A calculative cosmography: Geodesy and absolute space

Abstract

Visual signifiers of absolute space such as grids, points, and straight lines are often identified with absolute space as a concept, to the extent that critiques of one are taken to apply to the other. This article argues that this is a misidentification that forecloses attention to meaningful dimensions of the coordinate grid while muddling the concept of absolute space. Attending to the geodetic science that gives rise to these visual signifiers shows that the space they are used to construct is entirely relational, and that the mythless rationalism with which they and absolute space are commonly associated can be productively questioned through attention to geodesy’s performative and cosmological implications. This raises the question of how we might better understand absolute space. The suggested answer is a cosmological claim that can be pursued and pictured but never realized. Absolute space is absolute as a sovereign can be: neither empirically nor visually, but as a motivating idea that presents itself as an explanation.

Introduction

Theories of space are statements about cosmology. A claim about what space is is necessarily a claim about what the world is like, and about how things might be placed in such a world. Much of the time, human geographers concern ourselves with consequences of such claims further downstream: the spatial assumptions involved in social or economic valuation and oppression, modes of relation, assignments of responsibility, and so forth (e.g. Kabachnik, 2012; Katz and Smith, 1993; Lefebvre, 1991; Santos, 2021). While these concerns also bear on what the world is like, the specifically cosmological stakes of theories of space typically come to the forefront only in philosophical debates.

While attending to the societal consequences of such ideas is essential, at times the nature of a spatial theory’s cosmological stakes is taken for granted or obscured. This is particularly evident regarding the concept of absolute space. While absolute space is widely critiqued on political grounds as a practice that overwrites lived, social configurations to enable capitalist, colonial, and state exploitation (e.g. Katz and Smith, 1993), geographers who view it as simply another mode of conceptualizing space agree that it is associated with “a pre-existing and immovable grid amenable to standardized measurement and open to calculation” (Harvey, 2006: 272) and without ambiguity or social meaning: an inert container of, by implication, an empty cosmos (Agnew, 2011: 320). The geometric locations it offers as a mode of placing are directly contrasted with lived “understanding” (Agnew, 2011: 317): not themselves meaningful but, at best, a part of a spatial substrate to which meaning is somehow attached or associated. Indeed, in the history of cartography, the advent of this mathematical approach to space in mapping is commonly considered to be an inflection point at which the mythic, meaningful richness of the world evident in earlier mappae mundi or cosmographies was abandoned in favor of rationalist scientism (Cosgrove, 2001; Edney, 2011). This thinness of absolute space tends to be presented as identical with the use of grids and coordinates: e.g. “To think of space as absolute, means understanding it as existing in and of itself without any relations to substance, as mere point or container: a particular intersection of longitude and latitude or an enclosed area. . .just empty and without reference to similar emptinesses elsewhere” (Cox, 2021: 3). In other words, absolute space is identified with what it looks like, to such a degree that different visual and mathematical approaches are hailed as conceptual challenges to absolute space (O’Sullivan et al., 2018; Smith, 2014).

And yet, as this article will argue, these grids and coordinates and the locations they define are not without relations to substance, references to elsewhere, social meaning, or ambiguity. Tellingly, these qualities of the grid and its locations become most evident when considering them in the cosmological context required for their production. As we will see, doing so reveals an unsettled pluriverse shot through with cosmological relations and social investments. Equally telling, neither Newton nor Descartes—the two thinkers to whom the invention of absolute space is commonly assigned—thought he was proposing an empty cosmos, and yet the cosmological concerns central to their arguments regularly disappear in geographers’ discussions of the absolute even as their names are cited.

This state of affairs renders both absolute space, and the grids, coordinate locations, and Euclidean geometry that have come to stand as its signifiers somewhat caricatured ideas, defined as “empty” from the start such that further dimensions—which do not negate but can coexist with the familiar calamities of the gridded absolute—are foreclosed. The result is a twofold confusion: about what we precisely mean by “absolute space,” and about what the visual and spatial practices of grids, coordinates, measurement, and calculation can be and do. In this article, I address both issues via an extended discussion of geodesy, or the science of measuring, dividing, and figuring the earth. I do so for two reasons. First, in underwriting our knowledge of the earth’s size, shape, and surface distances and locations, geodesy gives rise to the coordinate grids and geometries identified with absolute space. If these are to be taken as a characteristic of absolute space, then geodesy is in the business of constructing it. Without geodesy, the gridded, “scientific” maps and coordinate locations used in service of empire, state governance, and capitalist enterprise could not be made. One might then expect geodetically constructed space to at least approximate absolute space—but, once examined, it turns out to be entirely relational.

Second, geodesy is unavoidably cosmological: it requires relating the earth’s surface, its interior, astral bodies, and time together. Attending to it reveals the persistence of cosmological and indeed fantastical elements usually seen as lacking in rationalist, modernized understandings of space (Bordo, 1986; Cosgrove, 2001; Edney, 1993) through the making and effects of geodesy’s technical products. In this way, we might ask about the cosmological claims of geodetically constructed space, and what they can tell us about those of absolute space.

On a broader note, geodesy has been neglected in geography despite that it has much to offer. Critical literature on maps (e.g. Cosgrove, 2001; Crampton and Krygier, 2006; Harley, 1989) and GIS (e.g. Pavlovskaya, 2017; Pickles, 1995), and, more recently, on the geoweb (e.g. Leszczynski, 2012) and locative media (e.g. Galani and Kidd, 2019), have rarely attended to geodesy’s role in how these spatial products come about. I do not mean to overstate the case: of course, scholars in these fields are aware that further technical practice lies behind the phenomena they critique or investigate. However, the identification of spatial absolutism with grids and coordinates convinces us we already know what work the latter do, and their production goes overlooked in studies of the production and representation of space. We thus risk-reducing and foreclosing their significance. Meanwhile, in geodesy, to my knowledge, no critical movement like those regarding cartography and GIS in geography has occurred ¹ ; neither discipline has given much thought to geodesy’s implications for critical inquiry. While much more work could be done, in this article, I argue that geodesy reveals that a spatial location is a powerful bundle of meaning worthy of interest, and reminds us that geometry, measurement, and calculation are not only tools of reduction and erasure but rich spatial practices whose histories and uses are plural. If “Geometry gives spatial expression to mathematical relations; it originates in the measurement of actual terrestrial and celestial spaces” (Cosgrove, 2001: 26), the second half of the statement bears more attention than it often gets.

