What question did this study set out to answer?

The aim is to explore four philosophical questions related to computation using the Conway Machine framework.

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April 25, 2026Open Access

Four Lenses on the Conway Machine: Lucas–Penrose, P vs NP, Simulation, Taxonomy

Key Points

The aim is to explore four philosophical questions related to computation using the Conway Machine framework.
Utilized the Conway Machine framework to analyze four foundational computational lenses.
Examined the Lucas–Penrose dialectic through numeric and loopy regimes.
Unified a parameter space for hypercomputation as a taxonomy.
Lens I differentiates between methodological and ontological claims in computation.
Lens II reinterprets P vs NP as a challenge of eliminating fuzziness across regimes.
Lens III connects the simulation hypothesis with complexities of closed-timelike curves.

Abstract

This paper applies the Conway Machine (CM) framework, formally introduced in the companion paper 22, to four foundational questions in the philosophy of computation. Lens I examines the Lucas–Penrose dialectic through the choice between numeric and short/loopy regimes, distinguishing methodological from ontological claims. Lens II reformulates P vs NP as a question of “fuzziness elimination” across CM regimes. Lens III explores structural resonances between the simulation hypothesis and closed-timelike-curve complexity (after Aaronson–Watrous). Lens IV unifies the (S, α) parameter space as a taxonomy for hypercomputation. These are interpretive lenses, not attempts at resolution; each depends on the formal framework developed in 22.

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