What Is Complexity Science?
Thinking as a Realist About Measurement and Cities and Arguing for Natural History

David Byrne
University of Durham, ENG


One of the more attractive developments in contemporary science studies is the inductive turn. In other words, the nature of science is established not only, and perhaps not at all, by the abstract specification of the scientific method. Instead, workers in science studies employ the frames of reference of history, sociology, and other social sciences in empirical investigation of the actual work of scientists. My effort at answering the question set for this special issue is going to take that form, albeit in what the polite might call a reflexive and the blunter identify as a solipsist fashion. In other words, I am going to engage in self-examination and seek to identify the nature of complexity science by reflecting on my own practice.

I work on and with complexity. When I say I work on complexity, I mean that a large part of my intellectual activity is methodological and technique oriented. That is to say, it is concerned with how we can understand complex systems given a specification of their nature1the methodological issue setand with how, given that form of understanding, we might develop a set of tools enabling us to grasp something useful about the nature of complex systems and the range of their possible future trajectoriesthe issues of technique. When I say that I work with complexity, I mean that I attempt to use the complexity frame of reference both in retrodictive exploration of the development of social systems and as a guide to social action that might determine the future trajectories of social systems. Much of my work is concerned with urban systemswith the combinations of location in nature, built environment, and local social systems constituting particular urban places.

In this article I am going to work through these elements in turn. I will begin with an ontologically derived argument about measurement in relation to complex systems, continue with a discussion of classification across time as a way of exploring the nature of complex systems, and conclude with a demonstration of the implication of this combination of understanding and method in relation to the general issues regarding the form and implications of the recent shift from industrial to postindustrial character in many urban places. Overarching all of this is a commitment to complex realism”—to the synthesis of critical realism as a philosophical ontology and complexity theory as a scientific ontology proposed by Reed and Harvey (1992).

One of the components of any specification of what something is, is an eliminatory assertion of what it is not. I will now assert that complexity science is not an activity directed toward the production of any set of master equations, even of nonlinear master equations, that can describe the essential workings of any complex system. Equation building may well have a limited role in our activities, but we do not derive complexity from it. It is at best part of a general descriptive process when integrated with other methods. My specification will in part be founded on a respectful but critical engagement with approaches to urban and other systems developed by those associated with the International Ecotechnology Centre at Cranfield University, UKrespectful because their work has always made me think and because their idea of integrative method is one that seems to me to be entirely appropriate, and critical because I think they have a hankering for the master equation set as the objective of complexity science. This is coupled with a less respectful and substantively more critical rejection of those approaches to complexity that seek to derive emergence solely from the interaction of simpler elementstypified by Holland (1998)that in general leads to a turn to microeconomic/rational choice-style specifications of agents and/or game theory-style rules in attempting to generate artificial analogs of real complex systems. This implies that for me, complexity science has to be decidedly skeptical about simulation.

Let me conclude this introductory section with some remarks about that word science. Monoglot English speakers are impoverished by the general association of the English word for organized knowledge with a specific privileged location of that knowledge in the domain of the physical sciences, a general specification of the appropriate form for obtaining that knowledge through experimental method,2 and a belief that the optimal form of the presentation of that knowledge is through mathematical forms describing laws of nature. In other words in colloquial, and even most academic, use, the English word science carries a heavy positivist burden. This is not true of the Slavic word nauk, which is usually translated into English as science but means all systematically organized knowledge regardless of its disciplinary location, the method through which it was obtained, or the form of representation. This article is committed to science as nauk, not science as science.


Emergence is above all a product of coupled, context dependent interaction. Technically these interactions, and the resulting system, are non-linear. The behavior of the overall system cannot be obtained by summing the behavior of its constituent parts. (Holland, 1998: 121-2, original emphases)

I used to worry about the combination of analysis and emergence typified by Holland's discussion above. I came to complexity to a considerable degree through a concern with the implications of statistical interactionthe sure trace when employing statistical procedures based on the General Linear Model that something was going on that did not fit either the linearity of that model or the general analytical approach in which variables were considered to have a real existence separate from the entities that had variate properties. Sociologists, as opposed to social statisticians, have always worried about the reality of variables, but the argument has often been one centering on the validity of operationalizations. In a typically Platonist fashion, a real variate entity was assumed to exist somewhere out therein the natural world's equivalent of the nineteenth-century physicist's etherto which our measurements were approximations.

