Empirical Encounters with Computational Irreducibility and Unpredictability
- 168 Downloads
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.
KeywordsComputational irreducibility Unpredictability Problem of induction Algorithmic epistemology Halting problem
We want to thank the anonymous reviewers for their valuable suggestions.
- Deutsch, D. (1998). The fabric of reality: The science of parallel universes and its implications. Penguin (Non-Classics).Google Scholar
- Israeli, N., & Goldenfeld, N. (2004). Computational irreducibility and the predictability of complex physical systems. Physical Review Letters, 92(7).Google Scholar
- Joosten, J., Soler, F., & Zenil, H. (2010). Time vs. program-size complexity: Speed-up and slowdown phenomena in small turing machines. International Journal of Unconventional Computing (forthcoming).Google Scholar
- Meyer, A. R., & Fischer, P. C. (1972). Computational speedup by effective operators. Journal of Symbolic Logic, 37(1), 55–68.Google Scholar
- Schnorr, C. P. (1973). Does computational speedup concern programing? In M. Nivat (Ed.), Automata, languages and programming. (pp. 585–592). Amsterdam: Elsevier.Google Scholar
- van Emde Boas, P. (1975). Ten years of speedup. In Proceedings of MFCS (pp. 13–29).Google Scholar
- Wolfram, S. (2002). A new kind of science. Wolfram Media.Google Scholar
- Wolfram Mathematica Documentation Center, FindSequenceFunction. http://reference.wolfram.com/mathematica/ref/DifferenceRoot.html. Accessed October, 2011.
- Wolfram Mathematica Documentation Center, DifferenceRoot. http://reference.wolfram.com/mathematica/ref/FindSequenceFunction.html. Accessed October, 2011.
- Zenil, H. (2010). Compression-based investigation of the dynamical properties of cellular automata and other systems. Complex Systems, 19(1), 1–28.Google Scholar