From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6916 Path: news.gmane.org!not-for-mail From: "Ellis D. Cooper" Newsgroups: gmane.science.mathematics.categories Subject: Natural Functorial Categorical Intuition Date: Tue, 27 Sep 2011 17:20:41 -0400 Message-ID: Reply-To: "Ellis D. Cooper" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Trace: dough.gmane.org 1317163576 28257 80.91.229.12 (27 Sep 2011 22:46:16 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 27 Sep 2011 22:46:16 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Sep 28 00:46:10 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 1R8gPh-0001VH-Bg for gsmc-categories@m.gmane.org; Wed, 28 Sep 2011 00:46:09 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:36253) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R8gNo-0008Py-KE; Tue, 27 Sep 2011 19:44:12 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R8gNn-00053V-3d for categories-list@mlist.mta.ca; Tue, 27 Sep 2011 19:44:11 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6916 Archived-At: 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. 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. 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? Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]