Minds and Machines

, Volume 22, Issue 3, pp 149–165

Empirical Encounters with Computational Irreducibility and Unpredictability

  • Hector Zenil
  • Fernando Soler-Toscano
  • Joost J. Joosten

DOI: 10.1007/s11023-011-9262-y

Cite this article as:
Zenil, H., Soler-Toscano, F. & Joosten, J.J. Minds & Machines (2012) 22: 149. doi:10.1007/s11023-011-9262-y


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.


Computational irreducibilityUnpredictabilityProblem of inductionAlgorithmic epistemologyHalting problem

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Hector Zenil
    • 1
  • Fernando Soler-Toscano
    • 2
  • Joost J. Joosten
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of SheffieldSheffieldUK
  2. 2.Grupo de Lógica, Lenguaje e Información, Departamento de Filosofía, Lógica, y Filosofía de la CienciaUniversidad de SevillaSevilleSpain
  3. 3.Departamento Lògica, Història i Filosofia de la CiènciaUniversitat de BarcelonaBarcelonaSpain