Article

Minds and Machines

, Volume 22, Issue 3, pp 149-165

Empirical Encounters with Computational Irreducibility and Unpredictability

  • Hector ZenilAffiliated withDepartment of Computer Science, University of Sheffield Email author 
  • , Fernando Soler-ToscanoAffiliated withGrupo de Lógica, Lenguaje e Información, Departamento de Filosofía, Lógica, y Filosofía de la Ciencia, Universidad de Sevilla
  • , Joost J. JoostenAffiliated withGrupo de Lógica, Lenguaje e Información, Departamento de Filosofía, Lógica, y Filosofía de la Ciencia, Universidad de SevillaDepartamento Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona

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Abstract

The paper presents an exploration of conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines, in particular results of a test that may spur experimental approaches to the notion of computational irreducibility. The test involves a systematic attempt to outrun the computation of a large number of small Turing machines (3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function for that purpose. The experiment prompts an investigation into rates of convergence of decision procedures and the decidability of sets in addition to a discussion of the (un)predictability of deterministic computing systems in practice. We think this investigation constitutes a novel approach to the discussion of an epistemological question in the context of a computer simulation, and thus represents an interesting exploration at the boundary between philosophical concerns and computational experiments.

Keywords

Computational irreducibility Unpredictability Problem of induction Algorithmic epistemology Halting problem