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
