Quantitative methods II: How we moved on – Decades of change in philosophy,focus and methods

I Introduction

The future of geography is inextricably bound to the future of spatial analysis. (Golledge, 2009: 481)

Whilst engaged on that defence, however, human geography’s quantifiers substantially changed their practices, which now differ very significantly from the original conceptions. This report reviews those changes under the three headings in the first report, giving most attention to philosophy; most of the methodological changes have been covered in detail in earlier reports by previous writers.

II Philosophy

The revolution’s underpinning philosophy, made explicit by Harvey (1969), was positivism – to some, logical positivism aimed at identifying geographical laws. That was attacked: from outside the ‘quantitative community’ the revolution was important because it stressed analytical rigour and the necessity of theory, but critics claimed it was the wrong sort of theory (e.g. Cox, 2014; Peet, 1998; Barnes and Christopher, 2018); from insiders it reflected growing awareness of the original research agenda’s limits – philosophical, methodological and substantive.

Two geographers long aware of those limitations had been disregarded. Crowe (1939: 11), the pioneer quantitative geographer (Johnston, 2019a), claimed geographers should seek ‘scientific synthesis…[in] statements of tendencies similar to those of the social sciences’. Jones (1956: 370) contested Martin’s (1951) claim that ‘laws must be formulated which could be applied in human geography with the same exclusiveness and rigor as scientific laws are applied in the physical world’, concluding that

however broad the generalization, it might fail in strict application to any single phenomenon. Any pattern which emerges does so as the statistical mean of the behaviour of a mass of human individuals, and any generalization which the human geographer might find useful must be based on this behaviour. (Jones, 1956: 373)

This shift of philosophical foundation involved no longer emphasising spatial form but stressing process. The early focus was on spatial patterns – points and hierarchies, lines and flows, surfaces and diffusions – resulting from human actions rather than the actions themselves. Increasingly attention focused on spatial order in decision-making – behavioural geography (Cox and Golledge, 1969, 1981; Golledge and Stimson, 1987, 1997), for which ‘Few, if any, of the classic positivist tenets now seem to be necessary’ (Couclelis and Golledge, 1983: 332). Positivism set ‘standards of clarity, consistency, and rigor in the development of argument and in the conduct of inquiry’, shifting it away from ‘fuzzy-mindedness, verbosity, muddled thinking and obscurantist discourse’ (p. 334) – hence they chose the term ‘analytic geography’, which studied ‘human existence…anchored in a shared external world’ (p. 337) and that did not need ‘the survival of the old-fashioned physicalism that sees the model of all knowledge in science and in particular that science of three centuries ago’.

There was also a growing acceptance that much human geography was insufficiently developed theoretically and, unlike the hard sciences, lacked the foundations for predicting outcomes. Gould (1981: 174), for example, preferred to ‘start with the data and try to make the data speak for themselves’, within a ‘frame of meaning’ that ‘must be derived by phenomenological and descriptive methods before they can be used in the empirical and explanatory part of a science…[deploying] descriptive analyses [that] should help us identify the geometries and mathematical structures that will not crush the phenomena’. (Gould’s (1980) chosen method/approach for this, Q-analysis, gained virtually no followers, however.) Some promoted what others interpreted as little more than naïve empiricism (e.g. Openshaw, 1991, 1992; Taylor and Overton, 1991); Openshaw’s ‘data-led’ discipline (1991: 622) explored the ‘increasingly spatial-information-rich world’ (Openshaw, 1992: 465) – exemplified by his Geographical Analysis Machine (Openshaw et al., 1988) and Geographical Explanation Machine (Openshaw, 1998b), which used computers’ ‘brute force’ to identify spatially significant clusters of, for example, particular diseases. This involved exploring patterns and their possible causes within broad theoretical structures rather than, as some argue (e.g. Taagepera, 2008, 2015), developing theories with precise, testable hypotheses. Not all accepted that argument, however (e.g. Plummer et al., 2012).

Such approaches paralleled arguments in sociology. Goldthorpe, quoting Neyman (1975: 417), argued that:

The common feature of…populations was that, while their individual elements were subject to considerable variability and might appear, at least in some respects, indeterminate in their states and behaviour, they could nonetheless exhibit aggregate-level regularities of a probabilistic kind. (2016: 7; emphasis in original)

