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quantitative revolution

  The \'radical transformation of spirit and purpose\' (Burton, 1963, p. 151) which Anglo-American geography underwent in the 1950s and 1960s following the widespread adoption of both inferential statistical techniques and abstract models and theories. In the process, an old idiographic geography characterized by a focus on areal differentiation and regional geography was displaced by a new nomothetic discipline, spatial science. As in most revolutions, tracts were written (such as Ian Burton\'s, 1963, quoted above), slogans coined (e.g. Harvey\'s, 1969, \'By our models you shall know us\'), heroes lionized (the gendering is appropriate in this case), and villains vilified. All of which attests to the fact that the revolution was as much social as it was intellectual.

In many ways both the adjective and the noun in \'quantitative revolution\' are misnomers. The noun is wrong because geography has been quantitative since its formal institutionalization as a discipline in the nineteenth century. The widespread use of formal statistical techniques from the 1950s onwards therefore represented evolution rather than revolution (Chisholm, 1975). The adjective is wrong because what was so significant about the 1950s was the introduction of theory not numbers; it was a theoretical revolution. Indeed, the new-found theoretical sensibility has been the period\'s most enduring legacy. Initially it secured the discipline\'s membership within the social sciences but also, and perhaps more importantly, prepared it for the inordinate range of theoretical \'isms\' that were to come — including, ironically, many \'isms\' that were diametrically opposed to the original conception of theory proffered at the time. (Note that Burton\'s, 1963, paper did link the \'quantitative revolution\' to \'theoretical geography\' — clearly getting the order of the adjectives wrong but illustrating the contemporary emphasis placed on quantification.)

As a discipline that is descriptive and practical, it is not surprising that geographers have a long history of using numbers. In Britain, the Royal Geographical Society (RGS; cf. geographical societies) founded in 1830 was a classic \'centre of calculation\' (Latour, 1987) providing resources for foreign expeditions, the products of which were sorted, sifted, displayed and presented back in London in the form of maps, tables, and figures (Livingstone, 1992, ch. 5). Similarly, in the US between 1852 and 1871 the American Geographical (AGS) and Statistical societies were formally twinned, and even when they went their separate ways, the mandate of the AGS remained \'the collection, classification and scientific arrangement of statistics and their results\' (quoted in Berry and Marble, 1968, p. 1). The point, then, is that geographers have always been numerate. Even within the discipline\'s reputedly least numerate paradigm which preceded the quantitative revolution, areal differentiation, Richard Hartshorne (1959, p. 161) still affirmed that \'scientific knowing … and objectivity … can best be accomplished … by quantitative measurements … through the logic of mathematics\'.

When the quantitative revolution began in the mid-1950s it was as a series of local affairs crystallized around one or two key individuals (see Johnston, 1997, pp. 62-73). In America the Department of Geography at the University of Washington, Seattle, was pivotal, as was the University of Iowa, Iowa City. At Washington, the presence of Edward Ullman, and especially William Garrison, was key. In 1954 Garrison gave the first advanced course in statistical methodology in a US Department of Geography, and in an early advertisement for the Department, the Head, Donald Hudson (1955), boasted about the departmental use of an IBM 604 digital computer, also a national first. The first cohort of graduate students from that department, which included Brian Berry, Michael Dacey, Arthur Getis, Richard Morrill, John Nystuen, and Walter Tobler, was critical in diffusing the Washington message, which they did by quickly establishing themselves and their research agenda at several prestigious US universities including Chicago, Northwestern and Michigan. At Iowa, the work of Harold McCarty was central. Again, he attracted a number of graduate students, including some from Australia and New Zealand (such as Leslie King and Reginald Golledge), all of whom were to prove vital in spreading the word about numbers. Outside the US, the University of Toronto became important in the mid-to-late 1960s, while Peter Haggett and Richard Chorley in the UK (the \'terrible twins\' of British geography) and Torsten Hägerstrand in Sweden were crucial in establishing a European beachhead. The influence of Chorley and Haggett on British school teachers through the Maddingly Hall lectures and concomitant publications was especially important sociologically (Chorley and Haggett, 1965, 1967). Those lectures brought pressure for change from those entering the discipline at the bottom, making the message of quantification more deeply entrenched in the educational hierarchy than in the US.

