comprehensive survey. Controversies around the borders of literary study have inevitably centred on the textuality of cartography: the extent to which maps themselves can and should be read like literary texts, and the relationship maps and texts have had in generating meaning. The second half of this article constitutes my own contribution to this debate.
- Some of the most influential interdisciplinary studies of cartography to date have analysed cartographic textuality in terms of wider rhetorics of power, government, property and empire, looking for analogies with literary discourse on this broad common ground. I will be arguing for the involvement of specifically early modern cartography with a rhetoric of representation itself, on which any further rhetoric of power, government, etc. must depend. I think the meaning and value of early modern cartography is grounded and sustained in distinctly "literary" discourse signifying its capacity to "carry over" meaning and effectivity between the generalities of abstract science and the specificities of worldly experience. Without the persuasion of this "literary" discourse, early modern sceptics were all too ready to suggest that the world was the world, and the map just a map. Eventually this work of persuasion is more or less done. Once the map is naturalised we rarely bother to ask whether what we are looking at is "representation" or "the world," and cartographers rarely bother to tell us. J.H. Andrews may be right, at least for the eighteenth and nineteenth centuries, when he writes: "before about 1930, cartographers made few general pronouncements of any kind about their subject" (5). But for a substantial part of the sixteenth and seventeenth centuries, cartography was a noisily rhetorical art, signifying not just "outwards" to the spatial world, but "sideways" to discourses of legitimate and truthful representation. And in that the metaphors and allegories through which these discourses work all signify the capacity of cartography to mediate, early modern cartography does not just signify the two-sided-ness of metaphor, it constitutes itself as equivocal: ambivalent between abstract frame and particular content. Ultimately the uncertainty of a new, critical history of cartography poised between materialism and abstraction can seem to echo the rhetorical ambivalence of the early modern map itself.
I Traditional Cartographic History
- What is traditional cartographic history? For one thing it is teleological. It tends to imply that early modern changes in cartography move consistently in the direction of a map-making practice and a text which is properly scientific and properly modern. Conventional cartographic history celebrates the sixteenth-century "Renaissance" of mathematical, and thereby recognisably modern methods of cartographic representation. Previous geographies, as exemplified in medieval T-O maps and mappae mundi, were (so the story goes) pictorial, partial and subjective. The story of modern geography as told in such history is one of the displacement of rhetoric by science, of individual skill by duplicable technology, of hierarchies of place by abstract space, and in general of the particular by the universal. E.G.R. Taylor prefaces her 1934 Late Tudor and Early Stuart Geography with the suggestion that the 67 years which her indispensable survey reviews
bring the reader to the threshold of that period in which for the first time he feels fully at home: the period in which truth is sought by experiment and observation instead of as formerly by reference to authority and revelation. (v)
Taylor's "threshold" metaphor, evocative of the map's own ideology and semiotics of boundary-making, suggests that whilst she is documenting a reasonably substantial, 67-year journey, arrival at the "home" of modern cartography is as concrete and absolute as crossing a national frontier. Mapping does not really become any more modern once this threshold has been crossed, any more than France becomes any more French between Calais and Paris. Similarly, in The Mapping of America, Seymour Schwartz and Ralph Ehrenberg suggest that the series of maps their book collects "reveals a metamorphosis from artistry to science" (9). This survey, like Taylor's, may cover substantial historical ground, but the conceptual metamorphosis from the discrete practices of Medieval artistry to the universal technologies of modern science is made to seem as immediate and at the same time as irreversibly absolute as the transformation from caterpillar to butterfly.
It is not only the modern map which Schwartz and Ehrenberg depict emerging blinking into the bright light of historical day. As well as self-reflexively chronicling their own "metamorphosis," the American maps they collect provide "a graphic picture of the nation and an illustrated chronicle of its evolution" (9). This is a double teleology, doubly paradoxical in its fusion of temporal process and punctual transformation. On the one hand the successive developments of the map mirror the successive stages of an American "evolution." On the other, each map pictures a "nation" with a concrete, ready-made identity common to all. The butterfly of America and the butterfly of modern cartography emerge together and in symbiosis, each identity as absolute and irreversible as the other. This simultaneous narrative of national/cartographic home-coming, where home is the here-and-now of modernity, permeates Schwartz and Ehrenberg's account of American cartography, just as it does many other older histories of the map. Like the antiquarian promoters of early modern exploration these historians relate seductive fables of unknown maps "discovered" in archives, in private collections, and even, in one instance, in a butcher's shop. And beyond the early phase of discovery, they figure the mapping of America and its physical colonisation as gradual, but irreversible, symbiotic struggles.
II Maps, Knowledge and Power
In the last two decades this narrative of homecoming has been significantly disrupted. Rather than a cartography whose accuracy cleanly mirrors the enlightened clarity of the modern nation's frontiers, devoid of the thickening particularities of "artistry" and politics, we are more often presented with a cartography designed and deployed as an instrument of political power. A key figure in a new history of cartography has been the late J.B. Harley. In a 1988 essay titled "Maps, Knowledge and Power" Harley regrets that cartographic history has been dominated to date by a technicist teleology of evolving accuracy. What this history elides, suggests Harley, is the partiality of even modern maps as simply one kind of "way of conceiving, articulating, and structuring the human world" (278). In fact, Harley argues, the "Euclidean syntax" privileged in post fifteenth-century cartography did not just reflect the world, but "structured European territorial control" (282). It was, in other words, a tool of power. The particular rhetoric of "authority" explicit in the Medieval map had not gone away, but was now simply hidden beneath the increasingly non-verbal, non-pictorial, generalised cartographic surface. The mathematical modern map was and is, for all its lack of apparent religious, political, imperial argument, nonetheless an integral "part of the intellectual apparatus of power" (282). Moreover, the relative invisibility of its rhetoric, proportionate in conventional terms to the enhancement of its scientific objectivity, has rendered the modern map, in Harley's terms, all the more serviceable a political instrument. General science has masked particular political interests. The objective, mathematical map de-socializes the territory it represents, thereby silencing resistance, divorces power from responsibility, and conducts warfare by remote control (282-284).
Harley's essay lays out the ground for a critical history of cartography which rather than simply celebrating accuracy, or the "Renaissance" of what was in fact another Eurocentric perspective masquerading as universal truth, instead explores the role of maps in the social making of knowledge. Harley comments, towards the end of his essay, that his ideas "remain to be explored in specific historical contexts" (303). A great deal of work is now being done to answer this call for specific, contextualised explorations of the cartographic power/knowledge nexus. Much of this work has explored the role of developing cartographic practices in early modern English/British imperial ventures in Ireland and America.
There is a general critical consensus in work of this nature that, as Harley suggests, it was the universalism of a newly mathematised geography/cartography that rendered it an attractive instrument of colonial ideology and domination, allowing colonial representation to transcend and thereby contain both details of prior occupation and details of struggles for authority and control. In his 1988 article "Inventing America" William Boelhower depicts the successive phases of an increasing cartographic mathematisation and abstraction not as an evolution towards enlightened accuracy, but as responses to the needs of successive phases in the chronology of imperialism (480). As the final phase in this honing of imperialist tools, Boelhower characterises the American "scale map" as a "panopticon": that epitome of the totalising spatial logic of Michel Foucault's "disciplinary society" (496).  The analogy draws upon Foucault's account of a persistent "movement" between modern "discipline" in its governmental and in its scientific senses: working to "fix" its social/natural subject matter through the application of universalising frameworks which establish "calculated distributions," arresting movement and dissipating particularity ("Panopticism" 208-209). Boelhower's cartographic history plays out this struggle to establish the disciplinary "frame," dramatizing a semiotic conflict on the surface of the map wherein "on the one hand we have the image/the Indian/local dwelling and on the other the line/the European/global circulation" (490). The aesthetic demise of a pictorial, subjective and variously particularistic cartography is thereby simultaneously the demise of the native. Such a narrative is the direct obverse of Schwartz and Ehrenberg's celebratory national/cartographic dawn-chasing. Boelhower sees "the line's regime cast[ing] its geometrical scheme over more and more of the new continent" like an ominous shadow, "fixing," and thereby obliterating native movement and locality in its wake (488). Accounts of Irish colonial cartography tell much the same story of universalising mathematical imperialism. Writing in 1993, Julia Lupton urges us to see the early modern Irish map "not only as a tool for military strategy, but more fundamentally as a structuring fantasy, a fantasy of structure" (101). 
