Complexity and Scientific Modelling

CPM Report No.: 97-23
By: Bruce Edmonds
Date: April 1997

Presented at: 20th International Wittgenstein Symposium, Kirchberg am Wechsel, Austria, August 1997.

Published as: Edmonds, B. (2000). Complexity and Scientific Modelling. Foundations of Science. 5: 379-390

Abstract

There have been many attempts at formulating measures of complexity of physical processes. Here we reject this direct approach and attribute complexity only to models of these processes in a given language, to reflect its "difficulty". A framework for modelling is outlined which includes the language of modelling, the complexity of models in that language, the error in the model's predictions and the specificity of the model.

Many previous formulations of complexity can be seen as either: a special case of this framework; attempts to "objectify" complexity by considering only minimally complex models or its asymptotic behaviour; relativising it to a fixed mathematical structure in the absence of noise; misnamed in that they capture the specificity rather than the complexity.

Such a framework makes sense of a number of aspects of scientific modelling. Complexity does not necessarily correspond to a lack of simplicity or lie between order and disorder. When modelling is done by agents with severe resource limitations, the acceptable trade-offs between complexity, error and specificity can determine the effective relations between these. The characterisation of noise will emerge from this. Simpler theories are not a priori more likely to be correct but sometimes preferring the simpler theory at the expense of accuracy can be a useful heuristic.

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