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Issue 18 Autumn 1997

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Complexity Theory and Social Research

David Byrne

David Byrne is Senior Lecturer in Social Policy at the University of Durham. He has a long standing interest in the use of measurement as a way of describing social change and is currently completing a book on Complexity and Social Theory for Routledge.

Trisoglio defines complexity as

... not a single discipline, but a process that represents the sharing of ideas, methods and experiences across a number of fields. (1995:1).
Hayles puts it more forcefully : ‘When a dichotomy as central to western thought as order / disorder is destabilized it is no exaggeration to say that a major fault line has developed in the episteme.’ (1991:16) What we are dealing with is a recognition of the limits of science understood as the use of linear mathematical formalism in describing the world. This constitutes a challenge to the Newtonian foundation of western science. The elements of this challenge include: (i) a recognition of the centrality of Poincaré’s conception of deterministic chaos in both mathematics and science, dismissing both randomness, the foundation of stochastic modelling in science, and certainty, the foundation of linear determinism; (ii) a revalidating of the idea that systems have emergent properties which are not to be understood by reductionist analysis of the systems into lower order components -- that is an assertion of holism; and (iii) a rejection of the tradition of a two valued logic in which order and disorder are dichotomous and opposites and its replacement by a conception of them not as antagonistic and fixed states but rather as stages in a process of dynamic and transformational becoming.

The implications of this reformation have been identified by the Gulbenkian Commission on Restructuring the Social Sciences (1996). Not only are the boundaries which constitute disciplines in the social sciences rendered irrelevant by this perspective, but it offers a challenge to the demarcation of the social from other sciences. This does not amount to prioritising any domain of knowledge. What we are dealing with here is not a new envy of physics founded on reductionism -- quite the contrary. There are three points which need to be made before turning to the implications of complexity theory for the form and content of the social research programme.

The first is that we now have available an account of dynamics which centres on non-linear changes in the properties of systems as a whole rather than the linear trajectories of the elements which are located within those systems. As Prigogine and Stengers (1984) put it, we should replace mechanics with thermodynamics as our central analogy. The second, which follows from the first, is that systems are inherently evolutionary and that changes over time are not reversible -- systems are essentially historical1. This means that such systems have emergent properties and provides us with a way of conceptualising time which permits a proper understanding of the relationship between the temporal and the social. Finally, we have available a developed, sociologically located discussion of the meta-theoretical character of complexity theory which identifies it as a scientific ontology complementary to the philosophical ontology of critical realism developed by Bhaskar (see Reed and Harvey 1996).

For social research the most important implication of this is that the long running problem of relating the quantitative and qualitative programmes no longer matters, apart from to those who deny any substantive reality to anything other than social actions and therefore regard all measurement as inherently reifying. The rest of us are now able to see the quantitative as itself inherently qualitative, given that the nonlinear and emergent character of social and other significant systems means that we can never establish general non-contextual laws and that the quantitative account itself is simply, but very usefully, a way of describing local contexts and transformation of systems as a whole.

This way of thinking corresponds very closely to the idea of the transformation of modes of production. The idea that systems are nonlinear means exactly that changes happen in them which are discontinuous and represent transformations of kind. Local quantitative descriptions of such bifurcation points are the measured history of such qualitative transformations of state.

A not very useful way of going on

Social scientists have responded to this new way of thinking in a variety of ways. One has been explicit imitation of the approaches of physical scientists. Such approaches involve the search for chaotic order in dynamic data sets measured across very large numbers of time points (for an accessible introduction to chaos theory see Peak and Frame 1994). This imitation of the method of physics is described in a set of chapters in Kiel and Elliott dealing with what they refer to as ‘mathematically rigorous approaches to the statistical analysis of chaotic dynamics in social science data’ (1996:9). Approaches including the use of spectral analysis (McBurnett 1996), Lyapunov exponents (Brown 1996) and ‘near neighbour techniques’ (Jaditz 1996) are all intended to enable the identification of chaotic determinism in what appear to be purely random/stochastic2 systems. Spectral Analysis techniques involve the examination of the pattern of oscillations in a time series in relation to the frequency of those oscillations. They originated in the analysis of oscilloscope readings. The Lyapunov exponent is used to measure the extent to which small changes in initial conditions generate large scale divergence over time. Near neighbour techniques use the idea of attractors. If there are chaotic attractors, the next state of a system may be predicted by examining the history of its near neighbours because they are all drawn towards the same attractor.

