Undecidability and Irreducibility Conditions for Open-Ended Evolution and Emergence

Is undecidability a requirement for open-ended evolution (OEE)? Using methods derived from algorithmic complexity theory, we propose robust computational definitions of open-ended evolution and the adaptability of computable dynamical systems. Within this framework, we show that decidability imposes...

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Bibliographic Details
Published in:Artificial life Vol. 24; no. 1; p. 56
Main Authors: Hernández-Orozco, Santiago, Hernández-Quiroz, Francisco, Zenil, Hector
Format: Journal Article
Language:English
Published: United States 2018
Subjects:
Biological Evolution
Models, Biological
Synthetic Biology
Open-ended evolution
complexity
dynamical systems
adaptation
emergence
undecidability
ISSN:1064-5462
Online Access:Get more information
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Summary:Is undecidability a requirement for open-ended evolution (OEE)? Using methods derived from algorithmic complexity theory, we propose robust computational definitions of open-ended evolution and the adaptability of computable dynamical systems. Within this framework, we show that decidability imposes absolute limits on the stable growth of complexity in computable dynamical systems. Conversely, systems that exhibit (strong) open-ended evolution must be undecidable, establishing undecidability as a requirement for such systems. Complexity is assessed in terms of three measures: sophistication, coarse sophistication, and busy beaver logical depth. These three complexity measures assign low complexity values to random (incompressible) objects. As time grows, the stated complexity measures allow for the existence of complex states during the evolution of a computable dynamical system. We show, however, that finding these states involves undecidable computations. We conjecture that for similar complexity measures that assign low complexity values, decidability imposes comparable limits on the stable growth of complexity, and that such behavior is necessary for nontrivial evolutionary systems. We show that the undecidability of adapted states imposes novel and unpredictable behavior on the individuals or populations being modeled. Such behavior is irreducible. Finally, we offer an example of a system, first proposed by Chaitin, that exhibits strong OEE.
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ISSN:1064-5462
DOI:10.1162/ARTL_a_00254