Computing and modelling: Analog vs. Analogue

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Highlights

  • Computing involves two distinct types of representation.

  • Computing implies the existence of epistemic agents.

  • An account of the distinction between analog and digital computing is proposed.

  • The account relies on the semantic and syntactic properties of all representations.

  • Analog computational modelling and analogue modelling are epistemically different.

Abstract

We examine the interrelationships between analog computational modelling and analogue (physical) modelling. To this end, we attempt a regimentation of the informal distinction between analog and digital, which turns on the consideration of computing in a broader context. We argue that in doing so, one comes to see that (scientific) computation is better conceptualised as an epistemic process relative to agents, wherein representations play a key role. We distinguish between two, conceptually distinct, kinds of representation that, we argue, are both involved in each case of computing. Based on the semantic and syntactic properties of each of these representations, we put forward a new account of the distinction between analog and digital computing. We discuss how the developed account is able to explain various properties of different models of computation, and we conceptually compare analog computational modelling to analogue (scale) modelling. It is concluded that, contrary to the standard view, the two practices are orthogonal, differing both in their foundations and in the epistemic functions they fulfil.

Section snippets

Historical examples of mechanical computing devices

We will briefly review some typical examples of machinery-aided computation, carried out by scientists and engineers before the advent of electronic, stored-program, digital computers. These examples will be slide rules, nomograms, planimeters, and general purpose analog devices.

The purpose of this short survey of representative cases is to identify common underlying features that justify our viewing of all of them as tools of (scientific) computation. We will argue that what is responsible for

Differential analysers and the general purpose analog computer

The first general purpose analog computer was built under the supervision of Vannevar Bush, in the 1930’s at MIT, known as ‘Bush’s Differential Analyser’. This was a mechanical analog computer, mainly based on disc and wheel implementations of integrators – similar to the ones constructed by Maxwell and Thomson – and on the feedback technique, first discovered by Kelvin.5 Bush’s

Regimenting ‘computing’: representation and agents

Having the above representative cases in mind, we are ready now to examine computing from a wider perspective. In this section, we consider standard and non-standard (i.e., non-digital silicon-based) computing together. Our purpose is a first attempt to regimentation of the informal, pre-theoretical notion of ‘computing’ that will take into account the great variety of guises under which computation appears, and at the same time pin down the common aspects that make us consider them all

Accounts of ‘analog’

What makes an analog computer analog? Generally, the distinction has been discussed in the literature relatively little, and usually in passing either in introductory chapters to computer science texts or in computing history surveys or in literature relevant to philosophy of mind issues. There are some notable exceptions, such as Beebe (2016), Goodman (1976), Haugeland (1981), Lewis (1971), Maley (2011), which include substantial discussion of the distinction itself, but they are rather

Analog vs. digital computation: the proposed account

Drawing on Goodman’s theory of analog and digital symbolic systems, and based on the general picture about computing we have drawn, we are ready (at last!) to articulate a precise account of analog and digital computing.

Recall that, according to our framework (Section 3 and Fig. 9), computing simultaneously involves two, distinct kinds of representation: one related to how the mathematical part of the computed problem is represented in the computing system, and the other related to how the

Kinds of physical models

Analogue (or physical)43 models are still widely in use in scientific practice today (engineering, fluid mechanics, etc.). We propose a distinction between two classes of such models. The first class contains models used for demonstration purposes, such as the examples mentioned before. The second is the class of scale models (largely neglected in philosophy of science until recently), on which we will mainly

Comparison with analog computing

We are now ready to set off for the comparison between the two practices, analog computing and analogue modelling. The paradigmatic case of the former will be computing with electronic analog computers, implemented by arrays of operational amplifiers (OpAmps). For the latter, we draw on the wing design example from above. We will be arguing that the two practices are orthogonal, fulfilling different epistemic purposes, by focusing on their differences.

Perhaps, the easiest difference to notice

Final remarks and open questions

We distinguished between two kinds of physical models: models that serve only demonstrative purposes, such as the famous DNA model constructed by Watson and Crick, and scale models used in similarity theory, such as scale wings in wind tunnels. We then examined the connection between analogue modelling and analog computing. To that end, we had to formulate an account of computing in general, and of analog and digital computing in particular. We argued that, generally, analog computing and

CRediT authorship contribution statement

Philippos Papayannopoulos: Conceptualization, Methodology, Investigation, Resources, Visualization.

Acknowledgements

I am indebted to Wayne Myrvold for discussions on some of the topics dealt with here. An early version of the paper was presented in 2019 at the philosophy colloquium of the University of Cyprus (Department of Classics and Philosophy). I am thankful to that audience for very stimulating comments. I am also thankful to the participants of the Workshop on Computation in Scientific Theory and Practice, held in 2019 at the Munich Center for Mathematical Philosophy, for useful discussions. I am very

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