These approaches are founded in the US centred tradition of the search for chaos rather than in the European interest in the emergence of order from chaos. Porush spells out the implications of the difference:

Although Prigogine’s term “dissipative structures” hasn’t sold as well (as chaos) it is in most senses much more accurate. First, it focuses on the dynamic system which undergoes the sudden transformation from apparently chaotic to apparently ordered (original emphasis) on the other side of the bifurcation point. Second, it implies the structure in Prigogine’s mathematical model which specifies when such orderliness is not only possible, but likely to arise. (1991:59)

In other words there is not much point in searching for nonlinear equations which will serve to describe the deterministically chaotic form of a chaotic dynamic system and thereby provide a means of predicting the behaviour of that system. Moreover, chaos identification methods require the availability of very large runs of time specified measurements of a kind which are generally not available for social time series. However, people are doing this kind of thing and the cited references explain how.

A much more useful approach

Another part of the chaos / complexity programme is simulation. The availability of computers permits both ‘experimental mathematics’ and the development, through simulations, of very elegant graphical representations of the behaviour of uninterpreted deterministic chaotic expressions. These are simulations in which parameters are specified so as to describe the initial conditions of real systems, or at least of meaningful analogues of real systems (see Khalil 1996 for an discussion of the meaning of metaphor in this context). Given the general (but not absolute) impossibility of solving nonlinear equations which describe the evolutionary behaviour of dissipative systems, it has proved necessary to turn to what Reed and Harvey call ‘iconological modelling’ in which ‘ the gaze is more important than deductive logic in grasping the evolution of a chaotic structure.’ (1996:310, emphasis in the original). There are relevant discussions of simulation in Gilbert and Doran (eds. 1994) and Gilbert and Conte (eds. 1995) and a discussion of Modelling Complex Phenomena in Lam and Naroditsky (eds. 1992).

A particular advantage of simulation noted by Gilbert and Conte (1995:5) is that it allows for the investigation of ‘sociality’, that is, of whole system properties corresponding exactly to Durkheim’s conception of social facts, and allows for examination of their emergence and transformation over time. This is an important corrective to the overwhelming emphasis on the individual case in quantitative social science, where the individualistic focus involves an implicit and erroneous assumption that it is possible to derive the macro properties of social systems from the aggregation of the properties of the individuals constituting them.

Thinking differently about what we already do and bringing time into it always

Another way of doing social research in a complexity informed way is to think somewhat differently about the procedures and methods of both quantitative and qualitative social investigation as we are already doing them. The quantitative case is more straightforward. We have available a number of what the Economic and Social Research Council calls ‘large and complex data sets’, for example the products of annual UK General Household Surveys. The ‘complexity’ in these datasets derives from their hierarchical character. At its simplest this means that they contain data about individuals within households. The data also constitute a time series and so what we have in effect is a series of snapshots of the nature of UK society describing individuals and households. With a panel study such as the British Household Panel Study we find that during successive passes the focus remains on the same individuals and households over time allowing for an examination of exact dynamic change3.

We also have descriptions of higher system levels. From standard time series as published in Social Trends and Regional Trends we have accounts of the history of national and regional systems within which individuals are located within households. We can see how people’s lives change within a changing social world.

A simple method of looking for system changes is the construction of time ordered classifications of the entities at any level within a hierarchical data set, such data sets being conceptualised as operationalizations of the nested systems described by Reed and Harvey (1996). The advantage of this is that the forms of social structures can be examined in relation to parameters which are characteristic of the system as a whole. Of particular interest is the relationship between the actual level of inequality in a social system, which, however operationalized, can only be a whole system property, and the forms of real socio-spatial division within that system. The relative neglect of numerical taxonomy techniques in analyses of social structure in general and of class forms in particular is puzzling. Time sequential classifications are a useful exploratory device. This can be done rather easily for successive time ordered data sets such as the General Household Survey cohorts using readily available cluster analysis procedures e.g. quick cluster in SPSS. Bryne (1997) has an example of such an approach using the invaluable Cleveland Social Survey which described household characteristics while locating households in neighbourhood zones within a single locality, and did so over an eighteen year period.

Several authors (e.g. Faia 1996) have proposed the use of logistic regression and loglinear procedures in analysing time orderable data sets. This approach has attractions because it represents a way of handling statistical interaction. Interaction is essentially equivalent to that demarcating characteristic of nonlinear systems, the breakdown of the property of superposition. It has been unfortunate that the emergent complexity generated by interaction has so often been reduced to terms in linear equations. A way of thinking informed by complexity leads us to treat procedures which enable the identification of significant interaction as qualitative exploratory devices rather than as ways of establishing law like models. In practice this is what social scientists really do (see for example Gilbert’s (1993) discussion of the use of G2 as a criterion for model selection). Instead of generating models which seek to describe the determinants of outcomes, and writing interactions as terms in those models, we can see interactions as signs of the presence of complexity in general. This kind of approach is likely to be particularly fruitful with panel surveys in which interactions with time are included, these terms being interpreted as indicating nonlinear changes.

