Scale in a digital geographic world

The representative fraction, the metric traditionally used by cartographers to characterize the level of geographic detail in a map, is not well defined for digital geographic data. Increasingly complex and unsatisfactory conventions are needed to preserve this legacy of earlier technology. A series of requirements is defined for replacement metrics. For digital representations of fields, six cases can be identified, but in only two cases is there a straightforward solution to the requirements. For digital representations of discrete objects, the representative fraction can be replaced with any ordinal index of specification. We conclude that simple metrics having dimensions of length are preferable to the complex conventions required to specify the representative fraction for digital geographic data. Introduction , In times of rapid technological change, it is frequently observed that the first uses of a new technology emulate those of an old one. An oft-cited example is the first 'horseless carriage', which simply replaced the motive power of the horse with that of the internal combustion engine, and left other aspects of the traditional mode of transportation largely unchanged, at least initially. It would have been very difficult at the time of the first horseless carriage to have anticipated the eventual form of the automobile, or the impacts that it has had on urban structure, land use or human spatial behavior. Recently, much attention and popular writing has been devoted to the long-term impacts of the very rapid advances being made in digital technology, particularly digital computing (Negroponte, 1995; Toffier & Toffier, 1995). Human society is in the midst of a transition to digital technology in all aspects of information transmission, storage and use. Almost all information communicated between individuals, with the notable exception of communication by direct personal contact (but see the literature on computer-supported collaborative work; for example, Densham et al., 1995), now adopts a form of digital representation at some point in its existence. Some digital data are structured in highly formalized ways--tables of information in spreadsheets are one example, or vectorized maps~while other information uses very general forms of representation, such as those associated with facsimile transmission, digital encoding of voice phone communication, or remotely sensed images of the Earth. Michael F. Goodchild and James Proctor, Department of Geography, and National Center for Geographic Information and Analysis, University of California, Santa Barbara, CA 93106-4060, USA. E-mail: { good,jproctor }@geog. ucsb. edu. 1361-5939/97 IOI 0005-19 © 1997 Carfax Publishing Ltd 6 M. F. Goodchild & J. Proctor When the first digital computers appeared in the mid 20th century, they were designed as responses to well-defined needs, and the inadequacies of older technologies. The digital computer's powers of numerical calculation vastly exceeded those of mechanical calculators or analog devices like the slide rule, and were quickly applied to the massive computations needed by nuclear research. Similarly, the computer's abilities to process large amounts of information.rapidly and to examine vast numbers of alternatives were of very substantial benefit to the cryptographic community. But in both cases the applications of the new technology reflected those of the old, or tried to solve its perceived problems and inadequacies, and it was not until many years after the advent of digital computers that new ideas began to emerge about their long-term significance. Ideas of graphic user interfaces, artificial intelligence, individual empowerment, electronic games, virtual realities-all of the ideas we now routinely associate with digital technology-would have been largely irrelevant and perhaps almost inconceivable to the developers of the 1950s. Without embarking on a discussion of the varied meanings of the term, it is useful to think of these technological transitions as occurring in a social and institutional context which we will refer to as 'culture'. These examples illustrate the short-term role of technological change in serving the needs of an existing culture (for general discussions of the interactions between technology and culture, see Hardison, 1989; Marx, 1988; Ross, 1991; Street, 1992; Volti, 1995). But in the longer term, technological change stimulates cultural change, as institutions, societal expectations and a wide range of social activities adjust in response. In this model, it is implicit that cultural change occurs more slowly than technological change-the technology to support our modern patterns of land use was available long before those patterns emerged in response to changing cultural practices. The term 'legacy' has a useful meaning in this context; legacy ideas are those aspects that are inherited from previous technologies, and tend to guide how we think about new ones. In other words, legacies are embedded in the old culture, but persist in the short term as one technology is replaced by another. Legacies help ns to adopt new technologies by giving them the 'look and. feel' of old ones-for example, the calculating function of a laptop computer may be presented on the screen in the form of a familiar electronic calculator. The electronic calculator's interface may not be optimal in any sense, but its familiarity allows the user to master the new technology quickly and to overlook its awkward aspects. While legacy ideas have benefits, they also tend to constrain thinking, and impede the emergence of new ideas. Although the metaphor of the desktop and its graphic icons was defined by the Xerox Palo Alto research laboratories in the late 1960s, it was not until the Macintosh was announced by Apple in the mid 1980s that it reached widespread application, and not until Microsoft released Windows 95, or arguably Windows, that it achieved its current status as the dominant paradigm for interaction in the general computer user community. The appropriate balance between new ideas and legacies is an important question for the research community, as it tries to push the 'cutting edge' of technology while at the same time ensuring that its results are useful enough to be widely adopted. In other words, there are good reasons why new technology should be embedded simultaneously in both the old and the new cultures. Much of the information now being collected, manipulated, communicated and stored using digital technology is geographic-we define geographic information here as collections of facts and other evidence about places on, above and below the surface of the Earth. As with other information types, almost all geographic Scale in a Digital Geographic World 7 information now passes through one or more forms of digital representation at stages in its life, making use perhaps of digital remote sensing and image processing (e.g. Jensen, 1996), the Global Positioning System (GPS; Leick, 1995), geographic information systems (GIS; Maguire et al., 1991), and a range of alternative representation schemes or data models (Peuquet, 1984; Molenaar & de Hoop, 1994). We may choose to think of a GIS as a container of maps, with a database that is built by digitizing maps, and outputs that frequently emulate the appearance of maps, because again these ideas and metaphors are familiar, and encourage adoption of the new technology by a wide base of users. But such legacies tend to constrain our ability to think about the long-term future of geographic information technologies, and their impacts on society's activities. The impacts of the transition from older geographic information technologies such as manual cartography have been the subject of several studies and essays (Tomlinson & Petchenik, 1988). In this paper, we examine one specific and important aspect of this legacy-the description of the level of geographic detail characteristic of a given geographic data set. We assume for the sake of argument that the level of detail is uniform for a given data set, and ignore the interesting implications of 'mosaic' data sets that incorporate varying levels of detail (as proposed, for example, for the National Spatial Data Infrastructure; National Research Council, 1995). 'Scale' is the term most often used to describe level of geographic detail, but we show that its meaning is confused in a digital geographic world. Its primary metric, the cartographer's 'representative fraction', compares distance on a map or image to the same distance on the ground-but in a digital world, there is no equivalent of map distance, and thus the measure is not defined. This failure of the most commonly used metric of geographic detail as a legacy of earlier technologies is our main motivation for this paper, and the need to replace it with metrics that better survive the digital transition. In this paper, the 'old culture' is that of manual cartography, paper maps and photographic images; the 'new culture' is that of digital geographic information technologies. We show that in the old culture a tension existed between the cartographer's view of geographic detail as the representative fraction, and that prevailing in the general scientific community, but argue that in the new culture this tension is no longer necessary, or founded on rational argument. We show nevertheless that it has persisted as a legacy into the new culture. The next section of the paper expands on the importance of the concept and its metaphors, and gives examples of its applications. This is followed by an analysis of the term 'scale' and its surrogates and correlates, first in the cartographic world, and then in science generally. We then present a series of requirements for metrics of geographic detail, and metaphors suitable for use in interacting with digital databases, and examine various alternatives. Finally, we present our suggested