A more fundamental attack on the reality of variables can be mounted if we take a relational view:

Sociologists today are faced with a fundamental dilemma: whether to conceive of the social world as consisting primarily in substances or in processes, in static things, in dynamic, unfolding relations. Large segments of the sociological community continue implicitly or explicitly to prefer the former point of view. Rational-actor and norm-based models, diverse holisms and structuralisms, and statistical variable analysesall of them beholden to the idea that it is entities that come first and relations among them only subsequentlyhold sway throughout much of the discipline. But increasingly, researchers are searching for viable analytic alternatives, approaches that reverse these basic assumptions and depict social reality instead in dynamic, continuous, and processual terms. (Emirbayer, 1997: 281)

This has much in common with the realist understanding of causation, and we might extend Emirbayer's critique beyond its immediate social referent to cover all complex order. For realists, causes do not derive from single simple entities. Rather, they reside in complex unobservable mechanisms that are inherently not analyzable and generate contingent consequences in the world that may or may not be observedBhaskar's (1978) domains of the real, the actual, and the empirical. If we accept a relational and complex realism, we cannot separate out through analysis aspects of complex systems because the systems are themselves, not aggregates of parts that we assume exist prior to the system. In other words, complex systems are not made up of pre-existing variables, although we can properly describe them through the measurement of variate traces. In realist terms, the traces are actual things in the world that are the products of the generative real system, and the interior working of the system is not reducible to elements existing separate and analyzable outside the system.

We have to be careful here. I am not saying that complexity theory is equivalent to holism. Price has reminded us that:

General systems theory focuses on the totality rather than its constituent parts. Thus, it adheres to the holism in the conventional sense of the word. Complexity theory views this type of holism as just as problematic as the reductionism it nominally opposesthe conventional theory holism is reductionism to the whole. Holism typically overlooks the interactions and the organization, whereas complexity theory pays attention to them. (Price, 1997: 10)

We cannot just deal, as postmodernism would have us do, with surfaces we need to look in, but we need to be very careful of what we are looking into. Here our idea of state space-phase space-condition space has to be very carefully clarified. Describing a system by mapping its position in a multidimensional space in relation to a series of coordinates measured for attributes of the system, each of which constitutes a dimension of the space, is a very convenient way of describing system trajectories and hence patterns and quality3 of changes. However, we must not think that the dimensions are real outside the system.

There are real variables, but these are things that act externally on systems. In social and biomedical experiments in the form of randomized controlled trials, things are done to individual systems: people are given drugs, classes of children are taught to read in a particular way. In social action, things are likewise done: specific planning regimes are imposed in particular places, particular policing strategies are employed around issues of public order. We must reserve the term variable for that which is done to the system from outside or by actors within it operating autonomously, and consider our measurements of the system to be variate traces of what it is doing, not as real things doing something to the system from inside.

This distinction between variable and variate trace has to be handled carefully. Complex systems are open systems, which means that distinguishing between a system and its environment is at best a provisional activity carried out for a specific purpose. If we think about the word intervention”—literally putting something intowe can usefully, but carefully, think about a special set of actions as external to systems, potentially variable, and therefore classifiable as variables. Note the suggestion above that in social systems willed action based on knowledge can be an innovative force. We can intervene from inside.

It is important to emphasize that the idea of variate trace is something to do with what we measure, not with what really iswith the elements of existence. It is not that there is nothing inside the complex system to which we should pay attention. We should go beyond surfaces. Rather, it is that our understanding of complexity should inform us that the significant entrails into which we look to prophesy the future and record the past are likely themselves to be complex components rather than single variates. This point can be made by distinguishing the kind of exploration being proposed here from the analytical strategy of factor analysis-type techniques, in which variate traces are reduced by mathematical manipulation in order to generate a smaller set of real, latent, causal variables. From a complexity perspective, any new state of the system is not caused by any single variate as measured, but by any combination of internal generation and external factors. Complex systems can change as a consequence of internal change, external change, or both together.

