Complexity Theory and the Social Sciences

An Introduction

David Byrne

• Publisher: Routledge
• Year: 2002
• eBook ISBN: 9781134714735
• Edition: 1
• Topic: Social Sciences
• Subtopic: Sociology
• Index: Social Sciences

Chaos and complexity are the new buzz words in both science and contemporary society. The ideas they represent have enormous implications for the way we understand and engage with the world. Complexity Theory and the Social Sciences introduces students to the central ideas which surround the chaos/complexity theories. It discusses key concepts before using them as a way of investigating the nature of social research. By applying them to such familiar topics as urban studies, education and health, David Byrne allows readers new to the subject to appreciate the contribution which complexity theory can make to social research and to illuminating the crucial social issues of our day.

1
UNDERSTANDING THE COMPLEX

Nonlinear Science(’s) . . . aim is to provide the concepts and the techniques necessary for a unified description of the particular, yet quite large, class of phenomena whereby simple deterministic systems give rise to complex behaviours with the appearance of unexpected spatial structures or evolutionary events.

(Nicolis 1995: xiii)

Introduction

The language of chaos/complexity¹ is relatively new in science in general, and in the social sciences in particular. It is, therefore, necessary to begin this book with this chapter, to which I had considered giving the title ‘naming of parts’. However, one of the most important things about the approach is precisely its rejection of the validity of analytical strategies in which things are reducible to the sum of their parts. We are dealing with ‘emergent properties’ and must begin with a holistic statement.²

The quotation from Nicolis provides us with much of that statement. It tells us that we are dealing with aspects of reality in which changes do not occur in a linear fashion. In reality, as opposed to mathematical models, the crucial dimension along which changes occur is time. In non-linear systems small changes in causal elements over time do not necessarily produce small changes in other particular aspects of the system, or in the characteristics of the system as a whole. Either or both may change very much indeed, and, moreover, they may change in ways which do not involve just one possible outcome. Nicolis says that there is a large set of systems which have this character. I would suggest that this set includes most of the social and natural aspects of the world, particularly interrelationships between the social and the natural.

There is a third component of ‘chaos/complexity’ in addition to nonlinearity as mathematical description, and realism as an ontological principle, which can be found in Nicolis’ statement. He uses the term ‘evolutionary’. This means that we are dealing with processes which are fundamentally historical. They are not time reversible. As Adams (1994b, 1995) has pointed out these approaches involve an explicit rejection of the Newtonian concept of time as reversible in macroscopic systems of significance to us in general. The work of Prigogine (see Prigogine and Stengers 1984) replaces the clock as the iconic symbol of the modern with the heat engine. Mechanics gives way to thermodynamics. That notion appeals to me very much indeed, as a native of one of the world’s oldest locales of carboniferous capitalism and as a descendant of pitmen and collier seamen and their wives, whose labour provided precisely the thermal energy input which underpinned the transformations which led to modernity.

The principle of holism³ is implicit in Nicolis’ description but Hayles provides us with a succinct explicit assertion of it, which completes the preliminary specification of subject matter:

From the system’s point of view, there is only the totality that is its environment. So strong is our belief in analysis, however, that we take the environment to be the artificial and the collection of factors to be the reality.

(Hayles 1991: 16–17)

The two themes of evolutionary development and holistic character have to be taken together. This is what is meant by the title of Kauffman’s influential book The Origins of Order (1993). At the points of evolutionary development through history, the new systems which appear (a better word than ‘emerge’ because it is not gradualist in implication) have new properties which are not to be accounted for either by the elements into which they can be analysed (i.e. they are holistic), or by the content of their precursors. The approaches we are dealing with are necessarily and absolutely anti-reductionist, although this point is not always appreciated even by those who propose them. Gell-Mann’s remark (in an interesting book on these themes) that:

In general, scientists are accustomed to developing theories that describe observational results in a particular field without deriving them from the theories of a more fundamental field. Such a derivation, though possible in principle when the additional special information is supplied [my emphasis], is at any given time difficult or impossible in practice for most cases.