III The Seductions of Structure
There is, however, a note of warning in Lupton's words here, sounded in her insistent reference to "fantasy," and this note of warning has in recent years become an increasingly audible counterpoint to theses exposing the cartographic, and more generally spatial power/knowledge nexus. In the introduction to Enclosure Acts, their 1994 collection of essays on early modern "sexuality, property and culture," Richard Burt and Michael Archer express unease about the predominance of new historicist approaches to what they call "the most familiar type of Enclosure": the spatial and economic appropriation of land resources (91). The new historicist approach, they note, promotes "a spatial model of subversion and containment" whereby "power," rather than seeking to repress or conceal that which resists it, works to "produce" resistance against which to define itself (2). This leaves the historian obliged to regard any resistance they may discover as always already accounted for and contained. Burt and Archer's unease, shared by a host of recent critics of new historicism, arises from the way in which the structuralist spatial model embedded within this critique seems in fact to further the work of the representational practices it describes, perfecting their forms and re-incorporating that which escapes them as part of the "system." Responsibility for this theoretical totalising can be traced directly to Foucault, a key thinker for new historicism: firstly for the closure which he attributes to the modern "disciplinary society" and its "indefinitely generalizable mechanism of panopticism" ("Panopticism" 206), and secondly for his aesthetic reinforcement of such social closure through the abstract structurality by which he models it. As he himself was once brought by a group of geographers to acknowledge, Foucault often used a descriptive language full of the metaphors of a modern, mathematised geography: metaphors of "implantation, delimitation and demarcation the organisation of domains" ("Questions on Geography" 72).
Although their primary concern is not with cartography, Burt and Archer's concerns about an over-attachment to structure clearly apply not just to the recent history of the English enclosure movement, but also to the new critical history of cartography, that other, closely related discourse and practice of spatial appropriation. Postcolonial critical analysis of colonial maps typically discovers in them colonial settlements rising out of a landscape purged by a generalising cartography of particular history and social content. But there is always a danger that analysis itself might repeat and reinforce this process of purgation. If we are to heed this danger, we must be wary of overstating the successes, or understating the failures of early modern cartography in making visible and containing that which resists it. We must be wary, in fact, of taking fantasy for reality, the aesthetic for the real, and of eliding the gap between what is, after all, only an analogy between aesthetic containment and real territorial control. We must even ask to what extent this analogy is an early modern analogy, and to what extent it is ours.
So it could be suggested that we critics and historians, in the last twenty years, have become a little too keen on maps. We might be accused of being as drunk with maps as a much-quoted cartographic rhapsody from the magus-mathematician John Dee suggests many of his late sixteenth-century contemporaries were.  In each case what intoxicates seems at least in part to be the latitude that the map appears to allow for clear thought and vision, uncluttered by inconvenient obscurities and inconsistencies.
William Boelhower's analysis of cartographic power/knowledge is more than aware of the dangers of such structural intoxication. Boelhower foregrounds those elements both in the cartographic subject and in the representational syntax of cartography that resist the universalising tendency of its mathematical frame. Similarly, Julia Lupton insists upon the failure of Irish colonial surveying, and resistance to the penetration of English cartography by "obdurate enclaves of Irish alterity" (93). There is, however, a problem with these re-discoveries of spatial "resistance." In The Production of Space Henri Lefebvre complains not just at the closure of Foucault's modelling of power/knowledge, but at its unexplained slippage between spatial representation and spatial practice:
[Foucault] never explains what space it is that he is referring to, nor how it bridges the gap between the theoretical (epistemological) realm and the practical one, between mental and social, between the space of the philosophers and the space of people who deal with material things. (4)
It might similarly be objected that not just their descriptions of cartographic power, but also the space Boelhower and Lupton allow for resistance often slips without warning from the practical into the aesthetic. Having given agency to the geometric "line" itself, Boelhower envisages evasion of its universalising influence via cartographic toponyms whose inherent particularity opens "a trap door in the written surface of the map" (494). Lupton writes of rebel resistance "cracking, piercing and mutating" the colonial geometric plane (93).
Rather than looking for resistance to cartographic representation in and through the map, a more flexible reading of cartography may well need to look elsewhere. Perhaps it is an awareness of the intoxication and exhaustion of the structuralist power/knowledge paradigm of map-reading that has led much of the most recent cartographic criticism to turn away from the map itself. It seems to be possible to identify two manoeuvres within what could be called this general "aversion." One tends to stay close to the individual map itself, and indeed its individual authors and users, but looks away from the map-as-text to the material, social, political relations which determined its production and use. The other uses the individual map principally as illustration and prompt for an exploration of the cultural codes in which cartography in general participates. The first approach tends to resist the textuality of the map, over-emphasised in the post-structuralist and New Historicist privileging of the language-model, and to treat it instead as a material element amongst others in material culture. The second approach remains committed to map-reading, but within a textual context which exceeds the bounds defined by the mathematical "science" of cartography, and reinforced by the post-structuralist power/knowledge paradigm.
IV Process not Product
Several essays in Denis Cosgrove's recent collection Mappings suggest that while we may have moved beyond the traditional evaluation of cartography in terms of accuracy and function, critical preoccupation with the aesthetics of the map, however much it acknowledges that this is an aesthetics of power, is merely another de-historicizing universalism. Cosgrove's concerns are anticipated in a review by Roger Starling of the conference "Paper Landscapes," held in 1997 at Queen Mary and Westfield College, University of London. Starling worries:
Could it be, after all, that maps lend themselves almost too easily to our current methods and approaches? In other words, are they so obviously implicated in relations of power, their social and cultural inscriptions too easy to read, to provide anything more than a performative confirmation of our critical paradigms and resources?" (106-7)
Cosgrove's introduction to Mappings expresses impatience with the buzzing of post-structuralist bees around his subject, keen to recognise blatant archetypes of imperial domination and difference in the map. What Cosgrove and, with reasonable consistency, the other contributors to his volume would have us recognise is that there are more important stories to be told about maps than those which meditate only on the finished product. These historians echo a warning inherent to J.B. Harley's own mission statement for a new critical history of cartography: that whilst it should regard maps as textual and rhetorical, it should not make the conventional mistake of treating them as self-evident and easy to read. Maps, writes Harley with David Woodward in the introduction to their six-volume History of Cartography,
require painstaking interpretation in relation to their original purpose, their modes of production, and the context of their use ... it would be a mistake to think they constitute an easily readable language. (3)
In Denis Cosgrove's case, an ambivalence about map-reading could be regarded as a symptom of the liminal location of his work. Where Cosgrove has spoken primarily to geographers, in his many contributions to the last two decades of cultural geographic debate, it has often been to argue for the textuality of landscape and the map.  Where he has spoken primarily to literary scholars, late entrants to this debate, it has often been to warn them against a rush to textual interpretation. Crystal Bartolovich has written of a reconstitution of cultural geography in recent years which, whilst "killing the fathers" of an older, un-critical cultural geography with theoretical weapons borrowed from literary and cultural studies, still codes the textual focus of these disciplines as "excess," "so that cultural geography, on the other hand, can become the science of the sensible middle" (9).  Cosgrove and other scholars contributing to literary debate from the disciplinary vantage point of geography seen keen to occupy this middle ground.
