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--- 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." altloc: - http://www.cpm.mmu.ac.uk/cpmrep23.html chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: [] creators_name: - family: Edmonds given: Bruce honourific: '' lineage: '' date: 2000 date_type: published datestamp: 2001-08-30 department: ~ dir: disk0/00/00/17/73 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: - family: Aerts given: Diederik honourific: '' lineage: '' eprint_status: archive eprintid: 1773 fileinfo: /style/images/fileicons/application_postscript.png;/1773/1/compsciA4.ps|/style/images/fileicons/application_pdf.png;/1773/5/compsci.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: pub issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'complexity, modelling, representation, specificity, noise, error rate, simplicity, language, order, disorder, randomness' lastmod: 2011-03-11 08:54:46 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: 3 pagerange: 379-390 pubdom: FALSE publication: Foundations of Science publisher: Kluwer Academic refereed: TRUE referencetext: | Cambridge. [2] Chaitin, G.J. 1966. On the Length of Programs for Computing Finite Binary Sequences, Journal of the Association of Computing Machinery, 13, 547-569. [3] Crutchfield, J.P. 1994. The Calculi of Emergence: Computation, Dynamics and Induction. Physica D, 75, 11-54. [4] Edmonds, B. 1995. A Hypertext Bibliography of Measures of Complexity. [5] Edmonds, B. (forthcoming). What is Complexity?: the philosophy of Complexity per se with application to some examples in evolution. In F. Heylighen & D. Aerts (eds.): The Evolution of Complexity, Kluwer, Dordrecht. [6] Grassberger, P. 1986. Towards a Quantitative Theory of Self-Generated Complexity. International Journal of Theoretical Physics, 25, 907-938. [7] Kauffman, S.A. 1993. The Origins of Order. Oxford University Press, New York. [8] Kolmogorov, A.N. 1965. Three Approaches to the Quantitative Definition of Information, Problems of Information Transmission, 1, 1-17. [9] Murphy, P.M. and Pazzani, M.J. 1994. Exploring the Decision Forest: An Empirical Investigation of Occam's Razor in Decision Tree Induction, Journal of Artificial Intelligence Research, 1, 257-275. [10] Pearl, J.P. 1978. On the Connection Between the Complexity and Credibility of Inferred Models, International Journal of General Systems, 4, 255-264. [11] Popper, K.R. 1968. Logic of Scientific Discovery, Hutchinson, London. [12] Quine, W.V.O. 1960. Simple Theories of a Complex World, in The Ways of Paradox, Eds., Random House, New York, pages 242-246. [13] Rissanen, J. 1990. Complexity of Models. In Zurek,W.H. (ed.). Complexity, Entropy and the Physics of Information. Addison-Wesley, Redwood City, California, 117-125. [14] Sober, E. 1975. Simplicity. Clarendon Press, Oxford. [15] Solomonoff, R.J. 1964. A Formal theory of Inductive Inference. Information and Control, 7, 1-22, 224-254. relation_type: [] relation_uri: [] reportno: ~ rev_number: 14 series: ~ source: ~ status_changed: 2007-09-12 16:40:10 subjects: - comp-sci-mach-learn - phil-sci succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: Complexity and Scientific Modelling type: journalp userid: 192 volume: 5