By focusing on geodesy, in this article, I give it some attention. After some historical context for geodesy, I further detail the critical view of absolute space that focuses on points, lines, and grids. With that done, I show that geodetic measurements retain a cosmographic meaning while dealing with some technical details necessary to understand the argument; I then show that the space produced through geodesy is not absolute at all. Finally, I offer a rethinking of absolute space as a claim, rather than an effect.

Figuring the earth

“Geodesy” etymologically means “the division of the earth.” This is accurate insofar as dividing the earth involves measuring and surveying it, but geodesy is also “the age-old quest for the size and shape of the earth” (Fischer, 2005). That is, it is equally about wholeness. The two sides feed into and depend on one another: calculating a distance between two places depends on knowing the size of the earth they are part of, and the size of the earth can only be known by measuring such distances.

The history of geodesy does not recognizably diverge from those of cartography, navigation, and geography until the 17th century. Its telling typically begins with Eratosthenes’ calculation of the size of the earth based on the distance between Alexandria and Aswan, the angles of the sun at noon in each place, and the assumption that the two lie on a single meridian. He was off by 16.7% (Schcheglov, 2016) because the distance as measured could not be very accurate—small inaccuracies add up quickly at the scale of a planet—and because they are not on one meridian. The story illustrates what the work of geodesy as developed in Europe ² from the mid-17th century was about: finding out where places are on the earth, in finding out the figure of the earth.

Direct historical treatments of geodesy are few. Hoare’s (2005) intellectual history concerns, on the one hand, scientific disputes between followers of Newton and Descartes from the late 17th century into the 19th, and the development of astronomical and surveying instruments. On the other hand, it is a history of interimperial diplomacy, as French expeditions to measure a degree brought academicians to Lapland and Quito bearing English-made instruments and Spanish permissions. Capello (2018) details Andean Indigenous contributions to the 1730s Quito mission and its 1901–1906 follow-up, as well as the considerable role this geodetic history has played in Ecuadorian state-building. By the mid-18th century, these expeditions “entered deeply into the Enlightenment consciousness” as “The quantitative precision that had hitherto been the preserve of astronomy was given a terrestrial dimension; the previously humdrum profession of the surveyor acquired global significance” (Hoare, 2005: 2). The global significance was “cosmopolitical” in Toulmin’s (1990) sense: an intellectual and (geo)political reworking of how to place terrestrial order in the cosmic order. The suddenly urgent question of what and where the earth might actually hide just in the wings of many works on quantification, measurement, space, and intellectual history (Cohen and Wakefield, 2008; Elden, 2005a; Frängsmyr et al., 1990; Gillispie, 2016; Kula, 1986).

Geodesy similarly sits in the background of the history of cartography, and of the Cold War’s political-scientific shaping of contemporary geography (Barnes and Farish, 2006). Burnett’s (2000) study of colonial surveyors in Guiana elaborates on the practical difficulty and narrative significance of pinning a notional coordinate to a physical place for both colonists and geography’s scientific “progress.” Edney’s reviews of the misleading nature of such “progress” (1993), and of the relative scholarly neglect of topographical surveys (2011) and map scale (2019), underline the continuing importance of terrestrial and celestial measurement in the development of modern maps. Rankin’s (2016) examination of geo-epistemological shifts in “the mapping sciences” in the 20th century features geodesy as one of these sciences. Here, geodesy’s increasing precision and changing methods shape and are shaped by the demands of aerial navigation, artillery targeting, and the geopolitics of map and data production, as well as the resulting technologies’ eventual role in coordinating civilian space. Cloud (2001: 232) highlights the geodetic underpinnings of the first U.S. network of reconnaissance satellites as “a missing chapter in Cold War science and technology.” Fischer’s (2005) autobiography as a leading geodesist from the late 1950s to mid-1970s gives her vantage on the institutional science serving these demands from within the U.S. Army Map Service, including the rise of satellite data and the increasing importance accorded to refining the earth’s figure. Warner (2002) summarizes the institutional and technical history of the same period. All of these developments have both spurred and responded to amendments in the figure of the earth.

Centering geodesy in these familiar histories foregrounds overlooked elements—not least the degree to which scientific debates, technical challenges, visual shifts, and political developments remain tied up with the cosmological problem of imagining the earth as a place, in its cosmic place. Whether called picture, myth, or physics, cosmology is always an effort to imagine what kind of universe this is and what place we (however, defined) have in it (Merleau-Ponty and Morando, 1971). In geography, interest in cosmology has typically been confined either to the explicitly global (Cosgrove, 2001) or to experientially oriented studies of meaning in places treated as unrelated—indeed, sometimes opposed—to abstraction, measurement, and calculation (Bachelard, 2014; Tuan, 1996). As will become evident, cosmology remains present in the modern construction of space and in abstract processes of calculation and measurement. Geodesy highlights this presence because it strives both to figure the earth and to locate what is on, in, and around it, and because the practical imperatives of doing so bring together the earth’s interior, its surface, the stars, and time. The history and practice of geodesy thus trouble the notion that modern science and global imaginaries entail an objectification of the earth as something observed from outside, rather than lived and practiced from within (Edney, 1993, 1994; Ingold, 1993). The geodetic work on which anything from GPS navigation to geophysics depends operates, in fact, from the classically ecumenical position between the depths and stars.

The confusions of absolute space

Academic critiques of absolute space rightly focus on its effects: the problem with absolute space is primarily the way it allows people to view and shape the world. If space is pregiven and fixed, it is separate from ourselves. If it has no content or substance but posits locations as entirely independent from what is there (or whether anything is at all), it cannot be affected; therefore, its production is not to be investigated. If it distributes everything in a Newtonian mathematical system of locations that are immutable and evident in themselves, then alternate views of what it means for something to be somewhere are “primitive,” unscientific misapprehensions not worthy of real consideration. If it does so by individuating bodies and placing them only against this system, not in relation to one another, this encourages Cartesian separations between the knower and the known world. Implicitly or explicitly, this argument asserts that absolute space is not a description of what the world is really like, but a way of seeing whose effects are made to seem natural. Therefore, one way to undermine absolute space’s power is to denaturalize these effects and demonstrate that their premises are false.