(Gell-Mann 1995: 111)

is simply wrong so far as the emphasised phrase is concerned. Quite the contrary. Not only can the complex not always be derived, even in principle, from the less complex, but, as we shall see, we can often only understand the simpler in terms of its origins in the more complex.⁴

Before going any further it is necessary to say something about the words ‘chaos’ and ‘complexity’. The best and clearest commentary on ‘chaos’ is provided by Hayles (1990, 1991) and what follows derives from her account. The word has its origins in the Greek for void and Hayles suggests that the contrast between chaos as disorder, and order, is a continuing dichotomy in the Western mind-set. She contrasts this binary logic with the four-valued logic of Taoism in which not-order is not equivalent to anti-order. This is persuasive and the point being made is that whilst ‘chaos’ in its popular usage is to be understood as a description of anti-order, to all intents and purposes as a synonym for randomness,⁵ the scientific usage is far more equivalent to not-order, and indeed sees chaos as containing and/or preceding order. The and/or is necessary because there are at least two approaches, which as Hayles indicates seem determined to ignore each other (1991: 12). One is concerned with the order that lies hidden within chaos and is essentially US-based. The other, European and represented particularly by Prigogine, focuses on the order that emerges from chaos.⁶

Actually I think that another synthesising account is implicit in both schools. Waldrop subtitled his popular text on Complexity (1992): ‘The emerging science at the edge of order and chaos’, and the account of bifurcation in complex systems certainly suggests that there is a domain between deterministic order and randomness which is complex. This is important in relation to the notion of ‘robust chaos’. For the moment the popularly oxymoronic but scientifically accurate expression of ‘deterministic chaos’ can be used to convey the difference in quality in the two usages.

Hayles leads us into this nicely when she remarks that: ‘In both literature and science, chaos has been conceptualised as extremely complex information, rather than as an absence of order’ (1991: 1). The point is that chaos remains deterministic – we are not, necessarily dealing with a scientific pessimism equivalent to the abandonment of rationalism by postmodernists. This means that we may have the basis of a technology in which we can use the understanding derived from chaos/complexity as a way of guiding purposeful action towards desired outcomes, although to do so we have to know a lot and be able to manage what we know in rather different ways. That is extremely important.

The rest of this chapter will be concerned with an exposition of the concepts and models which constitute the ‘chaos/complexity’ approach. It will not attempt to reproduce the more detailed accounts of the mathematical models associated with chaos/complexity, for which see Peak and Frame (1994), Casti (1994) and Nicolis (1995). Neither will it attempt to replicate the good scientific journalism of Waldrop (1992), Lewin (1993) or Johnson (1996), all of which in varying ways give an account of the US-based development and context of these ideas. Rather, it will contain a general account of the character of complex systems and of the way in which they develop over time, in order to provide an overview and a working vocabulary for the rest of the book.

We will begin with a consideration of chaos and discontinuity, continue with an examination of development through bifurcation, examine the character of strange attractors, and consider the nature of what Prigogine calls ‘far from equilibric systems’. Along the way, related ideas, and in particular that of fitness landscapes, will also be introduced and there will be a review of the importance of a complexity-based understanding of time and space for the social world. There is one important point which needs to be made here before we start, even though its development will form the conclusion to this chapter as a whole. In no sense whatsoever is the project of applying the ideas of complexity theory to the social driven by any sort of physics envy. That ought to be obvious from the explicitly antireductionist character of the form of the complexity programme which has already been endorsed in this book. However, I want to go further than ‘mere’ anti-reductionism. It is true that chaos/complexity emerges from experimental mathematics (think about the revolutionary implications of that expression) and thermodynamics, and has been particularly developed in physical chemistry and evolutionary biology. The social sciences have a good deal to learn from these fields. But, and it is a big but, once the social sciences get going, then other fields of inquiry will have a lot to learn from them. Indeed, this project is already well under way in relation to the development of fundamental metatheoretical ideas (see Reed and Harvey 1992, and Harvey and Reed 1994). There is no hierarchy here, no more or less fundamental field of science and/or disciplinary perspectives. We are in this together on equal terms.

