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The Phillips Machine, The Analogue Computing Traditoin in Economics and Computability

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  • K. Vela Velupillai

Abstract

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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  • K. Vela Velupillai, 2011. "The Phillips Machine, The Analogue Computing Traditoin in Economics and Computability," ASSRU Discussion Papers 1112, ASSRU - Algorithmic Social Science Research Unit.
    • Handle: RePEc:trn:utwpas:1112
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    1. William C. Brainard & Herbert E. Scarf, 2005. "How to Compute Equilibrium Prices in 1891," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 57-83, January.
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    4. Robert W. Dimand & John Geanakoplos, 2005. "Celebrating Irving Fisher: The Legacy of a Great Economist," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 3-18, January.
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    Cited by:

    1. K. Vela Velupillai, 2011. "DSGE And Beyond – Computable And Constructive Challenges," ASSRU Discussion Papers 1122, ASSRU - Algorithmic Social Science Research Unit.

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    More about this item

    Keywords

    Phillips Machine; Analogue Computation; Digital Computation; Computability; General Purpose Analogue Computer;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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