Published as: Edmonds, B. (2005) Simulation and Complexity – how they can relate. In Feldmann, V. and Mühlfeld, K. (eds.) Virtual Worlds of Precision – computer-based simulations in the sciences and social sciences. Lit Verlag, 5-32.

This is based on an invited talk at the workshop on “Virtual Worlds of Precision – Computer-based Simulations in the Natural and Social Sciences” at Oxford in January 2003.

For more information on the book see: http://www.lit-verlag.de/isbn/3-8258-6773-0

#### Introduction

When faced with some complex phenomena for which we can see no adequate analytic approach, it is easy to produce a simulation model, play with it and feel that we have gained some purchase on it. However simulation models can often give the illusion of progress and understanding due to the persuasive nature. A key question is thus to what extent this is real progress and understanding and how much sophisticated (if unintended) deception, i.e. “Do simulation models really help us understand complex phenomena?”

Equation-based and statistical modelling have a relatively long history and are relatively well developed. Simulation modelling has a much shorter history and its methodology is less well developed. In many (but not all) fields academics are still feeling their way as to how and when to use simulation modelling. Further, just as there are many branches of mathematics, there are many kinds of simulation modelling. Within each domain it takes time to develop ways in which equations can be usefully applied, what sort of ‘leverage’ it can provide one, what the pitfalls are and how to go about it. A similar sort of development is occurring within many fields of study with respect to simulation modelling. What works within one domain may well not work in another. However, just as with applied mathematics there are some more general guidelines that can be discovered and communicated, and, just as with mathematics, how one applies the formal machinery is more of an art than a science. The knowledge about applying the technique is not entirely formalisable, but consists, for the most part, of ‘rules of thumb’, scientific norms, approaches and frameworks for thinking about what one is doing.

Thus part of the intention in writing this chapter is to draw some of this more general knowledge out and put it into some sort of framework. Its scope is where the domain of study is sufficiently complex that equation-based or other analytic approaches are impractical or even impossible to apply. This sort of domain poses its own particular kind of problems, which go beyond the difficulties or solving (or otherwise finding solutions for) analytical models. In such domains it is not possible to produce a complete model of the phenomena, rather one is attempting to model parts or aspects of the phenomena in useful ways. Thus I am not concerned with simple numerical simulation of well-validated equations here, but more the art and science of applying partial computational models. Inappropriate use of any kind of modelling generates more confusion than it sheds light but this is even more of a danger with simulation modelling applied to complex phenomena.

Three particular problems in this regard are as follows.

The presentation of models that are intuitively plausible but with little solid relation to their intended domain. Such models are developed to aid conceptual or formal exploration but then convince their authors to such an extent that they then project the model upon their domain, drawing unjustified conclusions about it.

Different types of models are conflated in terms of use and judgement, so that a model that was developed and validated for one kind of use is then used or interpreted as if it were valid for a different use. For example a model may be developed as if it were a predictive model but then tested according to criteria suitable for an explanatory one.

Since programming is apparently much more accessible than doing mathematics (going by the numbers able to do each) – many more people can build models and discover something. This has both positive an negative aspects, its accessibility has the effect of democratising a field making it less prone to persuasion via mathematical opaqueness but on the other hand the lack of the implicit filter that mathematical competence means that there are more badly constructed or sloppily applied models around to confuse.

It is thus an open question whether a simulation models usefully inform one about some phenomena or whether they only give the comforting impression of doing so; simulation model is not a panacea but just another tool. I hope that in this chapter I will be able to sketch some guidelines to aid the useful use of simulation modelling and avoid the deceptive uses.

The chapter starts with an established and yet fairly simple account of the modelling process. This provides some of the reference for the terms and ideas to be used in the rest of the chapter as well as giving some idea of the nature of modelling and how it works. It then goes on to sketch some of what really happens when such models are applied in the process of research. This contrasts somewhat with what is presented in textbooks. The next section looks at some of the consequences when models are applied to complex phenomena. I then look at the problem of constraining our models, that is verifying and validating them. Finally I look at a neglected area: how a model comes to have meaning is not entirely clear. A successful predictive model with know conditions of application does not necessarily have any rich meaning. In the case of complex phenomena such black-box predictive models are rare and thus it is important to know what our models mean (and what they don’t) so that we have a better guide as to how to use them. All of this is illustrated with two example simulations developed at the Centre for Policy Modelling: that of modelling the interaction of mutual social influence on the domestic demand for water and that of integrating domain expertise with aggregate data in markets for fast-moving consumer goods.