However, focusing on effects obscures significant confusion about what we mean by absolute space both conceptually and empirically, and therefore, how it might be countered. The resulting arguments can be reductive about the things they criticize and overly enthusiastic about the alternatives they identify, which may not actually contradict the claims of absolute space. As a conceptual example, despite common references to both Newton and Descartes, discussions of absolute space conflate the two (e.g. Harvey, 2006: 272). Their very different views about motion (Belkind, 2007; Descartes, 1971; Newton and Thayer, 2005) and the relationship between matter and space (Curry, 1996; Descartes, 1971; Hoare, 2005; Newton and Thayer, 2005) recede behind their contributions to geometry and mathematics, such that “absolute space” comes to mean a Cartesian grid system with Newton’s, rather than Descartes,’ assumptions about space’s insubstantiality and immutability (Casey, 2013; Gillispie, 2016: 91). Despite that Newton was significantly concerned with relationships, his placement of distinct bodies in motion against immovable locations merges with Descartes’ isolating impulses ³ ; despite that Descartes regarded space as substantial, his interest in extension is assigned Newtonian immateriality. It is symptomatic of the slippage at work that Einsteinian spacetime has been hailed by geographers as overthrowing Descartes and Newton by privileging and recombining (Rynasiewicz, 1996) what are, in fact, their respective concerns of substance (Smith, 2014) and relationality (Massey, 1992; Unwin, 2000). Further conflations occur among Newtonian, Kantian, and Lefebvrian absolutes, which I deal with in the fifth section.

This fuzziness is facilitated by a tendency to fixate on what absolute space looks like grids, straight lines, Cartesian, and Euclidean geometry. These visual signifiers come to stand in for spatial absolutism, such that using them entails absolutist ideas and departing from them entails challenging such ideas. ⁴ When Harvey (2006: 281) presents tables to sort out possible spatialities, he remarks: “It may properly be objected that I am here restricting possibilities because a matrix mode of representation is self-confined to an absolute space.” It is taken as read that ideas presented in a grid could “properly” be seen as conceptually confined to absolutism by virtue of the shape of the table; this overlooks the relative and relational capacities of the grid. It situates ideas according to their relations to one another and in positions defined by their relative similarities and differences or conceptual distance. A call for recognition of quantitative methods’ ability to handle relational concepts of space offers “geometries that move beyond the Euclidean” as proof (O’Sullivan et al., 2018: 130). Katz and Smith (1993: 74) assert that “the power of cubism and surrealism [against perspectival geometry] was. . .that they fundamentally challenged the absolutist conception on which a wider web of social, economic, military and cultural relationships were modelled.” In a striking example of Curry’s (1996) contention that absolute space can never and has never been empirically instantiated but exists only as an “image” that convinces not only people at large but also geographers, too, of its concrete realization, in identifying absolute space with these visual signifiers, geographers convince ourselves of it as an actual phenomenon as much or more than a detrimentally convincing idea.

I must take a moment here to clarify this last statement. Curry (1996) is pointing to a disconnect between ontological ideas and practices in the world. Creating, using, and instantiating coordinate grids, Euclidean geometries, straight, dividing lines, and the like is a set of practices strongly associated with the ontological hegemony of absolute space by geographers of many stripes, as discussed in the introduction and just above. There are sound historical reasons for this association, despite the often oversimplified intellectual history around Newton and Descartes provided as its background. However, these practices are not, themselves, absolute. As the next section will detail, and much like Harvey’s (2006) matrix, they take place by relative means and to relational ends. Curry (1996) agrees with many other geographers that absolute space is a sort of chimera or illusion: he takes this further in disagreeing that the practices downstream of this illusion themselves are absolute or create a space that is absolute. They have very real effects in the world—they simply do not turn it into one of the absolute space. Thus, a common consensus that identifies such practices as constitutive of absolutism grants absolute space a concrete existence that it does not have and overlooks other dimensions of these practices to be detailed later.

The article takes geodesy as a particularly concrete way of demonstrating Curry’s (1996) disconnect and the elements it can overlook because it deals directly with the coordinates, grids, and lines so closely associated with absolute space. On the views described earlier, one would expect geodesy to proceed in absolutist spatial terms and to produce an absolute space. Geodesy is quantitative, geometric, and rationalist; it is the source of point locations, grids, and straight lines that fix and flatten the world to make it manipulable. If these modes of seeing, thinking, and acting are essential to absolute space, surely this must be what geodesy produces. Its rise to prominence with large, state-led field surveys is taken in the history of cartography as a key site of scientization, a “shift in emphasis among mapmakers from conceptualizing to measuring the world” (Edney, 2011: 288). Measurement in turn, in association with Descartes and quantification overall, has been understood as reducing the world into inert, valueless numbers and distancing it from the measurer (Bordo, 1986; Gillispie, 2016), much as calculation has in association with Kant (Ingold, 1993) and under the influence of Heidegger (Elden, 2005b).

Therefore, in the next section, I demonstrate that measurement and calculation need not be seen in only this way; in the fourth, that geodetically produced space is not absolute at all.

A calculative cosmography

With “calculative cosmography,” I mean to emphasize that the coordinate locations enabled by geodesy are not simply pairs of numbers, a dry convention only coincidentally related to places’ meanings. Historically, cosmographic maps figured the order of the cosmos beyond the places they portrayed, including gods, personifications of nature, and celestial bodies (Cosgrove, 2001; Edney, 1993:): in this mode, a place’s “design invokes its own position within a universal order” (Kargon, 2014: 104). In this section, I show that the same is true of a coordinate location—not only formally but substantively. The measurements required to locate a place establish relationships with the earth’s center, the stars, other places, and, through them, the earth as a whole. As will become clear, this invocation is accomplished through careful attention to the qualities of the place being located. In this sense, a location is not an empty abstraction. It is a thoroughly emplaced cosmological artifact dense with meaning, produced through performative acts of measurement (Kula, 1986). The coordinates that name it encode its cosmological relationships into a tight bundle, by means of which they are written into the figure of the earth and, in being used, onto its surface. From this perspective, the figure of the earth is itself a cosmography.

