Abstract
New England’s Prospect, written by the Puritan settler William Wood, and published in London in 1634, is a member of that class of texts produced to encourage early American colonisation. In it, Wood tells a story clearly intended to disperse English fears about the Indian menace. ‘The doubtful traveller’, he records, ‘hath often-times beene much beholding to … [the Indians] for their guidance thorow the unbeaten wildernesse.’1 ‘My selfe’, he continues, illustrating his point,
with two more of my associates bending our course to new Plimouth, lost our way, being deluded by a misleading path which we still followed, being as we thought too broad for an Indian path … which begat in us a security of our wrong way to be right, when indeed there was nothing lesse: the day being gloomy and our compasses at home … happily we arrived at an Indian Wigwamme … the son of my naked host … took the clew of his travelling experience, conducting us through the strange labyrinth, of unbeaten bushy wayes …2
Wood’s experience in the ‘wilderness’ is registered here both as exemplary and as exceptional. Exemplary in its illustration of Indian helpfulness; exceptional, in that without the temporary absence of the compasses, there would have been no need for such help, and indeed no story.
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Notes
William Wood, New England’s Prospect (London, 1634), p. 70.
Typical of such presumption is David Harvey’s comment in The Condition of Postmodernity: An Enquiry into the Origins of Cultural Change (Oxford: Basil Blackwell, 1989), p. 246, that the geometric aesthetic of Ptolemaic cartography made the world in general seem ‘conquerable and containable for the purposes of human occupancy and action’.
See, for instance, Homi K. Bhabha, ‘The Other Question: Difference, Discrimination, and the Discourse of Colonialism’, in Francis Barker et al. (eds), Literature, Politics and Theory (Colchester: University of Essex, 1986), p. 156: ‘Colonial power produces the colonised as a fixed reality which is at once an “other” and yet entirely knowable and visible.’ In insisting upon the inherence of human with environmental alterity, I take a similar approach to Paul Carter in his study of early European encounters with Australia, The Road to Botany Bay: an Essay in Spatial History (London: Faber and Faber, 1987).
In The Body Emblazoned: Dissection and the Human Body in Renaissance Culture (London: Routledge, 1995), Jonathan Sawday charts the emergence of a post-Cartesian language of the body as intellectually driven ‘machine’ — the ‘other’ of empiricism — displacing earlier modes of thinking of the body as the geographical unexplored, and at the same time as the grotesque condition of the soul/intellect’s secular imprisonment — the ‘other’ of idealism. This essay will tend to suggest that this displacement is incomplete in seventeenth-century discourse bearing on the division of labour between intellectual government and corporeal executive in mathematical art, and that the two modes are capable of co-operation.
For a full account of Ptolemaic projection, attended by reflections on the epistemological implications of its placement of the geographic viewer, see Samuel Edgerton, The Renaissance Rediscovery of Linear Perspective (New York: Basic Books, 1975).
See A. W. Richeson, English Land Measuring to 1800: Instruments and Practices (London: The London Society for the History of Technology, 1966) for an account of the advent and dissemination of triangulation.
See Spiro Kostof, ‘The Architect in the Middle Ages, East and West’, in Spiro Kostof (ed.), The Architect: Chapters in the History of the Profession (London: Thames and Hudson, 1991).
Marcus Pollio Vitruvius, The Ten Books on Architecture, translated by Morris Hicky Morgan (New York: Dover, 1960), pp. 11–12.
See Alfred Sohn-Rethel, Intellectual and Manual Labour: A Critique of Epistemology, trans. Martin Sohn-Rethel (London: Macmillan, 1978) for an exploration of the reductive metonymy ‘head’/‘hand’, which can be traced from Plato, through Vitruvius, to Vitruvius’s Renaissance disciples. Like me, Sohn-Rethel discovers the social/epistemological border between head and hand to be marked, typically, through mathematics.
Leonardo da Vinci, The Notebooks of Leonardo da Vinci, ed. Irma A. Richter, (Oxford: The World’s Classics — Oxford University Press, 1980), p. 118.
Leon Battista Alberti, ‘On Painting’ and ‘On Sculpture’, edited and translated by Cecil Grayson, (London: Phaidon, 1972).
