| Summary: | A working definition of a complex system is that of an entity which is coherent in some recognizable way but whose elements, interactions, and dynamics generate structures admitting surprise and novelty which cannot be defined. Complex systems are therefore 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 represent simplifications of a system in which salient parts and processes are simulated and given this definition, many models will exist for any particular complex system. In this paper, we explore the impact of complexity in validating models of such systems. We begin with definitions of complexity, complex systems, and models thereof. We identify the key issues as being concerned with the characterization of system equilibrium, system environment, and the way systems and their elements extend and scale. As our perspective on these issues changes, so do our models and this has implications for their testing and validation. We develop these, introducing changes in the meaning of validity posed by the use to which such models are to be put in terms of their users. We draw these ideas together as conclusions about the limits posed to prediction in complex systems. We illustrate our arguments using various examples from the fields of urban systems theory and urban science.
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