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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]