To demonstrate this understanding of location, the section introduces four main concepts: two in triangulation and two regarding what can be done with triangulated data. ⁵ I cover these in general terms to minimize details unnecessary to the argument to come. ⁶ I begin with two basic measurements: baselines and cosmographic measurement. ⁷ These obtain from 17th-century land surveying up to GPS geodesy today. While such work has gotten easier and the measurements much finer, the difficulties have changed in scope more than in type. It is these down-to-earth difficulties that require such careful attention to the qualities of the place being measured to locate it in the cosmos.

In triangulation, the aim is to discover distances by relating three points and determining the angles formed by the resulting triangle. If one knows the length of one of the distances involved, one can then calculate the others. In this way, it is possible to use the distance between two places as a baseline to triangulate their distances to a third place. Doing this repeatedly creates a network of “control points,” itself called a “control network.” This network of points and distances sets the terms by which other locations can be interpolated. The process includes vertical angles to account for elevation, and so also means measuring the direction of the center of the earth with a plumb line to establish which way is straight down. Since two places each offer angles toward the center of the earth relative to their shared baseline, one can use the same procedure to find the earth’s radius, which then allows calculating its size.

This might be simple if the earth was a sphere, if gravity was consistent over its surface, and if establishing a baseline was easy to do. None of these things is the case. The earth is an ellipsoid, longer across the equator than it is from pole to pole, and its curvature between those axes is irregular. A plumb line may not point to the center of the earth due to the local gravitational influence of topographic or geological features. Moreover, precisely measuring the distance between two places on the earth’s surface is very difficult. Physical units of measurement (e.g. a bar of defined length) may develop inaccuracies through repeated assembly and disassembly, or because the weather causes materials to expand or contract; there is no truly flat, unobstructed surface over which to lay them. With today’s electronic distance measurement, the atmospheric conditions at the place and moment of measurement must themselves be measured and corrected for.

Insofar as triangulation identifies a place via its relationships with others, it begins to be cosmographic by placing it in a wider order; cosmographic measurement extends this order beyond the surface of the earth. In local surveys, triangulation among places on the earth’s surface may suffice. For larger extents, “higher-order” control points with greater accuracy are needed. These must agree with the same model of the earth’s figure and, thus, can correct “lower-order” points for distortions over longer distances. Cosmographic measurement is the source of higher-order control points; it means triangulating with stars (or satellites—called, nonetheless, “constellations”) as a point in the triangle. It is this that allows locations to be referenced to a model of the earth, rather than only to one another on its surface. This process is just as vulnerable to instruments’ limitations, visual distortions introduced by the atmosphere, local weather conditions, and gravitational variation. It also depends on time. The measurements at the two earthly reference points must be astronomically equivalent, which is to say simultaneous, for the distances derived to bear on one another. GPS has made timing much easier, but not negligible. Since they require greater investment, higher-order control points are relatively few, whereas lower-order points are surveyed, tracked, or corrected based on them. Thus, while not all locations require their own direct relationship with the stars and time, all of them depend on some locations’ relationships with these elements of the cosmos. Notably, the locations produced this way are far from “existing in and of [themselves] without any relations to substance. . .and without reference to similar emptinesses elsewhere” (Cox, 2021: 3). They are deeply entangled with both, “internaliz[ing] relations with [their] area and reflect[ing] its characteristics” in the same manner that other phenomena described as relational do (Cox, 2021: 4).

Having established our “cosmological bundle” in the form of a location, it remains to write the cosmos back onto the earth. Geodesists have used these measurements to develop “reference ellipsoids,” or mathematically regular ellipsoids that fit the observed data closely. Even these are only approximations for the convenience of calculation: the earth does not have a constant curvature. This is so much the case that different ellipsoids are used for different parts of the world. A shape that approximates Europe well is unhelpful in South America. While, since 1960, there have been ellipsoids tailored to fit the whole earth—GPS is referenced to one of them—these World Geodetic Systems (WGSs) remain approximate; for some purposes, national or regional ellipsoids are still used for best fit. Even using an ellipsoid rather than only triangulation, the further away one interpolates from a cosmographic location, the more inaccuracy will be introduced with regard to the irregularities of the actual earth. To locate a place precisely requires going back to the cosmos, inquiring after the positions of stars or satellites and the center of the earth, then to be reconciled with existing cosmographic data. All this, in turn, leads to updates and adjustments in the reference ellipsoids as well as the geoid, the irregular approximation of the earth at sea level.

The types of projections used to generate maps from these data bring together the angular geometry of ground triangulation with the cosmographic data using the calculated size of the earth (Edney, 2019: 199–202). This is not simply a matter of reconciling two sets of references for flat surfaces. Cosmographic control points are height-sensitive. Thus, there are both geographic and projected coordinate systems. The former are three-dimensional and always affiliated with a matching ellipsoid; projected coordinate systems treat the earth as flat by defining one (secant) or two (tangent) lines of contact between the reference ellipsoid and a two-dimensional surface projected from it and applying linear coordinates to the resulting surface. Much like interpolating away from cosmographic control points, the projection’s accuracy will decrease with distance from its line(s) of contact. Therefore, some projected coordinate systems—commonly used for governance, military, and localized surveying purposes—accomplish this differently (e.g. Universal Transverse Mercator, British National Grid). Also called “grids,” these take multiple lines of contact and divide the earth into small strips around each line to avoid distortion; the strips, rather than one whole surface, are treated as flat. One corner of each strip is treated as the origin for Cartesian coordinates within the strip. Thus, the coordinates in grid systems are not continuous over the earth: they start over from one zone to the next. All of these ellipsoids, projections, and surfaces commonly discussed in cartography rely ultimately on the cosmological relationships defined and located through geodetic measurement. Between the suite of ellipsoids on the one hand, and the bevy of surfaces and grid strips on the other, geodesy offers a hidden pluriverse of approximations: to navigate, target, divide, and build accurately on our planet, we behave as though we were on several other, slightly different planets or planes very nearby—all held in place by cosmographic locations.

