Canada Archives Canada Published Heritage Direction Du Branch Patrimoine De I'edition

UNIVERSITY OF CALGARY

Andrew A. McLaren

A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FINE ARTS

DEPARTMENT OF ART

CALGARY, ALBERTA SEPTEMBER, 2008

395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada

Your file Votre reference ISBN: 978-0-494-44237-1 Our file Notre reference ISBN: 978-0-494-44237-1

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The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission.

In compliance with the Canadian Conformement a la loi canadienne Privacy Act some supporting sur la protection de la vie privee, forms may have been removed quelques formulaires secondaires from this thesis. ont ete enleves de cette these.

While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. •*• Canada Abstract:

This paper traces the intentionalities and heuristic research behind my installation

at the Nickle Arts Museum, Register of the Returning Earth. The practical / critical

implications of working with maps in Visual Art are contextualized in the author's work.

A neo-interdisciplinary practice, "Paracartography" is proposed. Artists using a

Cartographic sensibility in their publications are examined. A history of

Cartography/Geodetics is outlined, with notable speculative models of the Earth's structure. Literary (Borges) and critical (Deleuze and Guattari, Nancy) conceptions relating to Cartographic space are identified. The Semiotics of Charles S. Peirce is presented with reference to Cartography. Peirce's Quincuncial, and Laurence Lee's

Conformal Tetrahedric projections are discussed, as applied to Register...; conceptual / practical frameworks for the animations are described. Objects in the installation are detailed, referring to their appropriated functionality. Further developments in interactive media are proposed, while recognizing that the work only currently exists as a formal presentation.

in Acknowledgments

I would like to express my gratitude to many people in the University of Calgary community who have assisted me and/or otherwise offered their support as teachers, colleagues, technical advisors and in other capacities as friends and morale-boosters.

My advisory committee: Eric Cameron, Jerry Hushlak and Paul Woodrow, have been of great value in providing suggestions that have substantially assisted toward the development of this work. I would also acknowledge the ever-attentive Graduate Seminar instructor Linda Carreiro, without whose expertise in University protocol I may well have had difficulties. The office staff in the Department of Art, Sheila Harland, and Samira Jaffer, offered much real support in assuaging my caffeine dependency and providing printing services when my own machine finally bit the dust. Technician Anthony Reimer in the Fine Arts Media Lab was absolutely indispensible at times, when I had to address cross-platform issues with my digital output. Shop Techs Rick Calkins and Nathan Tremblay have been there at times I have needed them; I must also thank my fellow Graduate students collectively for contributing to a fantastically collegial atmosphere in which we have all able to further our development through all kinds of challenging, contentious and productive episodes.

Outside of the Art Department I must thank Shawn Mueller, PhD candidate at the Department of Geography, for sharing his wealth of knowledge and expertise in the area of digital cartography. Geography Department Tech Bart Hushlof was also invaluable in introducing me to ARC GIS in their labs.

One contributor to the substantial development of this project, for whom I must make special mention, is Research Assistant Doug Phillips from the I.T. Department, who made several scripts without which the visual aspects of this project would have been practically impossible.

Thanks are also due to Jonathan J. Davis and Jeff Haroutunian who pitched in with alacrity when they were able to help with technical issues.

I must also acknowledge the financial support of the University of Calgary and the Alberta Foundation for the Arts; additional support over the past two years has also been provided by the CRFA fund donated by John Lefebvre, and from the URGC, which provided funds that were applied to purchase a digital projector for the Department of Art.

Lastly I mention the Staff at the Nickle Arts Museum, to whom thanks are due for bearing with me and others in my graduating class, during the installation of our work.

IV Table of Contents

Title Page i Approval Page ii Abstract iii Acknowledgments iv Table of Contents v List of Illustrations vi

Press Release 1 Introduction 1 Prior Developments in World-Image 2 Richard Purdy: The Inversion of the World/ L 'Inversion du Monde 16 Arkady Nasonov (The Cloud Commission): Antipodes 18 The A tlas of Nowhere 19 Paracartography: a Semantic Analysis 20 A Non-Unitary World-Image: The Register of the Returning Earth 22 An Epistemology of Cartographic Representation 25 Genealogy of the World-Image: Archaic Models of the Extended Earth 26 Euclidean Space: Early Geographers 28 Typologies of Maps in Medieval Europe 30 The Ptolemaic Revival in Renaissance Europe 31 Baroque Visionaries and Later Speculations 33 Production of the Scientific Document 35 Empiricism and the Flat-Earth Theory 36 Theories oftheTetrahedral Earth 39 The Positivist Worl-View and the Space of Data-in-Formation (DIF) 40 Peircian Terms of Conventional Reference 42 The Map as Signifier of the Absolute (Jorge Luis Borges) 55 Deleuzo-Guattarian Conceptions of Space 56 Synthetic Constructions using Tessellating Map Projections 58 Using Discrete Global Grids as Locational Networks 61 Conceptual and Practical Frameworks for an Animation 64 Technical Aspects of Output 73 Physical Elements in the Installation 75 A Reversion to a Strategy of Display 78 A More "Down-to-Earth" Reading 80 References 84

v List of Illustrations

Fig. 1: Azimuthal Equidistant Projection centered at Calgary, Alberta. p. 7

Fig. 2: Azimuthal Equidistant Projection centered opposite Calgary, Alberta. p. 8

Fig. 3: Andrew McLaren, Gnomonic Tetrahedral Projection (South Polar Aspect), 1987 p. 9

Fig. 4: Andrew McLaren, LITTORAL #5, LITTORAL #6, Cyanotype Prints on Paper, 1995 p. 11

Fig. 5: Andrew McLaren, War Against Entropy, Digital Prints on Paper, 2001 p. 14

Fig. 6: Andrew McLaren, excerpted images (facing pages) from the Atlas of Nowhere, 2004 p. 19

Fig. 7: Tessellated Peirce Quincuncial Projection p. 22

Fig. 8: Sample Frame from test animation (Lee Tetrahedric Projection) May 2008 p. 25

Fig. 9: "Paralax" (Samuel Birley Rowbotham), Map of the Flat Earth, 1881 p. 38

Fig. 10:10242-point icosahedral Discrete Global Grid, panel 1 p. 65

Fig. 11: 10242-point icosahedral Discrete Global Grid, panel 2 p. 65

Fig. 12:10242-point icosahedral Discrete Global Grid, panel 3 p. 65

Fig. 13: 10242-point icosahedral Discrete Global Grid, panel 4 p. 66

Fig. 14: 10242-point icosahedral Discrete Global Grid, panel 5 p. 66

Fig. 15: Eight-Ball, in projection of tessellated Lee Tetrahedric maps p. 72

Fig. 16: Binder clip with envelope, in projection of tessellated Lee Tetrahedric maps p. 72

Fig. 17: 32" Replogle "Diplomat" library globe with brass meridian and light fixture, ca. 1970 p. 76

Fig. 18: Restored antique camera stand (tripod) adapted as projector support p. 77

Fig. 19: Registered and mis-registered Peirce Quincuncial maps (note register at right) p. 79

Fig. 20: Detail of two adjacent Peirce Quincuncial maps (registered) p. 80

vi 1

Register of the Returning Earth proposes a kind of parallel-world space that grows from an animated series of map projections. 10,242 maps of this otherworldly space are compiled into a potentially infinite space of multiple, shifting world-views. Created using digital cartography, what might be described as "anti-location maps" are projected onto the museum's walls, a plurality of colliding and emerging geographies which occur when the presence of a place becomes its own doppelganger.

(Press release written for the Faculty of Fine Arts, University of Calgary)

My thesis work addresses cartographic design, in the context of art, as a formal and conceptual construction of World-image. The histories of Visual Art and

Cartography each encompass a diverse scope of intentionalities and interpretive perspectives. There are, however, many historical and contemporary instances where these concerns overlap—both in print or electronic media for which some form of visual resolution is constructed, and among their practitioners, for whom either area presents a critical challenge. It can be argued, for instance, that in Medieval Europe both mapmakers and artists produced forms of didactic representation, whether their products were intended as a pilgrim's guide, or as an object of veneration. In a contemporary context, critical studies in both fields have long recognized that a description of Art or of

Cartography as practical disciplines must account for far more than such a naive sense of productive representation. Artists and Cartographers share a historical and cultural epistemology, and owe much to the literary, semiotic and logical milieus by which, or in spite of which, their activities are interpreted. 2

Prior Developments in World-Image

Among my critical engagements as a practicing visual artist, is the idea of World- image, as expressed in the formal systems of Cartography. I will outline the development of this abiding interest in my work: in terms of my intentionality; the propositional forms that have occurred in my practice; and, as I will further argue, with the contention that this activity is tangibly and conceptually negotiated as an artistic process. I will also examine the work of other recent artists who have adopted mapmaking as a viable strategy in their production. This will necessarily include the chronology of my heuristic studies since the 1980s, along with illustrations of my work in this area as it has developed, and some reference to related interests, in particular my development of schematic calendar systems.

My initial interest in Cartographic drawing grew partly from my enthusiasm for drawing and a habitual practice of delineating form. Among my early drawing experiments, were drawings of the complete range of my field of vision from my left and right eyes. The circular drawings would invariably include the perceived outline of my brow, nose and cheekbone, as I also discovered that the approximation of my peripheral vision necessitated the curvature of lines toward the perimeter, much as a fish-eye lens in photography. This somewhat naive experiment in empirical perception (which was in fact representative of a composite field of view, incorporating several orientations of my eyeball while facing a given direction) predates my interest in cartography by several years, but also demonstrates an attempt at exploring the limits of the retinal image, in a way, I would argue, that is analogous to a kind of surveying or mapping. 3

Another work that intrigued me at that time was a print of global map projections by the early Conceptualist and Feminist artist Agnes Denes, which was displayed by the front desk at the library of the Nova Scotia College of Art and Design (NSCAD), where I began borrowing books while at High School. I was exposed to many documents of critical and conceptualist artists, and was particularly impressed by the philosophical implications of the (1960's French art movement) Groupe de Research d'Art Visuel

(GRAV), whose 1961 manifesto, I found personally and politically challenging:

General Propositions of the 'Group for Research in the Visual Arts' (1961)

Relationship of the artist with society: This relationship is presently based upon: The unique and isolated artist The cult of the personality The myth of creation The overestimation of aesthetic and anti-aesthetic conceptions Elaboration for the elite The production of unique works of art The dependence of art on the marketplace

Propositions to transform this relationship: To strip the conception and the realization of works of art and to reduce them to simple human activity To seek new means of public contact with the works produced To eliminate the category 'Work of Art' and its myths To develop new appreciations To create reproducible works To seek new categories of realization beyond painting and sculpture To liberate the public from the inhibitions and the warping of appreciation produced by traditional aestheticism, by creating a new social-artistic situation

Relationship of the work to the eye This relationship is presently based upon: The eye considered as an intermediary Extra-visual attractions (subjective or rational) The dependence of the eye on a cultural and aesthetic level 4

Propositions to transform the relationship: To totally eliminate the intrinsic values of the stable and recognizable form be it: Form idealizing nature (classic art) Form representing nature (naturalistic art) Form synthesizing nature (cubist art) Geometrizing form (constructivist art) Rationalized form (concrete art) Free form (informal art, tachism, etc.) To eliminate the arbitrary relationships between forms (relationships of dimension, placement, colour, meanings, depths, etc.) To displace the habitual function of the eye (taking cognizance through form and its relationships) toward a new visual situation based on peripheral vision and instability To create an appreciation-time based on the relation of the eye and the work transforming the usual quality of time

Traditional plastic values These values are presently based on work which is: unique stable definitive subjective obedient to aesthetic or anti-aesthetic laws

Propositions to transform these values: To limit the work to a strictly visual situation To establish a more precise relationship between the work and the human eye Anonymity and homogeneity of form and relationships between forms To stress visual instability and perception time To search for a nondefinitive work which at the same time is exact, precise and desired To direct interest toward new variable visual situations based on constant results of the eye-art rapport To state the existence of indeterminate phenomena in the structure and visual reality of the work, and from there to conceive of new possibilities, which will open up a new field of investigation1

In proposing an historical teleology of vangardist practice, consistent with the reductionism of critics such as Jack Burnham and Lucy Lippard, I cannot claim to have followed all of its prescriptive suggestions. I had not at that time considered working in terms beyond static presentation (for example, in adopting a more performative or time-

1 Cited from Harrison, Charles, and Wood, Paul, Art in Theory 1900-2000, Oxford, Blackwell, pp 726-727 based approach to making art), but I felt that the GRAV document represented a rigorous

and responsible critique of art, as an ideological entity, and as a personal practice. In

particular I felt that the production of non-unique art, using techniques and materials that

could be accessed by 'anybody,' was an imperative basis from which to consider my own

work. Although encouraged to experiment in a variety of media and exercise different

sensibilities over the next few years in post-secondary Art studies at NSCAD and the

Byam Shaw School in London (and not fully resolving my intentions or productive

strategies during most of that period), an aversion toward expressive, or virtuosic mastery

of traditional media, persisted with me, and I largely eschewed the use of high-art

materials in favour of drafting supplies, commercial print output and such stuff that I

could find at Canadian Tire stores.

I was always interested in work that explores anamorphic pictorial space. Jan

Dibbets' 1969 piece Perspective Correction, consisting of a trapezoidal section of

removed turf from a sports field, intrigued me as the documentary photograph (which

must be considered part of the work, as its remaining artifact) showing this excavation at

an angle giving it a square appearance.2 During my studies in the UK (1981-5) I was also

introduced to the photographer John Hilliard, whose work at the time often consisted of

paired images, based on the same setting, but differing in the relation between the camera

and its principal light source. Illuminated by a moving bulb, the mise en scene would be

first shot with a static camera, recording a blurred arc of light with the tableau clearly

visible, and then again with the camera moving to follow the trace of the light, resulting

2 Ursula Meyer, Conceptual Art, New York, E.P. Dutton, 1972, p.] 20 6

in a close definition of the lamp's shape set against the conversely motion-blurred setting

of the lens' field of view.

At around that time I developed an interest in the Azimuthal Equidistant (AZED),

or Great Circle map projection. The AZED projection is conventionally used in

aeronautics and ham-radio applications, as it is designed to measure distances

consistently in a radial direction from its point of origin. This form of map interested me

as an anamorphic technique, and also reminded me of the appearance of a RADAR

screen, where a radial sweep of surrounding aircraft or other signaling devices is tracked

on a circular field. I still use this projection as a source-material for generating other map projections, including those in my thesis exhibition, Register of the Returning Earth. The

AZED projection describes a complete global map, relative to specific locations, from

which the rest of the Earth is circumscribed in a surrounding circular projection. I made my earliest attempts at drawing these using globes, which I inscribed with concentric

circles using point dividers, and radial lines with a flexible drawing curve. From these models I drew the circular map projections by eye, onto radial grids drafted on large

sheets of tracing paper, to make dyeline (positive blueprint) prints.

