Abstract
In this paper we shall relate computational complexity to the principle of natural selection. We shall do this by giving a philosophical account of complexity versus universality. It seems sustainable to equate universal systems to complex systems or at least to potentially complex systems. Post’s problem on the existence of (natural) intermediate degrees (between decidable and universal \(\Sigma _1^0\)) then finds its analog in the Principle of Computational Equivalence (\(\mathbf{PCE }\)). In this paper we address possible driving forces—if any—behind \(\mathbf{PCE }\). Both the natural aspects as well as the cognitive ones are investigated. We postulate a principle \(\mathbf{GNS }\) that we call the Generalized Natural Selection principle that together with the Church-Turing thesis is seen to be in close correspondence to a weak version of \(\mathbf{PCE }\). Next, we view our cognitive toolkit in an evolutionary light and postulate a principle in analogy with Fodor’s language principle. In the final part of the paper we reflect on ways to provide circumstantial evidence for \(\mathbf{GNS }\) by means of theorems, experiments or, simulations.
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Notes
- 1.
This requirement can be relaxed as a universal CA can mimic any other CA too.
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Acknowledgments
I would like to thank Barry Cooper and Hector Zenil for fruitful discussions on the subject.
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Joosten, J.J. (2014). Complexity Fits the Fittest. In: Zelinka, I., Sanayei, A., Zenil, H., Rössler, O. (eds) How Nature Works. Emergence, Complexity and Computation, vol 5. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00254-5_3
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DOI: https://doi.org/10.1007/978-3-319-00254-5_3
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