These approximations bring the calculative cosmography very close to the earth; it is the measurements’ uses on the earth that bring it the rest of the way. Grids were developed to allow quick, highly localized surveying and orientation by users (first soldiers, then civilians) wherever they are, not a few experts in a few offices. Therefore, from North America to the Republic of Korea, they have been physically built into the landscape as markers and monuments for reference. This means putting two-dimensional coordinates into the three-dimensional world; as Rankin (2016: Chs. 3–4) observes, this is essentially the map’s becoming the territory, its coordinates placed at a scale of 1:1. This may sound like the nightmare apotheosis of absolute space. However, making the grid physical is not simply replacing places with abstractions. Rather, having rendered places’ cosmological relationships with the stars and the earth’s center, composition, and atmosphere in geodetic terms as “location,” these markers then build that information back into the places. This is our calculative cosmography—a quantitative writing of the universe as the earth (its figure, known only via other elements of the cosmos) and onto it (in distances, elevations, coordinates, and grid markers). In the next section, I show that this calculative cosmography is significant to places’ social meanings and embodied lives.

The geodetic production of space

This section demonstrates that geodetically constructed space is not absolute but relational. If absolute space is a priori, neutral, separated, and fixed, what geodesy produces is constructed, hierarchical, relational, and in flux. There is perhaps no more literal demonstration of space’s social construction than via geodesy. This ought to call into question the idea that grids, points, and straight lines are characteristic, even constitutive, of absolute space. It supports the contention that “absolute space’s very nature. . .has prevented its use as anything other than an image” (Curry, 1996: 22); that is, that absolute space cannot and has not been instantiated or practiced, not even through the phenomena attributed to it.

As seen in the previous section, geodetic measurements and calculations are altogether relative, and in no sense a priori. By “relative,” I mean Leibniz’s notion of space, wherein a distance only exists by virtue of what it separates, within a bounded rather than infinite extent (Alexander, 1956). Nothing has an independent value prior to that of anything else; everything is located and calculated relative to other locations and distances, on a finite earth or within some smaller, defined area (e.g. a national survey). Coordinate systems are equally relative. They refer, in two or three dimensions, to a point of origin that had to be chosen. There is no pregiven (0,0) of the world. A good attempt at one is the Earth-Centered Earth-Fixed (ECEF) coordinate system, whose origin is at the center of the earth; but even this required choices about which center (the center of mass, rather than a geometric center), and about the directions of the axes intersecting there.

This so far suggests that while the quantities are relative, the nonhierarchical, neutral aspect of absolute space holds geodetically: mathematically, no direction or location has any particular significance. However, this is not the case. In setting locations relative to the stars and earth and creating shared points of reference, these measurements enact spatial hierarchies of significance and belonging in a broadly Aristotelian sense (Aristotle and McKeon, 2001; Curry, 1996): things are where they are because they belong there, and where they belong says something about what they are. In coordinate systems, the choice of origin is hierarchical in two senses. First, by definition, it makes one point and two or three lines more important than any other possible points and lines. That is what it means for them to be references (much as the center of the earth was a fundamental reference to Aristotle). Second, in setting up such a hierarchy, the choice is inevitably signifying: where and to whom do sites of importance belong? And therefore, who and where is important? Hence, to take the simplest example, geopolitical and postcolonial disputes about which should be the Prime Meridian—through Greenwich, Paris, or somewhere in the Pacific Ocean (Cosgrove, 2001: 12; Edney, 2019).

Cosmographic measurements have a similar effect: which places, and so which people, have been significant to figuring the earth? The most striking case is Ecuador’s very name—“equator.” The history of geodetic missions to Quito, aimed at measuring the length of a degree at the equator, became a significant part of that country’s geopolitical self-assertion and invented tradition, and eventually a focus for Indigenous contestation as well as the tourist trade (Capello, 2018). Monuments commemorating cosmographic measurements dot landscapes from India to Canada (Capello, 2018); France commemorated one of its early meridians with a line of trees intended to be visible from outer space (Hoare, 2005: 257), while lines of latitude and longitude such as the Arctic Circle and Prime Meridian serve as tourist attractions (Timothy, 1998). It is not only in technical terms that some locations are of a “higher order.”

The technical status of higher order is not to be dismissed, however. The significance of cosmographic measurements means that, in one sense, truth is concentrated at particular spots on the earth, decreasing with distance, forming a network of not only control but geognosis—knowledge of the cosmic order “extracted from the earth itself” (Grapard, 2012: 375). ⁸ These are literal axes mundi: places “where terrestrial space connects with celestial time” (Cosgrove, 2001: 20). This is still true with GPS; maintaining continuous, precise tracking of “the dynamic Earth” (Bock and Melgar, 2016: 2) depends on a network of stations that constantly talk to the GPS constellation (3-5). In either case, these spots offer “higher-order” knowledge of the earth and stars, which structures and guarantees knowledge of a “lower order.” This geognostic, quasi-Platonic significance is evident in the design of many of the monuments just discussed (Capello, 2018). Moreover, given the pragmatic role played by cosmographic locations in the coordination of life, the higher order shapes not only lower-order knowledge but what would, in earlier times, have been called the lower orders.

So, geodetically constructed space is neither a priori nor neutral. But surely it is fixed: what else is a “control point” for? The answer once more is no, but in two ways. “Fixed” can mean unmoving; it can also mean settled—decided once and for all, an approximation of a priori status. In absolute space, these are the same thing. Geodetically, they are not. The distinction turns on the fact that geodesy strives for accuracy, and accuracy is contextually defined: it depends on the instrument, what one wants to do with the information, and how it is stored (Brady, 2018; Fischer, 2005: 29–31; Hoare, 2005: Ch. 3). Thus, geodetically produced space is undecided because it supports multiple uses in multiple places. Depending on the user and use, different ellipsoids and coordinates, and therefore different locations, apply. Equally but distinctly, it is unfixed because it is constantly being changed due to refinements in metrology and calculation. This may seem esoteric: changing the mathematical description of something does not automatically change it. But the nature and function of geodesy means that this kind of difference makes a difference in the world, both materially and in the meaning of location—for location is a meaning.

