Abstract
It is argued that the vector space measures used to measure closeness of market prices to predictors for market prices are invalid because of the observed metric of commodity space. An alternative representation in Hilbert space within which such measures do apply is proposed. It is shown that commodity exchanges can be modeled by the application of unitary operators to this space.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cockshott, P., Cottrell, A.: Value’s Law, Value’s Metric, research report University of Strathclyde, Dept. of Computer Science (1994); Reprinted in: Freeman, A., Kliman, A., Wells, J. (eds.): The New Value Controversy and the Foundations of Economics, Edward Elgar, Cheltenham (2004)
Cockshott, W.P., Cottrell, A.: Labour-Time Versus Alternative Value Bases: A Research Note. Cambridge Journal of Economics 27, 749–754 (1997)
Cockshott, W.P., Cottrell, A.: A note on the organic composition of capital and profit rates. Cambridge Journal of Economics 21, 545–549 (2003)
Cockshott, W.P., Cottrell, A., Michaelson, G.: Testing Marx: Some New Results from UK Data. Capital and Class 55, 103–129 (Spring 1995)
DiVincenzo, D.: Quantum Computation. Science 270, 255–261
Farjoun, E., Machover, M.: The laws of Chaos. Verso (1983)
Iverson, K.: A programming language. Wiley, New York (1966)
Iverson, K.: Notation as a tool of thought. In: ACM Turing award lectures, p. 1979. ACM, New York (2007)
Kantorovich, L.V.: Mathematical Methods of Organizing and Planning Production. Management Science 6(4), 366–422 (1960)
Kliman, A.: The Law of Value and Laws of Statistics: Sectoral Values and Prices in the US Economy, 1977-1997. Cambridge Journal of Economics 26, 299–311 (2002)
Kurz, H.D., Salvadori, N.: Von Neumann’s Growth Model and the ‘Classical’ Tradition. Understanding “classical” Economics: Studies in Long-Period Theory (1998)
Ochoa, E.M.: Values, prices, and wage–profit curves in the US economy. Cambridge Journal of Economics 13(3), 413–429 (1989)
Petrovic, P.: The deviation of production prices from labour values: some methodology and empirical evidence. Cambridge Journal of Economics 11(3), 197–210 (1987)
Remak, R.: Kann die Volkswirtschaftslehre eine exakte Wissenschaft werden. Jahrbücher für Nationalökonomie und Statistik 131, 703–735 (1929)
Ryabev, L.D., Smirnov, Y.N.: The Atomic Project, Science, and the Atomic Industry. Atomic Energy 99(2), 519–527 (2005)
Shaik, A.: The Empirical Strength of the Labour Theory of Value. In: Bellafiore, R. (ed.) Marxian Economics. A reapraisal Essays on Volume III of Capital. Profits, Prices and Dynamics, pp. 225–251. St. Martins Press, New York (1998)
Shaikh, A.: The transformation from Marx to Sraffa. In: Freeman, A., Mandel, E. (eds.) Ricardo, Marx, Sraffa, pp. 43–84. Verso, London (1984)
Sraffa, P.: Production of commodities by means of commodities. Cambridge University Press, Cambridge (1960)
Valle Baeza, A.: Correspondence between labor values and prices: a new approach. Review of Radical Political Economics 26(2), 57–66 (1994)
Steedman, I., Tomkins, J.: On measuring the deviation of prices from values. Cambridge Journal of Economics 22, 359–369 (1998)
von Neumann, J.: A Model of General Economic Equilibrium. Review of Economic Studies 13(33), 1–9 (1945)
von Neumann, J.: Mathematical Foundations of Quantum Mechanics, Engl. transl. of the 1931 German edition by Beyer, R.T. (1955)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cockshott, P. (2009). Hilbert Space Models Commodity Exchanges. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds) Quantum Interaction. QI 2009. Lecture Notes in Computer Science(), vol 5494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00834-4_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-00834-4_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00833-7
Online ISBN: 978-3-642-00834-4
eBook Packages: Computer ScienceComputer Science (R0)