My first exhibition of the maps (1984) at the Byam Shaw was in a closed space, with an ultraviolet light illuminating the interior (and supposedly exacerbating the fading of the prints) and efflorescing upon strings pigmented with Day-Glo colours, which extended between selfsame locations as situated upon the different global maps. I also made stencils using the distorted landforms that these projections produced, later making 7 spray-painted negative images of these maps on acetate. Adopting a kind of self-taught cartographic drawing strategy, I felt that I fulfilled a kind of anonymous, or common ground of practice, engaging a kind of visual language (i.e. anamorphic drawing) and developing a critique of representation (with Global map projections), which demonstrates a particular mutability between generic and specific qualities of the World- image. I was also interested in the AZED map as a displacement of the conventional

World-view, which is polarized along the North and South axis. With this displacement comes a shift from the diurnal time zones defined along the longitudes; I had read a quote from Paul Virilio around then, directly referencing the AZED map projection:

Today we're in Chrono-Politics. Geography is the measuring of space. Now, since the vectors of the post-Second World War period, geography has been transformed. We have entered into another analysis of space which is linked to space time. What we call azimuthal equidistant projection is the geography of time. Geography of the day by speed, and no longer a geography of the meteorological day.3

Fig. 1: Azimuthal Equidistant Projection, centered at Calgary, Alberta.

3 Virilio, Paul, Lotringer, Sylvere, Pure War (trans: Mark Polizotti), New York, Semiotext(e) 1983, p.6 8

An opposite projection, constructed from the same polarity, with anamorphic inversion:

Fig. 2: Azimuthal Equidistant Projection, centered opposite Calgary, Alberta.

After graduating from the Byam Shaw I continued to work independently for a couple of years in London, producing other variants of the AZED maps, while investigating other types of map projection. My methodology remained one of hand- drawing, based on anamorphic reckoning and rendering from mass-produced globes.

After being introduced to the Dymaxion maps of R. Buckminster Fuller in 1986,1 developed what I believed to be a new kind of map projection, based on the lattice of a triangular grid wrapped around a globe, subtended upon a spherical tetrahedron. Fuller's maps were first composed of six square and eight triangular panels, defining a semi- regular platonic solid, the cuboctahedron, over the globe (later versions were defined by an Icosahedron, and these are the better-known examples). Jasper Johns produced a painting,Map (Based on Buckminster Fuller's Dymaxion Airocean World) between 1967-

71, now in the permanent collection of the Museum Ludwig in Cologne. 9

I produced two versions of a tetrahedral lattice, measured from the North and

South poles. My methodology was crude, using flexible curtain wire, connected at the four vertices with hooks and loops, divided evenly into segments across which I strung threads to define a triangular grid at 10° intervals. In constructing the spherical tetrahedron I used a single reference, which established the measurement of the angle subtended by an edge, at 109° 28' 16".4 I recognized that the tetrahedral map could

'unfold' in a similar manner to Fuller's Dymaxion design, but would also seamlessly tessellate upon an infinite plane. I am still employing similar map projections in some of my current work: the properties of tessellating maps are critical to the proposed work in this thesis, Register of the Returning Earth; these characteristics are further analyzed in that context, later in the paper.

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Fig.3. Andrew McLaren, Gnomonic Tetrahedral Projection (South Polar Aspect), 1987

After returning to Canada to complete my NSCAD BFA program during the early

1990s, I continued my work with an emphasis on perspectival drawing experiments, and resumed my activities with map projections. I also became familiar with Bruce Barber's

4 Williams, Robert, The Geometrical Foundation of Natural Structure, New York: Dover, 1979, p.63 10 ideas about Littoral Practice. For Barber, Littoral practice is discursive, an act of giving, and interdisciplinary:

Littoral art describes the intermediary and shifting zones between the sea and the land and refers metaphorically to cultural projects that are undertaken predominantly outside of the conventional contexts of the institutionalized artworld.5

A defining aspect of Barber's teaching philosophy, which is consistent with the premises of Littoralism, is that a person's skill-sets, even (and perhaps especially) those not ordinarily considered in the context of Art, can be recruited in an independent or collaborative artistic practice. It was Bruce Barber who first used to word

"paracartographer" to describe my activities in constructions with global maps. I have adopted this name, along with its proper classification, Paracartography, as a description of my agency and activities in adopting (some of the) strategies normally associated with

Geography, Geodesies, and Cartography; a more thorough semantic analysis of this proposed term is elaborated further below in this paper.

I produced a series of cyanotype prints following my graduation from NSCAD in

1995, which I titled LITTORAL. Despite my studies with Barber, this choice of title did not directly refer to Littoral Practice, but rather to the outlines of coasts that create a familiar pattern-recognition by map readers. These drawings superimpose two projections onto one graticule (lattice of latitude / longitude lines). The projection used in these is an oblique Mollweide, or elliptical projection, which is equal-area, but due to its disposition of latitude and longitude lines, not conformal (shape-equivalent). The superimposition of north and south hemisphere maps onto the bipolar grid along with the text cut into the

5 Barber, Bruce, Sentences on Littoral Art, 1998 http://www.novelsquat.com/index2.html 11 cyanotype print is intended to question the dominance of one "world view". Cut-out text in a lighter tone from underexposed prints was applied onto the final copies. The phrases are intended to reinforce the dualities which are present or assumed in cartography, or in media in which it is often used. These were exhibited at the Khyber Centre for the Arts

(now the Khyber ICA) during the June 1995 G-7 meeting in Halifax.

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Fig. 4 Andrew McLaren, LITTORAL #5, LITTORAL #6, 1995 Cyanotype Prints on Paper

After 19961 began to work more intensively with digital media, having enrolled in a 3D animation course at McKenzie College, in Halifax. My previous experience with computers was limited to rudimentary word-processing and a few experiments in Quark

Express, while at NSCAD. After roughly eighteen months of formal and self-directed studies in Photoshop and 3D Studio (on a DOS platform) followed by some work with

3D Studio MAX in Windows, this experience affected a significant shift in my approach to working with cartographic elements in my art; working with scanned maps, and vector-based drawings derived from these, I began to create work which could exist in several iterations, with multiple files based on variations of an initial image. Although I had already been aware of Peirce's and Lee's Projections since my studies at NSCAD, it was not until 2000 that I produced work that incorporated these particular designs. 12

At this time I was also exploring other kinds of formal construction, particularly with regard to structures based on the calendar. In the sense that our conventional measurements of time are based on the rotation and orbit of the Earth, graphic systems. based on calendar units can be considered as relational projections of the World, as a kind of temporal cartography. This research was published in my book Time Machines +

Paragogic Almanac (2001), where patterns and geometric structures, mostly derived from the numbers 365 and 366, as used in the Western (solar) calendar are elaborated in variable configurations. The weekly and monthly cycles of time, numbered as 7, 28, 29,

30 and 31 are also constructed as repetitive patterns in other diagrams, as well as those particular to the Islamic (lunar) calendar year, which is based on 354 days. My work in this area has not yet incorporated other calendrical structures such as the highly elaborate

Judaic (lunar-solar) calendar; but more notably at the time of these researches, I had also devised a pair of three-dimensional calendar models, which satisfy in other formal and conceptual respects, the arbitrary assignment of number-values to the conventionalized charting of time. These models, also incorporating the number-values 365 and 366, assume the schematic forms of six- and eight-sided dice.

Other abiding interests in my work at this time were historical, mythological, or nostalgic borrowings, especially those derived from the diagrams and symbolology of alchemical manuscripts from the Renaissance and Baroque periods. While maintaining a critical perspective upon these trappings, as such artifacts of Western mysticism are easily appropriated to a romantic, and ultimately obscurantist kind of speculation, seen in

New Age 'psychology' and worse; I adopted many of these iconographic motifs as 13 emblematic of a kind of totalizing World-view. In historical Alchemy, for example, a summary procedure of metallic transmutation is often codified by various figures which define an understanding of the material elements then believed to constitute the Universe.

Totalizing correspondences, such as those between the seven (then-conceived) planetary bodies, the seven (then-conceived) bodily organs, and seven (then-conceived) metallic elements, are directly referenced within this symbolic language, which speaks largely toward a will to understand the World in terms of logical properties.

My intentionality in using these motifs or related mythological figures was not one of New Age-type revivalism, but rather wanting to reference an emblematic artifact from a genealogical archeology of thought, in the sense that similar motifs often appear within the history of printed maps, as a mark of the authority of knowledge. The persistent authority of the printed map maintains its credibility as a generalized representation, as the kinds of correspondence it proposes—relative locations, recognizable coastline shapes, political boundaries—are reinforced by their consistency with other conventionalized versions of the same information. Reference to a more archaic proposition, such as that of Astrology or of figures personifying the prevailing

Mediterranean winds can also be understood as representative of conventionalized information, given a particular historical reading. In my diptych print, War Against

Entropy (2001) I incorporated a digitally altered image of the early 14th Century Zodiac from the Limbourg Brothers Tres Riches Hews de Due de Berry, placed within the inner perimeter of an annular tessellated map, based on the Peirce Quincuncial projection. 14

Fig. 5 Andrew McLaren, War Against Entropy, Digital prints on paper, 2001.

My continuing production of map-based art work as large-format printed output occupies an awkward space between gallery exhibition, in which it is summarily viewed as an image, in a pictorial reading, and the private space of the map-reader, attentive to detail in a more information-oriented engagement. The space of the gallery is not as conducive to this latter approach; the closer focus demanded by the more literary and minutely schematic construction in cartographic material is generally better served in forms more accessible to the space of the 'reader,' rather than that of the 'viewer.' As a lot of my output is in the form of self-published (and occasionally funded) book projects, there have been several instances where motifs in larger printed works and bookworks have been transposed from one format into another. The space between map as image, and map as information-document is variable in either case, and this variance may be 15 considered in the general terms of Semiotics (in this regard I refer to Peircian sign-theory later in this paper). The typologies of Semiotics, however, make no fine distinctions within the general and pervasive conditions of space and time, wherein an artwork exists on different terms, within an exhibition context, or in the necessarily regimented order of a book. A book, especially one in the form of an Atlas, is not necessarily meant to be read sequentially, from beginning to end, but the particular compilation of pages is bound to a particular contiguity. The pagination determines for the reader which elements are adjacent, facing, overleaf, or remotely placed; in this sense there is a particular milieu of differentiation in the materiality of books, distinct from the resolute linearity of alphabetic, narrative, and other sequential tropes within the order of writing and reading text. A book is given the formation of a beginning, middle and end, despite the most arbitrary possible arrangement of its contents. Scrolls, accordion books and folios of unbound pages differ in some ways from the spine-bound volume, but the situation of one side of a page is always in contraposition to its opposite surface overleaf (I make no exception here for the contrivance of the moebius strip); along with the virtual dualities implied by the propositional structures of language, there is also a material duality in the surfaces of the page.6 Thus, it is the form of the printed book that I next examine, with examples of my own and other artists' publications that refer to a paracartographic criticality.

I would characterize most of my early work in map-based art as tending to a play of opposite terms. A common development within propositional language is a tendency

6 In strictly digital media, this material contrariety does not apply, although there are other relations of contradistinction: inclusion and exclusion, sequentiality and non-sequentiality, conformity and non conformity (with codified protocols, such as URL addresses and security features), and in the final analysis, all binary signals that substantiate the complete extent of digital coding. 16 toward dialectic constructions. This kind of implied opposition is implicit in any logical statement: it is - is it not - it is not. For the classical formalist, every thesis implies an antithesis. These kinds of binary propositions exist in cartographic construction, and also in works by many artists using mapmaking strategies, including some of my own.

Richard Purdy: The Inversion of the World / L'Inversion du Monde

The Quebec-based poet and artist Richard Purdy, in his publication The Inversion of the World/ L'Inversion du Monde (1990), proposes a World in which the elevation and depth values of landmasses and oceans are reversed. The book is similar to that of an atlas, printed in an oversize format with foldout pages. The World inversion scenario, which proceeds from a dystopian account of cataclysmic flooding and submarine upheavals, details the changing geographic implications in place names, and speculates upon the political ramifications of migrating populations fleeing their now-submerged former lands to settle on newly emergent topographies. The maps are laid out in the typology of the general reference Atlas: World and Continental (formerly Oceanic) areas are specified, with formerly bathymetric details overlaid with the beige-brown hues denoting topographic features. The map projections used are not specified, although

Purdy's methodology in drafting these inverted maps appears to be based on existing bathymetric charts. The former landmass areas are overlaid with blue gouache, with rivers extending onshore between the newly defined bodies of water. Masking, fine layers of translucent medium, spattering and other paint techniques are employed to build up a sense of elevations, with borderlines drafted along the course of rivers and ridges in 17

Purdy's imaginary Continents. National territories and regions are given new names, which are superimposed in digital text over the map images.

Purdy's project relates in its broadest definition to the liminal differentiation between land and sea; as the familiar shapes of Global maps are defined by the coastal outlines, The Inversion of the World suggests an alternate relation to this liminality. The surfaces of land and sea are transposed, but it is an inversion of the surfaces themselves which must be imagined, with the subtending floor of the ocean now defining an exterior protrusion, rather than an interior displacement. Likewise the former elevations of the land must be reconfigured as the negative space (displacement) of the submarine floor, like the interiority of a die from which a coin is struck. The submersion and reversed orientation of the surface itself is not addressed, nor is the new Ocean floor mapped;

Purdy's primary concern is with the situation of new Geographic entities following the flipped stratification of the World's surface:

The transplantation of the human and animal population of the earth onto the sea beds produced many changes, like the re-orientation of east and west. Halifax, for example, is on the west coast of North Atlantica facing its east coast neighbour Galway on the Sea of Ire. New York and San Francisco are no longer part of the same country or continent, since New York is now in North Atlantica and San Francisco is on the east coast of Pacifica. A railway link between the new New York and Lisboa, both at 40' [sic] north latitude, is inevitable.7

The Inversion of the World fits well into the milieu of Speculative Fiction, also exemplified by Edgar Rice Burroughs's Lost World or Jules Verne's Voyage to the

Center of the Earth; as a document, however, it encompasses a broader, extra-narrative

World view. As an imaginary dissolution of the land, and a filling-in of the Lakes and

7 Purdy, Richard, The Inversion of the World, a Geo-Metaphorical Atlas, Toronto: Art Metropole, 1990, p. vi (introduction). 18

Oceans, it fulfills the premises of Alfred Jarry's 'Pataphysics, or the Science of

Imaginary Solutions. I propose for this reason, that Purdy's work can be considered an example of 'Patacartography.

