Neutral Emergence and Coarse Graining

Weeks, Andrew; Stepney, Susan; Polack, Fiona

doi:10.1007/978-3-540-74913-4_113

Cited by 3 publications

(1 citation statement)

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“…This was seen clearly with certain class II rules, where at one scale they have a high E, but a minimal at higher scales. The change of the measures across scales provides a useful tool to study dynamical systems (Wolpert and Macready, 1999;Polani, 2004;Weeks, 2010), as it has been formalized by Krohn-Rhodes theory (Rhodes, 2009;Egri-Nagy and Nehaniv, 2008). For example, a system with a high (but not maximum) E across scales can be said to be more emergent than one with E close to maximum at one scal e but close to minimal at other scales.…”

Section: Resultsmentioning

confidence: 99%

Complexity and information: Measuring emergence, self‐organization, and homeostasis at multiple scales

2012

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Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales. Nontechnical AbstractThere several measures and definitions of complexity, emergence, self-organization, and homeostasis. This has led to confusion reflected on the carefree use of these concepts. We provide precise definitions based on information theory, attempting to clarify the meaning of these concepts with simple but formal measures. We illustrate the measures with experiments on discrete dynamical systems.

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Section: Resultsmentioning

confidence: 99%