Complex Spatial Systems

The Modelling Foundations of Urban and Regional Analysis

Alan Geoffrey Wilson

• Publisher: Routledge
• Year: 2014
• ISBN:
  9781317875680
• Edition: 1
• Topic: Politics & International Relations
• Subtopic: City Planning & Urban Development
• Index: Politics & International Relations

A comprehensive core text from the expert in the field introducing students to the main issues of spatial systems modelling and analysis.

1
Introduction

Cities and regions and ‘big science’

Understanding cities and regions represents one of the major scientific challenges of our time. They provide the habitats of the world's populations; and urban and regional analysis should provide the underpinnings of well-being in the same way as the biological and medical sciences underpin health and medicine and the physical and engineering sciences underpin industry. But the science of cities and regions has not, as in these fields, been treated as 'big science'. None the less, the scientific foundations have been laid in the last three decades and the purpose of this book is to present an overview of what is known, and what can be achieved — albeit from a relatively limited perspective. Of course the social sciences are essentially different from the physical sciences. Human behaviour cannot be understood or predicted in the same way. But many features of cities and regions can be understood, and the knowledge productively applied, and the prime aim of this book is to offer a sketch of what has been achieved to facilitate further development.

The approach adopted has a number of distinctive features. Cities and regions are seen as complex systems and it is argued that a general perspective can be adopted which provides a framework for making effective decisions for building system models. The approach has to be interdisciplinary. This framework shows the weaknesses in some of the traditional approaches to urban and regional analysis and provides a viewpoint for the analysis of classical approaches to urban and regional model-building. The core of the argument is the presentation of a set of mathematical and computer model-building techniques. These are shown to be precursors of complexity theory and this means that insights can be offered about complexity theory in one of its detailed applications. The focus, therefore, is on complex spatial systems. Classical theory can be rewritten in a very powerful way, and this is important for a number of disciplines. More importantly, a research agenda can be articulated which shows tremendous potential for the future.

Cities and regions as complex systems

It is self-evident that cities and regions are complex systems, and methods exist for representing the theory of such systems, for example as mathematical and computer models, which represent the foundations for analysis and planning. In this century, tremendous progress has been made in the formulation of these models for cities and regions. The late twentieth century is a particularly exciting time to review what has been achieved because it can now be seen that the developments of the last 30 years can be integrated through the ideas of what is becoming a common approach in many fields of science — complexity theory.

Complexity theory perhaps represents the most important territory in contemporary science. However, presentations are not always complete or clear. It is sometimes misnamed — with labels like 'chaos theory'. Some critics belittle it, but are attacking obscure targets — particular and poor representations. Some proponents oversell it. The danger is that important directions for academic development are inadequately charted. It will be argued that there is tremendous potential for urban and regional analysts which can be unlocked through complexity theory and new interdisciplinary collaboration. Interestingly, it can be argued that this presentation is important to complexity theory as well as to the substantive field for two reasons: first, because in all the excitement of the new developments in complexity theory, the social sciences have been seriously neglected; secondly, because urban modelling in particular demonstrates how the ideas of complexity theory can be made to work in a real context.

We therefore need a good broad understanding of what complexity theory is about. The issues can be usefully addressed in two stages: the substantive subject matter, which is discussed here in terms of systems; and the methods. There is a preliminary exploration of these topics in the rest of this section. More detailed arguments are presented to complete the preliminaries in Chapters 2-4, and the ideas developed will be used in the context of examples in the rest of the book.

Components of cities and regions can be called systems — simply because they involve a large number of interacting components. Complexity theory can then be thought of as theory about complex systems. Urban and regional analysis can then be seen as concerned with complex spatial systems. There are then two initial questions: what is distinctive about complex systems? What is distinctive about the theory of complex systems?

It was Warren Weaver in the 1940s and 1950s who (to the author's knowledge) (Weaver, 1948, 1958) first introduced a useful distinction between simple and complex systems. In the scientific context, simple systems were those describable by a small number of variables; complex systems needed a large number of variables to describe them. He made a further subdivision of complex systems into those of disorganised complexity and those of organised complexity. It should now be recognised that a particularly important subset of systems of organised complexity (perhaps the whole set?) are nonlinear systems. Nonlinearities can arise in a variety of ways: when rates of change are anything other than constant; for the geographer, when distance effects, as in the gravity model for instance, involve a power or an exponential function. It is the nonlinearities that are at the basis of what is interesting in complex system behaviour. It turns out that a number of important analytical issues associated with urban and regional systems can be solved using methods for systems of disorganised complexity. However, the most interesting problems, as in most other sciences, are those of systems of organised complexity.

What Weaver observed was that problems associated with simple systems could be solved by essentially the mathematics associated with, for example, Newtonian mechanics; the problems of systems of disorganised complexity by the mathematics of statistical mechanics; but, at the time, there were no mathematical solutions to problems of organised complexity. It is the systems of organised complexity, the nonlinear systems, which can, in current parlance, be thought of as complex systems — and some of the mathematics does now exist. Weaver, when he was writing in the 1950s, was the Science Vice-President of the Rockefeller Foundation, and he went on to argue that the Foundation, on the basis of this analysis, should be investing more of its funds in biological rather than physical sciences — a prescient analysis! Social scientists, of course, would now wish to be added to Weaver's 'interesting' list!

