(Holists - please read "complication" for "complexity" where
appropriate!)
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Complexity and Scientific Modelling
by Bruce Edmonds
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.
Accessible from URL:
http://cfpm.org/cpm/cpmrep23.html
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Bruce Edmonds,
Centre for Policy Modelling,
Manchester Metropolitan University, Aytoun Bldg.,
Aytoun St., Manchester, M1 3GH. UK.
Tel: +44 161 247 6479 Fax: +44 161 247 6802
http://bruce.edmonds.name