What cultural historians should be concerned with, argues Cosgrove, is less the map itself as text than "processes of mapping" (Mappings 1). When we shift our focus from product to process, we soon see the "aesthetics of closure and finality dissolve" (2). Process, in Cosgrove's eyes, means proper history, rather than post-structuralist universalism, and there are two ways of interrogating process which he regards as of pressing importance in historicizing the map. One examines "the complex accretion of cultural engagements with the world that surround and underpin the authoring of a map," and the other "the insertion of the map, once produced, into various circuits of use, exchange and meaning" (9). The first treats the map "as a determined cultural outcome," the second "as an element of material culture" (9). Any map can in its turn be "mapped," suggests Cosgrove, if we take bearings on it from these two critical perspectives. Another way of conceiving such a mapping, he suggests, is to consider the map as a hinge around which these two kinds of meaning system pivot.
The work of cartographic historian Jerry Brotton is a good example of this particularising materialist shift from aesthetic product to historical process. The significances of Brotton's maps are, most importantly, individual: they are not the significance of some master-textual, epistemic "map." Moreover, Brotton's maps do not signify, in the transparent textual present tense embraced by most literary analysis, they signified, or perhaps rather functioned, or were used, in a sense which only well-informed historicism can help us to retrieve. Amongst Denis Cosgrove's criteria for the proper mapping of the early modern map, Brotton gives "exchange" particular emphasis. The "engagements with the world" that precede and follow the authoring of his maps are predominantly commercial and diplomatic.  The map, for Brotton, is both a "thing," a commodity which itself has value and is traded, and a "cipher" through whose mediation values and exchanges are represented and thereby facilitated (22). And where the geographic category is allowed due latitude, the elaborate preciosity of the globes and even tapestries which Brotton principally examines helps us to see the map as "at an even deeper level material" (22), or at an even deeper level, in the terms of a metaphor which Brotton favours, dirty rather than clean. 
V The Culture of Mapping
There is, however, a limit to this "deep" materiality. The authority which the map and the geographer draw upon to justify their engagement in the big deals of European history is in large part intellectual and even, as Brotton here and there acknowledges, beyond any issue of straightforward technological "accuracy," esoteric. Despite concessions to the map's status as "cipher," and its circulation in "circuits" of "meaning" as well as material exchange, what Brotton and Cosgrove's instructively materialist contentions about cartographic meaning can appear sometimes not to take into account, and sometimes even actively to resist, is precisely those circuits of meaning which can be identified with a respectable degree of historical specificity and yet which exceed the boundaries of, or do not "hinge" exclusively upon the individual map.
Where Bernhard Klein remarks, in his 2001 Maps and the Writing of Space, that his discussion of cartography "is ultimately less motivated by an interest in the history of maps than in the culture of mapping" he is clearly making a commitment to a more generalising mode of history than Brotton's (8). In Klein's work, as in the work of Richard Helgerson, John Gillies, Garrett Sullivan and Rhonda Lemke Sanford, all contributing to the new history of cartography from the vantage point of literary studies, subscription to this notion of a general "culture of mapping" is part of a broader willingness to consider history in terms of a general "poetics of culture." Such work is likely to go looking for, and is likely to find what Helgerson calls a "deep, if unexpected likeness" between categories of texts held separate by disciplinary boundaries, and especially between literature and geography (Forms of Nationhood 14).
The nature of this likeness does vary from study to study. Helgerson's seminal 1992 Forms of Nationhood found common ground between late sixteenth-century English literary and cartographic works in their textualisation of various forms of imagined community. The common ground with which John Gillies is concerned, in his 1994 Shakespeare and the Geography of Difference, is shared by Renaissance geography and Renaissance theatre, and is somewhat broader, ultimately expressing not just contemporary political consciousness, but subconscious human impulses to stratify and thereby textualise space, marking the scene, the obscene, and so on. This poetics of spatial representation subscribes to the phenomenological account of spatial "images," whether verbal or graphic, as expressions of primitive bodily desires and strategies. 
In their own recent publications on literature and cartography Sullivan, Klein and Sanford all pay considerable heed, like Helgerson before them, to the historical transformations within which early modern cartography and literature are co-implicated. In some cases they claim to pay more attention than their predecessors to this aspect of the map.  But it is an essentially literary, metaphorical latitude in their understanding of spatial representation, often informed by phenomenology, which licenses the connections these critics make between map and literary text. The "circuits of meaning" they trace, as Cosgrove's own, rather post-structuralist metaphor implies, make hidden and far-reaching connections which exceed the conscious human relations and material exchanges of commerce and politics and the official architecture of culture. In Literature, Mapping and the Politics of Space in Early Modern Britain, a recent collection of essays edited by Klein and Andrew Gordon, the contributors re-place strictly cartographic codes of meaning within a wider circuitry of interlacing cultural codes: the codes, for instance, of anatomy, poetic genre, the theatre, national symbolism, military "science" and royal/civic pageantry. 
Ultimately, the worst that could be said of these literary cartographies of "the culture of mapping" is the worst that materialist critics have said of any "poetics" of culture: that whilst it may avoid being mesmerised by the pessimistic totalisations of the Foucauldian power/knowledge model, it nonetheless risks generalising particular historical processes, where discrete interventions and transformations were possible, into static constellations of cultural codes.  In the terms of Cosgrove's prescription, it risks eliding two processes of "cultural engagement with the world" into one static circuit board of meaning, so that any individual map can only mean what maps already mean.
VI Pure Fantasy: Mathematical Poetics
The two approaches I have described offer two "takes" on the textuality of cartography: one broadly hostile, regarding the map-as-text as a map cleansed of history; the other more prepared to consider cartography as part of the architecture of cultural communication. At the same time, these two approaches offer two responses to cartographic mathematics: the structural "fantasy" legible in the modern map. One treats it as a false idealism: an exaggeration of the universal for which it compensates by exaggerating the particular "transactions" which surround the authoring and primary uses of each map. The other treats it as an artificial disciplinary constraint: merely one, de-privileged code amongst a diverse "circuitry" of cultural codes.
Where these approaches are united is in their strategic transgression of the mathematical cartographic frame: their refusal to meet the map, as a traditional history of cartographic science might have done, on its own, disciplinary terms. If maps have proved too legible, and too self-evident to a post-structuralist cartographic criticism addicted both to structure and to language, it seems to be mathematics that they hold to blame. But whilst this critical sidelining of mathematics may allow us to see how much more open and contingent cartographic meaning may be than an attention purely to mathematical structurality might suggest, it leaves the actual work of mathematics in cartography unexplored. I think that it's precisely in mathematics that the key to the peculiar currency of early modern cartography lies: a currency that flickers between Brotton's deep and dirty materiality and the abstraction theorised in the Foucauldian panopticon, inviting both interpretations of cartographic form and function.
