From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5425 Path: news.gmane.org!not-for-mail From: Dusko Pavlovic Newsgroups: gmane.science.mathematics.categories Subject: Re: additions Date: Thu, 24 Dec 2009 23:55:43 +0000 (GMT) Message-ID: References: Reply-To: Dusko Pavlovic NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1261773457 15047 80.91.229.12 (25 Dec 2009 20:37:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 25 Dec 2009 20:37:37 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Fri Dec 25 21:37:30 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 1NOGuf-00043s-JE for gsmc-categories@m.gmane.org; Fri, 25 Dec 2009 21:37:29 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NOGVt-0002tS-Al for categories-list@mta.ca; Fri, 25 Dec 2009 16:11:53 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5425 Archived-At: bob coecke proposed to add quantum computing to andre joyal's list of important directions of categorical research, but andre rejected it. i cannot overstate my respect for andre's work and judgement. but this left me pondering. like andre, i must confess that i am quite ignorant about quantum computing. (unlike andre, i am also ignorant about many other categorical topics on his list.) but we probably all know the following. most results in quantum computing are theorems about hilbert spaces. quantum computing is a *tensor calculus*. but it is a tensor calculus of a special kind: it attempts to describe a wildly unintuitive world. even the greatest contributors, like von neumann and feynman, deplored the gap between the quantum world, imposed on us in the lab, and the intuitions imposed on us in everyday life. now category theory often helps where the common intuitions fail. many of its applications demonstrate this. so quantum computation might be an opportunity for an effective application of *geometry of tensor calculus*. is it really wise to reject an attempt to develop this, as objectionable as it might be in any details? physicists like string diagrams, category theorists like string diagrams. most communities would actively reach out... is it just my impression, or are category theorists a little more sceptical about the value of applications than most mathematical communities? they seem to seek a recognition that categories are useful across mathematics, but then hesitate to recognize the depth and value of the applications in the other areas. --- can it be that we suffer from a superiority complex of some sort? the questions raised in the *well kept secret* thread were: 1) why are the achievements of category theory not recognized publicly? 2) what have we done to deserve the opprobium? 3) how can we convince the sceptics? please allow me to add one more: 4) how can the achievements of category theory be used to expand its future developments and applications, and not to constrain them? with best wishes, -- dusko [For admin and other information see: http://www.mta.ca/~cat-dist/ ]