Agency and the physics of numbers

TL;DR

This paper explores how physical theories depend on agents making guesses beyond computation, proposing a symbol-handling agent model that bridges the gap between theory and experiment, and underpins the development of spacetime and motion management.

Contribution

It introduces a novel representation of symbol-handling agents that compute and receive guesses, linking agency to the foundations of physics and the management of spacetime.

Findings

Physics depends on agents making guesses beyond computation.

A model for symbol communication among agents is developed.

Communication among agents underpins theories of spacetime and motion.

Abstract

Analogous to G\"odel's incompleteness theorems is a theorem in physics to the effect that the set of explanations of given evidence is uncountably infinite. An implication of this theorem is that contact between theory and experiment depends on activity beyond computation and measurement -- physical activity of some agent making a guess. Standing on the need for guesswork, we develop a representation of a symbol-handling agent that both computes and, on occasion, receives a guess from interaction with an oracle. We show: (1) how physics depends on such an agent to bridge a logical gap between theory and experiment; (2) how to represent the capacity of agents to communicate numerals and other symbols, and (3) how that communication is a foundation on which to develop both theory and implementation of spacetime and related competing schemes for the management of motion.