Understanding this ambivalence is impossible without a commitment to understanding cartographic, and ultimately mathematical discourse. I want to argue for a radically discursive understanding of mathematics itself. To suggest that there is no mathematics except the discourse on and practice of mathematics (and discourse, after all, is practice) is to provoke a certain degree of materialist irritation at the "excesses" of "literary" theory. Yet how can any mathematics, and any mathematically constituted map have value or meaning beyond and without discourse? The discourse of cartographic geometry, I want to suggest, is a way of wrapping the general into the particular, the abstract map into the world. It is the basis of cartographic textuality and the very reason why both the early modern users of the map and its modern critics were and still are able to take the aesthetic for the real.
The first premise of this mathematical double vision is Plato. Simply expressed, Plato believed the temporal world of sensibly perceived particular things to be governed by an a-temporal world of intellectually conceived universal ideas.  Plato's "real" world was not the natural one, which he considered ephemeral and illusionary, but the supernatural, which was permanent and true. Plato considered the objects of mathematics (triangles, circles and so on) to belong in the realm of the ideal "real" as much as any other pure ideas, with the special qualification that whereas part of the perfection of other immaterial ideas lay in their unitariness, instances of mathematical objects such as the triangle could be many, even infinite. In their qualified perfection, Plato allowed that contemplation of mathematical objects might serve as a preparatory study, or "propaedeutic" for pure philosophy.
Such a propaedeutic mathematics as Plato advocated is far from being the practical mathematics of the workshop, or even the procedural mathematics of the classroom and study, both of which Plato rejected utterly as contaminated with the world.  Indeed Plato refused the philosophically inclined mathematician not just the physical props of a worldly mathematics (drawings of circles and triangles) but even a dynamic language that spoke metaphorically and imagined the construction of such props.  Such a refusal is consistent with Platonic epistemology in general, which concedes the visual and verbal figure no role in truthful thinking. But Plato's own metaphysical discourse, and subsequent philosophical discourse still heavily invested in his dualist ontology, inevitably uses props from the physical world to help the would-be philosopher think his way from the particular to the universal, the most famous of which is his metaphor of the "ladder." And many of Plato's classical and medieval disciples strained to make a more concrete reality out of his metaphors. Mathematical objects, they suggested, the things we "mean" when we talk about or draw triangles, circles etc., might be considered not just as metaphors for, or images of the material inhabited by the ideal, but also as a third realm of being, and a stepping stone between the temporal and the absolute.  This position was taken to an extreme by those medieval and renaissance magi who, embracing the mystical Platonism of the Hermetic tradition, believed they could find the "seeds" of the divine not just metaphorically but actually in nature.
The importance of Neoplatonic ideas in renaissance visual representation of and intervention in the physical world has been well documented. Particularly useful in this regard is Denis Cosgrove's The Palladian Landscape. Cosgrove is interested in the permeation of a strain of geometric Platonic idealism, which he calls a "Euclidean ecstasy," through sixteenth-century discourses ranging from the pure metaphysical to the determinedly practical, and through discourses concerned with newly dignified and "intellectual" arts such as perspectival painting in between. But whilst he makes a convincing case for the investment of such practical arts as surveying with an idealist impetus, Cosgrove is not particularly interested in the mechanisms of such investment. For him, this is a merely textual matter. In his own words, sixteenth-century writing demonstrates a "drawing together" of the speculative and the practical (211); an "alternation" between the two aspects of such a science as mathematics (209). Writers on practical mathematics might make a "disingenuous" claim to pure pragmatic surface (213), but even their practically oriented readers were "not unaware of the philosophical depths" beneath (209). What I want to examine in the following part of this essay is the textual substance, even the "literariness" of this clearly ambivalent attitude to the liberal and the practical: an ambivalence which Cosgrove's spatial metaphors leave merely implicit and indeed reproduce.
We are of course very used to recognising an ambivalent attitude towards the world in renaissance "literature" as conventionally defined, and indeed we regard an ambivalent poise as an identifying feature of renaissance poetics. The capacity of literature for artful indeterminacy is celebrated by Sidney in A Defence of Poetry. Sidney, whose investments in Platonic philosophy were explicit, works to ground the value of poetry in its expression of pure ideas rather than mundane realities. He associates such an ideal foundation with the architect's design, arguing that "any understanding knoweth the skill of each artificer standeth in that idea or fore-conceit of the work, and not in the work itself" (Miscellaneous Prose 79). But whilst Sidney may ground the truth of poetry in its ideality, he maps its territory as a profession between the truthful generalities of the philosopher and the useful particularities of the historian (84). In a variation of the Neoplatonic ladder, Sidney describes poetry as "first nurse, whose milk by little and little enabled them [its readers] to feed afterwards of tougher knowledges" (74). Sidney doesn't tell us how it is possible to pass between worldly and intellectual knowledge. Instead, illustrating the theory with the practice of poetic indeterminacy, he exchanges one metaphor, the Neoplatonic ladder, for another: physical nourishment and growth.
Renaissance writing represents and thereby constitutes the Neoplatonist's ambivalent poise through a variety of literary techniques. Some works project man's dual angelic and beastly nature through highly figurative anatomies.  Others chart the desirable "middle course" of human life through allegories of the choice of Hercules or Daedalus's flight.  Others again match conflicting impulses towards and away from the world in the tight-rope balance of the metaphysical conceit. Famous amongst these of course is Donne, whose Platonic faith in divine law over worldly custom and the senses is so consistently qualified by his worldly, often specifically geographic knowledge. 
Donne's ambivalence between the free Platonic essences of nature and what he calls the "new nature" of worldly use is conspicuous more generally in Renaissance attitudes to geography.  Robert Appelbaum and Richard Helgerson have both written of a persistent vein of rhetoric which runs counter to renaissance interest in and valorisation of the new geography, debunking it as folly and producing extravagant fictional geographies which undercut the claims of science.  An ambivalence about geography is certainly widespread in Renaissance literature, and often expressed through the language of a distinctly Neoplatonic double vision on the world.  I want to suggest, however, that this discursive ambivalence is not just an aspect of the reception of geography, an effect of the passing of geography and maps through literary "circuits of meaning," but is inherent to geography itself. Disingenuous about its true orientation in much the way Donne's metaphors are, geography is itself a poetic art.
I'm not interested in proving or even arguing for an explicit thread of conscious Neoplatonism in early modern mathematics or geography such as we commonly find in renaissance literature. Although such a thread is substantial enough, it is easily dismissed by teleological histories of science and culture seeking the roots of modern empiricism as eccentric and a dead end. Even Denis Cosgrove, after making a forceful argument in The Palladian Landscape for the saturation of sixteenth-century Italian artistic culture with mathematical idealism, sees it giving way, "radically undermined," in the "seventeenth-century scientific revolution" (192). What seems to me of more importance is the way in which Platonic associations persist (more or less explicitly; more or less consciously) in a whole range of early modern texts involved in the reproduction of mathematical and visual culture. And whilst there may seem in retrospect to be a great distance between the mystic "visions" of medieval Neoplatonism and the positivist observations of the empiricist enlightenment, it seems that, as Martin Jay has put it, the "positive associations of geometrical order" residual in the latter still owed no small debt to the former (54). What I would argue is that this debt is carried forward through discourse. Early modern discourses of mathematics and visual/spatial culture inevitably combined both the materialist and Neoplatonist impulses which have been identified in rival histories as characteristic of European culture of the period. Such a combination of logically contrary impulses may not, perhaps, sit comfortably in explicit statements of artistic and scientific theory. It is, however, more likely to subsist in the more popular metaphors, allegories and rhetorics that adhere to and help to determine the meaning of early modern geometry and vision.
