From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9212 Path: news.gmane.org!.POSTED!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Re: History of string diagrams Date: Sat, 6 May 2017 16:45:02 +0000 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1494164765 19718 195.159.176.226 (7 May 2017 13:46:05 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sun, 7 May 2017 13:46:05 +0000 (UTC) Cc: "categories@mta.ca" To: Ross Street , Aleks Kissinger Original-X-From: majordomo@mlist.mta.ca Sun May 07 15:46:00 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1d7MVa-0004se-CP for gsmc-categories@m.gmane.org; Sun, 07 May 2017 15:45:58 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51660) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1d7MVc-0004NP-VU; Sun, 07 May 2017 10:46:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1d7MV3-0007JG-96 for categories-list@mlist.mta.ca; Sun, 07 May 2017 10:45:25 -0300 In-Reply-To: Accept-Language: en-US, en-CA Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9212 Archived-At: Some more comments.=0A= =0A= I always imagined that Penrose was inspired by Feynman's diagrams,=0A= but Max's story is casting doubts on this idea; Penrose=0A= may have been chiefly concerned with the syntax of tensor calculus.=0A= =0A= Let me point out that Eduardo Dubuc invented an "elevator calculus" in =0A= the early 70's which is a form of the string diagram notation.=0A= It was never published.=0A= =0A= Best regards,=0A= Andr=E9=0A= =0A= =0A= =0A= ________________________________________=0A= From: Ross Street [ross.street@mq.edu.au]=0A= Sent: Friday, May 05, 2017 6:48 PM=0A= To: Aleks Kissinger=0A= Subject: categories: Re: History of string diagrams=0A= =0A= On 4 May 2017, at 1:19 AM, Aleks Kissinger > wrote:=0A= =0A= A short note: This idea that string diagrams are, due to technical=0A= issues, only useful for private calculation, is said explicitly by=0A= Penrose. Penrose and Rindler's book "Spinsors and Spacetime" (CUP=0A= 1984) has an 11-page appendix full of all sorts of beautiful,=0A= carefully hand-drawn graphical notation for tensors and various=0A= operations on them (e.g. anti-symmetrization and covariant=0A= derivative).=0A= =0A= Some random comments:=0A= =0A= The person who told me of the Penrose-Rindler reference and the earlier=0A= =0A= R. PENROSE, Applications of negative dimensional tensors, in ``Combinatoria= l Mathematics and its Applications,'' (D.J.A. Welsh, Ed., Academic Press, 1= 971) 221--244=0A= =0A= was Iain Aitchison who found a coloured string-diagram Pascal-triangle-like= algorithm for producing the n-cocycle condition arising from the oriental= s and their cubical analogues. While Iain's more recent=0A= =0A= The geometry of oriented cubes, arXiv:1008.1714v1 [math.CT]=0A= =0A= has incredible diagrams in comparison with 1984 technology, the string vers= ions are not there.=0A= =0A= Speaking of Roger Penrose, Max Kelly used to tell the following story about= their time (mid 1950s) in Cambridge. Max thought Roger must be very visua= lly impaired. Two reasons:=0A= =0A= 1. When Max first met him he was wearing very thick glasses. It turned out = Roger was conducting an experiment to test whether one would adapt to weari= ng lenses that inverted the world. After a few days apparently the brain ad= justs and it believes everything is the right way up.=0A= =0A= 2. Looking over Roger's shoulder on lectures using tensors, Max noticed tha= t Penrose was not using the usual notation at all. He was using the string = notation instead. When Max asked why, Roger said that all the i_1, j_2, 1_1= , . . . sub- and super-scripts were impossible to read, whereas the connect= ing strings made it clear.=0A= =0A= Who knows what lies in one's subconscience! However, I think the string not= ation Max used when talking about his work with Eilenberg on extraordinary = natural transformations (not the more general Set-based dinatural transform= ations Dubuc and I wrote about) arose quite independently of Max's Penrose = experience. Sometimes when Graeme Segal was in Sydney, I was around while h= e and Max discussed comparisons of the Eilenberg-Kelly string diagrams=0A= =0A= (which do not appear in their paper: A generalization of the functorial cal= culus, Jour. Algebra 3 (1966) 366--375)=0A= =0A= and string diagrams in physics.=0A= =0A= Best wishes,=0A= Ross=0A= =0A= =0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]=0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]