I dont believe your interpretation of the diagonal argument is correct there, but it is anyway the wrong branch of maths since what one has to deal with here are information measures over vector and real spaces. ________________________________________ From: [email protected] [[email protected]] On Behalf Of raghu [[email protected]] Sent: Wednesday, July 20, 2011 4:48 PM To: Progressive Economics Subject: Re: [Pen-l] Ingo Elbe: Between Marx, Marxism, and Marxisms, Part I.3
On Tue, Jul 19, 2011 at 10:23 PM, Joseph Green <[email protected]> wrote: > But no, there is *no* reasonable way to map a two or more dimensional vector > space onto an ordinary numerical scale without losing essential information. > Period. That's the end of the story. > > It isn't a matter that this is a complicated problem. It isn't a matter that > one can use fancy methods of linear programming to do this. Or shadow prices. > Or Lagrange multipliers. Or non-linear functions. Or whatever. It simply > isn't possible. A two-dimensional vector space, for example, obeys different > laws than a simple numerical scale. That's no way around this. > > Or, to put it another way, if one reduces a two-dimensional vector to a > single number, one loses essential information. You are wading into deep mathematical waters here. The famous Cantor diagonalization argument does precisely what you claim to be impossible: reduce an order pair of numbers to a single number in a one-to-one fashion. http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument -raghu. _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l The University of Glasgow, charity number SC004401 _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
