From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5824 Path: news.gmane.org!not-for-mail From: soloviev@irit.fr Newsgroups: gmane.science.mathematics.categories Subject: Re terminology: Date: Thu, 20 May 2010 09:58:09 +0200 (CEST) Message-ID: References: Reply-To: soloviev@irit.fr 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 1274385167 16326 80.91.229.12 (20 May 2010 19:52:47 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 20 May 2010 19:52:47 +0000 (UTC) To: "Ronnie Brown" Original-X-From: categories@mta.ca Thu May 20 21:52:45 2010 connect(): No such file or directory 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 4.69) (envelope-from ) id 1OFBnQ-0008PK-Lq for gsmc-categories@m.gmane.org; Thu, 20 May 2010 21:52:44 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OFBK0-0000cl-Ow for categories-list@mta.ca; Thu, 20 May 2010 16:22:20 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5824 Archived-At: My personal opinion is that this process is very much influenced by the pressure of "bibliometry", "impact factors" and other "modern trends" - people often not very scrupulously invent and reinvent terminology to be better cited, and, conscious or not, it often very much smells of imposture. Sergei Soloviev > Peter Sellinger writes recently: > > --------------------------------------------------- > > I think this is a very apt illustration of what happens if a term with > an existing meaning is redefined to mean something else. Henceforth it > is impossible for anybody to use the term (with either meaning) > without first giving a definition. > > --------------------------------------------------- > > I completely agree. My own problem is with term `infinity groupoid' whi= ch > is used to describe something which is not even a groupoid, and whose u= se > seems to me to militate against the understanding of what has been > achieved with the original and much earlier definition. I once asked > Gian-Carl Rota about such change of terminology, in connection with a > refereeing job, and he agreed that mathematicians are used to creating > confusion in this way. > > There are two easy tendencies: one is to use an old name in a quite > different way, and the other is to use a new name for an old idea, so t= hat > the use of the old term looks old fashioned, and a lot of work may be > consigned to the dustbin of history, becoming not easy of access for n= ew > students. > > It seems to be an example of these confusions is the way the simplicial > singular complex of a space is called an infinity-groupoid, even the > `fundamental infinity groupoid', when what seems to be referred to is t= hat > it is a Kan complex, i.e. satisfies the Kan extension condition, studie= d > since 1955. The new term sounds like `dressing up' an old idea to look > new. My personal objection to this change of terminology (i.e. axe to > grind!) is that this distracts from studying the not so simple proofs t= hat > strict higher homotopical structures exist, which mainly are for > structured spaces (in particular filtered spaces (Brown/Higgins, Ashley= ), > n-cubes of spaces (Loday), and more recently smooth spaces (Faria > Martins/Picken)). The analysis and comparison of these uses should be > made. It was certainly a relief to Philip and I that we could do someth= ing > with filtered spaces which we could not do for the absolute case; the > significance of the fact that these constructions work and lead to > specific calculations should be thought about. > > The term `higher dimensional group theory' which was published in a pap= er > with that title in 1982 was intended to suggest developing higher group= oid > theory and its relations to homotopy theory in the spirit of group theo= ry, > which meant specific constructions relevant to geometry and calculation= s, > even computer calculations, of many examples, in which actual numbers > arise as a test of and examples of the general theory, and in which som= e > aspects of group theory are sensibly seen as better represented in the > higher dimensional theory; and example of this is the nonabelian tensor > product of groups, where group theorists have found lots of pickings. > > I am not sure how these terminological problems will be resolved, and I > know the term (\infty,n)-groupoid has been well used recently but the > problem of relation to the older ideas, which have had a certain succes= s, > should be recognised. > > Ronnie Brown > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]