A key term here is control parameter. In other words, in changing the character of systems some things matter more than others, even if the things that matter are themselves complex. The abandonment of the idea that there are bits in a complex system that we can analyze out as variables does not imply that there are no subsets of a complex system, change in which changes the system as a whole.4 Any prospect of agency in relation to systems depends absolutely on the possibility of first the existence and then the understanding of control parameter subsystems. The big question for any complexity science is: Can we get at these subsystems? Can we in any useful way understand them?

Cilliers has developed an important way of addressing this issue through his discussion of the use of models as devices that we use in an:

attempt to grasp the structure of complex systems. Complex systems are neither homogenous nor chaotic. They have structure, embodied in the patterns of interactions between the components. (Cilliers, 2001)

specifying that in his account the notion of structure:

refers to the patterns of interaction in the system, and underplays a distinction between the structure on the one hand and the activities within that structure on the other. Structure is the result of action in the system, not something that has to exist in an a priori fashion. (Cilliers, 2001, original emphasis)

This dynamic and generated notion of structureone wholly familiar to engineers like Cilliers in his original incarnation but rather foreign to social scientists, although Lévi-Strauss's (1978) structuralism is similar is very important. It seems to me to summarize rather well our ontological specification for methodological investigation. We can seek to establish the nature of structure. The next question is: Can we develop techniques of research investigation that will enable us to do this?


There are four processes in a practical complexity science; indeed, I will argue that inductive complexity science consists of the application of these processes to complex systems. The processes are:

There is at the very least a useful metaphorical referent for us in the procedures of natural history, which involve classification as the precursor to an account of evolutionary development. Here, what is interesting is not so much the origin of species as the development of ecosystemssomething that is particularly relevant for any urbanist concerned with the interaction among social systems, including the built environment and the natural environment in which the urban is literally embedded.

Biological taxonomists have developed a set of procedures, variously known as cluster analyses or numerical taxonomy (see Everett, 1993), which assign cases to categories on the basis of measurement. Cluster analysis proceeds through the construction of a matrix of cases and variate traces and the calculation of some sort of coefficient, either of similarity or, more commonly, dissimilarity, which is employed to allocate cases to categories. Typically, a hierarchic fusion procedure may be employed in which the number of categories is successively reduced until a level that appears substantively significant is identified. I have always found cluster analysis useful, but what makes it particularly attractive in relation to complex systems is the nature of dissimilarity matrices underpinning the whole exercise. Essentially, the multivariate description of any case in terms of an array of values for particular variate traces can be considered to represent a set of coordinates for that case as a system at a given time point. We can relate that case to other cases through classification and in effect construct attractors of ensembles of systems, i.e., a set of cases that occupy the same domain in the state space and are necessarily isolated from other sets. This is not an attractor as dynamic in any given single time measurement. Rather, it is a snapshot of a given time instance, somewhat along the lines of a Poincaré slice.

The construction of cluster sets for a given time point involves the execution of two of our processes: exploration through exploratory measurement of variate traces, and classification in terms of cluster membership. Let us turn to ordering and interpretation. In a sense, ordering is simple. We can often employ a timeline: not a version of calendar time with time written as a continuous variable, but rather something that we might think of as a very slow film, with each of our slices being a frame in that film.7 What interests us is the sudden and qualitative change in the form of our image.

Given such a change, exemplified by the very real change in the character of urban places in what used to be called advanced industrial society, we have two interrelated tasks as scientists. These are attempting to elicit the causes of change and, for social scientists and those concerned with understanding the intersection of natural and social systems, attempting to elicit the meanings informing significant human action. In the first instance our understanding is directed at retrodiction: the explanation of what has happened by the use of models that fit the data. We engage in retrodiction in part to establish a basis for prediction of futures. However, if our retrodictive story is contextual and local, the retrodictive account may not serve as a basis for understanding even the range of possible alternative futures. This is not a postmodernist epistemological pointwe can know what has happened; we can construct a valid history. It is rather an ontological pointcontingency and context mean that we cannot construct even a complex and emergent account of the range of future possibilities. We may be able to, but we cannot simply assume that this is the case. Our claims always have to be grounded and contextualized.

