The Turing machine of a harmonic oscillator: from the code to the dynamic system

TL;DR

This paper explores the formal equivalence between a damped harmonic oscillator and a Turing Machine, proposing that dynamic physical systems can implement computational processes traditionally associated with digital computers.

Contribution

It formalizes a Turing Machine based on a harmonic oscillator and discusses its potential as a physical realization of algorithmic processes, suggesting new directions for non-computerized computation.

Findings

Established formal equivalence between oscillator and Turing Machine

Linked FOR loop computational model to physical oscillator dynamics

Discussed implications for medical device technology

Abstract

In this work we consider a dynamic system consisting of a damped harmonic oscillator and we formalize a Turing Machine whose definition in terms of states, alphabet and transition rules, can be considered equivalent to that of the oscillator. We prove that the Turing Machine of a FOR loop corresponds to that of the oscillator and we ask ourselves if it is possible to obtain the dynamic system of the harmonic oscillator as a physical realization of the FOR loop. We discuss the relationship between the results found and the science of Can and Can't. We discuss the possibility of an evolution of computer science also towards non-computerized specialized machines whose operating principle is designed as an automatic process starting from a source code instead of as a work of human ingenuity. The approach to the implementation of algorithms in dynamic systems instead of universal computers can be particularly interesting for the field of both diagnostic and implantable medical devices.