John Dee, ‘Mathematicall Preface’, in Euclid, Euclides Elementes of Geometry: The First VI Books, trans. by Thomas Rudd (London: 1650), sig.B2v. Rudd’s is one of several recyclings of Dee’s essay, which originally prefaced Sir Henry Billingsley’s first English Euclid.
Robert Recorde, The Pathway to Knowledg (London: 1551), sig.A1r.
Jean Leurechon, Mathematical Recreations, translated by William Oughtred (London: 1633), sig.A2r.
For an exploration of supplementarity which makes particular reference to the spatial logic of the map, see Jacques Derrida, The Truth in Painting, translated by Geoff Bennington and Ian McLeod (Chicago: Chicago University Press, 1987).
R. A. Skelton, Decorative Printed Maps of the Fifteenth to Eighteenth Centuries (London: Staples Press, 1952), p. 18.
See, for instance, John Norden, The Surveyor’s Dialogue (London: 1607), p. 24.
See, for instance, Leonard Digges, Pantometria (London: 1571), sig.K4v — sig.L3r.
John Smith, ‘The Generali History of Virginia’, in Philip L. Barbour (ed.), The Complete Works of Captain John Smith 1580–1631) vol 2, p. 52.
Smith, ‘Generali History’, Complete Works, vol. 2, p. 52.
Giovanni Pico della Mirandola, Oration on the Dignity of Man, trans. A. Robert Caponigri (Los Angeles: Gateway Editions, Inc., 1956), p. 9.
Nicomachus of Gerasa, ‘Introduction to Arithmetic’, in Robert Maynard Hutchins (ed.), Euclid, Archimedes, Apollonius of Perga, Nicomachus, Great Books of the Western World 2 (London: Encyclopaedia Britannica Inc., 1952), p. 812.
Proclus, A Commentary on the first Book of Euclid’s Elements, translated by Glenn A. Morrow (Princeton, New Jersey: Princeton University Press, 1970), p. 4.
William Cuningham, Cosmographical Glasse (London: 1559), sig.A2r.
Quoted in Edward W. Strong, Procedures and Metaphysics: A Study in the Philosophy of Mathematical-Metaphysical Science in the Sixteenth and Seventeenth Centuries (Hildesheim: Georg Olms, 1966), p. 11.
See Aristotle, ‘Posterior Analytics’, A.II.71b.33–72a.5, in W. D. Ross (ed.), The Works of Aristotle (Oxford: Oxford University Press, 1908–1952).
See Philip Merlan, From Platonism to Neoplatonism (The Hague: Nijhoff, 1960), pp. 62–83.
See, for instance, Jacques Derrida, ‘White Mythology’, Margins of Philosophy, translated by Alan Bass (Brighton: Harvester Press, 1982) for a discussion of the disavowed necessity of metaphor and the impossible horizon of a private language, in metaphysical discourse from Plato to Husserl. Derrida argues in this and other texts that the ‘endangerment’ of closed structures of denotation through the discursive and material embodiment of language is essential for meaning to ‘settle down’ into the world.
For the thesis that the ascendancy of ‘empiricism’ led in some cases to the ‘codification’ rather than the ‘refutation’ of Platonism, see Ernst Cassirer, The Individual and the Cosmos in Renaissance Philosophy, trans. Mario Domandi (Oxford: Basil Blackwell, 1963), p. 152. For a characterisation of the early seventeenth-century scientific community as ‘protean’ and ‘heterogeneous’, rather than divided into rigorously aligned camps, see Mordecai Feingold, The Mathematician’s Apprenticeship: Science, Universities and Society in England, 1560–1640 (London: Cambridge University Press, 1969).
Michel Foucault, Death and the Labyrinth: The World of Raymond Roussel, trans. Charles Ruas (London: Athlone Press, 1987).
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Edwards, J. (1999). ‘The Doubtful Traveller’: Mathematics, Metaphor, and the Cartographic Origins of the American Frontier. In: Fudge, E., Gilbert, R., Wiseman, S. (eds) At the Borders of the Human. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-27729-2_8
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