Emergence and computability

TL;DRAbstract

This paper presents a discussion of the possible influence of incomputability and the incompleteness of mathematics as a source of apparent emergence in complex systems. The suggestion is made that the analysis of complex systems as a specific instance of a complex process may be subject to inaccessible 'emergence'. discuss models of computation associated with transcending the limits of traditional Turing systems, and suggest that inquiry into complex systems in the light of the potential limitations of incomputability and incompleteness may be worthwhile. Introduction We suggest that what we intuitively define as (strongly) emergent systems may include processes which are not computable in a classical sense. We ask how incomputable processes would appear to an observer and, via a thought experiment, show that they would display features normally defined as 'emergent'. If this conjecture is correct, then two important corollaries follow: first, some emergent phenomena can neither be s

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