Re: History of string diagrams

["Joyal, André" <joyal.andre@uqam.ca>]

Some more comments.

I always imagined that Penrose was inspired by Feynman's diagrams,
but Max's story is casting doubts on this idea; Penrose
may have been chiefly concerned with the syntax of tensor calculus.

Let me point out that Eduardo Dubuc invented an "elevator calculus" in 
the early 70's which is a form of the string diagram notation.
It was never published.

Best regards,
André



________________________________________
From: Ross Street [ross.street@mq.edu.au]
Sent: Friday, May 05, 2017 6:48 PM
To: Aleks Kissinger
Subject: categories: Re: History of string diagrams

On 4 May 2017, at 1:19 AM, Aleks Kissinger <aleks0@gmail.com<mailto:aleks0@gmail.com>> wrote:

A short note: This idea that string diagrams are, due to technical
issues, only useful for private calculation, is said explicitly by
Penrose. Penrose and Rindler's book "Spinsors and Spacetime" (CUP
1984) has an 11-page appendix full of all sorts of beautiful,
carefully hand-drawn graphical notation for tensors and various
operations on them (e.g. anti-symmetrization and covariant
derivative).

Some random comments:

The person who told me of the Penrose-Rindler reference and the earlier

R. PENROSE, Applications of negative dimensional tensors, in ``Combinatorial Mathematics and its Applications,'' (D.J.A. Welsh, Ed., Academic Press, 1971) 221--244

was Iain Aitchison who found a coloured string-diagram Pascal-triangle-like   algorithm for producing the n-cocycle condition arising from the orientals  and their cubical analogues. While Iain's more recent

The geometry of oriented cubes, arXiv:1008.1714v1 [math.CT]

has incredible diagrams in comparison with 1984 technology, the string versions are not there.

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 visually impaired. Two reasons:

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 wearing lenses that inverted the world. After a few days apparently the brain adjusts and it believes everything is the right way up.

2. Looking over Roger's shoulder on lectures using tensors, Max noticed that 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 connecting strings made it clear.

Who knows what lies in one's subconscience! However, I think the string notation Max used when talking about his work with Eilenberg on extraordinary natural transformations (not the more general Set-based dinatural transformations Dubuc and I wrote about) arose quite independently of Max's Penrose experience. Sometimes when Graeme Segal was in Sydney, I was around while he and Max discussed comparisons of the Eilenberg-Kelly string diagrams

(which do not appear in their paper: A generalization of the functorial calculus, Jour. Algebra 3 (1966) 366--375)

and string diagrams in physics.

Best wishes,
Ross


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