Few quantitative human geographers expressed this changed philosophical foundation in presentations aimed at wide audiences. Quantitative Geography: Perspectives on Spatial Data Analysis (Fotheringham et al., 2000: xi; see also Fotheringham, 2006: 5) was written to ‘redress the rather antiquated view of quantitative geography held by many outside the research area’ but may not have reached many critics. The goal is ‘to accrue sufficient evidence which makes the adoption of a particular line of thought compelling’ regarding ‘variation in relationships over space’ but rarely searching for ‘hard evidence that global “laws” of human behaviour exist’. Kitchin (2006: 24) recognised that difference, but claimed that a consequence of arguing that ‘the scientific method [is] the most sensible and robust (rather than the only) approach to geographical enquiry’ (as in the pioneering text on statistical analysis in geography – Gregory, 1963; Johnston, 2018) is that much quantitative geography has ‘relatively weak and unstable philosophical underpinnings (much of it backsliding into empiricism) and [is] vulnerable to theoretic critique and challenge for which it has little response’ (p. 27). ¹

III Focus

Many among quantification’s early promoters were stimulated by location theories assuming economically rational spatial behaviour (Taylor, 1981; Haggett’s (1965) pioneering text is a paradigm exemplar); geometry was their mathematical language (Bunge, 1966).

To Bennett and Wrigley (1981: 6):

the paradigm of spatial geometry has been weakened…many of the questions deriving from the methodology of spatial geometry have been left behind…[being replaced] by an emphasis on spatial process.

There was a considerable broadening of substantive interests. Within urban geography, for example, sociologists’ development of social area analysis and factorial ecology (Johnston, 1971; Timms, 1971 – later the basis for geodemographics: Harris et al., 2005) stimulated mapping residential patterns, deploying factor/principal components and classification analysis (Taylor, 1981), and the resulting segregation (on which there is a very extensive literature: e.g. Lloyd et al., 2015; Piekut et al., 2019; Yao et al., 2018). Exploration of neighbourhood effects built on these studies, investigating how local contexts influence behaviour, and how they might be inferred from aggregate data without committing ecological fallacies (a non-geographical survey of that large literature is Galster, 2019). Those aggregate studies were accompanied by investigations using survey data to analyse individual behaviour patterns in, for example, voting (Johnston and Pattie, 2006), with the greater availability of relevant data facilitating explorations at a range of spatial scales (e.g. Harris, 2017).

IV Methods

In the quantitative revolution’s early decades statistical procedures were mainly used to test (usually verify) hypotheses using methods within the general linear model, notably regression and correlation. Mathematical approaches were adopted by only a few and were rarely covered by introductory texts (Taylor, 1977, is an exception). ² Substantial work was, however, led by Alan Wilson at Leeds (Johnston, 2019b), embracing mathematical modelling (Wilson, 1970, 1981, with introductory texts; Wilson and Kirkby, 1975) in a variety of contexts (Rees and Wilson, 1977), stressing particular views on location theory (Wilson, 1974, 2016a, 2016b) and deployed in applied locational exercises (Birkin et al., 1996). ³

Geographers became increasingly aware of the limitations of standard statistical procedures when applied to spatial data. Addressing them stimulated growing sophistication of spatial analysis – engaging the interest of statisticians and computer scientists plus other social scientists (Fotheringham and Rogerson, 2009), illustrated by work in several areas.

V Conclusions

The 1960s to 1980s saw considerable intra-disciplinary conflict as proponents of different approaches struggled for dominance in human geography’s research and teaching agenda. Such conflict is now muted as accommodations were implicitly reached whereby the separate approaches co-exist with relatively little interaction. There are occasional outbursts and attempts at re-defining, either by promoting a particular approach or side-lining another (excluding it from introductory textbooks, for example: Johnston, 2006), but adherents to separate positions now operate in relative ignorance of others’ activities. Some attempts at overviews of the entire discipline either exclude or misrepresent some of its component parts, however; quantitative human geography has been presented by some as if its current practices differ little from those deployed 50 years ago (for example, Cresswell, 2013; Couper, 2015; see Johnston et al., 2014). Hence the formulation of these three progress reports, providing a broad overview of a rapidly changing, vibrant subdiscipline that many human geography texts largely ignore.

Not only is quantitative human geography technically more sophisticated now (see, for example, Kwan, 2010; Legates et al., 2003), but its philosophy, substantive foci and methodologies are very different. For many decades human geography’s key metaphor, using Buttimer’s (1993) terminology, was the mosaic. The quantitative revolution sought to change that to machine (with all the potential dangers of instrumentalism, of ‘is becoming ought’) but the remaking of the quantitative approach outlined here has returned it to mosaic – a focus on places more than on spaces. Some features of the revolution’s early years, such as the primacy of central place theory, have almost entirely faded: others remain – gravity models are still fitted to flow data and the spread of diseases explored with diffusion models (Cliff et al., 2009) and spatial forms are investigated (D’Acci, 2019), as in the pioneering application of fractal theory (Batty and Longley, 1994; more generally on systems approaches, see Batty, 2005, 2013). But these extensions of traditional concerns have occurred alongside an explosion of changes in philosophy, focus and methods whose nature has been briefly reviewed here, as the foundation for the final report in the series that will set out the contemporary agenda.