Arkady Nasonov (The Cloud Commission): Antipodes

The Russian artist Arkady Nasonov, working in the collective The Cloud

Commission (with Tania Detkina, Dmitry Ligeros, Vladimir Mogilevsky and others), published a bilingual (English and Russian) book Antipodes in 2000, which compiles a series of narratives, maps, and other documentation in vignettes based on opposite points of the World. Anecdotal correspondence, historical events and mythological figments are recruited, in many such pairings, which are printed on opposite sides of the pages. (In my book The Atlas of Nowhere, there are also pairings of antipodal locations, although I chose to display these across the facing pages.) Nasonov's Antipodes is bound as a flipchart rather than as a conventional (laterally opening) volume, penultimately concluding as an unresolved correspondence with a museum curator at the Rijksakademie in Amsterdam, with written requests to examine fingerprints on paintings in the collection

(for which permission is not granted). The entire project is thus framed as an enquiry into an indexical mark of authenticity, within the institutional context of the public archive or museum. Nasonov's Livre d'Artiste finally documents an act of espionage, by enlarging the surreptitiously photographed fingerprints in minute detail, where aberrations among the ridges of their imprinted trace become Rorschach-test models for the "Habel theory of the beginning of the Universe."8 Even while concluding with this fabulously contrived

8 Nasonov, Arkady, Antipodes, Amsterdam: Sanatorium, 2000 {xmp&gmated), passim. I believe that Nasonov refers, albeit parodicaily, to the idea of Geophany (the origin of the World as expressed in 19 exemplar of the macro- and microcosmic, Antipodes maintains a dialectic approach to its scope of the real, even to the extent of contrasting the scientific study of Dactylographic

(fingerprint) patterns and mystical speculations of Universal origins.

Fig. 6 Andrew McLaren, excerpted images (facing pages) from The Atlas of Nowhere, 2004

The Atlas of Nowhere

The Atlas of Nowhere, which I developed over 2003-4, is also a fairly eclectic work, which defines its points of departure with maps centred on opposite points of the

World. Most of these are derived, like much of my cartographic output from that period, from AZED projections. A defining characteristic of the AZED projection is the relation of polarity and opposition between centre and perimeter. I have used this projection extensively to construct the animations Returning Full Circles on my website www.paracartography.com (2007) and in tandem with distortion and other filters in

Genesis) described by Norman Habel in Habel, Norman, and Wurst, Shirley, The Earth Story in Genesis, Sheffield: Sheffield Academic Press, 2001. Pp. 236. Adobe Photoshop to generate maps of the World that resemble human eyeballs (these also appear in the Atlas).

Paracartography: a semantic analysis

I also identify this investigation as ancillary to the quantitative study of

Cartography, as a deconstructive and discursive practice situated under a broader definition, as Paracartography. The use of 'Para-,' as a prefix, is conventionally understood as a modification for a noun or adjective, and may, in this instance, be considered in several senses. In the sense of being near, or beside, indeed as a. parallel to

Cartography, this application evokes the two superimposed lines in text-symbol for equality, '=' (if not necessarily that exact signification of equivalence). 'Para' may also imply a certain distance, in the sense of 'beyond' the normal, as 'paranormal' implies an otherworldly being9, which is especially germane to the virtuality of geocoding in digital

Cartography, like a "Ghost in the Machine." 'Para' can imply a falsity of sorts, as seen in the paranoiac, where an aberration of psychic affect is implied. Another sense of 'Para' is that of similarity, or resemblance, as a paraphrase might be drawn to resemble any definition of mapping that might be proposed. The accepted meaning for 'Para' may shift, as in the word paradigm, which conventionally referred to something as epistemologically exemplary (and which for Ferdinand de Saussure, referred to a class of linguistic elements with similarities), but became adopted as emblematic of entire World-

9 "Paracartography" is also used by Toronto Speculative Fiction author Robert Wilson in The Inner Inner Citv (from his compilation The Perseids and Other Stories, TOR, Toronto, 2000), as the improvised religion of a group of friends seeking to divine the presence of urban ghosts by cartographic location. To borrow a literary device in this case, I should propose to demonstrate the presence of several ghosts in the machine of Cartography, not least within its pedigree of objectifying the World as a summary of Properties. 21 views in themselves, proclaimed as "paradigm shifts" by Thomas Kuhn in 1969.10 'Para' can be parasitical, or paraprofessional, in the present work, given my use of existing models and software which are used in the professional practice of Cartography. In most senses that it is used, the prefix 'Para' implies a distinction, separation, or difference, from the principle, object, or normative agency of the word to which it is appended. In the context of my development as a visual artist, Barber's use of the word

"paracartographer" to describe my activities can be understood in the last sense described above, as an auxiliary or paraprofessional engagement with the methods of Cartography.

The Paracartographic strategy that I propose in the present work is an animated, pluralistic deconstruction of the global map projection, through which the totalizing, unitary representation of the World (as typically informed by the terms of the map's construction) is destabilized. This production could be described as a series of anti- location maps; although familiar spatial references within a complete global context remain legible. The database from which stills in the animation are located allows for interactive viewing: it is intended that the viewer(s) can navigate through different iterations of the pluralized World-image (although the apparatus for this interaction is still under development, as of 2008).

Kuhn, Thomas S. The Structure of Scientific Revolutions, 3rd Ed. Chicago and London: Univ. of Chicago Press, 1996. A Non-Unitary World-image: The Register of the Returning Earth

Fig. 7. tessellated Peirce Quincuncial projection

A pervasive World-image associated with traditional maps has assumed an iconic status in mass media and reinforces a false notion of the World as a stable, neatly encapsulated entity. All two-dimensional map designs privilege certain characteristics of form at the expense of others, in terms of shape, scale, area, or consistency of linear direction—as, for instance, the Mercator projection, which while well suited to charting transoceanic navigation, also exhibits progressively exaggerated distortion towards the poles. In seeking to resist the conventionally framed world-views implicit in typical global maps, my strategy is to work with a trans-marginalized plurality of re-presentation, using map projections which can be regularly tiled into a multiplicity of cartographic spaces. In my digital drawings based on the Lee Tetrahedric projection, the 'orientation' 23 of the projection shifts by geodic translation from an initial placement of the graticule (or grid of latitude and longitude) into other configurations where the grids are displaced around other parts of the world. The resulting maps tessellate in unique unfolding patterns, and engender a more nuanced and relativistic space. The results of my work using these kinds of map projection have, thus far, been in static form; I propose, with

Register of the Returning Earth, to create an installation using animated sequences that transform the maps themselves, via the reorientation of their projection.

The use of tessellating maps radically changes the roles of centrality and marginality in the global map projection. Unlike the animations Returning Full Circles, which are based directly on the AZED projection to create a generative sequence of centres of maps, the animations in Register of the Returning Earth make merging and separating places occur at the marginal limits of the modular design. Seen in a dynamic context, these singular points become something like input and output zones; relations of approach and departure are followed through, and a duality or doppelganger of hinterland and/or frontier is present at that instantiation.

Navigation within the static tessellation of the map can be continued indefinitely, as the repetition of tiled triangles or squares extends upon the infinite plane. The animations will also work their way through a sequence of reoriented versions of the map projection, thus affecting a kind of trans-navigation that engenders different unfoldings of the map's repetition, suggesting an additional dimensionality within its projected differentiations. As these developments in paracartographic space will only be apparent within a time-based medium, the implications of visual 'parallels' appearing simultaneously within a linearity of time are unavoidable. Although the prospect of interactive animation—in which the viewer determines the progressively navigated map- frames—goes some way toward breaking a necessarily linear timeframe within the presentation of the work, the limitations of choice would still remain defined by the closed system of the work as a whole. It will suffice at this stage of development to present the visual possibilities within the range of tessellated maps that are generated.

The image of a 'changing World' evokes the terms from Structural Anthropology, detailing synchronic and diachronic subjectivities with respect to the experience of time.

Although diachronism, by definition, assumes the recognition of change and development in time-consciousness, synchronism does not imply a static view of the World; as Roman

Jakobson suggests, asking somebody to describe the action on a movie screen will elicit a synchronic [play-by-play] response, but not a static description.11

The presentation of The Register of the Returning Earth, based as it is on tessellating map projections, does follow a necessarily geometric framework, articulated through the repetition of forms; there is some precedence for this in early 20th Century

Constructivist and Futurist Art. The poet Vladimir Majakovskij, strongly associated with these tendencies, considered the idea of an ideal future in which subjectivity transcends

11 Roman Jakobson, Dialogue on Time in Language and Literature (in interview with Krystyna Pomorska) from Verbal Art, Verbal Sign, Verbal Time, University of Minnesota Press, Minneapolis MN 1985, p. 12 25

the diachronic dimension, and all time is experienced in a singular apprehension,

suggesting a radical synchronistic consciousness.12

Fig. 8 sample frame from test animation (Lee Tetrahedric projection) May 2008

An Epistemology of Cartographic Representation

The minimal terms, by which Cartographic practice can be conceived, is as a graphic information system, which references aspects of the real in proposing a delimited representation with a symbolology established in a formation of measured data.

In a development with respect to the virtual and in the case of simulacra, a cartographic strategy may be applied as an interpretive model. In the sense that a cartographic model

[Many of] The Artists of the Russian avant-garde... (Majakovskij in particular) drew from the dialectics of time an absolute inference, one particularly characteristic of the avant-garde: they wanted to vanquish time, to overcome its immutable march. Like Kirillov in Dostoevskij's The Devils, Majakovskij believed that in the Utopian future time would "fade from consciousness" and cease to be experienced by men. Krystyna Pomorska cited in interview with Roman Jakobson, ibid., p.14 13 The word 'real,' in Charles Sanders Peirce's account, originates among scholastic philosophers in the 13" century, and was first used to mean "having properties;" this can be assigned to a tangible thing or experience (in which sense even a dream is a real experience, for the dreamer) which is known by its attributes. C.S. Peirce, A Neglected Argument, from Values in a Universe of Chance, Selected Writings of Charles S. Peirce, P. Wiener, ed. Doubleday, New York, 1958 p. 358 may be considered as pure abstraction within a (e.g. programming) language, an instance of virtuality or simulation may be directly (or incidentally) informed by its prescriptive or procedural norms. It would be a mistake, however, to argue that such schematic formalism bears a direct agency upon the constitution of the real, as advocates of

'intelligent design' would propose.

The authority of cartographic conventions can be traced through a historical genealogy of terms, by which the idea of mapping has been variably constituted, and through a semiotic reduction, to the normative means (in geometric and other codified language) by which these representational modalities operate in inscription and interpretation. A discursive elaboration of these two approaches in understanding the authority of maps must overlap considerably in attribution to 'principles' of meaning that have become conventionalized, and to a more nuanced, interpretive polyvocality. The intentionalities 'behind,' and perceptions 'before' these formal constructions, are in themselves, not idealistic abstractions, but must be answered in a phenomenological, as well as political, perspective. For the purposes of this paper, however, the conventionalized history of Cartography, and the semiotic/phenomenological models by which I propose to interpret the 'grounding' of Cartography in its operational milieus, will be addressed separately in that order.

Genealogy of the World-image: Archaic models of the extended Earth

Among the ancient Vedic figures of Earth is that of a hemispherical World supported on the backs of four elephants, standing on the hemispherical shell of a 27 gigantic tortoise floating on the surface of a Universal Sea.14 Aztec Cosmology and

Theology also refer to a World-view constructed by figurative elements, with the Sun god

(also an earthquake and thunder god) Quetzalcoatl supporting the firmament of the stars above the Earth. The Cosmology of ancient Egypt invokes a Creation myth in which the separation of the sky from the Earth is explained through Theogenic figures, with the Air god Shu forcing apart the starry goddess Nut from her husband, the Earth god Seb. These animalistic and anthropocentric World-views merit more extensive analysis elsewhere, but exemplify, for this paper, a predisposition to envision the totality of the World according to synthetic and symbolic models, constructed by elements abstracted from

Human experience. The Astronomical observation and record-keeping of these ancient civilizations recognized a systematic order in the celestial bodies, although this, too, would be defined in their terms as similarly anthropocentric figurations.

The more abstracted configurations, by which a progressively knowledge-based

World-image developed, were expressed using numbers and geometries that were based on the observations of the night sky. The Babylonians, for whom records survive documenting their use of a 360° circular measurement, were certain to have used that metric as an approximation for the number of days in the sidereal year. Besides calendrical purposes, the number 360 would also have been known for its consummate factorability, divisible in whole numbers from one to ten, with the exception of seven, a quantity reserved for the days of the week. The origin of Geometry—a notion which I will further examine in epistemological and phenomenological contexts—can not be

14 Kenton, Edna, The Book of Earths, Morrow, New York, 1928, pp 41 -42 28 accurately or precisely identified, according to the relics of History, and it is highly probable that the 'discovery' of some Geometric laws occurred in several independently remote archaic scenarios.

Euclidean Space: Early Geographers

Most Early Geographers, of whom historic records exist in the Western canon of

Mediterranean and Middle-Eastern literature, were in consensus that the World is of spherical form. The earliest well-documented didactic records of Geometry, as this relates to an understanding of Geodic space, are those of ancient Greece; it is speculative at best to consider any other epistemological origin for the practical application of Geometry, in terms of Geodetics and Cartography as they have developed historically. I will briefly outline a Historical overview of some Euclidean geometers with references to their articulation of the Earth as sphere: Pythagoras, Philolaus, Aristarchus, Eratosthenes,

Hipparchus, Strabo, and Ptolemy.

The first recorded postulation of the Earth's sphericity is ascribed to Pythagoras15 in the 6th Century BCE. Pythagoras' pupil Philolaus proposed that the spherical Earth also revolved around a "central fire," in diametric opposition to a twin planet, Antichthon, which was also in tandem with the more distant orbit of the Sun. This is perhaps the first mechanistic cosmological model of a 'parallel world.'16 In the 3rd Century BCE,

Aristarchus of Samos was known to have proposed a heliocentric model of the Universe, predating Copernicus (who gave him credit) by seventeen Centuries. The work in which

15 Brown, Lloyd A., The Story of Maps, Dover, New York, 1977, p.25 16 Kenton, pp. 173-176 Anstarchus proposed this is lost, but was referenced by his contemporary, Archimedes in his book, The Sand-reckoner}1 In that book Archimedes estimated the circumference of the Earth as 300,000 stadia, the equivalent of 30,000 miles (approx. 49,180 km). The earliest known measured calculation of the Earth's circumference, however, was that of

Eratosthenes in ca. 240 BCE. Taking measurements of the Sun's cast shadow at noon at two separate locations (Alexandria, Egypt, and the Southern outpost of Syene, on the same meridian of Longitude, separated by 500 miles (820 km)), Eratosthenes was able to calculate that distance as corresponding to one-fiftieth the arc of a circle, implying that the Earth (if a perfect sphere) is approximately 25,200 miles (41,311 km) in circumference, a figure very close to that of the actual Geoid. 18 However, his geodetic work, beyond this relatively successful instance, was a haphazard patchwork of astronomic observations relating to arbitrarily placed meridians and parallels. His contemporary Hipparchus, who wrote a pamphlet Against Eratosthenes, was the first to propose a systematic construction of lines which he named latitude and longitude. The exact placements of these were never truly established, according to Hipparchus' suggested method of measuring the longest and shortest days of the year, in correlation with astronomic observations; nevertheless, the conceptual model that he devised was constructed with far more precision than that of Eratosthenes. Hipparchus' compilation of trigonometric tables and extensive interpolation of Babylonian and Assyrian astronomic records also led to his calculation of the length of the solar equinox, with a margin of error between 9 and 14 seconds.

