Dear Zoran, You misunderstood my posting, or I phrased it badly, because On Tue, Dec 22, 2009 at 11:59 AM, zoran skoda <zskoda@gmail.com> wrote:

Dear Zinovy,

I can say that I dislike your selling/marketing despair and do not share excitement in the existence of an easy niche market you propose.

in the list "despair-excitement-easy niche", only the second term is true. Building mathematical models for engineering problems is a hard business, and the suggestion to view it as a fruitful area for categorical applications stems from optimism about the power of category theory, rather than from despair. I'm not going to defend the market metaphor -- it's doubtful anyway. Still, I'd like to clarify a couple of points. 1) I think that both sources of mathematical development, the internal one based on aesthetic criteria and consistency, and the external one based on applications, are equally important and mutually beneficial. Apart from posing interesting problems, applications provide novel interpretations of formal constructs, which is always fruitful. After all, effectively applicable mathematics turns out to be aesthetically appealing as well (Eugene Vigner wrote a famous paper about this "On inaccessible effectiveness of mathematics in natural sciences") 2) The problem of "category theory vs. mathematics" is beyond mathematics as such. A lot of problems could be avoided if a taste for categorical thinking were cultivated in high school, and the basics of category theory were taught to mathematicians, scientists, engineers at the undergrad level. But education is one of the most conservative social institutes with a huge inertia. Turning mathematical education towards category theory needs financial and administrative support, and an external demand. Applications of category theory to engineering problems would be beneficial in this respect too. Z. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] Status: RO