IDEAS home Printed from https://ideas.repec.org/a/mul/jb33yl/doi10.1428-35926y2011i1p39-62.html
   My bibliography  Save this article

The Phillips Machine, the Analogue Computing Tradition in Economics and Computability

Author

Listed:
  • Velupillai K. Vela

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 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.

Suggested Citation

  • Velupillai K. Vela, 2011. "The Phillips Machine, the Analogue Computing Tradition in Economics and Computability," Economia politica, Società editrice il Mulino, issue 1, pages 39-62.
  • Handle: RePEc:mul:jb33yl:doi:10.1428/35926:y:2011:i:1:p:39-62
    as

    Download full text from publisher

    File URL: https://www.rivisteweb.it/download/article/10.1428/35926
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://www.rivisteweb.it/doi/10.1428/35926
    Download Restriction: no

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stefano Zambelli, 2011. "Flexible Accelerator Economic Systems As Coupled Oscillators," Journal of Economic Surveys, Wiley Blackwell, pages 608-633.
    2. 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.
    3. Richard Stone, 1951. "Simple Transaction Models, Information and Computing," Review of Economic Studies, Oxford University Press, vol. 19(2), pages 67-84.
    4. Robert W. Dimand & John Geanakoplos, 2005. "Celebrating Irving Fisher," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 3-18, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    More about this item

    Keywords

    C02; C63; E27; E37;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mul:jb33yl:doi:10.1428/35926:y:2011:i:1:p:39-62. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: https://www.rivisteweb.it/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.