To illustrate locations’ undecidability: during WWI, the demands of artillery firing made it important for allies to link up their control networks. It was found that the French and Belgian networks shared two points at the border but gave different locations for these points because one network started from Paris, the other from Brussels, and each had interpolated using different values for the size and shape of the earth (Rankin, 2016: 153). The two networks were incommensurable—there was not a simple conversion to be made. The same places were not in the same locations, depending on whether they were known from the French or the Belgian capital. These locations had political meaning: even without a territorial dispute, one set of locations made these places belong to France, the other to Belgium. However, this political divergence was entirely quantitative. That the two states used different numbers for the figure of the earth did not reflect some characteristic national difference in cosmology, as each regarded the earth as an ellipsoid of similar dimensions. Rather, because political and metrological control have long gone hand in hand (Kula, 1986: 18–23), the fact of two states resulted in two different sets of figures. These two sets of locations meant sovereignty; they therefore could not be reconciled.

Meanwhile, accuracy renders geodetic locations unfixed. Because accuracy depends on its context, even with ever-finer measurements—now sometimes to the micrometer—there is no final, proper location good for all time and all purposes. Refinements in geodetic accuracy can have significant material and meaningful consequences. They do not mathematically relocate things in a pregiven space: refinements also affect ellipsoids and the figure of the earth. Nor do they merely redescribe locations, or reduce uncertainties. They remake space. Consider that the height of the U.S. relative to sea level has been adjusted five times since 1900 thanks to finer measurement and calculation, and is set to adjust again in 2022–2024. The downward adjustment, increasing westward up to 6.5 feet in Alaska, means that Coloradans may no longer be able to brag about the heights of their mountains and West Texans may need to buy flood insurance they never needed before, without anyone’s or anything’s moving an inch (Mitchell, 2020). Thus, the unfixed nature of geodetically constructed space is not only about mathematical precision. It concerns the nature of places and what it means to live there. The infixity and undecidability of geodetic location go hand in glove: even if locations could be mathematically finalized, there would always be more than one valid location. There is a sense in which no one knows, absolutely, where anything is.

We have established that geodetically produced space is relative, hierarchical, and unfixed. This leaves the question of relations. The above should already have demonstrated that geodesy produces space not only through relative means, but to relational ends. In contemporary human geography, to say that space is “relational” means that it is the product of social relations, which themselves mutually define the participants in the relationship; relations are prior to space, which then further affects relations. We have already seen some ways in which geodetic space shapes and is shaped by social relations: flood insurance in West Texas, incommensurably sovereign control networks. However, as Cox (2021) points out, relational space can be a physical as well as social concept: when space is united with substance (as indeed Descartes believed it to be), the physical relations between things in space are also the relationality of space, or what Leibniz called “the relation of situation” (Alexander, 1956: 70). We saw in the third section how geodetic locations fulfill this condition on the basis of the substantive and cosmological relations that give rise to them. The Aristotelian hierarchy of geognostic significance also does so: to paraphrase Cox (2021: 3–4) no Prime Meridian without its lessers, no lower-order locations without higher-order counterparts. It is these relations that geodetic space is made of.

However, I would like to emphasize a different sense, which somewhat integrates both physical and social relations. In addition to mediating human relations through geopolitics, surveying, and navigation, geodesy and its products also serve to relate people to the cosmos. Varying our educations and cultures, the shape of the earth, the geodetic hierarchy written into it, and the astronomical, geological, and geomorphological knowledge to which geodesy contributes (Bock and Melgar, 2016) play a meaningful role in our ability to imagine the cosmos and our place in it: the earth as a place, in its cosmic place (Merleau-Ponty and Morando, 1971). Cosmologically, the physical and substantial relations of the situation are socially significant in themselves; at a planetarium, children learn not only about the sun and solar system but also the precise measurements of how far away each is “from us.”

Abstract as contemporary scientific cosmology may be, to live in it, people require ways of relating to its features; geodesy’s lines and locations provide these. There is a reason the effort to determine the figure of the earth is consistently called a quest. Thus, Fischer (2005) tells us that on a ship crossing the equator, passengers rushed to the side to see “The Line” (39) and that the first satellite measurements, having made their way into a Peanuts comic, prompted a call from a schoolteacher asking what she should tell the children about the earth’s shape (69). While the significance of geodetic monuments from Ecuador to Kenya to England differs for Indigenous critics, those profiting from the tourist trade, and the tourists (Capello, 2018), they remain an attraction because they let visitors put themselves in touch with something they would never otherwise see or feel, but which has significance in their understanding of their place in the world. Millions of visitors per year are photographed straddling lines of longitude or latitude and buy certificates attesting that they have stood in two hemispheres at once; these attractions are promoted in terms of points, lines, and divisions (Timothy, 1998), whose significance lies in being taken for granted as actually constituting and composing the earth. Even those who firmly oppose basic premises of the geodetic cosmology think in its terms: the Flat Earth Society’s website dedicates an entry to WGS84 (which turns the geodetic process inside out to argue that the system is derived from the real geognostic truth of flat maps), and its entry on the “Ice Wall” starts with a story about an attempt “to determine the position of the South Magnetic Pole.” ⁹

To sum up, then, an understanding of the geodetic production of space shows that a gridded, geometric, quantitative, coordinate-laden, point-based space is hierarchical, in flux, and defined in relative terms to relational purposes and effects. It is socially constructed and socially causal. In other words, it is indistinguishable from relational space. A relational geodetic space is no less implicated in the modern state, capital, warfare, and colonialism than the usual picture of absolute space: these are, after all, relations. Geodetic relationality does, however, suggest that grids, points, and straight lines are not what make absolute space absolute, and that alternatives responding to such visual cues will not easily translate to its conceptual or political overthrow.

If “absolute space’s very nature. . .has prevented its use as anything but an image” (Curry, 1996: 22), images still have certain uses. One of these is a vision, in the sense of an ambition. In the next section, I present a different view of what makes space absolute.