What characterises systems of organised complexity is essentially that they are made up of large numbers of parts — and that these parts are strongly connected; that is, they each interact strongly with a number of others. Obvious examples of systems of organised complexity are human beings, brains, ecosystems, economies and cities. Most of these figure in the popular literature of complexity theory though the social sciences are seriously under-represented. Other dimensions figure in this literature too: time is important (in fields such as evolution); methods, such as nonlinear mathematics and computer science, are important. Many of the ideas employ analogue or metaphor: neural network computing for instance. It should be clear even at this stage of the overall argument that urban and regional systems of interest are typically systems of organised complexity.

What Weaver had not foreseen was the extent to which the methodology to be developed in the four decades since his analysis would be multidisciplinary and generic — and hence the term complexity theory. In any particular discipline, it will be particularly important to work towards an understanding of what can be achieved through the deployment of generic tools and what has to be developed which is specific to that discipline.

I will take as a working definition that theories are about understanding systems; and that methods are important elements in theory-building. We should also recognise that most interesting theory-building is concerned with process — the nature of change over time for the system of interest. Scale is particularly important. The same systems can be characterised at different scales, and if we do not insist on absolute clarity in this respect then confusion can ensue. It is obvious intuitively that there are fundamentally different spatial scales at which we can perceive the 'same' systems. It is important to recognise that there are interesting (scientific) phenomena at each of these scales — though sometimes there are important interactions between scales. It can then be argued that the methods which are valuable in theory-building at one scale may be different from those for the same system (or an element of it) at another scale. In the case of temporal scale, as in the study of a biological system for example, the approach will be different if the study is concerned with contemporary function or with evolution over a long time period. In effect, we work with a hierarchy of knowledge about real complex systems. This notion is pursued in more detail in Chapter 2.

Key Idea 1.1

Scale is a form of hierarchy and clarity of vision in this respect is critical.

This then takes us to method. Nonlinearities fundamentally change the nature of the mathematics needed to describe complex systems. This was why Weaver in the 1950s recognised that problems of organised complexity were then insoluble in mathematical terms. What has changed (in the last 20 years or so) is that appropriate mathematical tools have become available. There is now a broad understanding of the mathematics of nonlinear systems and we need to chart out the essence of the ideas involved so that we can understand, at least intuitively, the range of application of each. What is more, as happens in scientific development, these ideas are at least broadly understandable in less technical ways.

Authors such as Holland (1995) argue that there are properties of complex systems which demand a kind of mathematics that is not yet available to us: these properties are based on adaptation. The agents and subsystems which make up cities and regions are capable of adaptation; they evolve over time. As we will see later, this capability is very difficult to model.

However, there is another aspect of the methodological tool-kit needed for theory-building which needs to be brought into play here. Most interesting complex systems are very large. So even though some of the mathematics exists in principle, either not enough is known substantively about the system to make mathematical analysis possible, or the system is simply too large for feasible analysis; there are too many variables. This is where another major impact from discoveries of the last 20 years contributes to method: powerful computers. These have meant that many of the problems which are not solvable in analytical mathematical terms can be tackled through computer simulation — generating great understanding and insight. Much of the power derives from the fact that it is possible to combine human intelligence with computing power — and we should not underestimate the impact of computer graphics, developed with the advent of PC cultures, in this context. In many cases, it is easier to work directly with ideas of computer modelling and simulation rather than the more traditional systems of mathematical equations. In the context of urban and regional analysis, these ideas have even manifested themselves in impressive computer games, such as the bestselling SimCity (for a geographer's review, see Macmillan, 1996).

There is a third element to the methodology of complexity theory: the effective deployment of metaphor. This arises from the multidisciplinary power of complexity theory: essentially, in fact, the main concepts are supradisciplinary.

These ideas will allow us to map out (systematically!) in turn the territory of complexity theory and the range of methods which are potentially valuable in systems of interest — in this case, cities and regions.

This argument generates the basis of an approach that will be formalised in the rest of the book, i.e. that there is a three-stage approach to achieving understanding: the articulation of systems of interest; theory development for that system; and the deployment of appropriate methods to operationalise the theory. The particular and more specific focus of this book is the representation of this knowledge as system models.

By adopting a systems' modelling focus, as in this chapter so far, it might be argued that an essentially functionalist approach is being adopted. That is, the forms of organisations and institutions are taken as given and the emphasis is on the way they function both individually and in relation to each other. It is also necessary to explore the deeper structures and forces which create these particular forms of organisation, i.e. to adopt a structuralist approach. The position adopted here is as follows. It is argued that a functionalist analysis is usually valuable, at least to provide a framework, and also that this is a useful starting point in comparing contemporary theory with 'classical' urban and regional theory. The approach will be spelled out in more detail in Chapter 3.

Key Idea 1.2

A focus on systems and models of systems provides some valuable contributions to theory in its own right, and a framework within which other theories can be developed.

We have already noted that there is one discipline which has a prime concern with cities and regions in a holistic way — and that is human geography. To an extent in what follows, 'urban and regional analysis' and 'human geography' can be used interchangeably, albeit with the recognition that this is in respect of the overlapping territories in the Venn diagram which represents the two areas — one multidisciplinary, one a discipline. It is helpful in this context to review briefly the broad stages of the evolution of human geography in this respect. We do this in Chapter 4, in the broader context of all the disciplines which contribute to urban and regional analysis.

The structure of the rest of the book

In the light of the argument thus far, we can now state the objectives of the book through a commentary on the way the remaining chapters are organised. In Chapter 2, we adopt a substantive systems focus and try to establish from first principles what the subject matter of urban and regional analysis is. In Chapters 3 and 4, w...