17 Brown, p.27 18 Brown, op.cit., p.29 30

The Geography of Strabo, first disseminated in approx. 20 CE, proposed an equirectangular cylindrical projection:

...if instead of the circles, i.e., the parallels and meridians with which we show the 'Climata,' the winds and other differences, and also the positions of the parts of the earth with reference both to each other and to the heavenly bodies— drawing parallel lines for the parallels, and perpendicular lines for the circles perpendicular to the parallels, for our imagination can easily transfer to the globular and spherical surface the figure or magnitude seen by the eye on a plane surface.19

Claudius Ptolemy's Planisphaerium, and Geographia, written in the middle of the 2nd

Century CE, document three Global map projection types which are still in use: the

Stereographic (translating the sphere into a circle by projecting perpendicular lines onto a plane); the Conic (projecting lines onto a cone subtending or variably intersecting the sphere); and a modified Spherical projection, combining the Cylindrical approach of

Strabo with a converging series of lines for the meridians, which anticipates the sort of compromised geometries which have been devised in their hundreds during more recent

Centuries.20

Typologies of maps in medieval Europe

The pervasive myth that the World was widely regarded as flat in Europe "until

Columbus" is a nineteenth century fable, although the maps of the medieval era made no particular reference to the Earth's curvature. A typology of medieval representations of

Geographic space consists of three distinct mapping practices: that of the Mappamundi

(or World Map, commonly referenced as "T-O" due to a typically circular format with a

19 Brown, op.cit., p. 55 20 Brown, op.cit., pp.58-80, passim 31

perpendicular configuration of Africa below Europe and Asia), Portolan Charts (used in

plotting bearings for navigation), and Cadastral (or regional) maps. The Mappasmundi

conventionalize a World centred on Jerusalem, and examples of these are even seen in a

very small, iconic scale. It is important to point out that these were not considered 'maps'

as the word might imply; "Mappa" is literally "napkin" and the connotation is more

accurately defined as a plan or schema. Portolan Charts were designed and interpreted by

traders and merchants, and are also very selective documents, outlining only what was

necessary to follow a known bearing, along an overland or marine route; the need for

accurate scales of distance, proportion and coastline detail, however, made these the most

geographically realistic maps of the middle ages. Cadastral maps are as much a pictorial

convention as one of cartography: they would present an oblique view of the landscape,

often portraying the details of buildings in a city.

The Ptolemaic revival in Renaissance Europe

After the 'rediscovery' of Ptolemy's The Geography in the early 15 Century a

more geometrically-based methodology was adopted.21 The text by Ptolemy (who as

noted above, was well aware of the Earth's spheroid form) was the first of the

rediscovered texts in which the terms of latitude and longitude was encountered. The

charted voyages of Columbus and Magellan in conjunction with newly revived designs of

map projection made more comprehensive visualizations of the Earth as a globe viable.

The methodology of map construction up to the first truly successful schematization of

21 The influence of Ptolemy's work, first translated into Latin in 1410 by Jacopo d'Angelo, is also apparent in the development of perspectival geometry by Brunelleschi and Alberti over the following three decades. Peta Mitchell, A Genealogy of Cartography. A Genealogy of Space, from Cartographic Strategies of Postmodernity, Routledge, New York, 2008, p.44 32 the known World in Mercator's projection followed a cross-reference of astronomical/calendrical, land-survey, and geomagnetic reckoning, in addition to the aggregation of already-recorded data-in-formation that was cribbed from pre-existing maps. Graticules and perspectival grids employed by Ortelius, Mercator, re-initiated the reformation of totalizing space. Renaissance Ptolemaic maps made obsolescent both the totalizing mappa;mundi and the non-uniform portolan chart conventions. The Mercator projection adopted the functionality of both these supplanted codifications, bringing a navigable equivalence in bearing (or consistency of linear direction) into the cylindrical model that had served as the totalizing World-view of The Geography.

The codification of Renaissance space into a formalized logic by Rene Descartes inherited the prescriptive linearity of Euclid, while making a rigid distinction between the res extensa of passive, empty space and matter, and the res cogitans of pure abstraction.

Motion within the res extensa of Cartesian space is an expression of linear values. The entire formal conception of Descartes, based on an ontological criterion of self-evidence, as a first principle, is a codification in rationalizing quantity and degree, to the ends of verification and the establishment of the evident. The transcendental subjectivity that establishes the absolute identity of self-reflection as cogitatum, extends to the identification and identity of the object.

Newton's cosmology, although engaging with curvilinear motion, retained the sense of space as an absolute dimensionality, with a first law of motion that expressly 33 describes inertia as a linear force. In contrast to both Descartes and Newton, Leibniz held that all extension is relative and localized, and not subject to an absolute formation. The independent contributions to the development of the calculus by the latter two can be attributed to different motives, as Newton proceeded from the basis of differentiation, and

Leibniz from instances of integration. >.

Baroque Visionaries and Later Speculations

Along with the rationalized World-image that emerged from the late Renaissance, speculations regarding unknown parts of the World were rampant, in belief that the northernmost latitudes must be surmounted by a significant region of land—hosting the colossal Lodestone of the North Magnetic Pole—as well, that a very large Southern landmass must necessarily exist, in order to balance the proliferation of newly discovered terrain in the Northern Hemisphere. During the Counter-Reformation and Baroque era there were several rather outlandish claims regarding the World's structure, among them the "Rygge Forme" as recounted by Robert Recorde (1556), and the Hollow Earth theories of Athansius Kircher (1664), Thomas Burnet (1681) and Edmund Halley (1692).

For the Welsh Mathematician Recorde, best known as the inventor of the symbol of equivalence, the equals sign '=':

[the World] has been, at one time, a "rygge forme,"—"a three-cornered forme," says Recorde's The Castle of Knowledge (1556), "like the rygge of an house where one syde lyeth flatte, and the other two leane a slope. And thys forme they judged better for twoo causes. Firste they thought that it was more steddy than a cube forme, because it hath a broader foote, and a lesser toppe; and secondly for that they thought it a more apte forme to walke on and more agreeable to the nature of the earthe, where sometimes there risyth highe hill, and sometimes again men may see greate vales descendyng.... Againe they thinke this Rygge forme meetest for the standing of the sea and for the running of rivers, for in the first forme [a cube] if the sea should rest on the outermost plaine, then wolde it over runne all that plaine, and so flow over all the earthe; where as in this seconde forme it mighter reste about the foote of the earthe, and yet the slope risyng wyll not permit it to over run all the earthe. And so for rivers if there is no slopenes (as in a cube there is none) then cannot the rivers runne well."22

Edmund Halley's proposal that the Earth consists of several concentric, hollow

spheres was grounded in Newton's incorrect calculation of the Earth's and the Moon's

respective masses, in one of his notebooks, from which Halley estimated the Earth's mass

to be approximately five-ninths of its correct value:

Now if the Moon be more solid than the Earth as 9 to 5, why may we not reasonably suppose the Moon.. .to be solid.. .and this Globe to consist of the same Materials, only four ninthes thereof to be Cavity, within and between the internal spheres, which I would render not improbable.

Earlier variations of the hollow or subterranean World had existed since antiquity, and

Halley, before his pronouncement in 1692 would have been aware of then recent

literature by the German Anansius Kircher (Mundus Subterraneus, 1664) and English

cleric Thomas Burnet {Sacred Theory of the Earth, 1691), both proposing the World as a hollow shell, with firey (Kirchner) or watery (Burnet) interiors. Kircher proposed that the

2Z Kenton, Edna, op.cit, pp 9-11 The Welsh Mathematician (1510-1558) Robert Recorde's lot in the 16th century was fraught with a personal and political rivalry which led to his early demise; Counter- Reformation politics, with the assumption of Mary I to the throne in 1553, were also in his disfavour. The vigorous persecution of heretics by the re-established Catholic authorities left Recorde in a position where the promotion of then-current Copernican ideas was extremely inadvisable. In The Castle of Knowledge he also writes: "Copernicus a man of great learning, of much experience, and of wonderful diligence in observation, hath renewed the opinion of Aristarchus Sainius, and affirmith that the earth not only moveth circularly about his own centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundred thousand miles: but because the understanding of that controversy dependeth upon profounder knowledge than in this Introduction may be uttered conveniently, I will let it pass till some other time." cited from http://www-history.mcs.st-and.ac.uk/Biographies/Recorde.html

23 Halley, Edmond, "An account of the change of the variation of the magnetical needle with an hypothesis of the structure of the internal parts of the Earth." Philosophical Transactions of the Royal Society xvi (1692): p.595 Cited in Griffen, Duane, What Curiosity in the Structure: The Hollow Earth in Science, manuscript prepared for the forthcoming book From Mercator Projection to Freudian Phantasm: The Myth of the Hollow Earth in Literature, Science and Culture, Hanjo Berressem and Uwe Schwagmeier, eds. 35 hollow Earth hosts a vast underground circulation of Oceanic water, draining into massive whirlpools at the North Pole, being heated in the Earth's interior, and emerging from the South Pole to replenish the Seas. Burnet's vision of the Earth, grounded in Neo-

Platonist idealism, was a kind of eggshell containing yolk-like aqueous matter in an interior space. Halley's model proposed that the interior hollow spheres of the Earth correspond in proportion to the Planets Venus, Mars and Mercury, with a 500 mile

(800km)-thick outer crust, an empty space for a further 500 miles, with the same thicknesses for successive layers, ultimately surrounding the solid innermost sphere,

2,000 miles (3200km) in diameter, corresponding to the size of Mercury. Despite the categorically erroneous basis of Halley's hypothesis, these measurements are very close to modern estimates for the thickness of the Earth's mantle (700 km) and the diameter of the inner core (2432 km). Halley's conception of the hollow Earth was widely ridiculed; however, his influence upon subsequent proponents of the "inner world" occasionally resurfaced over the following centuries. The American John Symmes was well-known for his promotion of the Hollow Earth in the early 19th Century, first published in 1818, citing Halley's idea as a supporting argument. Symmes' model of the interior World was different; in his view the Planet has broad openings at either Pole.

Production of the Scientific Document

The determination of longitude and approximation of the Earth as an oblate spheroid were established in the 18th century. Charles Harrison's timepieces from the 18th

Century24 enabled further refinements of Cartographic representation, having set the

Sobel. Dava, The Search for Longitude, New York: Penguin Books \995, passim. standard for consistent global measurement of longitude. With this development, the older practice of determining location by astronomical triangulation gradually fell into disuse. The terrestrial map, in tandem with the apparatus of measurement, thus assumed a greater autonomy from the cosmological model of pre-Enlightenment space. The standardization of longitude was complemented by the development of the metric system of measurement, which based the standard measurement of one metre on the distance between the Equatorial Latitude and the North Pole. A Cartesian global grid based on the measurement of time (longitude) and space (latitude) was now established, against which the res extensa of Descartes could be rationally ordered. Immanuel Kant categorized geography as a science, which describes simultaneous appearances in space, while typifying history as the study of immanence, of becoming in time. Kant found in

Geography a discipline ultimately capable of providing a complete physical, moral and political map, against which the temporality of history is referenced.25 With this characterization of the map as a document of qualitative and quantitative space, cartography assumes a literary as well as mathematical dimension, a repository of factual information, and a symbolic typology of political orders.

Empiricism and the Flat-Earth Theory

Among the alternate World-views promoted in the 19th century, few were more stubbornly promoted, in the face of all commonly held Scientific opinions, than the Flat

Earth theory of Samuel Birley Rowbotham, who under the pseudonym "Parallax," lectured extensively throughout the British Isles, promoting what he called Zetetic

Philosophy. The full title of his book, inscribed in the third edition of 1881 is:

25 Mitchell, Peta, Cartographic Strategies ofPostmodernity, New York: Routledge, 2007, pp. 52-53 37

Zetetic Astronomy. Earth Not a Globe. An Experimental Enquiry into the True Figure of the Earth, Proving it a Plane, Without Orbital or Axial Motion, and the Only Known Material World; Its True Position in the Universe, Comparatively Recent Formation, Present Chemical Condition, and Approaching Destruction by Fire, &c, &c, &c.26

Rowbotham's arguments for the Flat Earth, based on highly selective techniques for empirical measurement using theodolites, spirit levels and telescopes, propose that distantly observed lighthouses, bridges and other features would necessarily be several, to many hundreds of feet below the horizon, assuming that the Earth were spherical. In a laboriously constructed piece of reverse-engineered logic, adapting the measurement of data to the form of the experiment, distant observations made on a canal barge are correlated with incremental measurements along the intervening distance, in a "forward" process of measuring.27 Recruiting the "law of perspective" to explain the disappearance of the hull of a sailing ship on the horizon, while its mast is still visible28, and further claiming that circumnavigation of the World is no less viable on a circular plane than it is on a sphere, Rowbotham establishes a model of the Earth as a flat, circular non-moving surface, similar in form to an Azimuthal Equidistant projection map (fig. 9).

26 "Parallax" (Samuel Birley Rowbotham), Earth Not a Globe, London: self-published, 1881 Reprinted by Kessinger Publishing, Whitefish, MT, 2003, title page

27 Ibid. pp. 9-21 28 Ibid, pp. 201-201-212 2 2929 Ibid,pp.224-Ibid, pp.224-2302 . Rowbotham argues that the magnetic pole establishes North and South as absolute directions on a plane, and East and West as relative directions, at right angles ro North and South. 38

yy — Wf

Fig. 9 "Parallax" (Samuel Birley Rowbotham),*Map of the Flat Earth, 1881

The Copernican model of the Solar System is refuted by experiments with the trajectories of cannon balls to 'deduce' the lack of rotational or orbital motion;30 triangulations are measured to establish "that all the visible luminaries in the firmament are contained within a vertical distance of 1000 statute miles."31 Other convoluted arguments, rivaling the complexity of Ptolemaic epicycles, are put forth to explain the declination of the

30 Ibid, pp. 69-73 31 Ibid. p. 104 39

Sun's seasonal variability within its daily circuit overhead,32 and to suggest the agency of atmospheric refraction as an intermediary cause of day and night.33 Rowbotham's vision of the World, suited to his further elaboration of a creationist and mystical agenda, unwittingly assumes the form of a map, partially illuminated by a revolving desk lamp.

