From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5396 Path: news.gmane.org!not-for-mail From: Zinovy Diskin Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Mon, 21 Dec 2009 10:46:58 -0500 Message-ID: References: Reply-To: Zinovy Diskin NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1261442596 12471 80.91.229.12 (22 Dec 2009 00:43:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 22 Dec 2009 00:43:16 +0000 (UTC) To: John Baez , categories@mta.ca Original-X-From: categories@mta.ca Tue Dec 22 01:43:09 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NMsqC-00072w-Ao for gsmc-categories@m.gmane.org; Tue, 22 Dec 2009 01:43:08 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NMsPv-0006RA-9i for categories-list@mta.ca; Mon, 21 Dec 2009 20:15:59 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5396 Archived-At: >> =C2=A0I think there are enough very interesting simple examples of categ= ories >> that the language and diagrams could be introduced to high school studen= ts. >> I've heard that Piaget experimented, successfully, with teaching category theory to 12-year-old children (but I do not have any references). > > > Math trickles down. =C2=A0Right now we need more category theory taught a= t the > graduate level, so someday enough professors will understand it well enou= gh > to teach it at the undergrad level, so that eventually enough high school > teachers will know enough to teach it at the high school level. > > If this seems overly optimistic, it's worth thinking about calculus, whic= h > in Newton's day was regarded as comprehensible only by a few experts. > For calculus, the transformation of an esoteric into a basic discipline was largely driven by engineering applications. After mathematicians demonstrated that calculus could be applied to practical engineering problems, and developed a methodology for such applications, engineers recognized that calculus should be taught at the then-undergrad level. This created a demand in professors capable of teaching calculus to engineers, and further along the chain, as John described. This mechanism should work for category theory as well: software engineering is saturated with problems to which categories have something essential to offer. The situation is even more favorable because software engineers themselves reinvent categorical constructs (more accurately, their inventions can be seen as a reinvention of categorical constructs). I believe that software engineering is ready (theoretically :) to accept categorical methods. Of course, much needs to be done to adapt category theory as a basic mathematical discipline for software engineering but it would not be a waste of time and effort. This work should be profitable for categories in two ways: 1) Public appreciation, funding etc. 2) Engineering applications are a source of interesting problems and interpretations that may be mathematically fruitful. Focusing on engineering allows treating "the opprobrium issue" in a different way (my apologies if it is too vulgar). Category theory provides methods and tools, and there are other tools on the market. At least part of the attempts to sell category theory to a general mathematical public is like selling it to a competing vendor, and hence doomed to fail from the very beginning. It's more fruitful to sell (whatever that means) to prospective users/customers. Working mathematics, physics, computer science are such users, and they do appreciate category theory. However, these groups of customers are not particularly numerous. A very promising prospective user is software engineering: it's massive, dynamic, and eager (as any other engineering) to adapt any widget helpful to do the job, be it calculus, vector algebra or abstract nonsense. Having such a customer would dramatically change the market situation for categories similarly to the case of mechanical engineering-calculus. Z. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]