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  An idealized and structured representation of the real (cf. abstraction; ideal type). Model-building has a long history in many sciences, but its incorporation into geography is of comparatively recent origin. It is usually most closely associated with post-war attempts to establish geography as a spatial science. Indeed, scientificity was central to the bench-mark collection of essays edited by R.J. Chorley and P. Haggett as Models in geography (1967). They argued that model-building depends on what they called \'analogue theory\', which treats models as \'selective approximations which, by the elimination of incidental detail [or \'noise\'], allow some fundamental, relevant or interesting aspects of the real world to appear in some generalized form\'. The accent on generalization was vital, and it was given a particular inflection by the architects of spatial science. Generalization can take many different forms, but spatial science relied heavily on two strategies: (i) the construction of schematic diagrams to represent geometric schemes in visual terms; and (ii) the formalization of their \'spatial structures\' as statistical and mathematical models. These twin devices played an important role in the search for general theories of spatial organization that, so it was believed, could underwrite the seemingly endless heterogeneity and differentiation of human landscapes. Ten years later, P. Haggett, A. Cliff and A. Frey (1977) spoke of \'essential links\' between model-building in these terms and the so-called quantitative revolution, and many of the first-generation models were attempts to represent the abstract geometry of an idealized landscape through various transformations of distance-decay functions. Because the itinerary from abstraction through generalization to disclosure was supposed to provide for further extensions and explorations, model-building was seen as a necessary moment in the \'puzzle-solving\' activity required for the foundation of a new scientific paradigm. It was no accident, therefore, that Chorley and Haggett\'s advocacy of a model-based paradigm for geographical inquiry should have been based in resolutely Kuhnian terms.

Since Chorley and Haggett wrote, however, the claims and concepts that provided the architecture for their pioneer collection of essays have been re-evaluated on five main levels.

The locational models of spatial science have been subject to a (limited) reformulation. In the second edition of Locational analysis in human geography (Haggett, Cliff and Frey, 1977) the authors admitted that \'the present stock of models may be unprepossessing\', and a comparison with the first edition (1965) shows that the intervening years had seen remarkably few attempts to construct new locational models, although some of the old ones had been reworked: e.g. Hägerstrand\'s contagious diffusion model was shown to be a special case of a more general epidemiological model, the classical gravity model was shown to be an instance of a more general class of entropy-maximizing models and the von Thünen model was recast as the dual of the transportation problem in linear programming.

This limited advance was, in part, because the autonomy of location theory had been compromised by the construction of more inclusive models of the space-economy outside the domain of spatial science. Those who continued to work within the conventional modelling framework were more interested in developing statistical and mathematical models that could break open complicated datasets than with seeking to establish in any direct way the theorems of a general spatial science. Elsewhere in the discipline, however, model-building took radically different directions, and when Peet and Thrift compiled a collection of New models in geography (1989) their sub-title identified a tectonic shift in the foundations of model-building: \'the political-economy perspective\' signalled a range of different approaches that had a common grounding in forms of critical social theory attached in varying degrees to historical materialism.

Partly as a consequence, the original claim for analytical model-building as the object of geographical inquiry was displaced and efforts were directed towards methods as means rather than as ends in themselves. This effort was originally entangled with the critique of (logical) positivism, but the use of analytical methods was subsequently resituated within a wider intellectual landscape that was much more sensitive to the limitations of such methods. So, for example, Sheppard and Barnes (1990) \'recognize that many aspects of society and economy are not subject to analytical treatment, and even those aspects that are may well be more sensitively treated by non-analytical methods\'. The same authors direct modelling towards the identification of substantive processes and causal mechanisms rather than mathematical processes and idealized landscapes:

Distances are not some physical constraint to which all realizations of a process are subject in identical ways, as in the laws of physics, because spatial structures are socially constructed and far more complex than the isotropic and stationary spaces that are generally relied on in [locational] analysis. (Sheppard and Barnes, 1990)Those reformulations had some impact on conventional modelling, and an international conference held in 1987 to mark the twentieth anniversary of the original Models in geography included both revisionists who sought to rethink spatial modelling and dissidents who were sceptical of its ability to address important practical questions. On one side, Harvey claimed that \'those who have stuck with modelling since those heady days [of the late 1960s] have largely been able to do so by restricting the nature of the questions they ask\'. To Cosgrove, modelling was a quintessential expression of (high) modernism and the privilege it accorded to abstraction, parsimony and generalization was altogether incapable of responding to the challenges of \'difference\' being articulated through a diffuse postmodernism. On the other side, the conference included a large number of unrepentant spatial scientists who had no time for such concerns, and who reaffirmed their faith in the central importance of formal modelling as a way either of making an accommodation with the New Right (Bennett) or of meeting the demands of the commercial market-place (Openshaw: see Macmillan, 1989). Their priorities have since been boosted by the rapid expansion of geographical information systems and by a robustly contentious statement of the importance of securing human geography as a \'real\' science — a computational human geography — that would eschew \'soft methodologies\' and incorporate new approaches to modelling at its core (Openshaw 1998).

What most exercised Openshaw was the counter-claim that human geography also had roots in the humanities and the social sciences, and in particular the rapid advance of post-structuralism through the discipline. There is no doubt that post-structuralism calls into question the epistemology on which conventional model-building relied: the separation between \'the real\' and \'representation\' (Dixon and Jones, 1998). But its practitioners do none the less provide heuristics — usually in words rather than schematic diagrams or mathematical formulations — and they do offer vignettes that purport to illuminate larger propositions. Openshaw (1998) claimed that these constructions are at once too complicated and too singular: \'difficult-to-read texts\' that offer merely \'descriptions of unique experiences that do not generalize\'. This appears to reinstate the much misunderstood distinction between idiographic and nomothetic approaches, but Sibley (1998) believes that what is really at stake is abjection: \'anxiety about disorder\' that is inimical to the model-building enterprise of classical spatial science and its successor projects. \'That there is more order in the world than appears at first sight is not discovered till the order is looked for\', Chorley and Haggett (1967) often reminded their readers. Post-structuralism draws attention to the radical non-innocence of just \'looking\', and its interventions have unsettling implications not only for the formal modelling of spatial science but also for the \'new models\' of political economy and social theory (cf. Sheppard, 1995). (DG)

References Chorley, R.J. and Haggett, P., eds, 1967: Models in geography. London: Methuen. Dixon, D. and Jones, J.P. 1998: My dinner with Derrida, or spatial analysis and post-structuralism do lunch. Environment and Planning A 30: 247-60. Haggett, P., Cliff, A. and Frey, A. 1977: Locational analysis in human geography, 2nd edn. London: Edward Arnold. Macmillan, B., ed., 1989: Remodelling geography. Oxford: Blackwell. Openshaw, S. 1998: Towards a more computationally minded scientific human geography. Environment and Planning A 30: 317-32. Peet, R. and Thrift, N., eds, 1989: New models in geography: the political economy perspective, 2 vols. London: Unwin Hyman. Sheppard, E. 1995: Dissenting from spatial analysis. Urban Geography 16: 283-303. Sheppard, E. and Barnes, T. 1990: The capitalist space-economy. London: Unwin Hyman. Sibley, D. 1998: Sensations and spatial science: gratification and anxiety in the production of ordered landscapes. Environment and Planning A 30: 235-46.

Suggested Reading Dixon and Jones (1998); Harvey, D. 1969: Explanation in geography. London: Edward Arnold, chs 10-11; Macmillan (1989).



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