Theories of the Tetrahedral Earth

In a paper read at the Royal Geographical Society on January 23, 1899, Dr. John

Walter Gregory expounded his theory that the Earth, which he recognized as approximating an oblate spheroid, would over many future millions of years gradually develop into the shape of a tetrahedron.34 Gregory, who was a renowned geologist and geographer, had explored many parts of the World including the Rift Valley in Africa and the Rocky Mountains in the USA, and based his theory on the placement and directional bias of the "main geographical lines" defined by mountains and undersea ridges, and at the broadest schematic approximation of their form, the roughly triangular shape of the major Oceans. He also cites the distribution of antipodal land and sea areas between the

North and South hemispheres: when two world maps are superimposed (as I had in the

Littoral prints in 1995, but with one inverted and turned longitudinally 180° over the other) to demonstrate the symmetrical balance of land and sea, Gregory suggests that underlying this disposition of higher- and lower-lying areas (relative to the averaged spheroid of the Earth's form) is a tendency toward a contraction of the Earth's crust in some areas, and an upheaval in others. The tetrahedral Earth theory was first proposed in

32Ibid. pp.105-110 33 Ibid. pp. 111-123 34 Gregory, J.W., The Plan of the Earth and its Causes, from The Geographical Journal, No. 3, March, 1899, Vol. XIII, pp. 225-251 1875 by Lowthian Green who had proposed that the planet was an oblate spheroid with slight deformations tending toward a tetrahedral form. Gregory suggests even further, that the earth is contracting into an even more tetrahedral shape:

When the earth solidified it would (neglecting the influence of rotation) have contracted into a spherical shape. It would have tended to acquire this form because the sphere is the body which incloses [sic] the greatest volume for a given surface. But as the earth contracts it tends to acquire a shape in which there is a greater surface in proportion to its bulk. Now, among regular geometrical figures with approximately equal axes the tetrahedron is that which contains the smallest volume for a given surface. Hence every hard-shelled body which is diminishing in size, owing to internal contraction, is constantly tending to become tetrahedral in form. .. .that it is considered probable by some geodists is shown by the following quotation from E.D. Preston [a contemporaneous American geodist]: "Nothing is more in accordance with the action of physical laws than that the earth is contracting in approximately a tetrahedral form. Given a collapsing homogeneous spherical envelope, it will assume that regular shape which most readily disposes of the excess of its surface dimensions, or, in other words, the shape that most easily relieves the tangential strains; for, while the sphere is of all geometrical bodies the one with the minimum surface for a given capacity, the tetrahedron gives a maximum surface for the same condition. Experiments on iron tubes, on gas bubbles, rising in the water, and on rubber balloons all tend to bear out the assumption that a homogeneous sphere tends to contract into a tetrahedron."36

The Positivist World-View and the Space of Data-in-Formation

It would be facile, but not entirely untrue, to suggest that the shape of the world as seen in the 21st Century now conforms variably to the shape of a computer monitor.

Performative readings in contemporary interactive media, that characterize the use of digital cartography (at the current refinement of Google Earth, and GPS applications), can be reduced as phenomenological episteme, analogous to the map-readings of earlier centuries. The situation of the reader, whether in actual space-time navigation or virtual

Ibid. pp. 236-237 Ibid. pp. 239-240 41 reckoning, is motivated by the map's speculative extension of the imagination. A genealogy of the digitized representation of the Earth can be traced through mid- nineteenth-century positivism in the development of the global map as schematic of a totality of accumulative, quantified and systematized data. The procedure of navigation in the digital source maps of GPS-based software is ultimately Cartesian, based on a grid with set values. Locations are thus appended to a polar-axial system, not from among the discrete terms of their own relational constructions. Google Earth and other animated , interactive maps have two basic levels of engagement: panning and zooming. Changing the orientation of the map is also possible: the 'compass-direction' toggle in Google

Earth, for example, can be turned like a steering wheel. Using another interactive control, oblique perspectives can be approximated, in which the general vertical perspective of the locally-framed view of the Earth is tilted into an Orthographic projection. Location, direction, and (virtual) altitude are defined by the frame of the viewer's computer screen or Graphic User Interface (GUI).

The illusion of place and space experienced through Google Earth and similar interfaces (e.g. those employed in flight simulation software) is as effective as the range of their resolution—which varies according to available (declassified) Satellite imaging on the one hand, and also according to the viewer's expectation bias, with regards to the display media. These factors become especially apparent when zooming in on urban areas, where the orthographic angle of the source photography remains fixed, while the oblique panning and shifting of the viewers' perspective is changed. At these more localized levels, the image reverts in some ways to the appearance of the medieval Cadastral map, in which a pictorial schematic (the particular orientation of street-level architecture) is integrated into the overall structure of a diagram (the surrounding aerial landscape). As the juxtaposition of image-within-map breaks down, the trappings of digital sign-language become exposed, and pixels on the viewers' screen reach the limit of their interpolated renderings.

In examining the space of digital Cartography, it is constructive to consider it within the broader context of systems of signification, or Semiotics. I am substantially indebted to the work of Charles Sanders Peirce, both for his innovations in Cartography, and the development of Semiotic theory; I will further elaborate upon this latter area of his research below.

Peircian terms of conventional reference

C.S. Peirce worked for the United States Coast and Geodetic Survey for over thirty years, and enjoyed a reputation as one of the World's leading authorities on

Geodetics during that time (1861-1891). During that time he devised a global map design

(discussed later in this paper) based on the transformation of a hemisphere into a square, which is usually referred to as the Peirce Quincuncial projection. Among the formal qualities of this map design is its ability to be tessellated regularly on an infinite plane; I shall return later in this paper to a more elaborate analysis of this projection. Peirce, who is recognized as the first to define Pragmatism and considered the founder of Semiotics, 43 wrote extensively as a Philosopher, but there is scant direct reference in any of this work to Cartography.37

Peirce's essay Logic as Semiotic: the Theory of Signs was compiled over thirteen years (1890-1903) and his formulation of Semiotic models underwent several revisions during that time. The three triple-modalities of signs outlined in the essay: Qualisign,

Sinsign, and Legisign, Icon, Index and Symbol, Rheme, Dicent, and Argument, correspond in kind to signs in themselves, connections of signs with objects, and constructions of signs for interpretants (this latter term corresponding to the reformulated sign, as understood by the observer). Additionally they are considered as categories of a triadic phenomenology which can be described as firstness (Quality), secondness (Fact), and thirdness (Law).

Modality: I. Signs in 2. Connections 3. Constructions of Themselves of Signs with and by Signs for Category: Objects Interpretants a. First, Quality a. Qualisign a. Icon a. Rheme b. Second, Fact b. Sinsign b. Index b. Dicent c. Third, Law c. Legisign c. Symbol c. Argument

As given signs are active within different modalities, and phenomenological categories,

Peirce outlined possible relations within these milieus, identifying ten configurations.

Daniel Maher has examined these ten formulations in detail, and considered their

37 Maher, Daniel H. Mapping in the Life and Thought of Charles Sanders Peirce, a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science (Cartography), Madison: University of Wisconsin-Madison, 1993 p.1-2 Peirce himself (having recently retired from his position with the US Coastal Survey) may have deliberately avoided such an analysis of Geodetic and Cartographic representation, as he sought to demonstrate his erudition in other academic fields and did not wish to be associated so strongly with his former vocation (although his desire for an academic appointment was sadly never fulfilled). 38 Peirce, Charles Sanders, Logic as Semiotic: the Theory of Signs, from Philosophical Writings (Justus Buchler, ed) New York: Dover 1955 p.98 44

potential application to Cartography. I have extended his suggestions, which mostly

concern the typology of representations in printed maps, into a broader analysis of the

premises of Totalizing Representation, which is a defining feature of my own work in

Paracartography. Peirce himself was fairly provisional about the particular cases in which

his ten categories could be exemplified, and had a greater interest in exploring the

mutability of signification. It is important to note that as a Pragmaticist, he was more

concerned with examining the implications of ideas, rather than establishing them as

idealistic principles. There are however ten types of Peircian sign; the classification of

these is outlined below (Peirce's shorter terms for the signs are in bold):

Modality Name of the Sign Example by Peirce (via Maher) 1. 2. 3. [modified by myself] 1. a a a Rhematic Iconic Oualisign A feeling [intuition] of 'red' 2. baa Rhematic Iconic Sinsign An individual diagram [actual] 3. b b a Rhematic Indexical Sinsign A spontaneous cry [in and of itself] 4. b b b Dicent Indexical Sinsign A weathervane [its measured trace] 5. c a a Rhematic Iconic Legisign A [design of a] diagram [virtual] 6. c b a Rhematic Indexical Legisign A demonstrative pronoun ['this'] 7. ebb Dicent Indexical Legisign A street cry [e.g. a sales pitch] 8. c c a Rhematic Symbol Legisign A common noun [nominal word] 9. c c b Dicent Symbol Legisign A proposition ["If..."]

10. c c c Argument Symbol Legisign A syllogism ["...therefore..."]

The ten configurations outlined above break down into one Qualisign (a general

phenomenological category), three Sinsigns (pertaining to particular (Single) instances of

empirical sense-data), and six Legisigns (synthetic and conventionalized language-

constructs). There are three instances of Iconic relation (pertaining to generic aspects of a

sign that are directly reduced into a quality of its representation); four Indexical

(references to known relational specifics); and three Symbolic (formal idiom relating to the object of the sign) orders in Peirce's schematic. Considering the ways in which the 45 interpretant is engaged with a sign, there are six Rhematic typologies (understanding a general form of representation-in-itself, the 'given'), three Dicent (recognizing the particularity of a representation) and one typology of Argument (judgments based on given premises, whether or not these are accurate) among the ten forms of signification.

Iconic signification is necessarily interpreted as a Rheme; Indexes are either

Rhematic or Dicent; Symbols may be seen in Rhematic-, Dicent- or Argument-based interpretations. A Qualisign corresponds to an instance of Henri Bergson's difference-in- kind; strictly speaking there is a wholly passive (Rhematic) phenomenological relation between the interpretant and these intuitive perceptions, which are necessarily denoted as generic qualities rather than specific things. An elemental and characteristic (Iconic) kind of signification is engendered, corresponding to the type of phenomenon or class of object in question. As such, the classification of Qualisigns stands as a unique and unmodified category in Peirce's Semiotics. ;

Sinsigns are more specific to a given instance of signification, with regard to an object's existential status as a thing-in-itself, beyond the generic qualities that typify a qualisign. In the phenomenological analysis Peirce considered the apprehension of a

Sinsign to be rhematic in most instances (as a 'given' entity). A Rhematic Iconic Sinsign is read according to its own terms of reference (as with the example of an individual diagram), unlike a Rhematic Indexical Sinsign, where the primary characteristic is its immediate attribution to another agency (given the example of "a spontaneous cry"). The special case of a Dicent Indexical Sinsign refers to a secondary characteristic of representation (Peirce refers to the indication of a weathervane); such a relation is seen in 46

negative-based photography, where the image is generated from the exposure of ambient,

reflective and incidental light onto a sensitized medium. Applications such as satellite

altimetry, radar and sonar, radio astronomy, and subatomic experiments using particle

acceleration in various ways furnish data which is interpolated at a secondary order; the

information derived from such equipment can be considered as Dicent Indexical Sinsigns.

This latter kind of signification is therefore of particular relevance to contemporary

Geodetics and Cartographic imaging.

Legisigns are of a third order of signification, of which in Peirce's schematics

there are three Rhematic types, two Dicent types, and one possible configuration as an

Argument. Thus, among all the classifications of Peircian signs, that of the Legisign is the

most apodictically complicated, from the phenomenological perspective, as these concern

conventions in language that bear a conditional, rather than necessarily existential

relation between the sign, its object and the interpretant. This conditionality is expressed

in Peirce's summary of the Semiotic project:

A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign. That sign which it creates I call the interpretant of the first sign.39

The sense in which a Legisign stands to somebody is predicated by the formal codes of the interpretant; these Peirce, borrowing terms from the Scholastic philosopher

Duns Scotus, references as pure grammar, logic proper and pure rhetoric. Pure grammar concerns the thing-in-itself, identified as such, for the purpose of establishing a correspondence of meaning. Logic proper is "the formal science of the conditions of truth

Ibid., p. 99 47 of representations40;" this may be considered as an active indexicality within language, or in more discrete and non-cognitive relations among objects and their indexical tracings

(e.g. the footprints of a wild animal). Pure rhetoric is the field in which the laws of generative meanings are deployed; this is the means by which a chain of signifiers within language can be used to construct a synthetic narrative or conditional argument. Thus, a

Legisign is rendered legible.

A Rhematic Iconic Legisign is exemplified by Peirce as "a diagram, apart from its factual individuality," by which he refers to the codification or virtuality of such a drawing or plan, by which it may be reproduced. In a contemporary example this could refer to the constructions of binary code that are used to format HTML, or a myriad of other types of digital documents, when these are considered in their own terms as a programming language.

A Rhematic Indexical Legisign is a more dynamic inscription which bears the second-order implications of language, for which Peirce provides the example of the demonstrative pronoun (e.g. 'this' or 'that'). Again borrowing a term from Duns Scotus, a secondness, or indexical reference is drawn to the emergent character of individuation, or haecceitas ('thisness')41, a term also adopted by Deleuze and Guattari in their characterization of discrete events in 'Smooth space.' Daniel Maher proposes an example of the Rhematic Indexical Legisign in Cartography, as the set of conventions determining figure-ground relations: for example, the general sense in which darker elements on a

40 Ibid, p.99 41 Almeder, Robert, Peirce's Epistemological Realism, from The Philosophy of Charles S. Peirce, A Critical Introduction Oxford: Basil Blackwell, 1980 p.123 48 map will be interpreted as features, and lighter areas, as the subtending area of land or a surrounding body of water.42

The class of Dicent Indexical Legisigns refers to signifiers within a known set of possibilities; Peirce describes this as

...any general type or law, however established, which requires each instance of it to be really affected by its Object in such a manner as to furnish definite information concerning that Object. It must involve an Iconic Legisign to signify the information and a Rhematic Indexical Legisign to denote the subject of that information. Each replica of it will be a Dicent Sinsign of a peculiar kind.43

Peirce's example of "a street cry" suggests that a distinction can be drawn in meanings, between the calls of vendors selling hot dogs, in distinction from somebody yelling

"Taxi!" to hail a cab. The intentionality of these expressions is considered as their

(Dicent) indexical relation, rather than their (Rhematic) incidental status as phenomena, which are exemplified above, with the Rhematic Indexical Sinsign (as "a spontaneous cry"). In Cartography, a Dicent Indexical Legisign is apparent in weather maps generated from Satellite observations, where white areas indicate cloud cover. However, it is also possible to depict snow coverage under clear sky conditions with a very similar appearance. The conventional depiction of cloud coverage in weather maps on television is not based directly on photo-imaging, but rather coded in different shades of grey to indicate the intensity of weather systems. This mimics the appearance of more or less dense cloud coverage as seen from below, effectively superimposing the shaded appearance of dense cloud cover over their outwardly exposed (and brightly illuminated) side. As a Dicent Indexical Legisign, this convention operates as a secondary

Maher, Daniel H., op.cit., 51-52 Peirce, op.cit, p. 116 49 representation, such that indexical references are made in a familiar Earthbound, rather than orbital perspective, from which the relative intensity of cloud patterns would not be as immediately apparent.