The cosmological claim of absolute space

The term “absolute space” has been used in more senses than its critics usually note. In this section, I compare three versions from Newton, Kant, and Lefebvre to illustrate that absolute space is not a description or an empirically realizable project but a cosmological claim: a way of placing the self in a particular kind of world and guaranteeing that placement. Curry (1996: 22) sums it up well: spatial absolutists argue “not that we have evidence that space is absolute and independent, but rather that we must believe that space is absolute and independent.” This is implicitly recognized in geographic critiques of absolute space’s political consequences. However, as illustrated earlier, the transfer of the claim to the grid muddies the distinction to imply that absolute space empirically exists. It is therefore worth elaborating on what it means for it to be simply and specifically a claim.

Newton’s assertion of “absolute space” as a dimension fundamental to the cosmos, pregiven, fixed, and independent of both matter and time had both scientific and theological motivations. To account for a body’s motion, it is necessary first to define it—what is part of it and what is not—and to put it in relation to something separately defined. Absolute space solves these difficulties mathematically by providing a stable background that will never be part of anything else (Belkind, 2007). Newton (Newton and Thayer, 2005) recognized that actually using this mathematical solution requires relativism and hierarchy (just as coordinates do in geodesy); true absolutism was for “philosophical disquisitions” (p. 20). In this philosophical sense, his absolute space was equally an assertion about the nature of the cosmos and its divine creator’s rationality and agency (Alexander, 1956).

Kant and Lefebvre used “absolute space” in quite different senses. For Kant (1929), space had to be absolute because people have an embodied spatial awareness that seems to precede conscious knowledge or experience. A sense of direction and orientation and automatic division of what one senses in this way into up and down, left and right is, he argues, basic to making sense of the encountered world. Thus, space is a priori. It is necessary to know anything about what else exists beyond oneself; it must exist because one does know something about what else exists. Kant’s absolute space was resolutely regional, not only in the way it organized perception but in that this sensed, proprioceptive knowledge was always only a partial experience of the world. Putting the pieces together required a different kind of thought (Ingold, 1993; Kant, 1929, 1998).

Lefebvre used “absolute space” in a third sense, although this has sometimes been misread as a reference to Newton (e.g. Unwin, 2000: 20). In The Production of Space (Lefebvre, 1991), “absolute space” means space fully imbued and united with a society’s social, cosmological, and sacred systems of meaning. The historical trajectory in “From Absolute Space to Abstract Space” (Ch. 4) is toward what is commonly identified as absolute space and for Lefebvre is “abstract”; the absolute space from which it departs is the kind of embodied, meaning-laden lifeworld usually seen as opposed to Newton’s absolute. “[. . .A]bsolute space assumes meanings addressed not to the intellect but to the body. . .. This space is ‘lived’ rather than conceived. . .no sooner is it conceptualized than its significance wanes and vanishes” (p. 236). This absolute space is a kind of dream of social wholeness and immersion, a fully immediate experience without gaps of abstraction. To be clear, Lefebvre’s absolute space is not his “social space,” which combines space as lived, conceived, and practiced. Whether anyone has ever experienced the totally-lived enfolding he describes as “absolute” seems doubtful. Rather, he uses it as an ideal type: something that still appears in moments and traces in social and abstract space, and toward which the balance could tilt further, into the lived and everyday life.

What can these three absolute spaces be said to have in common? It is simply this: the claim that the world is made of space, ¹⁰ and the claim to an unshakable mode of being in it. It is the condition for explaining how one finds oneself in a cosmos taken to be fundamentally spatial, rather than in an Aristotelian hierarchy of places (cf. Bordo, 1986). The spatial character of this existence may be externally fixed, insensible, and mathematically complete, as in Newton, or based in the senses of a roving body whose sensing is always partial, as in Kant; physically individuating and distinct from time, as in Newton, or socially enfolding and imbued with eternity, as in Lefebvre. Absolute space is absolute the way a sovereign can be: not empirically, but as a motivating idea that presents itself as an explanation. For Newton this motivating idea was mathematical; for Kant, epistemological; for Lefebvre, political. These men do not make the same claim, but their claims are of the same sort—claims that place the self in the world and assert some absolute, unbreakable mode of relation between the two: location (Newton), orientation (Kant), or immediacy (Lefebvre). It is to preserve this self-placement that Kant and Newton, at least, argued “not that we have evidence that space is absolute and independent, but rather that we must believe that space is absolute and independent” (Curry, 1996: 21). Lefebvre argues something close: “we must believe that space can be absolute,” in the sense “absolute” has for him. I do not argue these three ideas are equivalent because they use the same phrase to make similarly structured claims, but the observation illustrates that the absolute space geographers usually discuss is a claim.

A claim of this kind can be neither realized nor falsified, but it can be asserted, pursued, and pictured. Such picturing can indicate its absolutism, but never instantiate it. We have seen this already with the critiques of Newton’s absolute space that focus instead on the grids, points, and geometry that indicate it. Analogously, there are cartographies that indicate Kant’s and Lefebvre’s respective absolute spaces. Rankin (2016: Ch. 2) details maps that represent a global world through a regional perspective, a view from somewhere, resembling Kant’s orienting absolute (cf. Burnett, 2000: 116). Some efforts in immersive deep mapping aim at Lefebvre’s immediate absolute by trying to capture a small but total social world as it is lived, down to sounds and smells (e.g. Harris, 2016). In none of these cases can the absolute be achieved: the attempt contradicts itself from the start. Just as geodesy shows us that representing a locative absolute relies on relativism and hierarchy, to represent a perceptually regional view, you must figure the global first; to represent a place as lived, you must conceive of it first. But practitioners and critics of the mapping sciences do keep questing after such images.

At this point, I will briefly lay out how the pursuit of a specifically Newtonian, locative image has animated geodetic practice. This pursuit manifests primarily as a drive for accuracy—in the precision of measurements, in the quixotic attempt to fix locations, and in the characterization of the images these tools make visible, including the figure of the earth. As already discussed, accuracy is contextual and can never be final. Its unending pursuit in geodesy reflects Newton’s locating absolute, despite that it remains impossible and indeed undesirable in practice.

