Hilbert Space Models Commodity Exchanges

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. 1 Linear Price Models The context of this paper is the empirical testing of linear models of economic activity. Whilst these originated in an informal way in the work of Adam Smith and Quesney, and were partially formalised by Marx in volume 3 of Capital, an adequate formal treatment had to wait for von Neuman[21] and Kantorovich[9]. Both von Neumann and Kantorovich were mathematicians rather than economists. Their contributions to economics were just one part of a variety of research achievements. In both cases this included stints working on early nuclear weapons programs, for the US and USSR[15]...

• Type: Conference
• Year: 2009
• Where: QI
• Authors: Paul Cockshott
• Keywords: Physics, QI 2009, Vector Space Measures, Vector Spaces, Von Neumann