The class of Rhematic Symbol Legisign is exemplified by Peirce, using grammatical language, as "a common noun." In Cartographic terms the Rhematic Symbol

Legisign can be seen in the historical example of World maps that used the colour Pink to indicate countries in the (former) British Empire. Another Rhematic Symbolology is seen in relief maps, where the elevations of land are conventionally codified by a series of topographic shades, progressing from greens, yellows and browns, into purple and finally white areas at the highest altitudes. With both of these examples, the use of colour is particular to their respective milieu of Cartographic conventionality. Otherwise, in a post- colonial political map, the colour pink may be assigned quite arbitrarily according to the placement of other colours that identify adjacent countries; in the same map, the colour white might signify the icecaps of Greenland and Antarctica, regardless of altitude data.

In these cases, other rules of interpretation apply, in which the differentiation of colour- coding is assigned, as another Rhematic Symbolology altogether. Other Rhematic

Symbol conventions in Cartography, such as blue lines representing rivers, or directional lines with arrow points signifying the directions of Ocean currents, are more consistently employed.

The Dicent Symbol Legisign is characterized by Peirce as propositional:

...a sign connected with its object by an association of general ideas, and acting like a Rhematic Symbol, except that its intended interpretant represents the Dicent Symbol as being, in respect to what it signifies, really affected by its Object, so that the existence or law which it calls to mind must be actually connected with the indicated Object.44

As a prepositional sign, the Dicent Symbol conflates the discrete factuality of its Object within a relational field of agency (which could, for instance, be defined among the four causalities of Aristotle: material, formal, efficient and final); thus, when the World is described as "the globe," a proposal is made that it is formally defined by spherical geometry. A statement of'fact' (although in this case not entirely accurate) is engendered according to the terms of 'how,' 'why,' and (by) 'what' (other factors) it is so defined.

Such a proposition might be seen in the statement "Calgary, Alberta, Canada

(Latitude: 51° 4' 60" N, Longitude: 114° 4' 60" W)" which establishes a relationship of containment (Calgary, within Alberta, within Canada), and of orientation, relative to the standard means of geographic location (51° 4' 60" North of the Equator, and 114° 4' 60"

West of the Greenwich Meridian). This Dicent Symbol (in fact a composite Dicent

Symbol) proposes agencies by which means the location of Calgary is defined. These agencies are (considered within their own terms) indexical, for which reason the interpretant is of a secondary or Dicent order. The factual placement of Calgary according to those indexical relations (containment, location-coordinates) is, however,

Symbolic, the indexicality of which is not absolute. A placement of Calgary prior to the incorporation of Alberta as a Province in 1905 would read "Calgary, Northwest

Territories, Canada." In a remote prehistoric epoch (given what Paleogeographic information is available, according to our knowledge of continental drift and necessarily altered reference points for the locations of the North and South Poles), the position of

Peirce, op. cit., p. 117 51 what is now Calgary could certainly not be described as 51° 4' 60" North of the Equator, and 114° 4' 60" West of (what would have then been) the Greenwich Meridian.

The conventions that determine relative positions of (selective) features on a map are thus a Dicent Symbolology. When Peirce refers in his definition of this class of sign, to the indicated Object, his construction of that representation is as a logical extension of indexical relations, which are adopted as a Symbolic language. Maps based on different forms of map projection thus fulfill the propositional definition of Dicent Symbol. The

Symbol, in this case, is not a singular thing (in the sense that a Replica of a Rhematic

Symbol is a Rhematic Iconic Sinsign), but an aggregation of assertions, tending toward an existential hypothesis. Further developments of the Symbolic order, when the propositional facts-in-formation of Dicent Symbols are employed in the Rhetorical assemblages of statistical modeling (such as may be seen in animated Weather Forecast maps on television), are discussed in the final classification, the Argument Symbolic

Legisign.

Argument Symbolic Legisigns are characterized by Peirce as syllogistic constructions, predicating upon combined or differentiated propositions (Dicent

Symbols), conflated into synthetically derived formations which are held to be true:

.. .a sign whose interpretant represents its object as being an ulterior sign through a law, namely, the law that the passage from all such premises to such conclusions tends to the truth. Manifestly, then, its object must be general; that is, the Argument must be a Symbol. As a Symbol it must, further, be a Legisign. Its Replica is a Dicent Sinsign.45

Peirce, op.cit, ppl 17-118 52

The particular validity of an Argument notwithstanding, it may be judged according to hermeneutic (within its stated terms of reference) or contingent (implications among related factors, not directly expressed within the premises) considerations. If it is argued:

1. The direction "North" terminates at the North Pole; 2. A consistent direction of travel is maintained, crossing over the North Pole;

3. Therefore the direction of travel has been Northward;

.. .there is a limited truth-value within this syllogism, although that limitation is clearly expressed within the first and second premises. Expressly: that up to the point where the direction "North" terminates (1) and up to the point where the direction of travel crosses the North Pole (2), the argument is correct in surmising that a Northerly course has been maintained. Beyond that point, quite literally in this case, "everything goes South."

However, there is an extended circumstance (at the risk of seeming to construct a circular argument) when all the implications of this syllogism are considered:

4. If the consistent direction of travel is maintained, the South Pole is crossed;

5. Therefore the direction of travel is again, Northward.

While the terms in this argument are clearly shaped by their relational or absolute values,

I include it to demonstrate the non-exclusivity of its premises; thus, evincing a way in which terms within its predicates may invalidate a given conclusion, which conclusion may itself be re-validated by extending an initial premise (direction of travel) over a contingent circumstance (the bipolar opposition of directional termini). The structure of this transformed argument is categorically transferable to mathematical terms, although the formal equivalence of validation, of truth in such a model is that of equivalence, and non-equivalences, over a surface that is more accurately described as a Geoid. 53

It is equivalence that is paradigmatic of truth in Mathematics, expressed in the symbol '=' and an indispensible term in the formation of the most elementary differentiations, aggregations, and solutions in the metrics of numbers. For these, as well, are Arguments in the Peircian schema. Equivalence is both normative and constitutive within the rhetoric of Arithmetic, as a procedural closure, synthesis, and verification in the order of the constructed equation. The representative sign '=' is in these various senses, to the Interpretant, a Dicent Symbol Legisign which may be placed in differing syntactical positions in the rhetoric of maths-based codification, which comprise the

Argument of equivalence. Robert Recorde, the inventor of the notation of the equal sign:

'=' which first appears in his seminal Algebra textbook, The Whetstone ofWitte, published in 1557 explained his use of this graphic device of two parallel line segments:

Nowbeit, for easie alteration of equations I will propounde a few examples, bicause the extraction of their rootes, maie the more aptly bee wroughte. And to avoide the tediouse repetition of these woordes : is equalle to : I will sette as I doe often in woorke use, apaire of paralleles, or Gemowe lines of one lengthe [OED: gemew = twin, double or parallel], thus: ====, bicause noe .2. thynges can be more equalle.46

The very elementary dualism within this graphic sign stands as self-icon, one line in mimesis of the other; but the Equality that it expresses is not a Qualisign, despite the homonymy of those terms. A Qualisign, despite standing to somebody for something in some respect or capacity, is not an Equivalence for, but a nuance of the Interpretant, a first-order phenomenological perception which goes so far as "What You See Is What

You Get" (WYSIWYG). Equivalence is not a general predicate or absolute (static) quality in the field of duration, but the mark of an instance, in which sense it is a

46 Recorde, Robert, The Whetstone ofWitte, London, John Kyngston, 1557 cited at http://www.brown.edU/Facilities/University_Library/exhibits/math/nofr.html#rob.htmlThis textbook of Algebraic procedure was the firstt o be written in the English language. haecceity, an act of positing "here, it is true" at an intersection of the virtual and actual thus defined. In that sense, as a demonstrative pronoun, it is exemplary of Peirce's definition of a Rhematic Indexical Legisign.

The symbol '=' can be considered iconic, insofar as it expresses a static self- equivalence, as a mark. In that virtual sense, it is a Rhematic Iconic Legisign, but in the actual application of asserting equivalence, it is a Rhematic Symbolic Legisign. The concept of Equivalence, then, is as an Alchemical Universal Solvent to Peirce's schematics, intrinsic to the formation of his relational typology of signs, and potentially apparent in most of them. The triadic relations of Signs, Objects and Interpretants, and the categorical epitomes of Quality, Fact and Law, are all implicated in the formation of instances of Equivalence, but all independently fail to summarize the Semiotic entirety of what Equivalence is, or can potentially be.

Returning to the Mathematical milieu to which the mark '=' is native, it is constructive to reference the Incompleteness Theory (1931) of Kurt Godel:

That is, it can be proved rigorously that in every consistent formal system that contains a certain amount of fmitary number theory there exist undecidable arithmetic propositions and that, moreover, the consistency of any such system cannot be proved in the system.47

This logical point-of-no return is often cited in support of the general non-resolution of irreconcilable paradoxes in other studies, by appealing to the authority of this paradigm

47 This particular citation was added by Godel to the 1931 notes on August 28, 1963, a propos of Alan Turing's work in computational algorithms, and is introduced thus: "In consequence of later advances, in particular of the fact that due to A. M. Turing's work a precise and unquestionably adequate definition of the general notion of the formal system can now be given, a completely general version... is now possible" G8del, Kurt, On Formerly Undecidable Propositions of Principia mathematica and Related Systems 1. (1931) from Collected Works: Publications 1929-1936, Oxford: Oxford University Press, 1986, p. 195 55

of pure logic as a model of formally, rigorously determined justification for

inconsistency. In suggesting its similarity to the incompleteness of Peircian Semiotics, I

propose that the terms of Sign, Object, Interpretant, Quality, Fact and Law along with

their derivatives cannot adequately describe the entirety of its systematic implications. It

is irresolvable, for example that these relations could exist in a non-cognitive context.

The logical development of Peirce's Epistemological Realism as Semiotics does indeed

succumb to the limitations of pure Logic.

The Map as signifier of the Absolute (Jorge Luis Borges)

Jorge Luis Borges' fable of the 'absolute map' in his fable "On Exactitude in

Science" was first published in 1946. It has become the consummate figuration of the <

map as metaphor within post-modernist criticism, with interpretations by Umberto Eco,

Jean Baudrillard and Jean-Francois Lyotard. Borges' story speculates upon an Empire

which in which the pursuit of categorized knowledge developed to such an obsessive

degree, that the exhaustive summary of all its epistemological resources required a map

corresponding in exact scale, representing the terrain point-for-point, which extended

over the entire domain. Over subsequent generations the maintenance of this project was

neglected, eventually leading to the map's disintegration. For Eco, the subtext of Borges' parable is that of a necessary failure, as the totalizing Cartographic scheme is undermined

by the "paradox of the Normal Map;" this is subject to three corollaries. To wit: "every

1:1 map always reproduces the territory unfaithfully;" further, "at the moment the map is realized, the Empire becomes unreproducible;" and in the final case, "every 1:1 map of the Empire decrees the end of an Empire as such and therefore is the map of a territory 56 that is not an Empire. Baudrillard uses this parable to introduce his book Simulations, typecasting the story itself as an archeological relic; a prototype which has engendered the real, as a precession of simulacra, which expressed in terms of the real, remains as rotting vestiges:

If we were able to take as the finest allegory of simulation the Borges tale where the cartographers of the Empire drew up a map so detailed that it ends up exactly covering the territory (but where the decline of the Empire sees this map become frayed and finally ruined, a few shreds still discernable in the deserts—the metaphysical beauty of this ruined abstraction, bearing witness to an imperial pride and rotting like a carcass, returning to the substance of the soil, rather as an aging double ends up being confused with the real thing)—then this fable has come full circle for us, and now has nothing but the discrete charm of second order simulacra.49

For Baudrillard, the Lyotard contends that Borges' map is problematic because its maintenance becomes an absolute preoccupation of everyone in the Empire, leading to the breakdown of everything else.50

Deleuzo-Guattarian conceptions of Space

In A Thousand Plateaus, Deleuze and Guattari articulate nomadic space according to two tendencies: "striated space" typified by "sedentary thought," and governed by the principles of analogy, judgment, representation, reproduction, binary distinctions and identity51; these constructions are set against the backdrop of "smooth space," in the

Eco, Umberto, On the Impossibility of Drawing a Map of the Empire on a Scale of 1 to 1. in How to Travel with a Salmon and Other Essays (trans. William Weaver), New York: Harcourt Brace, 1994, pp93- 94 49 Baudrillard, Jean, Simulations (trans. Paul Foss, Paul Patton and Philip Beitchman) New York: Semiotext(e), 1983, p.l 50 Lyotard, Jean-Francois, The Post-Modern Condition: a Report on Knowledge (trans: Geoff Bennington and Brian Massumi) Minneapolis: University of Minnesota Press, 1983 p. 55 51 Deleuze, Gilles, and Guattari, Felix, A Thousand Plateaus, (trans. Brian Massumi) Minneapolis: University of Minnesota Press, 1987 pp. 361-380 virtual plane, "filled by events and haecceities, far more than by formed and perceived

things."52 Smooth space is expressed in normative rather than constitutive terms: while

populated by the (Bergsonian) qualitative multiplicities which enter "line-blocks of

becoming," necessarily changing in formation with other such multiplicities, these

delineations and genealogies do not constitute smooth space itself, which is a field of

differentiation, of nomadic virtuality.

These tendencies were previously designated by Deleuze, in Difference and

Repetition, with the expressions logos and nomos, as these relate respectively to the

division of space (from agrarian to urban constructions), and the nomadic distribution of

presence within open space, without property, enclosure or measure.53 It is in this sense

that we can reference the territorialization and deterritorialization of the map, which persists in the models of digitized Cartography. The categorical qualification of

differences-in-kind which populate the databases of ARCGIS, for example, are given a

hierarchical precedence, and divided among rhetorical syllogistic relations, when

functions modeling the quantification of data are formulated. Boolean-type functions of

intersection, subtraction and union cut across the categories, engendering new models; this scenario, however, is far from the smooth space envisaged by Deleuze and Guattari.

Even the space of 'interactivity' is delimited among a range of quantified and quantifiable operations; the implications of 'user-defined' actions within this milieu remain wholly within the system of Data-in-Formation (DIF).