In mathematical literature published in England at the end of the sixteenth century and at the beginning of the seventeenth it's possible to identify two polar positions between which approaches range. One pole represents a Hellenic classicism, seeking in an idealist mathematics the means for cultivating magical intellectual powers; the other an empiricist, pragmatic attitude closer to Latin humanism. These extreme stances might be identified with two giants of early modern educational reform: the English magus and propagandist both of geography and British "empire" John Dee, and the Huguenot martyr Pierre de la Ramée, known often to his contemporaries in the European scientific community by his Latinised name, Petrus Ramus. Both of these figures were responsible for publications which sought to broaden the audience of mathematics beyond the universities where it was felt to have fallen into neglect: Dee in his "Mathematicall Preface" to the first English vernacular edition of Euclid's Elements, translated by Sir Henry Billingsley and published in 1570; Ramus in his Geometria (1569), and in his published lectures and addresses on mathematics.  Moreover, the influence of these figures was not channelled only through their own much-reprinted publications. Dee's "Preface" attended other editions of Euclid over almost a century following its original appearance (French 172-177), and Ramus's Geometria, although excluded by other popular texts from universal usage in England, was cited and sampled with great frequency for its doctrines and its organisation by other mathematical publicists (Hooykaas 105).
A crucial point to retain, while I am setting up these figures as antagonists, is that in fact they perceived themselves as part of a unitary enterprise of reform (French 167). Both intended the revival of mathematical education, and both foresaw the benefits to be gained from attention to the relation between intellectual and craftsman, and published to this end. The pair corresponded as "friends," apparently concerning mathematical texts (French 142), and Ramus even sought to intervene with the Crown on Dee's behalf to gain him a university chair in mathematics which both Oxford and Cambridge at that time lacked (Hooykaas 105).
This spirit of co-operation between purveyors of very different philosophies of science demonstrates the social aspect of that textual alternation between practical and speculative that Cosgrove has discussed.  However textually Dee is generally the idealist and where he invokes the objects of mathematical study, they tend to take their place on the supernatural side of a Platonic binary divide. Dee's "mathematicals" are so "absolute," and so "free from all matter," that another name than "Geometry" "must needs be had" for a science which "regardeth neither clod nor turff: neither hill, nor dale" (sig. B2v-B3v, sig. E2r). Textually, Ramus is very much the pragmatist. Where Dee rails against the name "geometry," Ramus famously embraces a definition of the science as "ars bene metiendi" ("the art of measuring well") and vehemently opposes the medieval university tradition of dividing the quadrivial disciplines (geometry, arithmetic, astronomy and music) into the hierarchy of speculative and practical (Scholae Mathematicae 1, Hooykaas 25). Ramus bases his trust both in the rightness of usage and in the possibility of knowing usage rightly on his doctrine of "natural reason," by which he means the inherent capacity of even, and perhaps especially uncultivated human intelligence to follow nature, forming correspondences with the natural order of the universe (Hooykaas 51). Where an original Platonism discovers the origins of mathematics in the ideal, and medieval and renaissance Hermeticism seeks to harness the virtues of these ideal origins within mundane practice, Ramus discovers a "closed circuit" leading from and back to human use (Hooykaas 20-21).  This position, which structurally anticipates the more materialist modern historicisms, aligns with and extends to its logical conclusion the Latin humanist precept that theory is engendered and preceded by practice (Hooykaas 21). For Ramus, as for materialist histories of science, there "is" no pure mathematics.
But although both Dee and Ramus find textual space to be vehement in their commitment to seemingly incompatible philosophies of mathematics, they also leave plenty of room for such commitments to be fudged. Whilst Dee situates the foundations of mathematics in the pure, unsullied ideal, his rhetoric leaves the relationship between ideal and practical mathematics vague. It is full, like all Neoplatonic discourse, of spatial metaphors suggesting the possibility of "stretching," or of finding "ladders" or "bridges" between the ideal and material realms:
Though number, be a thing so Immateriall, yet by degrees, by little, and little, stretching forth, and applying some likeness of it as first, to things Spiritual: and then bringing it lower, to things sensibly perceived, as of a momentary sound iterated: then to the least things that may be seen, numerable: And at length (most grossely) to a multitude of any corporal things seen, or felt: and so, of these grosse and sensible things, we are trained to learn a certain Image, or likenesse of numbers, and to use Art in them ... (sig. B4v).
The latitude in Ramus's geometry lies in its legacy. Since Ramus believes metaphysical speculation to have no place in "proper" mathematics, the Euclidean geometry which he and his English disciples promulgate is left to "mean" anything its user likes. Those practically oriented texts which reproduce Ramus's geometry without its qualifying glosses beyond one or two well-worn dicta maintain a suggestive silence on the metaphysics that might ground a practical geometry. Most early modern mathematical texts that aspire to a popular audience inevitably fall into this "silent" category. In the more pragmatic text, Dee's intermediate "least things" become workaday abstractions, which may or may not represent something more. Introducing Euclid's elements in The Pathway to Knowledg (1551) the highly influential English humanist Robert Recorde abandons the indivisible, "unsensible" point of "onelye Theorike Speculacion," in favour of "that small printe of penne, pencyle, or other instrumente, which is not moved": a definition more suitable for "practise and outwarde worke" (sig A1r). Recorde turns away, averts his gaze from the ideal, but without denying its presence. Indeed he reminds us of what he neglects. In doing so he echoes the humanist pragmatism of Florentine practical mathematics a century before. In his writings on perspective in painting, Leon Battista Alberti advises that the painter should think, for instance, of the geometric point, or "signum," not so much as mere signifier of the ideal Euclidean principle of indivisibility, as the "mathematician" would, but more as "somehow a kind of thing between the mathematical point and ... finite particles like atoms" (qtd. in Edgerton 81).
Alberti claims to speak "not as a mathematician but as a painter," and to express himself in "cruder terms" than those of pure mathematics: terms which figure the mathematical line, for instance, as a "brim" and as a "fringe." (On Painting 36).  And it is precisely these crude, painterly, metaphorical terms that allow Alberti "the artist" to speak at all. A genuinely ideal mathematics endures no material or literary figuration, and a genuinely pragmatic one no special authority raising it above the realm of mute, anonymous craft. In a purely Ramean universe, rather as in the universe of some materialist history, the (mathematical) text has little status. The closed circuit of use-informing-use may be aided by textual education, but only in a supplementary, rather than a constitutive role. For Dee it is the mathematical text itself which builds the bridge between "real" mathematics and the world. But no less is true of those pragmatic texts which ostentatiously avert their gaze from "theory" and build an inescapably textual middle ground between abstraction and pragmatic use.
Lesley Cormack is resolute in trying to resolve the contradiction between Dee's textual idealism and social pragmatism, to the disadvantage of the idealist text. In footnotes to her essay for Gordon and Klein's collection she draws up sides between those older histories which have encouraged us "to see Dee as an Elizabethan 'magus,'" and those recent, more "balanced" accounts which separate Dee's "natural magic" from his "natural philosophy," and which "set the record straight" by "establishing the primacy" both of Dee's "geographical work" and of his social relationships with "court and government" (65). However this assurance about the "true," pragmatic nature of Dee's mathematics does not utterly disperse Cormack's evident perplexity that though he "seems to have kept separate" magic and geography "in his dealings with geographers," the symbolism of his texts "argues for a closer relationship" (66). The principal new account to which Cormack alludes is clearly William H. Sherman's John Dee, with whose refusal to subscribe to the traditional view of Dee as isolated Platonist it would be impossible to argue. Sherman's attention to the material transactions of Dee's life, to its material loci (most importantly Dee's library), and to the materiality of Dee's reading and writing practices is exemplary.  This materialist corrective ought not, however, lead us to downplay the role Dee's textual investments in transcendence played in securing worldly currency for mathematics and social influence for the mathematician himself.
