The Ontology of Digital Physics

Authors: Anderson BeraldodeAraújo Lorenzo Baravalle

Publish Date: 2016/12/19

Volume: 82, Issue: 6, Pages: 1211-1231

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Abstract

Digital physics claims that the entire universe is at the very bottom made out of bits as a result all physical processes are intrinsically computational For that reason many digital physicists go further and affirm that the universe is indeed a giant computer The aim of this article is to make explicit the ontological assumptions underlying such a view Our main concern is to clarify what kind of properties the universe must instantiate in order to perform computations We analyse the logical form of the two models of computation traditionally adopted in digital physics namely cellular automata and Turing machines These models are computationally equivalent but we show that they support different ontological commitments about the fundamental properties of the universe In fact cellular automata are compatible with a rather traditional form of physicalism whereas Turing machines support a dualistic ontology which could be understood as a realism about the laws of nature or alternatively as a kind of panpsychismIn this appendix we provide the details of the Proof of Theorem 41 We assume the definitions of Turing structure and computations as they are defined in de Araújo and Carnielli 2012 Let us begin by showing that the sorts of Turing structures cannot be approached in an isolated form That is to say states symbols cells and instants of computations must be relatedThere is no class of Turing structures mathcal A that corresponds to the class of Turing computations mathcal C such that mathcal A is defined over a signature with unary relational symbols for each of the sorts of a Turing machineThe second fact shows that there is no Turing structure that has all the sorts in just one predicate This means that states symbols cells and instants cannot be regarded as a unique object That is to say the minimal parts defined by Turing head and tape are necessarily differentThere is no class of Turing structures mathcal A that corresponds to the class of Turing computations mathcal C such that mathcal A is defined over a signature with relational symbols that have exactly one parameter for each sort of a Turing machine

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