52 Ibid, p. 479 53 Deleuze, Gilles, Difference and Repetition (trans. Paul Patton), New York: Columbia University Press, 1994 p. 36 58

Haecceity, as proposed by Deleuze and Guattari in A Thousand Plateaus, is a

marker of "this-ness" which also corresponds to Jean-Luc Nancy's singularity: a multiple

assemblage, defined, in their writing as "an intersection of latitude and longitude" which

is "inscribed on the plane of consistency," while defying the self-constitution of the

subject in Cartesian space.

Synthetic Constructions using Tessellating Map Projections

The British mathematician H.A. Schwarz (1843-1921) was the first to

successfully formulate the conformal projection of the interior of a circle into the interior

of other geometric forms, first publishing his results in 186954. He wrote a formula to

construct a tetrahedral map, along with conformal projections of the Globe onto the other

four Platonic solids, in 1872, based on Jacobian elliptic functions. These formulae were

first employed in actual map projections by Charles Sanders Peirce in 1877, who mapped

a hemisphere onto a square, via the stereographic projection (which maps the sphere onto

two circles). Peirce's square map consists of a double-sided square, with one side

diagonally cut into four triangles, which are then placed around the matching perimeter of the intact side. Having five singular points defining the four perimeter triangles, Peirce referred to this as the Quincuncial projection, although other configurations of the double-sided square projection are possible, that do not employ his configuration.

Lee, L.P., Conformal Projections Based on Elliptical Functions, Cartographica, Monograph no. 16, Toronto, York University Press, 1976, p.l The central areas of the square forms in the Peirce Quincuncial projection have a

more extensive degree of conformal fidelity, but this map exhibits even greater

distortions at the four mid-sections of the outer edges. Peirce's map is projected from the

sphere onto a square, double-sided plane, which is cut across the corners on one side and

* unfolded' into a larger square. Peirce referred to it as Quincuncial due to the five

corners, or points, defining the four flaps of the back side which become the perimeter

regions of the complete Global map. This projection, which is arguably of a more

primitive geometric construction than that of any of the solids, shares with the tetrahedral

projections the ability to be tiled into a continuous pattern in a two dimensional plane.

The liminal spaces of this and other tessellating map projections are variably conformal,

exhibiting a progressive attenuation of shape-distortion, with increasing proximity to their

singular points. Due to its characteristic tessellation, it is also referred in Jacques Bertin's

Semiology of Graphics, as Peirce's periodic projection.55 Other versions of the Square

projection, that are congruous with the Peirce Quincuncial model (and which are also

derived directly from the Stereographic projection), were devised by Emile Guyou in

1887 (in transverse aspect, with North and South Poles placed at the mid-points of the upper and lower margins) and Oscar Adams in 1925 (with the Poles placed at opposite corners of the square, rotated 45 °).

The tessellation of the tetrahedral projection is most directly expressed in a triangular pattern, although it is possible to rearrange the margins, changing the disposition of the map in such a way that the same contents are repeated in rectangular

53 Bertin, Jacques, Semiology of Graphics (trans. William F. Berg), Madison: University of Wisconsin Press, 1983, p.288 units. In common with all tessellating map projections, the adjacency of recursive margins project a 180° directional inversion upon their adjacent iterations, corresponding to the sum total of triangular angles. Tetrahedral map projections exist in Gnomonic and

Conformal configurations. Gnomonic construction is achieved through subdivision of the four spherical triangles of the spherical tetrahedron, into a triangular grid (this can be achieved through regular subdivision of edges into parallel subdivisions, creating smaller equilateral triangles); this gnomonic (or directional) lattice is directly applied to a two- dimensional triangular grid, to interpolate the anamorphic disposition of the map. My own early experiments with this form of map projection (1987-8) used a 12" globe with curtain wire, threaded eyelets, and threads wrapped across the six approximated tetrahedral edges. While very crude, this exercise, hand-drawn, demonstrated the marked distortion that is necessarily exacerbated toward the tetrahedral vertices. The reduction of angular conformity from a spherical triangle at the vertex, describing 120° of surface, into a flat triangle (where the same surface is described within a 60° angle) is severe, although the subdivided triangles toward the middle of the tetrahedral faces translate with a far greater degree of fidelity.

The New Zealand-based Cartographer Laurence Lee developed a more conformal version of the Tetrahedral projection in 1965; this is also based partly on the

Stereographic projection. The degree of shape-distortion towards the positions of the tetrahedral vertices (that are defined upon the sphere) is ameliorated by a progressive increase in relative scale for areas plotted towards those points. This projection produces

56 Lee, op. cit; the derivation of his formula for the Stereographic projection of spherical triangles subtending the form of a tetrahedron is outlined on pp. 27-29; his more detailed description of the Lee Conformal Tetrahedric projection is elaborated through pp. 50-59. 61 far more consistently conformal shapes of the familiar features of terrestrial Geography than the Gnomonic Tetrahedral maps I (and others since H.A. Schwarz in the 19

Century) had been using previously. I readily adopted the form of Lee's projection, hand- compiling and drafting digital variations in CorelDraw® based on visual reckonings between concentric grids placed on AZED maps (separate maps up to the circumference of the spherical triangles that would define the tetrahedron in different orientations), producing four of these 'handmade' digital maps (with graticules of latitude and longitude, rivers and coastlines) in 2002-3, and another seven in 2006-7. Several variations (along with additional anamorphic transformations) exist for these, mostly designed for printed output, as vector images. I am enormously indebted to the ingenuity of Lee, and to the programmers at Flaming Pear Software, who have produced the program I use to make Lee Tetrahedric, and Peirce Quincuncial map projections, at a scale of production that now takes a few seconds (for rasterized output), as opposed to many days (using guesswork and vectors).

Using Discrete Global Grids as Locational networks

The production of closely spaced orientations of maps, for interactive animations that navigate through successively parsed images of the tessellation, has to be programmed in a consistent distribution. The conventional (latitude/longitude-based) representation of Geographic data in databases such as WGS1984 is based on the

Universal Transverse Mercator (UTM) grid, against which a given location is referenced, with coordinate values appended using decimal Easting and Northing values within that quadrant. Locations in Polar Regions (above 84° North or below 80° South) are assigned values within corresponding Universal Polar Stereographic coordinate grids. While this

codification works very well for conventional map-reading purposes, the implicit

hierarchy of the Cartesian grid produces a progressive incongruity toward the North and

South, in which the real-world scale of longitude decreases markedly toward the poles.

Configured as such, GIS programming privileges the rectilinear output format of the

conventional map, over the dimensionality of distance and direction on the World's

surface (although these can be calculated by interpolation). Thus, the conventional

systems of global positioning based on a polar grid are not the most effective way to

determine an even distribution of locations. In fact, the gnomonic construction of

medieval portolan charts (which is more specific to the factors of location and local

congruity) would be more appropriate for this; in order to address all possible

configurations of navigation among maps, a similar, non-hierarchal approach in map

projection must be adopted.

The best solution for this is found in developments of spherical icosahedron

lattices, models developed by Buckminster Fuller and others, known in contemporary

Cartography as Geodesic Discrete Global Grids, or Geodesic DGGs. Icosahedrons, ;

having the smallest faces (in proportion to the whole structure) of all the regular

polyhedra, are the best basis for generating these variably tiling lattices in different

formations: triangular hierarchies, diamond hierarchies, and hexagonally-based

aggregations. The hierarchies within these grids are localized rather than generally polarized; there is however, a systemic inconsistency around the vertices of the

57 Keith C. Clarke, Locational Geocodes, from Analytical and Computer Cartography (second edition) Prentice Hall, Englewood Cliffs, New Jersey, 1995, pp.62-65 63 icosahedral matrix, where five-fold symmetries locally occur, restricted to the lattice cells immediately adjacent to those singular points. The principal developers of the grids that I found heuristically online were Computer Scientist Kevin Sahr from the Southern Oregon

University, Denis White, a Geographer working for the EPA in Oregon, and Prof. A. Jon

CO Kimerling, from the Geography Department at Oregon State University .

For the purpose of navigating among evenly distributed and regularly oriented maps, the strategies used by Sahr, White and Kimerling may be adapted to the inverse geospatial terms: the positioning of vertices. Having defined a series of points with congruencies and degrees of adjacency, among successive developments of DGGs, the best models for populating the database for the animation, Register of the Returning

Earth, are seen in the triangular subdivision of the icosahedral geode. In the fifth-fold resolution of the isometric triangular division of the geode there are 10242 vertices, spaced approximately 178 km apart at the scale of the Earth. In negotiating an isometric mesh, the linear distance to adjacent points is always consistent: the tessellation maintains a uniform but permutable form as a plane of passage, which may be reconfigured in approximation to any direction. The extension of this location matrix into a model of tessellating map (which is itself extensible without limit) opens up possible new relational mapping strategies in time based models, with divergent inscriptions: for instance, different statistical models could coexist in pluralistic schemata, current and historical timeframes could be displayed in adjacent 'worlds,' and various narrative elements could have separate 'worlds' as their contextual location.

58 Sahr, Kevin, White, Denis, and Kimmerling, A. Jon, Geodesic Discrete Global Grid Systems, from Cartography and Geographic Information Sceince, Vol. 30, No. 2,2003, pp. 121-134 64

Conceptual and Practical Frameworks for an Animation

Compiling the maps used in the animations of The Register of the Returning Earth

began with two directives: designing a series of map-orientations based on equal global

distribution (i.e. all maps being centered at equal distances from those adjacent to them),

and plotting maps centered on the locations prescribed by this series.

The computer-based model used for the location matrix was programmed by

Doug Phillips at the University of Calgary IT department, based on a 10,242-point

discrete global grid. This geodesic grid, based on triangulating the faces of a spherical

icosahedron, was broken into five panels (each comprising four triangular faces of the

twenty-sided platonic solid); each of these five panels is subdivided into a 33 x 65 point

lattice (defining values 0-32 and 0 - 64) from which 2,145 map locations are

determined. The points defined by all five panels thus totals to 10,725, which,

discounting overlapping points at the panel edges and corners, amount to the 10,242

points of the discrete global grid. Each point (at the origin of its AZED map projection) is

given an address according to panel number (1-5) and location coordinates within the

panel (i = 0 - 32; j = 0 - 64); thus they are designated as a series with file names from

1_00_00 to 5_32_64 (these particular points are ascribed to the North and South polar

locations). A simple graphic transformation of the five grid panels from the isometric

shape of four adjacent triangles, into a rectangle, results in an easily interpreted presentation (reproduced overleaf). 65

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Generating the digital source maps for the animations is possible using a variety of cartographic imaging programs. After experimenting with ARC GIS software in the U of C Geography Department, I determined some of the factors by which the eventual maps were made (specifically, the colour values for depth and elevation) but unfortunately scripting the automated output of a series of maps was not an option in the open access labs there. I was able, however, to generate maps, using the AZED projection, with topographic and bathymetric detail to the specifications I would

eventually use. The colour values were compiled with the ETOP05 dataset, imported into

the lab's copies of ARC GIS; this generates pixel values to a maximum resolution of

geographic detail of 5 arc minutes, or one-twelfth of a degree. This dataset is some twenty years out of date (although its substantial elements remain accurate), as far better resolution is viable with current computing speeds-the more recent ETOP02 dataset is

detailed to 2 arc seconds, or one-eighteen hundredth of a degree-but using a simplified dataset speeds up rendering time considerably, while also being more suitable for the

smaller scale of maps which can be effectively compiled into a projected animation.

After I determined that using ARC GIS to produce thousands of maps would require an enormous effort in manual data entry, which would certainly hazard an unacceptably high error rate (typographic errors, incorrectly entered values and mistakenly overwritten file names among these), I again contacted Doug Phillips, who suggested using a freeware program, Generic Mapping Tools (GMT), which could be scripted to produce AZED maps, using the ETOP05 dataset with the colours I specified.

This UNIX-based software is widely used in graphic and web applications to make vector-based and rasterized maps for illustrative purposes. 10,725 jpegs were generated on the U of C IT servers, with colour values only, at an output size of 1134 x 1134 pixels.

Although GMT software is also able to generate additional details such as coastlines, rivers, and national and regional boundaries, an appropriate level of detail-to-scale was unfortunately not possible using the AZED map projection; the rivers in particular are prone to a known bug in the program with this projection, especially in cases where the lines describing their course are situated near the terminal circle of the map, which can 68

create falsely closed shapes around the perimeter. Also, the coastline detail in GMT is set

according to parameters that are more suited to localized or regional mapping than global

map projections; with a lower level of detail appropriate to the resolution of a global map

at the scale of a medium-sized jpeg many significant features-coastlines of islands

including most of the Canadian Arctic and Indonesia (among many others)-are altogether

missing, while at a higher level of detail including all the major island coastlines, the

convolutions of many of these features coalesce at the 1134 x 1134px resolution, often

resulting in blotchy clusters of lines.

At this point I had reached an impasse; in order to make map-images with a reasonable level of graphic definition, linear detail is critical to maintaining legible shape- recognition, in more or less distorted areas of the final map projection. I found a solution in returning to an older Visual Basic program I had used previously (notably in The Atlas of Nowhere), a compilation by a Swedish Ham-Radio expert, Roger Hebdin, called Great

Circle Maps (GCM). This Windows95-era software uses the same WGS84 database as

GMT, but with more control over the detail as applied to the entirety of the AZED map.

After converting all the data supplied by Doug Phillips for locations based on the 10,242- point grid into an EXCEL document, I was able to copy-and-paste latitude and longitude values for each into GCM, and save the generated map (consisting of coastlines, boundaries, rivers and lakes) as bitmaps with three-part location addresses corresponding to the jpegs generated from GMT. The bitmaps were also proportioned to match the world-image size of the previously rendered jpegs. This work over two weeks was not without errors in data entry and file-saving (the expediency of partially overwriting 69

selected pre-existing file names in the 'save as' dialogue box of GMT led to a few

misnamed maps), but these were evident from reviewing the files in the Windows Picture

and Fax Viewer, and were readily corrected. One particular logistic problem was the size

of the files; uncompressed bitmaps at this scale (1361 x 1361px, to be trimmed into 1134

x 1134px maps edge-to-edge) are just over 7 megabytes apiece, with over 10,000 of these representing a sizeable amount of disk storage.

The compilation of jpegs and bitmaps into a single image represented another minor hurdle, as batching options in Adobe Photoshop do not (in the current CS3 release)

include the capacity to merge two different files as such. To this end I again drew upon the expertise of Doug Phillips, who wrote another script, using the freeware program

Image Magick, with which the bitmaps were superimposed as a darkening layer over the coloured GMT jpegs, and the resulting images saved as a new jpeg document. Although this script was most effective for compiling a number of the files, there were a number of cases (in fact 512) where it failed to recognize the relevant bitmaps and jpegs; in those instances non-automated compilations in Photoshop had to be created. This did cause some complications down the line as Photoshop scripting (for the final image output) for the UNIX (Image Magick) and Windows (Photoshop) compilations would transform differently when tiling the images. These cases were isolated and scripted independently to overcome this irregularity.

