Definability as hypercomputational effect

TL;DR

This paper explores the limits of classical simulation of physical processes and proposes using computability theory to understand hypercomputational aspects of physical phenomena, aiming to clarify their significance.

Contribution

It introduces a computability theoretic approach to analyze physical phenomena resistant to classical simulation, assessing the relevance of hypercomputation in science and philosophy.

Findings

Identifies limitations of classical models in simulating physical processes.

Proposes a deconstruction method using computability theory.

Aims to differentiate between practical hypercomputational effects and philosophical speculation.

Abstract

The classical simulation of physical processes using standard models of computation is fraught with problems. On the other hand, attempts at modelling real-world computation with the aim of isolating its hypercomputational content have struggled to convince. We argue that a better basic understanding can be achieved through computability theoretic deconstruction of those physical phenomena most resistant to classical simulation. From this we may be able to better assess whether the hypercomputational enterprise is proleptic computer science, or of mainly philosophical interest.