While the meaning and terms of the quest for the earth’s figure have changed over the centuries, it has always lent accuracy an existential weight due to the “enduring cosmographic urge to parallel the metaphysical with the geographical. . .order” (Cosgrove, 2001: 12). Early expeditions to measure equatorial and polar degrees were meant to settle what kind of ellipsoid the earth was, and therefore, whether Newton’s or Descartes’ theory of celestial motion was correct: it was an empirical question that turned on accurate measurements (Hoare, 2005). Yet, this empiricism reflected the post-Thirty Years’ War cosmopolitical imperative to recompose the cosmos. “What keeps the planets in orbit, what holds the world together, in a universe where motion persists?” (Gillispie, 2016: 91) was not merely a scientific but a cosmological problem: what holds the world together? One political answer lay in communication: the search for a universal language and knowledge, ideally mathematical in basis. Accordingly, innovations in coordinate systems, measures, and map scales have been consistently put forward as a universal language (Heilbron, 1990; Rankin, 2016: Chs. 1–2). The international character of the quest for the figure of the earth exemplifies the cosmopolitical effort “to build up a body of knowledge that would carry conviction with savants of different [Western European] countries and religions, and support a shared world view” (Toulmin, 1990: 105). Geodetically, this imperative appears as the pursuit of an image: the accurate figure of the earth.

The continuing refinement of the earth’s figure grants accuracy and existential weight in other ways. In the 1950s, the U.S. Department of Defense regarded refining the geoid as essential to nuclear deterrence (Cloud, 2001: 233). Army geodesists’ guilty consciences regarding the geoid’s role in conventional war were assuaged by assurances that geodetic accuracy would avoid loss of civilian life (Warner, 2002). Today, geophysicists call for yet denser networks of high-precision geodetic GPS tracking for “a holistic understanding of the Earth engine” (Bock and Melgar, 2016: 93) to allow better prediction and rapid response for earthquakes; and similarly of the atmosphere, for meteorology in the context of climate change. In these terms, better images of the earth’s figure, its wholeness, underwrite the possibility of life. In describing such things as “the Earth engine” as images, I do not suggest that the earth has no geophysical processes or that understanding them lacks practical purpose. Rather, in conceiving them holistically, they emerge as something like “cartefacts” (Wood, 2012): things that need to be intensively represented to be grasped as wholes—that is, as bodies individuated in Newtonian style against a background. “[Weather] fronts were discovered and promulgated on maps: [. . .] ‘I only gave the right kind of maps to the right young men, and soon they discovered the wrinkles in the face of the Weather’” (Wood, 2012: 291). No pursuit of accuracy will ever realize a face for Weather or an Earth engine, or locate their anatomies finally and perfectly in space. (Indeed, responding to earthquakes or climate change does not require it.) However, the quest to picture and locate them must believe in absolute space to see them at all, in the same way that the U.S. DoD needs an Earth figure to designate targets from thousands of miles away.

These practices do not add up to instantiating absolute space. Instead, they tell us about the practice and pursuit of the absolute image, which produces instruments, measures, modes of accuracy, and a variety of new images that certainly have consequences—but neither embody nor produce an absolute space of any description.

Conclusion

In this article, I have offered some history and technical basics of geodesy primarily to argue that absolute space, as an object of critique, has become misidentified with its signifiers, and that said signifiers’ further significance is too often overlooked. I have shown how this slippage occurs, and used the geodetic production of space to illustrate that grids, points, and Euclidean lines do not add up to spatial absolutism. This indicates that absolute space is used—and often critiqued—as an image in Curry’s (1996) sense. It further clarifies the nature of absolute space as a claim about not only the nature of the cosmos but also how one could come to belong in it, and the way absolute imagery is used in the impossible quest to try to make good on this claim. Notably, such rationalist efforts lead, in their entirely pragmatic problem-solving, to fantastical results: a hidden pluriverse of ellipsoids and grid strips grazing and bumping against the surface of the earth, networks of geognostical axes mundi, Earth engines and Borgesian landscape-maps. None of this is inherently virtuous, but its departure from the mythless neutrality of absolute space is worthy of notice.

This argument proceeded in the context of two broader contentions: that knowledge of geodesy is of interest to geographers, and that drawing on it specifically directs attention to elements of cosmology and measure in potentially fruitful ways. “Measure is intimately connected with man and the things he values above all others: land, food, and drink. It metes out to him what his destiny has failed to afford him in abundance” (Kula, 1986: 17). This is a geodetic concern in the sense of “division of the earth,” whose examination might deal with metric units or customary, highly localized measures. Geographers interested in political ecology and Indigenous knowledge already note the clashes between geodetic and customary measurements (e.g. Karnad and St Martin, 2020). The subject is significant to any history of territory (Elden, 2013), property (Brady, 2018), sovereignty, labor, or exchange (Kula, 1986), and the geodetic construction of space presents an intriguing subject for geographers interested in vitalist and new materialisms (e.g. Barad, 2001). Similarly, the continuing relevance of cosmology and its cosmographic expression in a variety of places, techniques, and practices offers a view of the relational connections of place where we might not look for them, in quantitative reductions and representations (Kargon, 2014). This subject might be particularly fruitful for geographers interested in non-representational space (e.g. Thrift, 2006). Rather than restrict this theme to the past (Edney, 1993), to the global scale (Cosgrove, 2001), or to a mythic realm held separate from science (Merleau-Ponty and Morando, 1971), we might find different cosmopolitical questions to ask in those interstices of place, technique, and image.

If there is no absolute space, only an image, and if that image has a variety of uses, geodetically speaking one of them is to perform ourselves into our world by measuring it. This, again, is not to deny that much of this process is violent and unequal. I do not propose geodesy’s cosmographic and metrologically performative aspects in opposition to the well-critiqued calamities of absolute space. Rather, I aim to show that they are not merely dimensions of the latter’s pursuit, but geographic phenomena worthy of study in their own right. They might tell us things about the production of space, and indeed of the world, that other approaches have not.