When does a control system compute? Digital, mechanical and open-loop systems

TL;DR

This paper uses Abstraction/Representation theory to analyze various control systems, demonstrating that all such systems perform some degree of computation, including mechanical and biological controllers.

Contribution

It introduces a novel application of ART to model control systems and establish their computational properties, expanding the understanding of computation in physical systems.

Findings

All examined control systems perform some computation.

The plant in a control system acts as the representational entity in ART.

Mechanical and biological control systems are shown to compute.

Abstract

Control systems are ubiquitous in modern technology, comprising an engineered plant to be kept within specific, often fine-tuned, limits, and a separate controller that ensures this is the case. While modern controllers often employ digital computers, other examples are purely mechanical, or even biological. It is an open question whether computation is happening within all controllers by virtue of them being part of a control system. Abstraction/ Representation theory (ART) has been developed to tackle just this question of whether a physical system is computing. Here, we demonstrate how to use ART to model control systems, and analyse them for computational properties. We determine that the plant of a control system is (a proxy for) the representational entity necessary in ART for the existence of any computation: the plant is the user of the controller. We consider specific systems: a digital thermostat, an electro-mechanical thermostat, the purely mechanical centrifugal governor, and an open-loop human-controlled heating system. We show that all these systems, and control systems in general, are performing some degree of computation. As an initial use of these results, we apply them to computationalism within cognitive theory: we show the governor is computing, so it cannot play its role of counter-example in the question of whether the brain is too.