**From:** Paul Cockshott (*wpc@DCS.GLA.AC.UK*)

**Date:** Wed Sep 22 2004 - 06:27:33 EDT

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I am not entirely sure on this point. I don't know enough of the history of the derivation of the correlation coefficient, and I have certainly used it in the past. However it looks very like an inner product operation which only make sense in a vector space. What one is basically doing with the correlation coefficient is measuring the angle between two vectors, or rather measuring the cosine of the angle between normalised unit vectors going along the same rays as the original vectors. But this whole procedure is only well defined for vector spaces. If one has for example a Manhattan metric, then the distance between the origin and the point (3,4) is not 5 but 7, so that the normalisation condition used in the correlation coefficient will be wrong. -----Original Message----- From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Ian Wright Sent: 21 September 2004 22:28 To: OPE-L@SUS.CSUCHICO.EDU Subject: Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott Hi Paul What is wrong with the Pearson correlation coefficient when comparing (price, value) pairs? I am unsure whether this measure assumes anything about an underlying metric space. -Ian.

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