The early modern practical mathematician is, as Daniel Defoe's Moll Flanders says of her "gentleman tradesman," another marker of modernity, a "land water thing." He is both liberal scholar and wage labourer, and he is neither gentleman amateur nor common mechanic, neither landlord nor tenant. The value and meaning of his role, his work and its product depend on a precarious rhetoric of intermediacy, which figures the mathematician's art as somehow in between. If we were to construct a "poetics" of such in-between-ness we would have to begin with the mathematical images which bridge the ideal and the material realms of Platonic idealism: the ladders and bridges of Neoplatonism, and Dee's, Recorde's, Ramus's, and Alberti's tiny points and momentary sounds. We might also conclude that one of the most characteristic images of intermediacy is the study. Several recent scholars of early modern cartography have noted the close association of maps with the studies in which writers imagine them being consumed. As Garrett Sullivan neatly articulates it: "the map performs the surprising function of realizing the spaces of textual consumption" (96). And the figure of the study, as Sullivan also notes, performs the distinctive and crucial cartographic function of eliding the distinction between representation and reality; between looking at and being in a place (97). Cosmographie, states William Cuningham in The Cosmographical Glasse (1559), "delivereth us from greate and continuall travailes. For in a pleasaunte house, or warme study, she sheweth us the hole face of all th'Earthe, withal the corners of the same" (sig.A6r). Elsewhere, the student of Cuningham's Platonic dialogue perceives that he has learnt how, by
observing this order of you prescribed, I may in like sorte at my pleasure, drawe a Carde for Spaine, Fraunce, Germany, Italye, Graece, or any perticuler region: yea, in a warme and pleasaunt house, without any perill of the raging Seas: danger of enemies: losse of time: spending of substaunce: wearines of body, or anguishe of minde (120).
The mathematician's study might be considered an important site of contention for the various schools of recent cartographic criticism. A Foucauldian map-reading sees in it the sinister profile of the panopticon. Critics tracing the cultural poetics of cartography have been inspired by phenomenology to soften these outlines and find in the study the traces of universal human desires for transcendence, secrecy and comfort.  A materialist history tends, on the other hand, to be interested in the mathematician's study principally as a concrete location of particular events and material exchanges.  I think it's important to appreciate the role of the study as a poetic bridge between philosophical idealism and pragmatic worldly use. John Dee's famous study, for instance, is both a signifier of liberation from the constraints of time, place and the body, and a room in a house at Mortlake where he reads and writes particular books and meets the movers and shakers of Elizabethan London. It is this "both"-ness of the study, like the simultaneous abstraction and concrete-ness of the pen-drawn geometric point, that fuses the mathematician's authority with his agency; his representation with reality.
VII Applied Fantasy: Circuits of Mathematical Meaning
For such literary scholars of the map as John Gillies and Garrett Sullivan, so close is the association between map and study that the map might be said always to connote or "realize" the comfortable study. And yet this can only be so if the map is taken to be in some way constantly attended by those literary discourses which maintain this association. I have argued so far that early modern geography is "literary" not just by virtue of literary consumption, but in the constitution of its first principles: the ambiguous principles of an applied Euclidean geometry. I want now to consider the more extensive discursive means by which the ambiguity of geography and the map is sustained in general currency.
Where we underestimate the role of both popular and literary discourse in propagating the meaning of mathematics and geography in early modern culture, we are likely to conclude with Lesley Cormack, in one of the most influential of recent studies in this area, that mathematical interest and knowledge in the late sixteenth and early seventeenth centuries was of a "closed and almost recondite nature" (124). But where we consider the meaning of mathematics and of the mathematical text (be it map, picture, surveyed landscape or whatever) to be more than a matter of knowledge narrowly and scientifically defined, then the constituency involved in reproducing mathematical meaning must surely be much broader. Rather than just asking who knew trigonometry or how to project a map, we might also ask who knew and used the mathematical metaphors and allegories that in my view gave and still give such technologies their meaning in and purchase on the world. Who hasn't now, or hadn't then, heard of Archimedes, so disinterested in the material world that he jumped naked from his bath in joy at the discovery of a formula to measure gold? Archimedes the designer of siege engines who was himself killed while contemplating mathematical designs in the midst of his city's siege? And who doesn't now or didn't then understand such a persona and such allegories to signify the scientist's paradoxical service to yet freedom from the world? I think that the double meaning of mathematics, and thereby its simultaneous authority and usefulness, is sustained through figuration such as this.
In the writings of Thomas Hood, another late sixteenth-century educational reformer, allegory is one element in a wider rhetorical fusion of an idealist and a pragmatic mathematics. In 1590 Hood published a translation of Ramus's geometry to support lectures given by him under the auspices of the London merchant Thomas Smith to an open audience composed in part of the militia got up to counter the Armada (Hooykaas 117). It is appropriate, given the worldly circumstances of its production, that the translation repeats Ramus's pragmatist dictum that geometry is "the Arte of measuring well" (1). The speech given by Hood in 1588 to inaugurate these lectures, in correspondingly humanist voice, determines the "subject matter" of the mathematical arts as "the world" (22). However parts of this speech also take on a tone very similar to Dee's then eighteen-year-old "Preface." Hood expresses Dee's Platonist distaste for "clod and turff" in exhortations to his audience not to be "looking grovelling on the ground as senceless beastes" (sig. A3v). He also expresses Dee's Platonist desire for transcendence in urging them to perceive instead the mysterious mathematical seeds of the absolute beyond/within a familiar "outward frame" (sig. A3v). Hood's rhetoric commits, in other words, to both an idealist and a materialist-utilitarian philosophy of science.
I think Hood's precarious balancing act between contemplative science and profitable craft hides a silent, disingenuous investment in both. Faced by an audience of practical men, speaking from within the third, and eminently most worldly "university" of London, and promulgating the mathematical teachings of that prophet of Protestant utilitarianism Ramus, Hood still cannot let go of the absolute. It is obvious why not. Like Archimedes, in the mathematical fables whose popular currency Hood's speech both presumes and works to extend, he wants both the authority of liberal transcendence and the agency of worldly use. And he needs his audience to share this equivocal fantasy with him to secure its currency. As Lesley Cormack suggests, it is not enough for a few savants to be privy to esoteric mathematical knowledge for that knowledge to be influential in a wider culture.
Hood's speech both maintains and undoes a division between geometry's abstract systematisation of social space and the lives of those who inhabit it, discovering a continuous, undivided vale of discourse, stretching from the crudest ideas of Ramean mathematician-craftsmen to the esoteric speculations of Dee's mathematician-philosophers. For practical mathematics to "work"; for it to have meaning and value for those whose lives it touches, all of them must be included in this discursive landscape and must share the same fantasies about mathematics. So, to return to Julia Lupton's phrase, maps may well embody a "fantasy of structure"; a fantasy of "pure" mathematics, but this fantasy is a real and substantial element in constituting their value, meaning and thereby currency in the world.
Granted that fantasies of pure, mathematical transcendence might attach to general maps of large areas, enjoyed by virtual travellers in the comfort of their studies, it might be argued that they are far less likely to be realized by local mapping, conducted with more pragmatic purposes in mind. This, once again, is what recent materialist history, with its commitment to the "local" story, tends to suggest. Lucia Nuti makes a clear distinction in her essay in Denis Cosgrove's Mappings between renaissance geography and chorography (93). Where geography tended to mark the total and the absolute through mathematics, suggests Nuti, chorography, dealing pictorially with local and "ephemeral" terrain, was constitutionally more open to argument. The pictorial arts of chorography, she argues, needed to be "persuasive" and "rhetorical," engaged as they were to such practical, rather than scientific ends as "boundary disputes, inventories of estates, sales of properties, military operations" (93).
