Abstract
A brief analysis of analog computation is presented, taking into account both historical and more modern statements. I show that two very different concepts are tangled together in some of the literature—namely continuous valued computation and analogy machines. I argue that a more general concept, that of model-based computation, can help us untangle this misconception. A two-dimensional view of computation is offered, in which this model-based dimension is orthogonal to the dimension concerning the type of variables used in components. I argue that this is a useful framework for assessing alternative computing devices and computational claims in an expanding landscape of computation.
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Notes
An earlier version of this paper originally appeared in Beebe (2016). This current paper has extended and improved upon the original by incorporating several new references, updating definitions and clarifying the argument structure, and by providing additional discussion of important points throughout.
We will see shortly that von Neumann, among others, used the term ‘organ’ for computational components.
Thus, in the remainder of this article, the reader should note that when I use the term ‘analog’, even as an adjective, it does not refer to continuity.
Also, Care (2010) advocates a deep relationship between analog computing and modeling in science supported by an in depth historical analysis.
Although it may be an open question whether all models are in fact rooted in analogy or similarity, I do not focus on such an argument here.
It is also interesting to note that a slide rule is typically called an analog computer. Under the misconception of analog computer as necessarily involving continuous variables, what role does continuity play in the use of a slide rule? It is arguable that the continuously adjustable aspect of the device is incidental to the actual use and function of the computer since outputs are also not real numbers.
The benefits or drawbacks of any specific device depends on the model involved, and thus it makes no sense to talk of ‘general’ speed-up (or slow-down) results for model-based computing.
Piccinini (2015, p. 203) also notes that we should distinguish between ‘general purpose’ as referencing computational universality (i.e. a Universal Turing machine for digital computation), and ‘general purpose’ in the sense that we can do many things with the same device. A model-based computer in the account offered here might be neither universal nor useful for many different things.
Even more so than Searle himself might have admitted.
Attempting to mitigate or explicitly accepting the HF is a required step, since as Searle notes, “...The homunculus fallacy is endemic to computational models of cognition and cannot be removed by the standard recursive decomposition arguments.” Searle (1990, p. 36) What can be done, I argue, is to put a new spin on the issue.
A similar point is made by Piccinini and Bahar (2013), however their re-structuring of the cognitive computationalism debate ends with a hybrid notion of computation for cognition that combines digital computation with the conflated notion of analog computation discussed earlier. Besides the obvious disagreement we have in defining analog computation, I think the notion of model-based computation discussed here supports in some ways their assertion that neural computation is a kind of its own (not particularly digital, not particularly continuous).
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Acknowledgements
I would like to thank Bernd Ulmann for introducing me to my own errors on the foundations of analog computation, and for motivating this present analysis. Among others, Michael Cuffaro, Ulrike Hahn, Stephan Hartmann, Christian Leibold, Gregory Wheeler, and Richard Whyman provided substantial feedback and discussion of the topic during the writing of this paper.
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Beebe, C. Model-based computation. Nat Comput 17, 271–281 (2018). https://doi.org/10.1007/s11047-017-9643-0
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DOI: https://doi.org/10.1007/s11047-017-9643-0