Abstract
Stephen Wolfram has maintained that almost any system whose behavior is not obviously simple is computationally universal and, consequently, its long term behavior is undecidable. Wolfram’s tenet is a direct consequence of his Principle of Computational Equivalence (PCE). In this paper, I propose an independent argument for the ubiquity of computational universality and, as a consequence, dynamical undecidability as well. My argument does not presuppose PCE and, in essence, it is based on the recognition of two facts: (1) the existence of a strong structural similarity between the transition graphs of any two computational systems; (2) the mapping needed for computational universality is emulation, which is itself a quite weak structural mapping.
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Giunti, M. (2019). Are Dynamically Undecidable Systems Ubiquitous?. In: Minati, G., Abram, M., Pessa, E. (eds) Systemics of Incompleteness and Quasi-Systems. Contemporary Systems Thinking. Springer, Cham. https://doi.org/10.1007/978-3-030-15277-2_11
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DOI: https://doi.org/10.1007/978-3-030-15277-2_11
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