**From:** Paul Cockshott (*wpc@dcs.gla.ac.uk*)

**Date:** Sat Apr 05 2008 - 18:15:07 EDT

**Next message:**Paul Cockshott: "RE: [OPE] Dialectics for the New Century"**Previous message:**Dave Zachariah: "Re: [OPE] Dialectics for the New Century"**In reply to:**GERALD LEVY: "RE: [OPE] Dialectics for the New Century: geometry and meaning"**Next in thread:**Dave Zachariah: "Re: [OPE] Dialectics for the New Century: geometry and meaning"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Gerry -------- Hi Paul C: What articles and/or research are you referring to? What areas of research in political economy do you foresee the usefulness of modeling with high dimensional vector spaces? Paul ----- We had a discussion on a paper I wrote a year or so ago on using Hilbert space to model commodity exchange. Well that is a higher dimensional vector space. Then obviously value theory uses higher dimensional vector spaces to determine the values of commodities, it models technologies as matrices whose dominant eigen value is the inverse of the maximal rate of profit. Well Google are apparently using Hilbert spaces to understand the semantics of documents on the web, the demos he gave were sufficiently good for him to be able to use them to get context specific appropriate translations of words between languages. In my case I invented the concept of commodity amplitudes in order to allow one to model commodity exchanges as the result of unitary rotation matrices on the state space of commodity and money holdings. In the case of what Domminic is doing he is using the same formalism with the vectors spaces representing the occurence of words in documents. (I have only started reading his book, so I am not in a position to give a very good explanation of just how it works yet), but the basic idea is that the inner product between the vectors representing two words occurences in documents over the web, is an amplitude whose square is the probability of co-occurence of the words, and thus of relatedness in terms of meaning of the words. The formalism is of course the same as that developed by von Neumann when he formalised quantum mechanics in the 30s. It is significant that he went on from that to develop the von Neumann growth model, which uses much of the same apparttus, and the development of I/O tables in the 40s and Sraffa and Morishima's work derive in turn from that. I am struck by how many different areas end up depending on the same conceptual tools. I first came accross it in economics with von-Neumanns growth model, then read his work on quantum theory, then I found that the same conceptual apprattus was handy for thinking through algebras for relating interacting concurrent systems, then it turned out to be useful in information coding. We used the same basic maths in the software we developed for the first mobile video phones. Then I found you could analyse exchange relations using it, then yesterday I find that people can derive aristotelean logic and the semantics of words from it! Paul Cockshott Dept of Computing Science University of Glasgow +44 141 330 1629 www.dcs.gla.ac.uk/~wpc/reports/ -----Original Message----- From: ope-bounces@lists.csuchico.edu on behalf of GERALD LEVY Sent: Sat 4/5/2008 10:40 PM To: Outline on Political Economy mailing list Subject: RE: [OPE] Dialectics for the New Century: geometry and meaning > Since the maths he uses is very similar> to the maths I use for modeling financial transactions I found it> particularly interesting. Hi Paul C: What articles and/or research are you referring to? What areas of research in political economy do you foresee the usefulness of modeling with high dimensional vector spaces? In solidarity, Jerry _______________________________________________ ope mailing list ope@lists.csuchico.edu https://lists.csuchico.edu/mailman/listinfo/ope

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**Next message:**Paul Cockshott: "RE: [OPE] Dialectics for the New Century"**Previous message:**Dave Zachariah: "Re: [OPE] Dialectics for the New Century"**In reply to:**GERALD LEVY: "RE: [OPE] Dialectics for the New Century: geometry and meaning"**Next in thread:**Dave Zachariah: "Re: [OPE] Dialectics for the New Century: geometry and meaning"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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