When does a physical system compute?

Abstract

Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however, no consensus on how to tell if a given physical system is acting as a computer or not; leading to confusion over novel computational devices, and even claims that every physical event is a computation. In this paper, we introduce a formal framework that can be used to determine whether a physical system is performing a computation. We demonstrate how the abstract computational level interacts with the physical device level, in comparison with the use of mathematical models in experimental science. This powerful formulation allows a precise description of experiments, technology, computation and simulation, giving our central conclusion: physical computing is the use of a physical system to predict the outcome of an abstract evolution. We give conditions for computing, illustrated using a range of non-standard computing scenarios. The framework also covers broader computing contexts, where there is no obvious human computer user. We introduce the notion of a ‘computational entity’, and its critical role in defining when computing is taking place in physical systems.

Heterotic computing: exploiting hybrid computational devices

“…This also illustrates another basic attribute of physical computation that is easily forgotten with the ubiquity of binary encoding: the fungibility of representation. The same computation can be embedded in different computational substrates and even embedded in different ways in the same substrate [5]. Henson et al [13] describe a system comprising a computer, a robot and a chemical reaction system, linked together in a fully automated experimental system to search for chemical products that exhibit interesting complex spatio-temporal dynamics (motile and dividing droplets).…”

“…The results and insights in this article represent Deciding whether biological entities are computing, or are maybe 'universal' in some other biological sense, requires a notion of what it means for a physical system to compute. Horsman et al [5] have recently developed abstraction/representation theory, to formalize when a physical system is indeed computing, rather than merely 'doing its thing'. Horsman [16] summarizes that theory, then shows how it can be applied to multiple substrates in the case of hybrid and heterotic computational systems.…”

“…The issue starts with Kendon et al [4], in which we extend our definition of physical computing [5] to include multiple substrates composed, in series or in parallel, into hybrid computational systems. We then flesh out what we mean by 'heterotic' computing through a collection of examples from quantum to biological.…”

Towards heterotic computing with droplets in a fully automated droplet-maker platform

“…However, we are so familiar with conventional computing architectures, driven by digital logic on a silicon substrate, that finding the correct process to convert potential natural computing architectures that take advantage of the laws of physics, chemistry and biology will require a new abstract 'translation' framework for constructing the computation [25]. In order to completely understand how to construct a new theory for computation, and then explore how existing physical systems may be better for one type of problem as opposed to others, we need to rigorously define the practical considerations for carrying out a computation.…”

Simple or Complex Bodies? Trade-offs in Exploiting Body Morphology for Control

“…Some authors would subsume this type of interaction under a computational framework as well-e.g., "embodied computation should be understood as a physical process in an ongoing interaction with its environment" [13, p. 6]. Other authors pose much stricter requirements on physical computation: according to Horseman et al [22], a physical system can be said to compute only if it was designed as such. That is, there needs to be a user that has an abstract computational problem that he wants to solve by a physical machine.…”