On Wed, Jul 20, 2011 at 2:52 PM, Joseph Green <[email protected]> wrote: > Hi raghu! It's nice to find someone else who is interested in set theory and > the philosophical foundations of mathematics. But what I said was that there > was no "reasonable" way to map a two or more dimensional vector space onto an > ordinary numerical scale with losing essential information. > > There are, as you point out, set-theoretic ways to map a two-dimensional > space onto a single numerical scale, but they destroy the mathematical > structures in these spaces, are not smooth functions, destroy any practical > approximations, etc. That's why you don't see these mappings used in > economics, and never will.
Indeed. I do understand what you are saying and agree on an intuitive level (to paraphrase, it is possible to create mappings of an ordered pair of numbers to a single number, but there is no way to design a calculus that is preserved over such a mapping), but it doesn't seem so easy to make this claim precise. Anyway you seem to be making what I would call an anti-Hayekian argument. Friedrich Hayek made a lot of mileage out ofthe so-called economic calculation problem which is really a rather trivial and obvious observation. Here's Wikipedia's summary of it: "Without money to facilitate easy comparisons, socialism lacks any way to compare different goods and services. Decisions made will therefore be largely arbitrary and without sufficient knowledge, often on the whim of bureaucrats." With money, it is certainly true that easy comparisons are facilitated, but this is not rational in any sense except a circular one. Your argument may suggest that having a single number (the price) to compare two disparate goods is only slightly better than having no numbers at all; it may convey some information, but only a meagre amount. -raghu. _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