Of course, one of the great attractions of the approach is that in fact we have been in it together for quite some time. Once we have the name we can recognise that we have been doing the thing – we have been talking prose for a long time without knowing it. For sociologists the work of Talcott Parsons provides an interesting illustration. Crooke et al. (1992) sum this up in terms which resonate very strongly with the complexity account:

Parsons makes a distinction between what might be called developmental processes and what might be called phase-shift processes. The former consist in a continuous and incremental elaboration and separation of sub-systems, which does not alter the general overall pattern of society. By contrast, phase-shift processes are fundamental differential leaps or evolutionary breakthroughs, typically caused outside the social realm (e.g. in the realms of culture or personality) which reorient the social pattern.

(Crooke et al. 1992: 5)

Here we find the language of complexity and chaos being used by contemporary commentators, as Hayles tells us we must reasonably expect to, given the current character of the Western episteme, but what really matters is that the perspective they are describing is so congruent with the approach, even though it predates chaos theory by many years.

And now for the naming of parts:

Small changes make for big differences and lots of things are out to play, together

Linearity in relationships is most simply expressed⁷ in algebraic terms by the equation:

γ = a + bX

Here the interesting thing which statisticians want to determine when they construct a bivariate regression equation of this form, is the value of b. b gives the amount of change in Y when X changes by one unit. Every time X increases by one, Y increases by b. Of course, interpreted regression equations where X and Y stand for real variables do not produce exact predictions of real Ys. The degree to which the real Ys differ from those predicted by the regression equation is used in both simple bivariate models and in the multi-variate extension into the general linear model in which lots of variables are brought into play together, as a measure of strength of relationship and explanatory, if not causal, power.⁸ It has been remarked that ‘regression equations are the laws of Science’ and indeed the search for laws in science has in essence consisted of attempts to find relationships which can be formalised in linear terms.

The search for linearly-founded laws is a search for predictive ability. If we can establish the relationships so that our formalised linear mathematical models are indeed isomorphic with the real world, and our ideal method for doing this is usually thought to be the controlled experiment,⁹ then we can predict what will happen in a given set of circumstances, provided we have accurate measures of the initial state of the system. Once we can predict, we can engineer the world and make it work in the ways we want it to. We can turn from reflection to engagement. This is a wholly honourable project so far as I am concerned. It is the technological foundation of modernity itself.

The trouble is that much, and probably most, of the world doesn’t work in this way. Most systems do not work in a simple linear fashion. There are two related issues here which derive from the non-linearity of reality, despite the availability of non-linear mathematical models which can sometimes be used in place of the general linear model and its derivatives. The first, which is generally discussed in the literature on chaos, is extreme sensitivity to initial conditions in non-linear systems. The classic, and by now well-known, expression of this is in relation to weather systems. Efforts to model weather systems in mathematical terms are faced with the major – and indeed essentially insurmountable – problem that variations in initial conditions of the scale of the force of a butterfly’s wing beat can produce vasty different weather outcomes over quite short time periods.

The problem that this raises is one of measurement in terms of accuracy. Lorenz originally encountered the phenomenon when he re-ran some weather data by re-inputting print-out results which were accurate to three decimal places instead of to the six the computer used in internal calculations. Re-inputting data produced very different outcomes because the measures differed in the fourth decimal place. It has to be stressed that the existence of chaotic outcomes of this kind does not involve an abandonment of causality in principle. If we could measure to the degree of accuracy we need then we could model the system, albeit in non-linear terms, and then we could predict what the outcome of changes would be. In practice we can’t. It is precisely this practical limit – that word: ‘limit’ – which seems to set a boundary on science and science-derived technology. This is why the idea of chaos is so attractive to postmodernists. Science seems to have come to the end of its capacities. Rationality seems to be exhausted as a general project. Is it hell as like!

