The Phillips Machine, The Analogue Computing Traditoin in Economics and Computability
In this paper I try to argue for the desirability of analog computation in economics from a variety of perspectives, using the example of the Phillips Machine. Ultimately, a case is made for the underpinning of both analog and digital computing theory in constructive mathematics. Some conceptual confusion in the meaning of analog computing and its non-reliance on the theory of numerical analysis is also discussed. Digital computing has its mathematical foundations in (classical) recursion theory and constructive mathematics. The implicit, working, assumption of those who practice the noble art of analog computing may well be that the mathematical foundations of their subject is as sound as the foundations of the real analysis. That, in turn, implies a reliance on the soundness of set theory plus the axiom of choice. This is, surely, seriously disturbing from a computation point of view. Therefore, in this paper, I seek to locate a foundation for analog computing in exhibiting some tentative dualities with results that are analogous to those that are standard in computability theory. The main question, from the point of view of economics, is whether the Phillips Machine, as an analog computer, has universal computing properties. The conjectured answer is in the negative.
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- Stefano Zambelli, 2010. "Flexible Accelerator Economic Systems as Coupled Oscillators," ASSRU Discussion Papers 1004, ASSRU - Algorithmic Social Science Research Unit.
- Richard Stone, 1951. "Simple Transaction Models, Information and Computing," Review of Economic Studies, Oxford University Press, vol. 19(2), pages 67-84.
- William C. Brainard & Herbert E. Scarf, 2000. "How to Compute Equilibrium Prices in 1891," Cowles Foundation Discussion Papers 1272, Cowles Foundation for Research in Economics, Yale University.
- Robert W. Dimand & John Geanakoplos, 2005. "Celebrating Irving Fisher," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 3-18, 01.
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