There is a relationship between retrodiction and retroduction, but they are not the same. Blaikie suggests that retroduction

be restricted to the process of building models of structures and mechanisms which characterizes the Realist approach ... The Retroductive research strategy involves the construction of hypothetical models as a way of uncovering the real structures and mechanisms which are assumed to produce empirical phenomena. (Blaikie, 1993: 168)

The kind of time-ordered classification described above is a method of quantitative exploration that employs a version of retrodiction as an aid to retroduction. I say a version, because the exploration of data does not involve the construction of models in the normal usage of that word. It yields a story of what has happened without depending on independent variables as causes.8 We might consider it to be a means toward the Aristotelian process of intuitive induction defined thus by Losee:

Intuitive induction is a matter of insight. It is an ability to see that which is essential in the data of sense experience The operation of intuitive induction is analogous to the operation of the vision of the taxonomist. The taxonomist is a scientist who has learned to see the general attributes and differentiae of a specimen. There is a sense in which the taxonomist sees more than the untrained observer of the same specimen. The taxonomist knows what to look for. This is an ability which is achieved, if at all, only after extensive experience. (Losee, 1993: 8)

However, I am not proposing it as more than part of the toolkit, and the name of the toolkit as a whole is, to use Lemon's expression, integrative method.


The idea of integrative method implies more than simple multidisciplinary or even interdisciplinary approaches. As exemplified by Lemon and his co-authors' work on water issues in the Argolid region of Greece (1999), it involves an engagement with human subjects as individuals and as collectivities whose agendas and decision spaces must be understood if the nature of potential future trajectories is to be established, and if the products of scientific research are to play a part in the determination of those future trajectories. Before proceeding any further, it is important to distinguish this approach to scienceone that emphasizes science as for usefrom that which in principle is concerned with the generation of knowledge for its own sake. The religious origins of western academia still resonate and the division between contemplatives and those engaged in the world still colors our conception of knowledge. It has always seemed to me that one of the advantages of modernity was that it asserted, through its commitment to progress, that knowledge could not be passive but was always engaged. For all their deconstructionist agenda, the postmodernists' equation of knowledge with power and interests has something of the same sort of implication. If there is one thing complexity science certainly is for, it is to be used.

If it is to be used, then it is always to be used in context, in relation to a history of human social action and the realities of human social organization. Moreover, we have to understand the absolute recursivity of any scientific project that engages with human systems and the interrelationship between human and natural systems. In other words, the science is part of the system, something Allen (1997) appreciates particularly clearly. I find nothing to disagree with in his declaration of intention:

The initial aim is not to describe a completely realistic model in microscopic detail, but rather to set out the basic framework, a matchstick drawing as it were, of the workings of a city, in the hope of being able to explore the long-term evolution, involving structural changes. In other words the aim is to build a model which, at least, can predict the sort of structure that may evolve under a certain scenario, with the accent on the qualitative features of that structure, rather than quantitative accuracy. (Allen, 1997: 177)

However, I do have a problem when Allen goes on to say:

We recognize the fact that evolution results from the dialogue between the deterministic equations of change expressing the average behavior of actors and a whole series of perturbations from outside the model, or from outside the level of description. (Allen, 1997: 216)

If this is referring only to the model as abstraction, then my problem is with the model being specified in a way that depends only on individual agents and with the absence of a sense of social structure, which is more than merely the product of emergent interaction among agents. If, as would seem pretty well inevitable, the model is being equated with reality, then we have a reification of variables and their relationships and a privileging of mathematical expression that seem to me to be misconceived. Jeffrey et al. (1999: 77) refer to the almost unnerving reliance upon mathematics as the basis of modelling physical phenomena, and this seems even more unnerving when we deal with the natural and social worlds as they intersect. The point is not to dismiss quantification, but to see it as part of the process of understanding, not as the ultimate representation of understanding.

