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Production of Ideas by Means of Ideas: A Turing Machine Metaphor

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  • Stefano Zambelli

Abstract

In this paper production of knowledge is modelled in terms of Turing machines or compositions of Turing machines. The input tape and the output tape of the machines are seen as the encoding of ideas generated by Turing machines. This allows us, among other things, to define and measure the complexity of ideas and knowledge in the simple terms of algorithmic and computational complexity. Moreover the very existence of the halting problem allows for the introduction of a non‐stochastic notion of uncertainty. Consequently uncertainty may be modelled not as the outcome of a predefined probability distribution, but in terms of the randomness associated with the halting problem. In this way the ‘frequency distribution of innovations’ is endogenously generated by the choices of the Turing machines. It is shown that a vast variety of alternative dynamic behaviours in knowledge evolution and hence in productivity can be generated. One can observe clusters of emerging innovations, persistent and increasing emergence of new discoveries as well as periods of explosive evolutions followed by stasis periods.

Suggested Citation

  • Stefano Zambelli, 2004. "Production of Ideas by Means of Ideas: A Turing Machine Metaphor," Metroeconomica, Wiley Blackwell, vol. 55(2‐3), pages 155-179, May.
    • Handle: RePEc:bla:metroe:v:55:y:2004:i:2-3:p:155-179
    DOI: 10.1111/j.0026-1386.2004.00188.x
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    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    3. Bridges, Douglas S., 1982. "Preference and utility : A constructive development," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 165-185, January.
    4. Rustem, Berc & Velupillai, Kumaraswamy, 1990. "Rationality, computability, and complexity," Journal of Economic Dynamics and Control, Elsevier, vol. 14(2), pages 419-432, May.
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    Cited by:

    1. K. Vela Velupillai, 2007. "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics," Department of Economics Working Papers 0722, Department of Economics, University of Trento, Italia.
    2. Kumaraswamy Vela Velupillai, 2013. "Turing's Economics. A Birth Centennial Homage," Economia politica, Società editrice il Mulino, issue 1, pages 13-32.
    3. Stefano Zambelli & N. Dharmaraj, 2013. ""Carry-on-Activity" and Process Innovation," ASSRU Discussion Papers 1306, ASSRU - Algorithmic Social Science Research Unit.
    4. Bartholo, R.S. & Cosenza, C.A.N. & Doria, F.A. & de Lessa, C.T.R., 2009. "Can economic systems be seen as computing devices?," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 72-80, May.
    5. K. Vela Velupillai & Stefano Zambelli, 2010. "The Epistemology of Simulation, Computation and Dynamics in Economics Ennobling Synergies, Enfeebling 'Perfection'," ASSRU Discussion Papers 1002, ASSRU - Algorithmic Social Science Research Unit.

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