Nuti concedes the evident point that mathematics came to play a role in the renaissance in local as in global mapping, and indeed in various kinds of pictorial representation. She identifies a seventeenth-century English writer, William Leybourne, as characteristic of those converts to practical mathematics who tried to bridge the gap between total and local representation. Leybourne, author of such texts as The Compleat Surveyour (1653), was far from the earliest writer in English with pretensions to total measurement, as Leonard Digges's 1571 title Pantometria makes clear. However Leybourne's confident instructions in "'How to draw'" even "'a mountainous land'" according to exact principles of geometry is rejected by Nuti as "pale pretence" (96): another fantasy. It fails to capture the particularity of the terrain. More pictorial, more conventionally chorographic, and, Nuti implies, more realistically useful, are the "subtler correspondences" promoted by a writer such as William Folkingham, who prescribes a cartographic colour for every variety of ground (97).
The absoluteness and abstraction that Leybourne and a host of his contemporaries writing on surveying and cartography appeal to is clearly what a Foucauldian cultural historian sees when they look at the hard boundaries and contained territories of a geometric map. And of course we must not take this fantasy and ideology of closure at face value. But to try to look beyond the graphic aesthetic of the finished map to the temporality of its production and the rhetorical nature of its use is not necessarily to set aside mathematics. Were we to take Cosgrove's cue and to read the history of a given map in terms of the "complex accretion of cultural engagements" that preceded and followed its making, we would find that geometry, despite its primary appeal to the a-temporal absolute, was in fact part of that process of accretion. During the production of the map, the surveyor uses geometry to manufacture the effect of an absolute, continuous representation in what is in fact an acutely discontinuous process. Where maps are used, far from simply "closing" meaning with its mute authority, cartographic geometry is itself constituted and sustained through a rhetoric of persuasion: a free-flowing circuitry of allegories and images which determine the meaning, value and currency of the map.
Cartographic narratives like Leybourne's provide us with a fascinating resource for tracing and unpicking the means by which a practical, but inseparably discursive process of accretion is turned into the apparent mathematical closure of the finished map. They also demonstrate the insufficiency of this "finished" mathematics without their own discursive support. Crystal Bartolovich has given a convincing account of the "advertising" function of early modern surveying tracts, which use "emblems, icons, and metaphors" in a struggle to effect a "'turn' from 'feudally' to 'mathematically' ordered spatial relations" ("Spatial Stories" 255). Bartolovich reminds us that in a period of agon between post-feudal and capitalist socio-economic values, usefulness was far from the only consideration in the promotion of an abstract, mathematical attitude to land. In fact, judging surveying texts by their practical functionality empties them of their politics. The purpose of Leybourne's text, as with Thomas Hood's speech, is not just to instruct in, but to advocate for the use of mathematics: to spread precisely a "fantasy" of mathematics to support its mute cartographic products. 
This advertising function of the cartographic narrative is acutely obvious once again in a text produced explicitly to attend and support not cartography in general, but a specific set of maps. John Norden's 1596 Preparative to His Speculum Britanniae is first and foremost an answer to a wide range of objections anticipated and sustained to his abortive collection of British county maps. The objections Norden records to the maps published in advance of his complete collection, along with his answers to these objections, are highly suggestive. Norden notes contention over the scale of counties: whether this should show their relative size or equalise them (2). He notes the desire of "some" that, rather than reflecting regional variations in the measurement of miles, his maps should make reference to some standard unit (3). He notes that "some" would have his localities framed by degrees of latitude and longitude, notwithstanding "that few shires will admit one degree" (12). He notes that "where it is objected by some that I observe too many perticularities," "some again thinke I cannot observe more then necessarie" (17). And he notes contention over the relative rights of particular houses to be represented. All of these are both technical and, to varying degrees, social, or political problems. They are local problems particular to the social production of the meaning of Norden's maps, and they are problems which could be further bodied out and particularised were we to identify various of the "some" whose interests Norden refers to. This is the direction an archival, materialist map history might take. But these are also problems general to the social making of a more widely conceivable cartographic meaning: problems inherent to the fraught negotiation between abstraction and particularity.
Norden's project sits on the cusp of change towards what cartographic historians old and new characterise as a modern cartographic practice and meaning. In fact, his surveying practice did not deploy the new technique of geometric triangulation, but relied on the old estate-surveyor's method of measuring with chains (Taylor 47). Norden's defence of this decision confirms Nuti's scepticism about Leybourne. "Such as have but Speculation in the Arte," he complains, may think it easy to perform, but "practisers" like himself know that proper triangulation, faced often by such obstacles as "Woodes" and "Mountaines," would take art so "infinite" and "intricate" that it would "require the whole time of a mans ripe yeares, to effect the description of England" (14). And yet Norden's objections and answers, including the latter, themselves confirm the degree to which a public of "speculators" comprising at least a constituency who wished to buy and/or see their locality and even property represented in the maps, desired that such "perticularities" be contained within a standard geometric frame.
The mathematical fantasies of these buyers and users of Norden's maps were already playing an essential role in securing their currency in the world. No wonder then that Leybourne embraced impracticality. And yet it was not only the owners and users of his inadequately mathematical maps that Norden had to sell them to. For these maps to have any meaning and value in the making and in use once made, Norden needed the cooperation of those ordinary people whose environment was being mapped and redefined. Norden's apology for his Speculum reveals not just the social politics inextricable from what was still only an embryonically "modern" scientific exercise, but also the inextricably social and particular nature of the science to come. Norden's master-excuse for a range of the faults and inconsistencies people have discovered in his maps is that he has had to depend in his surveying on guidance from such local people
as by discretion of men in Aucthoritie are thought fit to yeelde me direct information, who yet thru their simplicitie or partialitie, may miscarrie the most provident observer, holding that to bee in their conceites of moment, and of the contrarie, as their affections leade them . (17-18)
This dependence is structural to local mapping, however geometric it becomes. Almost as often as early modern cartographers boasted the capacity of the map to elide the vicissitudes of actual travel, they complained of the impossibility of making maps without the help and advice of reliable local inhabitants, whether of Sussex or Virginia.
Behind every cartographic text with any claim to authority lie buried histories of encounters: some violent and exploitative, some more co-operative and transactional. This is true both of the history which precedes and that which follows the making of the map. As finished text, the individual map can mediate encounters ranging from the violent military and colonial campaign to political diplomacy, commercial exchange and the humble local boundary dispute. The stories told by local people to surveyors, the decisions they make, their own needs and "affections" are integral to the social production of the map and of its meaning. These inherently particular elements of cartography may be "reduced" to geometric form in the map, to give it the effect of absolute mathematical authority, but they cannot disappear altogether if it is to be of any use. And equally integral to the currency of the map, its meaning and its value, are the beliefs held about mathematics and cartography not just by the makers, owners and users of maps, but also by the inhabitants of the territories they represent. These beliefs are no less "partial," no less affected than any others.
