Modelling and prediction in a complex world

A complex system is an entity, coherent in some recognisable way but whose elements, interactions, and dynamics generate structures and admit surprise and novelty that cannot be defined a priori. Complex systems are more than the sum of their parts, and a consequence of this is that any model of their structure is necessarily incomplete and partial. Models thus represent simplifications in which salient parts and processes are simulated, and given this definition, many models will exist of any particular system. In this chapter, we explore the impact of this complexity on validating models of such systems. We begin with definitions and then identify key issues as being concerned with the characterisation of system equilibrium, system environment, and the way systems and their elements extend and scale. As our perspective on these issues changes, then so do our models with implications for their testing and validation. We argue that changes in the meaning of validity, posed by the use to which such models are to be put, are central to this debate, drawing these ideas together as conclusions about the limits posed to prediction in complex systems.