So, let me define integrative method:

Let us turn to illustration by considering the use of complexity science in relation to understanding the urban.


Urban studies has taken a postmodern turn in recent years, although almost no urbanist is willing absolutely to forswear the grand narratives of political economy, currently dominated by theses of globalization. The tension between a more or less postmodernist culturalism and a story of economic cause drives academic argument. This is by no means merely an issue of academic debate. The globalization theses inform both political cultureespecially in relation to the intellectual collapse of European social democracy and laborismand the development of urban policies in most city regions. Nonetheless, there is a crisis in the episteme. Planners, both technical and political, generally are not convinced that they know how cities work and thereby are not sure about what may be made of them.

There has been a turn to simulation and even to ideas about complexity as a way of trying to provide once again a coherent model-based account of how cities work. It is important to note that such modeling now never forswears textual narrative or even iconic documentation. People who use numbers are not frightened to use words and pictures; the reverse is by no means true of many textual interpreters who seem to hold the view that innumeracy is a valid epistemological principle. There is now a school that sees cities as complex systems, typified not only by Allen and his co-workers but also by others who try to use abstract simulation to model complex development of urban space.

Although I have distinct reservations about abstract simulation (see Byrne, 1998), I have no problem with most of these approaches if they are understood as part of an exploratory program. However, I think we can go further if we are more confident about what a complexity science of the urban might be. Let us consider this in relation to a real instance.

I propose to do this by considering the city region of Katowice, the largest industrial/mining complex in Poland. Let us take it as given that city regions are complex systems and that all the problems of nestedness, embeddedness, and boundary determination apply to them. Let us also note that we have a great deal of information about city regions in all forms. We have quantitative trend information, hierarchically ordered for the region as a whole and for spatial components down, in principle if not always in practice, to a neighborhood level. We have household-level data and data about important subsystems in economic production, education, and ecology. We also have an enormous amount of documentation that is the product of systems of governance. We also have the product of ethnographic investigation and representations of a place as presented in mass media and in other more specific cultural forms. We have a lot of material. How can we organize this to generate a complexity-founded narrative and some form of understanding that might guide forward-reaching social practices?

At the level of descriptive retrodiction, this does not seem to me to be a particularly difficult task. In other words, we can establish that the Katowice region has, since 1989, begun to undergo a transformationthe process is still in train: the place and its people are still in a time of change. There is a range of material on the character of this change (see Byrne & Wodz, 1997; Wodz, 1994, 1995; Blasiak et al., 1994). In summary, we can say that Katowice is undergoing a profound industrial restructuring that involves the loss of many industrial jobs and is associated with a change in the internal sociospatial form of the conurbation, so that there is a much higher degree of internal differentiation of residential space, a residential differentiation that in this now essentially ethnically homogeneous place is constructed on class lines. We can chart this change by examining statistical trends and by documenting in images, documents, and through ethnographic experiences recording how people feel about the experience of these changes, which in summary is for many a profound sense of unease, dislocation, and disempowerment. In complexity terms we can pick out a phase shift.

Gorzelak (1996: 32-3) has advanced an account of the origin of those changes that I would certainly endorse. He argues that they are not to be understood simply as a product of the transformation from a centrally planned to a market economy. Instead, he contends, the dismantling of the political barriers of the soviet system in central Europe in 1989 meant that the forces changing industrial capitalism in the West could now penetrate zones from which they had been excluded. The changes in Poland are in essence those that the West had experienced, compressed into a much shorter time period. This is a story of globalization. Once the barriers were down the external processesthings operating at the level of the world system rather than the national system of Poland or the city regional system of Katowiceengendered changes in the character of the place. In complexity terms, the perturbations were external. Smith has attempted to qualify such accounts in a most pertinent way:

Societal evolutionism is still quite evident in the globalization discourses that have dominated urban theory in the past two decades ... I have sought to displace these evolutionary discourses with a social constructionist urban theory in which globalization is treated as an unfinished product of politically and culturally constructed social practices, rather than a structural force operating behind people's backs and inexorably determining their futures ... The turn to the realm of social practice does not mean that urban researchers must move from a global to a purely local gaze when conducting urban research ... By deploying the metaphor of transnational urbanism I have tried to capture the notion of the city as a crossroads of social relations constituted by the interactions of local, national, and transnational actors and the networks through which they operate ... Viewed in this light, the diversity of place-making practices, the dynamics of political conflict and accommodation, the variety of state policy-making projects, and the agency of social networks come to the forefront of urban analysis. (Smith, 2001: 184)

In other words, Smith argues for understanding at all levels. Indeed, those of us with an interest in the internal dynamics of urban systems would extend his spatial range downward to incorporate the neighborhood, andpace all my earlier criticisms of accounts that center solely on the behavior of individual actorspay attention to decision-making strategies by individual households.

I am arguing, quite strongly, that integrated accounts constructed around a complexity frame offer us the best narratives for describing change. The issue of action is whether they offer us a foundation for shaping change. My answer would be that they do. For example, a recognition of the significance of the local in systemic changeas expressed by Smithalready has the enormous significance of challenging the discourse of disempowering globalization. Local actions can matter in shaping urban forms. To my mind, the whole repertoire of our techniques can be brought to bear on exploring by extrapolation, an extrapolation that includes quantitative models of whatever form as part of the extrapolation of narrativesof stories of the future. We can have a foundation for some sort of action.

Cilliers has always expressed a concern for the ethical dimension of complexity reasoning. In a lecture given at the University of Durham in 1999, he suggested that for him it is unethical to reason about complex social systems while being outside of them. This point relates closely to sociological concerns about the social nature and implications of knowledge. In other words, scientists and technicians using that science cannot, as I interpret Cilliers's remarks, operate as expert knowers who do not engage with what they describe. I have no problem with this at all. It seems to accord very well with the prescriptions for the forms of social science as practical critique most coherently specified by Paulo Freire (1998). In summary, complexity science is inductive, integrative, engaged, and differentfor me, at any rate.


  1. For me this is provided by a synthesis of the arguments of Cilliers (1998) and Reed and Harvey (1992, Harvey & Reed, 1994, 1996) about the nature of complex systems, coupled with an endorsement of Khalil's (1996) argument for a soft foundationalism and his discussion of organization and structure order.
  2. Scientistic complexity theory has got beyond the experimentnecessarily, since it accepts emergence. However, the privileging of mathematicization remains.
  3. Quality of change indicates a necessary distinction between changes of position within the confines of a torus attractor and phase shifts: nonlinear movement to a whole new attractor set.
  4. We might think that such a subset is the system in the sense that changes in it, in a given sociotemporal location, are what change everything. However, in another sociotemporal location the generative set may be different. Moreover, and more immediately, we may still have consequent changes of important aspects that can be distinguished from initializing aspects. Again, our separations are likely to be at best heuristic because all relations among components are likely to be recursive.
  5. I am always reminded at this point of Williams' (1982) discussion of the meaning of the word determine in the Marxist dicta: base determines superstructure and social being determines social consciousness. Williams argued that we must understand determine here not in the sense of the specificity of an equation-expressed law, but rather in terms of the setting of boundaries within which a range of possibilities existed, something well expressed by the image of a torus attractor.
  6. There are of course other dimensions of ordering besides time, but when we are dealing with evolutionary systemsthe domain of both natural and human historytime is the most important dimension.
  7. This can be literally a series of images. Byrne and Doyle (1997) employed sequential images of the same scene as a way of documenting transformational change in cultural landscape.
  8. Cilliers's discussion (1998) of neural nets is worth noting here. Neural nets are unanalyzable devices. One of their best developed uses in practice is in classification through data mining. Whereas cluster analyses work with a pre-specified algorithm, in a neural net the training process generates a method that cannot be analyzed out from the operation of the net. The outcome is much the same: sets of things sorted as similar. There is an interesting debate about validation in relation to these classificatory devices. I have proposed (Byrne, forthcoming) a multi-processual approach: if similar classifications are generated from multiple methods and multiple but related data sets, e.g., from both cluster analyses and a neural net approach, we might take them reasonably seriously.


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