Towards a mathematics of complexity

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Abstract

There is a need for a unified, mathematical theory of complexity that is capable of expressing the structures and processes common to different phenomena. This account proposes three elements for such a theory. (1) Universal measurement generalises the concept of measurement to include many formal systems of observation. (2) Graphs, which are inherent in the structure and behaviour of all complex systems, provide possible units of measurement that are the equivalent of numbers for organisation. (3) Syntactic homomorphism, which identifies the underlying "programs" common to classes of patterns and processes, provides at least one analytical tool. As well as suggesting new techniques, the above elements imply a need to re-interpret many current ideas and methods. They also suggest a series of open questions for future research.

Original languageEnglish
Number of pages12
JournalComplexity International
Volume3
Publication statusPublished - Apr 1996
Externally publishedYes

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