By the mid-1960s a network of quantification (and symbolized by Taylor\'s, 1977, fictional Quantgeog Airlines flight plan — see figure) was in place that connected researchers and universities on both sides of the Atlantic. The network was both literal and figurative. It was literal because individuals, as well as reprints, data sets, and mimeographs ceaselessly moved among its nodes. Faculty and graduate students travelled to workshops (such as the Michigan Interuniversity Community of Mathematical Geographers: MICMOG), seminars and special conferences were organized, and papers circulated for discussion and criticism.

{img src=show_image.php?name=bkhumgeofig63.gif }

quantitive revolution Quantgeog Airlines flight plan (from P.J. Taylor, 1997, p.15)

It was figurative because the network was associated with two new sets of geographical practices: technique-based and theory-based. The new techniques included computerization (reading computer FORTRAN manuals, writing programs, interpreting printouts), and the study and application of ever more complex statistical methods (parametric and nonparametric, linear and non-linear, static and dynamic; for details, see Gould, 1969, and quantitative methods). The theory-based practices involved thinking about space and location in rigorously abstract terms (cf. locational analysis). Before the 1950s human geography was resolutely atheoretical. With the quantitative revolution, however, a flood of theoretical models from other disciplines were imported and applied. There were several sources: from physics came gravity and later entropy-maximizing models (and associated with macrogeography and social physics); from economics, often by way of regional science, came the holy trinity of von Thünen\'s model, Weber\'s location triangle (cf. industrial location theory), and Lösch\'s and Christaller\'s hexagonal central place theory; from sociology came the Chicago school, urban factorial ecology, and the rank-size rule; and from geometry came networks and graph theory and the analysis of topological forms which were incorporated into transportation models. More generally the quantitative revolution was defined by an innovative set of geographical practices that stemmed from a distinct set of technical and theoretical competencies. In the process human geography moved from a field-based, craft-form of inquiry to a technical, deskbound one where places were analysed from afar.

Whether these practices represented a self-consciously new philosophical approach, positivism, is unclear. Reflecting on what they had done, many of the early proponents of the quantitative revolution speak of their work in terms of a revolution of technique not of philosophical conviction (discussed in several reflections on the revolution in Urban Geography, vol. 14, 1993). Few had any philosophical training, and most had never heard of positivism before the 1970s; Richard Morrill (1993, p. 443), for example, in recalling his experiences as a graduate student at the University of Washington, said \'I never met a positivist\'. Rather, when people turned to positivism, such as Harvey (1969), it was in effect an ex post rationalization of quantification, and then, ironically, just as the movement was beginning its slow arc of decline.

Much more clearly marked than positivism was the role of sociological processes in both maintaining and extending the quantitative revolution. Most immediately the revolution required that the message be spread. This occurred through: establishing new journals (e.g. Geographical Analysis in 1969); hiring the \'right\' people (the Department of Geography at Ohio State was transformed following Edward Taaffe\'s appointment as Chair in the mid-1960s); securing funding to carry out research (mainly from the National Science Foundation (NSF) and the US Office of Naval Research: see NAS-NRC, 1965); and training the wider discipline to think in a new vocabulary (carried out under the auspices of NSF-funded summer workshops on quantitative methods beginning in 1961).

In all of this, circumstances, particularly in the US, were propitious. Higher education was expanding, the social sciences were burgeoning, and the broader instrumental, \'can-do\' attitude of the time resonated perfectly with the new geographical models and techniques (cf. instrumentalism). The old-style geography of regional description was being swept away by the new broom of the quantitative revolution. Peter Gould (1978), in fact, labelled the era \'The Augean period\' after the mythic Augean stables which after 30 years of neglect were cleaned all of a piece by Hercules.