Before turning to robust chaos, the basis of that robust rejection of postmodernism as state of mind,¹⁰ I want to pick up on the social sciences’ experience of non-linearity through encounters with interactions. The word ‘interaction’ here is not being used in the general sociological sense to describe social interactions among individuals, but in the statistical sense where in the simplest three variable case, the relationship between two variables is modified by the value of a third. This sort of thing crops up all the time in sociology.

The issue is that in the social world, and in much of reality including biological reality, causation is complex. Outcomes are determined not by single causes but by multiple causes, and these causes may, and usually do, interact in a non-additive fashion. In other words the combined effect is not necessarily the sum of the separate effects. It may be greater or less, because factors can reinforce or cancel out each other in non-linear ways. It should be noted that interactions are not confined to the second order. We can have higher order interactions and interactions among interactions. It is in principle possible of course to calculate interaction terms and enter them into linear models, and there are statistical programmes (elements in SPSS and the dedicated package GLIM) which exist to do exactly this. What this amounts to is the creation of new variables in the linear equation which represent the interaction among the measured variables. In essence the complexity is locked away in the interaction term. Once there are lots of variables in play this is, to say the least, a difficult business, and it always worries me because it seems to be a way of ignoring the complex character of the reality being investigated. In practical terms in contexts where chaos exists, the effect of interactions is to make the issue of precision of measurement even more important. The effects of interactions are not additive either in themselves or in relation to measurement errors. This means that complex causes can easily generate chaotic outcomes.

How and when things split

At this point we need to sort out some of the implications of the generally systemic character of chaos/complexity accounts. I want to do that by considering the difference between mechanics’ Newtonian interest in trajectories and thermodynamics’ interest in the behaviour of whole systems. The idea of a trajectory is generally to do with movements through space over time under the influence of forces. When I was doing A level Applied Maths we used to spend a lot of time working out the trajectories of artillery shells. Another applied example would be the kind of problems which had to be solved by a navigator in a coastal command plane flying blind by dead reckoning, i.e. without being able to fix position by reference to a fixed point achieved either by recognising a landmark or by getting a fix from either the sun or stars. The position of the plane would be a resultant of courses taken over time and wind speeds and directions.¹¹ The plane was within a system of wind, space and time, and had some autonomy (the effects of piloting and courses) within that system. What mattered was where it was as the result of its trajectory. When we come to look at individuals and households we will be interested in trajectories of just this kind within social systems.

However, here we are interested in the properties of the system as a whole. The nature of the kind of systems we are interested in will be considered subsequently, but we need a preliminary specification here. Prigogine and Stengers provide us with this:

The study of the physical processes involving heat entails defining a system, not as in the case of dynamics, by the position and velocity of its constituents . . . but by a set of macroscopic parameters such as temperature, pressure, volume and so on. In addition, we have to take into account the boundary conditions that describe the relation of the system to its environment.

(Prigogine and Stengers 1984: 105–6)

It is very important to note that whilst the state of the system may be described in terms of the values of a very large number of variables, it may be, and for the systems which interest us it is likely, that the actual character of that state is determined¹² by the value of a far smaller number (sometimes just one) of key control parameters. If the relationship of system form to the value of control parameter(s) is linear then small changes in them produce corresponding changes in the system, without a change in the system’s form. In non-linear relations at crucial points something very different happens.

Prigogine and Stengers deal with this in a discussion of chemical systems by reference to the law of large numbers. Social scientists should be familiar with this in relation to the con...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Acknowledgements
• Introduction
• 1 Understanding the Complex
• 2 The Reality of the Complex
• 3 Complexity and the Quantitative Programme in Social Science
• 4 Analysing Social Complexity
• 5 Complex Spaces
• 6 The Complex Character of Health and Illness
• 7 Complexity, Education and Change
• 8 Complexity and Policy
• 9 Conclusion
• Glossary
• Notes
• Bibliography