Quantitative geography: representations, practices, and possibilities

Representations of quantitative geography, both by practitioners and by others, have tended to associate quantification with empiricism, positivism, and the social and academic status quo. Qualitative geography, by contrast is represented as nonempiricist or postempiricist, sensitive to complexity, contextual, and capable of empowering nonmainstream academic approaches and social groups. Attempts to engage in debate between these positions rarely challenge this dualism, reproducing the representation of quantitative geography as logical positivism, and a dualism separating quantitative and qualitative geography. I argue that this dualism can be broken down, by deconstructing the underlying representation. I discuss why this representation came into existence and how it was stabilized; how close attention to the practices of quantitative geographers, and particularly to the evolution of these practices, reveals its inadequacies; and what new possibilities for quantitative practices emerge from this deconstruction. GIS, one of the recent manifestations around which representations of quantitative geography polarize, is used as a case study to illustrate these arguments. I pay particular attention to the question of the relevance of quantitative practices for an emancipatory human geography. DOI:10.1068/d307 (1) The distinction drawn here between quantitative and qualitative geography has developed since the late 1970s, after humanistic and radical human geographers began to develop critiques of the philosophical and methodological foundations of the geography of the quantitative revolution. Those advancing hermeneutic, feminist, realist, and dialectical methods as an alternative to logical positivist methods have increasingly seen themselves as pursuing a qualitative rather than a quantitative human geography. This is reflected in the recent growth of qualitative methods courses in Anglo-American geography departments, as an alternative to quantitative methods. For an overview, see Eyles and Smith (1988), Eyles (1993), Lawson (1995), Johnston (1997), Jones et al (1997), and Fotheringham et al (2000). (2) In this paper, I will use positivist as a shorthand for logical positivism; the Vienna Circle brand of positivism that became the norm for `normal' science in geography, as in most other disciplines. It is important to recall that, in its original Comtean form, positivism was conceived as a humanist enlightenment project, notwithstanding the ways in which, as logical positivism, much of this emancipatory concern has been set aside (Gregory, 1978). with marginal communities struggling to use GIS to better understand and improve their environments, I have long been convinced that progressive human geography can take advantage of quantitative practices. This seems to be an increasingly unpopular position. The rediscovery of the importance of qualitative and reflexive methods, their refinement under the influence of feminist geographers, and their establishment for the first time as a legitimate alternative to quantitative methods in many geography departments has been wonderful to see. But too often qualitative approaches are placed in opposition to quantitative/positivist geography (for a more constructive exception, see Dixon and Jones, 1998). At times this dualism has been stark indeed, as when the authors of a paper presented at an IBG meeting in the early 1990s began by apologizing to their audience for presenting some quantitative data in table form as part of their paper (David Rigby, personal communication). Reproducing this qualitative ^ quantitative dualism seems particularly paradoxical given that feminist and poststructural theory seeks to escape dualistic thinking. I argue here that this dualism should and can be deconstructed. Through tracing the evolution, reproduction, and contradictions of this representation, I suggest that it caricatures quantitative practices in geography in an overly narrow way, and that, in fact, the potential of quantitative geography for postpositivist geographical practices is significant. The argument is organized as follows. First, I trace how this representation has become hegemonic, arguing that its persistence is a result of how it serves the contrasting interests and identities of quantitative and qualitative geographers. I summarize periodic attempts to break down the dualism, and discuss why these have failed. Second, I briefly review the diverse practices of quantitative geography and contrast these with the dominant representation, drawing implications for the unrealized potential of quantitative practices. Third, I examine the case of GIS, around which the association of quantification with positivism has been resurrected. Finally, I discuss the possibilities for quantitative practices as one component of a progressive human geography in what I will argue is an increasingly quantified world. Prior to engaging in the argument, however, some preliminary remarks about mathematics as a language of theory are in order. I adopt the view that mathematics is a humanly constructed language for describing and conceptualizing the world (compare Barnes, 1998; Gould, 1999).(3) As with any language, it has been developed by social actors to carry out certain tasks, and continues to evolve in ways framed by our cultural context, our ability to use it, and the tasks to which mathematical communication is applied. Two consequences follow from this. First, mathematics is not a hermetically sealed logical system with its own internal rules that enable the truth of all mathematical statements to be determined (Go« del, 1931), nor is it a mirror of the natural order of the world. While mathematics is a better language than others for certain purposes, that is true of all languages, and we cannot conclude that mathematics is superior to other languages in general. But if claims that mathematics can be elevated above other languages because of its `rigor'öits ability to determine the truthfulness of statementsöare questionable, how is it that mathematics nevertheless has achieved the `structural effect' (Mitchell, 1999) of being elevated in this way, above and separated from other languages? I take seriously the arguments of Bruno Latour and others, that the answer to this question comes from examining the dynamics through which certain claims come to be taken as truthful and natural, as well as the processes and networks through which agreements about naturalness and truthfulness (3) It is important to recognize that mathematics is not simply numbers. In fact, it frequently has little to do with numbers per se. Its key features are not the objects manipulated in mathematical reasoning, whether these be numbers or letters, but the mathematical grammar through which relationships between these objects are expressed. 536 E Sheppard