NOTES TO THE READER
Although I use the term Complexity Theory as if it was a coherent body of scientific theory, this area of research is in fact still both young and evolving. I use it therefore as a shorthand term to cover a number of areas, each with its own distinct heritage. Broadly, it covers fractal structures, nonlinear dynamical systems, and models of self-organisation and self-organised criticality.
The research on which this book is based could not have been carried out without the help of a number of other people. Their contributions are, I hope, suitably acknowledged in the text. I would like to thank particularly Walter Perry (RAND), Susan Witty (Dstl), David Rowland, and Maurice Passman for their contributions. I am also most grateful to Professor Henrik Jensen for contributing the Foreword.
For the last couple of decades, attempts have been made to develop some general understanding, and ultimately a theory, of systems that consist of many interacting components and many hierarchical layers. It is common to call these systems complex because it is impossible to reduce the overall behaviour of the system to a set of properties characterising the individual components. Interaction is able to produce properties at the collective level that are simply not present when the components are considered individually. As an example, one may think of mutuality and collaboration in ecology. The function of any ecosystem depends crucially on mutual benefits between the different species present. One example is the relation between legumes, such as peas and beans, and their associated nitrogen-fixing bacteria: the bacteria collects nitrogen for the legume, which in turn produces carbohydrates and other organic material for the bacteria. Clearly this crucial arrangement cannot be studied by focusing on, say, the legume and neglecting the bacteria; the ecological function emerges first when the different components are brought together
and interaction is taken into account.
Another important feature of complex systems is their sensitivity to even small perturbations. The same action is found to lead to a very broad range of responses, making it exceedingly difficult to perform prediction or to develop any type of experience of a “typical scenario.” This must necessarily lead to great caution: do not expect what worked last time to work this time. The situation is exacerbated since real systems (ecological or social) undergo adaptation. This implies that the response to a given strategy most likely makes the strategy redundant. An example is the effect of using the same type of antibiotic against a given type of bacteria. Evolution soon ensures that the bacteria develop resistance and make the specific type of antibiotic useless. That complex systems adapt and change their properties fundamentally as a result of the intrinsic dynamics of the system is clearly extremely important. Nevertheless, for the sake of simplicity adaptation is often neglected in model studies. Sometimes assuming the existence of a stationary state might be justified (e. g., if one is interested in “toy” models of the flow of granular material under a controlled steady input of grains). But if one is dealing with more complex situations such as in ecology, and even more when considering social and political systems, ignoring adaptation is very likely to lead to erroneous conclusions.