Whilst the gentry customers of his county maps may have squabbled over their compromise between general frame and particular content and its ordinary contributors may have distorted them through their simple, un-mathematical affections, Norden's contribution to manorial estate surveying anticipated another, more trenchantly political form of resistance. In 1607 Norden published The Surveyor's Dialogue, a text which works, through staging a series of conversations between the surveyor and various figures in the agrarian scene, to persuade doubters of the truth and usefulness of applied geometry. During one of these conversations, a humble tenant farmer asks the surveyor: "is not the field it selfe a goodly map to looke upon, better than a painted paper ?" (15). This question reminds us of the historical agon played out in the argument for practical mathematics, and of the politics of mathematical "fantasy." For Norden's farmer the map is not a text. It is nothing more than the field itself: mere clod and turf. The farmer is refusing to participate in mathematical fantasy. But he is simultaneously refusing the authority of an art which would ultimately de-socialise and commodify English land, marginalizing the customary rights of its users and maximising the profits of their landlords.
If Norden's cartography were to have meaning and value beyond some mathematical in-crowd in which he himself was included, then he needed to persuade not just those who might buy and use his maps (the Landlords and governors of the nation) that they were more than painted paper, but also those whose lives they were expected to govern. This more is always some fantasy, however popular and unscientific, about mathematics. The problem with Norden's farmer is that he doesn't know or refuses to believe in any of the metaphors and allegories that might help him circulate the cultural capital of an ambiguous cartographic meaning and value. Beyond the spreading of any actual mathematical knowledge, the job of Norden's book, and many others like it, from Dee onwards, is to rectify this situation: to spread not just principles and techniques but fantasies of mathematics. The truth is that there is no difference between discourse and practice, between the cartographic frame and its content, between the goodly field and its representation, and this difference is itself an effect of discourse. Discourse is what turns both landscape and map into a text, wrapping representation into reality whilst still holding them apart. When we think about the geometry that frames a modern map, we should see neither pure mathematical abstraction, nor a "mere fantasy" concealing the material, political real. Instead, we should remind ourselves of the persuasive rhetoric that keeps the frame in place, dividing and hovering between the ideal abstraction of representation, and the dirty, pragmatic deals of the world, and encouraging us, as it encouraged its first users, to make analogies and slippages from one to the other. If a modern, critical history of cartography is tripping over itself in trying for the middle ground, and if it cannot make up its mind between materialism and the text, then it is simply yielding to the equivocal seduction of the early modern map.
1. See Koch for another version of this analogy.
2. See also Baker and Klein for broadly congruent accounts of the imperialist geometry of Irish colonial cartography.
3. "Some, forone purpose: and some, for an other, liketh, loueth, getteth, and useth Mappes, Chartes, & Geographicall Globes" (sig. A4r).
4. See "New Directions in Cultural Geography."
5. Bartolovich ascribes the discomfort of cultural geographers with cultural studies methodology to a simplistic understanding of textuality. To place an emphasis on textuality, she suggests, is not simply to suggest that maps and landscapes are like books, and can be read as such, but to denaturalise and foreground the constructedness of our most apparently transparent means of viewing the world and bringing it into discourse. Textuality simply draws attention to the problematic of representation: what Michael Ryan calls the "interweaving of inside and outside" (qtd in Bartolovich 9n).
6. See Gronim for another good example of a particularising, archival map history. Gronim places a series of maps of British colonial New York within the context of local territorial disputes in which they were deployed as instruments of political persuasion. Her maps make no sense at all as "texts" divorced from the immediate contexts within which they were used.
7. See, for instance, 48.
8. Many literary critics of map culture draw heavily on Gaston Bachelard's Poetics of Space and on Michel de Certeau's The Practice of Everyday Life, both of which interpret spatial representation as always already informed by the life of the body.
9. Certainly Sullivan expresses a little discomfort with the literary paradigm of cartographic study, and echoes Harley's warning about the too-legible textuality of maps divorced from the material circumstances of their production and use (95).
10. Once again Gordon and Klein's introduction bids for the middle ground, warning against "the often inflationary usage of this suggestive semiotic concept [mapping] in recent critical work [which] tends to ignore perhaps too easily the boundaries between the metaphorical and the material," but insisting nonetheless that "both realms mutually determine each other" (3).
11. See Ryan xiv-xv.
12. For an account of Plato's two divided realms, see Merlan.
13. For an account of the differences between what he regards as "proper" mathematics and what he calls Plato's "meta-mathematics," see Strong.
14. See Wedberg, 108.
15. See Merlan for a full account of "excessive realism," or, as he calls it, "realistic trialism," from the early Christian centuries to the Renaissance.
16. See Raleigh, The History of the World: "Man is the bond and chaine which tyeth together both natures" (II 30).
17. Exemplary here is Jonson's 1618 Masque Pleasure Reconciled to Virtue (in Complete Masques), which deploys both Hercules and Daedalus to suggest to his courtly audience, and in particular the young prince Charles, the possibility of artful compromise between apparently divergent paths.
18. Donne's lovers are "stiffe twin compasses" ("A Valediction forbidding mourning" 35-36 in Complete Poems 98), his tears "globes," his globes "nothing" made "All" ("A Valediction of weeping" 14-16 in Complete Poems 85), his body a "Mapp" to which his physicians as "Cosmographers" tend ("Hymne to God my God, in my sicknesse" 6-15 in Complete Poems 488). On the one hand, these figures can be regarded as evidence of the poet's awareness of and interest in the new geography, and as working to extend its currency in the circulation of geographic ideas and discourses. On the other, they might be held to emphasise the status of geography as an artificial substitute for reality rather than the thing itself: in Platonic terms a mere shadow. The macrocosm of the world to which geography aspires is characteristically reduced in these images to the microcosmic bathos of the human body whose scale its globes and maps more properly suit.
19. See "Elegie XVIII: Loves Progress" (11-16 in Complete Poems 179):
I when I value gold, may think upon
The ductilness, the application,
The wholsomness, the ingenuitie,
From rust, from soil, from fire ever free:
But if I love it, 'tis because 'tis made
By our new nature (Use) the soul of trade.
20. See Appelbaum, "Anti-geography" and Helgerson, "The folly of maps and modernity."
21. Ben Jonson bids his friend William Roe safe voyage in the poem which bears the latter's name, in the hope that Roe will come back "untouched," having travelled "perfect in a circle" ("Epigramme CXXVIII: To William Roe" in Complete Poems 84). So much, so like Donne's stiff compasses. Except that as well as wishing Roe a journey which he might as well make in the comfort of his domestic imagination, for all he gains or changes, Jonson also bids him "know" and "extract" the best of the "Countries, and climes, manners, and men" that he meets. Jonson is clearly interested in geography not just as a metaphor for more significant spiritual territories and journeys.
22. See Hooykaas for a thorough account of Ramus's mathematical works.
23. See Feingold 13-21 for an account which characterises the early seventeenth-century scientific community as "protean and heterogenous" rather than divided into rigorously aligned camps, and see Sherman for a polemic reinforcement of this case.
24. Any translations from Hooykaas are my own.
25. See Edgerton 80-81 for an account of Alberti's painterly geometry.
26. Sherman's focus on the textual marginalia of Dee's books, like Jerry Brotton's mode of cartographic history, is designed to reveal the "deep materiality" of Dee's participation in Renaissance literary culture.
27. John Gillies describes the physical comfort imagined in what he takes to be the always-implicit "ultimate scene of cartography": the domestic interior "in which maps are typically read" (121).
28. See William Sherman's fascinating account of John Dee's "living library."
29.Such a fantasy is composed of familiar "literary" ingredients such as the image of the study. Leybourne encourages his reader to imagine himself consuming his mathematically surveyed map "at pleasure" "in his study, or other private place" (275).
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Responses to this piece intended for the Readers' Forum may be sent to the Editor at L.M.Hopkins@shu.ac.uk.
© 2003-, Lisa Hopkins (Editor, EMLS).