A Behavioural Foundation for Natural Computing and a Programmability Test

TL;DR

This paper defines a new behavioural measure of programmability to determine if a physical system computes, based on its ability to respond to stimuli, and discusses its implications for natural and artificial systems.

Contribution

It introduces a measure of programmability for physical systems, linking their behavior to their computational capacity and comparing it with existing behavioural approaches.

Findings

Proposes a measure of programmability based on system responsiveness.

Classifies systems by the complexity of their evolution.

Connects the measure to Turing's test and natural computation.

Abstract

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical system to compute based on this notion. It proposes a behavioural characterisation of computing in terms of a measure of programmability, which reflects a system's ability to react to external stimuli. The proposed measure of programmability is useful for classifying computers in terms of the apparent algorithmic complexity of their evolution in time. I make some specific proposals in this connection and discuss this approach in the context of other behavioural approaches, notably Turing's test of machine intelligence. I also anticipate possible objections and consider the applicability of these proposals to the task of relating abstract computation to nature-like computation.