After compiling the relief / depth colours and linear elements, the series of AZED maps could be batch-processed using the (Flaming Pear Software) Flexify2 plug-in for 70

Photoshop. This filter allows for a sizeable variety of transformations in images based on the geometries of map projections. The more limited selection of input projections (21) includes Polar (AZED), and among the 116 output projections are the Peirce Quincuncial and Lee Tetrahedric (with an additional rectangular variant of the latter) as used in creating the tessellating maps of Register of the Returning Earth. Using Flexify on both

MAC and PC versions of Photoshop, the 10,242 maps were transformed into differently tessellating images based on each of these map projections, while retaining the location- address of the original file.

The first and simplest tessellations to produce were based on the Peirce

Quincuncial projection; the square maps are tiled 2.666 times horizontally and twice vertically, to make a 4x3 ratio frame as used in the SVGA format of 1024 x 768px native to most of the projectors at my disposal. This arrangement exhibits the characteristic tiling of the Quincuncial projection, as it is disposed on all four sides of each map, but the repetition of the global map 5.333 times per frame becomes more of a pattern than is appropriate for the format, referencing the rectilinear framing device of the image while overwhelming the particularity of each World map with the regular reduplication. This effect is only exacerbated by the display multiple projections of the image; for this reason it was decided to tile 1.333 maps per frame, extending from the right side of the square

Quincuncial design. When this image is projected by two adjacent SVGA-format projectors, with the left projector adjusted to cast an inverted image, a simple tiling of

2.666 World maps is effectively set up. Peirce's design works almost flawlessly in the

Flexify plug-in, although massive pixilated artifacts generated from the peripheral areas 71 of the original (AZED) map are apparent (which is to be expected from working with this resolution of source image).

Complete tessellations based on the Lee Tetrahedric projection are better suited to the HD digital video format with a 16x9 ratio frame; with four repetitions of the triangular map and a minor vertical adjustment (reducing to 97.36%), this arrangement fits very well in a 1280 x 720px image. When Lee Tetrahedric maps are made using

Flexify, a strongly diagonal aspect of symmetries is established. There is also an attenuation of pixel values toward the apexes of the triangle, particularly along the edges; thus another kind of patterned artifact is present in their tessellations. This roughly stellated or burst-like shape of lightened pixels is intrinsic to the filter's output in every instance of the 10,242 maps; it is retained, and positioned in the center of the tessellated images. This central illumination is used in the installation as a device to spotlight either of two objects mounted on the wall: an eight-ball from a pool table, and a black, one-inch binder clip, which holds an empty invitation-sized envelope (overleaf). 72

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Figs 15,16: eight-ball and binder clip with envelope, in projections of tessellated Lee Tetrahedric maps 73

Technical Aspects of Output

The entire range of these files could be animated as a simple slide show presentation at this point. The range of motion exhibited in these sequences is in regular runs of 64 images (corresponding to the third-order numbering of files, e.g. 13201,

1_32_02... 1_32_64) which refer to nothing more than the nominal construction of the

DGG, while also creating systemic interruptions in the continuity of the apparent motion.

It was decided that this presentation would not be suitable, as the progressive adjacency of each successive map (relative to each of their origins) was a more important quality than the nominally numerical order of their location-addresses. In order to make an effective presentation of the complete range of tessellating maps, the simplest strategy involves a progressive orbital sequence from one Polar position to the other. With the assistance of Mathematics Masters student Jeff Haroutunian, who compiled a Visual

Basic script for renaming the files from 00001.jpg through 10242.jpg, the final animations were compiled, and ready to import into QuickTime. I decided on a frame rate of 12 fps; at this rate the entire cycle of maps is played in 14 minutes 11 seconds.

At the time the final animations were compiled, there were two post-production issues to be addressed: the ability for the digital videos to loop, and the format suited to the output device that would be employed for differing animations and projectors. DVD media was ruled unsuitable due to the MPEG-2 codec that is used in standard (NTSC)

DVD output, which reduces and re-samples the image size to a 720 x 480px resolution.

That would represent a reduction to 43.9% of an SVGA image (or, 37.5% of an HD 74 image (720p at 1280 x 720px)), which is clearly unacceptable, representing a significant degradation of Cartographic detail from already downscaled jpegs.

Due to the variable linear detailing that would deteriorate rapidly under any appreciable degree of down-sampling, it was determined that a computer or similar device would be preferable, as the full screen resolution is directly generated. An AMD- based Lenovo PC with Windows Vista, along with an ASUS EEE PC running Windows

XP, was recruited, to output 1024 x 768px animations of the Peirce Quincuncial projection. For either of these devices, it was necessary to export wmv files native to

Windows Media Player. The option for looping the digital video is not difficult to select in either Windows XP or Vista versions of Media Player.

Another solution was the use of the Apple TV, which can output true HD (720p) mpegs, suitable for the 1280 x 720px animation of the Lee Tetrahedric projection. This device is a versatile media drive, but it required a somewhat convoluted nesting of the embedded mpeg4 file to make it possible for the ATV to play looping tracks. QuickTime movies can be saved with the 'loop' option enabled under the view menu; while this option can be saved in the exported mpeg4, the Apple TV does not have a preference or settings option to enable auto-repeat on movies. The way around this is found using the native Apple software for presentations, Keynote, into which the mpeg can be imported as an image in a slide presentation, with a further option to loop the images engaged. 75

Using Keynote's native ability to export to QuickTime, a codified loop is thus made legible to the ATV, and the mpeg4 animation is played seamlessly.

A total of five projectors are used in the exhibition: three later model NEC

GT1150 units, outputting 1280 x 768px Windows media files at 3000 lumens illumination, and two recently produced Optoma 1691HD projectors (1280 x 720px;

2500 lumens). Two of the NEC projectors are positioned alongside one another on shelves separated by 2.5 meters, and linked to emulate the same output from a Lenovo

PC. Their projections are registered immediately beside one another, with the left frame inverted; this effectively tiles the continuity of map-images between them. The third NEC projector is mounted on a restored antique camera-stand, and directed at the wall adjacent to the other projections, with the images abutting at the corner. This third projector is run independently with an EEE PC playing the same Windows media file (wmv) as the other two, without being synced. The real-time discontinuity at the corner between this projection and the others is in contrast to the split-screen between the matching pair; it is fair to characterize this juxtaposition of three projected images as displaying registered and mis-registered frames of the animation, with reference to the "Register" of the works title.

Physical Elements in the Installation

The current resolution of the work as presented at the Nickle Arts Museum incorporates two areas of projections, whose space is interrupted by a dismantled and suspended library globe. The globe, a 32" (812 mm) Replogle "Diplomat" model dating from approximately 1970, consists of a mahogany base, with a brass meridian and 76 interior light fixture. The base is suspended behind the rest of the globe, laterally positioned three feet below the ceiling bars. The equatorial ledge of the bases' top faces the globe which is placed four meters away, suspended in an inverted position (with the

North Pole pointing down) by the meridian. The light fixture inside is mounted with a 14 watt energy saver bulb in its incandescent fitting.

Fig 17: 32" Replogle "Diplomat" library globe with brass meridian and light fixture, ca. 1970

Two meters from the other side of the globe, a circular (101 cm diameter) plate of glass is suspended, situated two meters from the single mid-room digital projector which is placed on a reconstructed camera stand. This arrangement of globe and projector stand bears an object-based relation of instrumentality, alluding to a pre-existing model of representation, with particular reference to the era of Charles Sanders Peirce.

Fig 18: Restored antique camera stand (tripod) adapted as projector support

The circular glass and camera stand, like the globe, are appropriated objects; here detourned into a relation that approximates a conceptual scheme of the Stereographic projection, from which Charles S. Peirce's Quincuncial map projection (which is employed in the animation projected from the camera stand) was partially derived. The construction of the Stereographic projection, as can be recalled, derives from the inscription of the hemisphere inside a circle; Peirce's Quincuncial projection represents the development of a two-sided Stereographic projection into a two-sided square, which is again deconstructed into a single square. As appropriated objects, both globe and camera (projector) stand exhibit a detourned instrumentality. Both are a kind of foundational apparatus. When the base of the globe is suspended sideways it adopts the disposition of projection rather than support; the camera stand supports, in another sense, another kind of projection, rather than serving in its functional design as a camera tripod.

In tandem with the animated maps—which are themselves maps of maps rather than first- order representations—the presentation of supporting objects in the current59 installation of Register of the Returning Earth has adopted a shift in their functionalities.

A Reversion to a Strategy of Display

The practical resolution of my work as displayed at the Museum is in some respects an admission of the failure of representation: having adopted the language of

Geography, a discipline that occupies an ambiguous space between Art and Science, whose central conceit is the ability to categorically represent 'everything,' I have found that it has not been possible for me to live up to that ambition. For instance, the design of my location-grid, from which the origins of the maps in each frame of the animations are plotted, was conceived as an open navigation system, for interactive animations in which

(author's note) It is my intention that this thesis exhibition should be the prototype for further developments: gallery-based, publication-based, and in web and other interactive media. 79

the viewer could incrementally view adjacent maps; in effect, being able to accommodate

all possible routes of navigation among the different tessellations of maps. However, the project as it currently stands represents a display strategy for running through the range of maps that I have generated; indeed, I have reverted to a quasi-polar order of precedence among the maps, as the animation proceeds from the North Pole, moving along the diagonal lines defined by the five triangulated panels (these correspond directly to lines of latitude), gradually shifting to more Southerly levels before terminating at the South

Pole. As the most effective means of running through 10,242 maps, it is fair to call this prescribed order a register, as the title of this work identifies it. By happy accident, an actual register also appears in the space of the projection, at the far end of the room. This heating vent immediately at the foot of the mis-registered Peirce Quincuncial animation could be emblematic of another, archaic mapping convention: that of the Southerly zephyrs that appear in many Renaissance-era maps, as winged cherubs, blowing hot air.

Fig 19: Registered and mis-registered Peirce Quincuncial maps (note register at right) 80

A More "Down-to-Earth" Reading

Although the defining purport of this work addresses the idea of World-view, as framed in maps, in a very abstract sense, there are other readings and implications that relate to the cultural and historical dimensions of the maps as they might be 'literally' interpreted, as representative of the World we live or have lived in. In common with the

Globe that hangs above, off the Museum's ceiling grid, the maps in the animations appear somewhat out of date. The political boundaries are those of the Cold War era, with the

USSR, Yugoslavia and Czechoslovakia still intact as Nation-States. Although the reason for this is that the database for these graphic elements, from the Great Circle Maps software, provided the best overall detail-to-scale solution aesthetically, it is also true that this back-dated political landscape still persists in our consciousness of recent (twentieth century) history. As such, the figure of the "returning" Earth may also include the vestiges of the recent past, which continues to inform our conception of the present.

Fig 20: Detail of two adjacent Peirce Quincuncial maps (registered) 81

Another 'literalist' interpretation, which is more parodic, is engendered by the

multiplicity of World maps in these images. Reflective of a culture of over-consumption

and dwindling natural resources, this post-dystopian vision summons a World-view

which can accommodate our endless greed for more material and more political real

estate, by providing more Worlds for us to exist in. This skewed view of 'reality' may not

exist in our common-sense view of the World, but it does seem to have taken hold of our

desire for limitless uncontrolled growth as a species. Unlike the return of the recent past

evoked by the resurrection of old political boundaries, this multiplicity suggests an

eternal return of a phenomenological present, a scenario in which a limitless World can be manufactured in our collective imaginations.

These (propositional) interpretations relate strongly to a sense of temporality as well as the figuration of Geographic space; it could be argued, for instance that the historicist interpretation of my use of dated political boundaries represents a diachronic

World-view and the model of limitless multiplicity stands as an example of synchronistic thinking. These arguments, however, are limited to a static interpretation of the images; as they exist in animated form, in Register of the Returning Earth, a broader field of trans-Historic and pluralistic temporality is played out. The radical separation of place- ness (haecceity) into a relational space where it can exist in more than one instance can only be adequately expressed in a dynamic context, where these relations are able to be generated: separate elements are able to merge, and singularities to separate into diverse presences. In a field of multiple representations, the point of location for a given site is no longer specific, or exclusive; according to the degree of proximity to the singular 82 point(s) of the maps tessellation, the site of locality may be expressed as an anti-location: generic, regenerative and transitive. Locations are encountered and extended into a shifting, triangulated continuity by the configuration of the map, rather than being situated in a static geometry by the triangulation of fixed coordinates. Translation, displacement and relativity are activated, in lieu of location, containment and fixation.

The singular points in the Lee Tetrahedric and Peirce Quincuncial Projections engender a congruent (if reflexive) multiplicity when these configurations of the Global map are tessellated. This may be compared to the being of singularity proposed by Jean-

Luc Nancy in place of the notion of individuality. In this scheme, a person in communal existence is identified as a convergence of relative differentiations, rather than as an absolute essence of individuality. Singularity is beholden to exteriority and embraces finitude, unlike the 'indivisibility' of an absolute unity proposed by the ontological principle of individuality. While it is of course absurd to propose a 'multiple Worlds' scenario in describing the actual planet which we inhabit, such a model may certainly be applied to the plurality and proliferation of existing World-views. What is certainly the greatest ever repository of World-views, the World Wide Web, clearly owes its name to a

Cartographic perspective, based on horizontally-formatted global maps. Proposed maps of the Internet often assume a world-like shape, as a spherical form with numerous branching structures, not unlike the bearing lines on a portolan chart. This sort of structure identifies the domain addresses and server connections accurately enough, but in a very static form. A more dynamic, event-based model (or more importantly, series of models) for mapping multiple discrete 'navigations' on the WWW might be well-served 83 by the use of tessellating geometries that allow for relations among such events to be charted using pluralistic perspectives.

These models cannot stand as an 'absolute representation,' any more than the full- scale map in Jorge Luis Borges parable. With the possibility of multitudinous iterations of the map, in which different markings can be registered, and further, with the possibility of altering the relative space of the map itself in a (not necessarily linear) animation, the project of Paracartography, in creating such synthetic models, can express a new spatiotemporal narrative, in an interactive milieu that can accommodate a collaborative inclusion of additional (digital) contents. For the purpose of the present exhibition of

Register of the Returning Earth, I have decided that the most appropriate inclusion, or inclusions, for the animations that have a space clearly defined for such purposes (in the central singular points of the Lee Tetrahedric animations), are an empty envelope

(attached with a 1" black binder clip) and an eight-ball, which also serve as the inconclusive, and conclusive details of this thesis. 84

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