Assertions about the possibilities of qualitative analyses are even more speculative. However, given that procedures for computer based analyses of qualitative data are inherently founded around relational data bases, it does seem that in qualitative data sets which are in some way time ordered, we might use the perspective of emergent order with some profit. Certainly as Hayles (1990, 1991) has demonstrated there is considerable power in literary analyses based on these perspectives. An interesting example is provided by the work of Callaghan (in progress) who has interviewed a sample of young adults in Sunderland, both when they were 18 and when they were 23. The interviews can be analysed using Nud°ist, for example. The time ordering allows for the consideration of the existence of different types of trajectory over the transition to adult life. Such an approach allows for reflexive return to informants to assess their views about qualitative descriptions of processes of change.

The absolutely essential element in the approaches being suggested here is that the data are time ordered. We have to be able to examine processes of becoming. It is important to engage in Analyzing Social and Political Change (Dale and Davies 1994), but from a perspective which prioritises whole system emergent properties. Otherwise we are reduced with the authors in that collection to linear models buttressing the time honoured individualistic fallacy of quantitative social science.


1 The use of the terms evolutionary and historical to describe systems assigns two properties to them: first, they change over time and usually change by becoming more complex (the evolutionary property); and secondly, the changes are irreversible -- time has an arrow -- and the current state of the system is a product of irreversible evolutionary changes and the emergent properties at each stage (the historical property).

2 Statisticans usually use the terms random and stochastic as synonyms. However, stochastic originates in a Greek term for aiming an arrow. It has a dynamic directionality which is lacking in the idea of randomness.

3 Unfortunately we have no national UK data set which allows us to locate even successive non-panel passes of households and individuals at a local spatial level. This is possible with the Cleveland Social Survey (see Byrne 1995) for that conurbation, but the absence of the ability to handle spatial changes matters.


Byrne, D. S. 1995 ‘Deindustrialisation and Dispossession’ Sociology, vol. 29, 95-115.

Byrne, D. S. 1997 ‘Chaotic Places or Complex Places’ in S. Westwood and J. Williams (eds.) Imagining cities. London: Routledge, 50-72.

Brown, T. A. 1996 ‘Measuring Chaos using the Lyapunov Exponent’ in Kiel, L.D. and Elliott, E. (eds.) op cit 53-66.

Callaghan, G. (in progress) ‘Young people and social change in Sunderland’. PhD thesis University of Durham, to be submitted.

Dale, A., and Davies, R. B., 1994 Analyzing Social and Political Change London: Sage.

Gilbert, N. 1993 Analyzing Tabular Data: loglinear and logistic models for social researchers London: UCL Press.

Gilbert, N. and Doran, J. (eds.) 1994 Simulating Societies London: UCL Press.

Gilbert, N. and Conte, R. (eds.) 1995 Artificial Societies London: UCL Press.

Faia. M. A. 1996 'Comparative Analysis with qualitative variables : a loglinear view', mimeo, Dept of Sociology, College of William and Mary,Williamsburg, VA 23185,USA

Gulbenkian Commission 1996 Open the Social Sciences: report on the restructuring of the Social Sciences Stanford CA: Stanford University Press.

Hayles, N. K., 1990 Chaos Bound Ithica: Cornell University Press.

Hayles, N. K., 1991 Chaos and Order Chicago: University of Chicago Press.

Jaditz, T. 1996 ‘The Prediction Test for nonlinear determinism’ in Kiel, L.D. and Elliott, E. (eds.) op cit 67-88

Khalil, E.L. 1996 ‘Social Theory and Naturalism’ in E.L. Khalil and K.E. Boulding (eds.) Evolution, Complexity and Order London: Routledge, 1-39.

Kiel, L.D. and Elliott, E. (eds.) 1996 Chaos Theory in the Social Sciences Ann Arbor: University of Michigan Press.

Lam, L. and Naroditsky, V. (eds) 1992 Modelling Complex Phenomena New York: Springer-Verlag.

McBurnett, M. 1996 ‘Probing the underlying structure in dynamical systems: an introduction to Spectral Analysis’ in Kiel, L.D. and Elliott, E. (eds.) op cit 67-88.

Peak, D. and Frame, M. 1994 Chaos Under Control New York: W.H. Freeman.

Porush, D. 1991 ‘Fictions as dissipative structures’ in Hayles, N.K. (ed) op cit. 54-84.

Reed, M. and Harvey, D.L. 1996 ‘Social Science as the study of Complex Systems’ in Kiel, L.D. and Elliott, E. (eds) Chaos Theory in the Social Sciences Ann Arbor: University of Michigan Press 295-324.

Prigogine, I. and Stengers I., 1984 Order out of Chaos New York: Bantam.

Trisoglio, A. 1995 ‘Complexity : The Challenges’ Paper presented at workshop ‘Risk, Policy and Complexity’ IIASA Laxenburg.

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Autumn 1997 © University of Surrey

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