Empirical Encounters with Computational Irreducibility and Unpredictability

TL;DR

This paper investigates the unpredictability and irreducibility in small Turing machines through large-scale experiments, exploring the limits of prediction and decidability in deterministic systems.

Contribution

It introduces a systematic experimental approach to test computational irreducibility using integer sequence prediction on small Turing machines, linking philosophical and computational perspectives.

Findings

Rates of convergence of decision procedures analyzed

Decidability of certain sets examined

Unpredictability in deterministic systems discussed

Abstract

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines. We present the 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 (all 3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function finder program. This massive 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.