From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6919 Path: news.gmane.org!not-for-mail From: posina Newsgroups: gmane.science.mathematics.categories Subject: Re: Natural Functorial Categorical Intuition Date: Wed, 28 Sep 2011 10:27:58 -0700 Message-ID: References: Reply-To: posina NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1317249530 9829 80.91.229.12 (28 Sep 2011 22:38:50 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 28 Sep 2011 22:38:50 +0000 (UTC) Cc: To: "Ellis D. Cooper" Original-X-From: majordomo@mlist.mta.ca Thu Sep 29 00:38:43 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R92m0-0000TM-Lj for gsmc-categories@m.gmane.org; Thu, 29 Sep 2011 00:38:40 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:40363) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R92kg-0004BB-1Z; Wed, 28 Sep 2011 19:37:18 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R92ke-0001Ww-EX for categories-list@mlist.mta.ca; Wed, 28 Sep 2011 19:37:16 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6919 Archived-At: Dear All, My understanding, having studied in some detail the behavioural, psychological, and cognitive scientific studies, is that a serious study = of mathematics (beginning with Lawvere & Schanuel's Conceptual Mathematics) can inform cognitive sciences more so than the other way around, with all due respect to Dan Kahneman and those 'where mathematics comes from' guys= . Thank you, posina On Tue, 27 Sep 2011 17:20:41 -0400, "Ellis D. Cooper" wrote: > My motto has been "Rigor cleans the window through which intuition > shines." It seems to me that > a great deal more is known about mathematical rigor than about > mathematical intuition. >=20 > Economics Nobelist Daniel Kahneman recently published at www.edge.org > a survey of several > men-decades of research on flaws of human statistical intuition. A > paper, "The Intuitive Experience" in > "The View from Within" (Journal of Consciousness Studies, V.6 1999) > discusses in considerable > detail schema and methods of invocation of intuition in > psychotherapy, art, and biology research. >=20 > My overall question is whether there really are different kinds of > intuition depending on the research > discipline. In particular, is there some kind of kinetic intuition > specific to category theory that crucially > involves visualization of time-varying diagrams? Do conjectured > adjoint functors arise from distinct algebraic, or > geometric, or logical intuitions? Do categorists deploy special > methods to access their intuition, or > do intuitions just happen to those with a knack for category theory? > Does categorical intuition just > develop with experience, or is there a specialized training to > enhance it? Is categorical intuition > any different from mathematical intuition in general? >=20 > Ellis D. Cooper >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]