On Wed, Dec 23, 2009 at 9:35 AM, Ronnie Brown <ronnie.profbrown@btinternet.com> wrote:

First a slight correction:  The paper referred to was I think

Wigner, E.P., The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Comm. in Pure Appl. Math. (1960), reprinted in Symmetries and reflections: scientific essays of Eugene P. Wigner, Bloomington Indiana University Press (1967). Here are some quotations from this article: -------------------------------------------------------------------------

yes, I meant this paper, I apologize for the wrong reference. Actually, I literally translated the Russian translation of the title (that I remembered) back into English. The result turned out to be not an identity, and even not an isomorphism

... that the enormous usefulness of mathematics in the physical sciences is something bordering on the mysterious, and that there is no rational explanation for it.

Here's an absolutely rational explanation. Suppose that once upon a time there were two classes of people, say, A and B, with different logics and aesthetics and criteria of elegance. Correspondingly, they had developed different mathematics, MA and MB. It so happened that A-aesthetics and thinking based on it turned out to be inadequate for the reality, and people A were eaten by saber-toothed tigers. Mathematics MA was forgotten and its traces can now be found in ancient archives only. I'm afraid that the A-destiny is awaiting the opponents of cat theory and their non-categorical math. :) [Do not take it seriously, I understand that category theory is just a good mathematics, not a different mathematics]. Happy Holidays! Z. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]