Equating the quantitative revolutionaries with Hercules, and an earlier non-quantitative geography with unkempt, filthy Augean stables, also speaks to other sociological processes around the revolution that typically are not acknowledged. First, Gould\'s portrayal of the revolution in heroic terms, whether he wanted to or not, points to its masculinist nature. This is true in a number of senses: that its initial proponents and expositors were all men; that there were virtually no substantive studies of women carried out by that group; and that the disembodied, totalized knowledge proponents sought matched what later feminists would describe as phallocentric (see situated knowledge). Second, Gould\'s Augean metaphor also illustrates the extent to which quantifiers were desperately keen to separate themselves from the past. Clearly the main reason was intellectual, but, as Taylor (1976) argues, another was for internal sociological reasons within the academy. For in order to get ahead, to secure early promotion and academic status, it was, and still is, necessary to be original, and to do something different. For a group of very bright, ambitious and competitive young scholars emerging from graduate school, the quantitative revolution was the perfect vehicle to achieve such career goals.

At some point in the late 1960s, or early 1970s, these once-compelling sociological reasons began to slip, and with them the grip of the quantitative revolution on the discipline. There were at least two broad reasons for change. First, a different kind of world was emerging that was more restless, less innocent than before. Great debates were happening around issues of poverty, civil rights, the environment, gender and racial equality and war, but the quantitative revolution seemed unable or unwilling to address them. The ensuing relevance debate of the early 1970s left quantifiers flat-footed (cf. radical geography). As Harvey (1973, p. 129) damningly put it, \'There is an ecological problem, an urban problem, an international trade problem, and yet we seem incapable of saying anything of depth or profundity about any of them. When we do say something, it appears trite and slightly ludicrous. In short, our paradigm is not coping well. It is ripe for overthrow.\' Second, an academic generation had already passed since the first quantifiers, and the time was once more ripe for change. So yet a new vocabulary was forged to mark off the old from the new, in this case, one principally derived from Marxism (Harvey, 1973), and its later successor projects. But the important point, and why the quantitative revolution remains a watershed in geography\'s recent history, is that Marxism and the various intellectual movements that followed persisted with a theoretical vocabulary. Certainly since that time the meaning of theory has altered, but the continuity of some kind of theoretical vocabulary has proven more important in subsequently shaping the discipline than any rupture. (TJB)

References Berry, B.J.L. and Marble, D.F., eds, 1968: Spatial analysis: a reader in statistical geography. Englewood Cliffs, NJ: Prentice-Hall. Burton, I. 1963: The quantitative revolution and theoretical geography. Canadian Geographer 7: 151-62. Chisholm, M. 1975: Human geography: evolution or revolution? Harmondsworth: Penguin. Chorley, R.J. and Haggett, P., eds, 1965: Frontiers in geographical teaching. London: Methuen. Chorley, R.J. and Haggett, P., eds, 1967: Models in geography. London: Methuen. Gould, P. 1969: Methodological developments since the fifties. Progress in Geography 1: 1-49. Gould, P. 1978: The Augean period. Annals of the Association of American Geographers 69: 139-51. Hartshorne, R. 1959: Perspective on the nature of geography. Chicago: Rand McNally. Harvey, D. 1969: Explanation in geography. London: Edward Arnold. Harvey, D. 1973: Social justice and the city. London: Edward Arnold. Hudson, D. 1955: University of Washington. Professional Geographer 7(4): 28-9. Johnston, R.J. 1997: Geography and geographers: Anglo-American human geography since 1945, 5th edn. London: Arnold. Latour, B. 1987: Science in action: how to follow scientists and engineers through society. Cambridge, MA: Harvard University Press. Livingstone, D.N. 1992: The geographical tradition: episodes in a contested enterprise. Oxford: Blackwell. Morrill, R. 1993: Geography, spatial analysis and social science. Urban Geography 14: 442-6. NAS-NRC, 1965: The science of geography. Washington, D.C.: NAS-NRC. Taylor, P.J. 1976: An interpretation of the quantification debate in British geography. Transactions, Institute of British Geographers NS 1: 129-42. Taylor, P.J. 1977: Quantitative methods in geography: an introduction to spatial analysis. Boston: Houghton Mifflin.

Suggested Reading Barnes, T.J. 1998: The history of regression: actors, networks, numbers and machines. Environment and Planning A 30: 203-23. Gould (1978).



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