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James Fairbanks (Jun 01 2020 at 21:40):Hi @John Baez, I saw a comment on Azimuth about Tonti Diagrams
Hi! The last questioner was Morad Behandish, and he subsequently sent me a copy of Enzo Tonti’s book The Mathematical Structure of Classical and Relativistic Physics, which I’m currently perusing. You can learn more here:
• Wikipedia, Tonti diagram.
• Algebraic formulation of physical fields.
I’m not ready to say anything about this work.
Have you developed thoughts on Tonti Diagrams in the intervening years?
John Baez (Jun 01 2020 at 21:48):I've looked at them but haven't thought about them much. They seem pretty much subsumed by other ideas I know - sorry, I know that's an infuriatingly vague remark, but that's why I haven't dug into them more deeply.
James Fairbanks (Jun 01 2020 at 21:54):What subsumed them? I’d love to have a CT friendly approach that would work for that purpose
John Baez (Jun 01 2020 at 21:59):Well, first of all, discretized field theories have been extensively studied using chain complexes, CW complexes and other related structures.
James Fairbanks (Jun 01 2020 at 22:00):Thanks!
John Baez (Jun 01 2020 at 22:01):Here are some things:
https://vtechworks.lib.vt.edu/bitstream/handle/10919/27485/Arnold_RF_D_2012.pdf
John Baez (Jun 01 2020 at 22:02):https://www.amazon.com/Electromagnetic-Theory-Computation-Mathematical-Publications/dp/0521801605
John Baez (Jun 01 2020 at 22:03):https://arxiv.org/pdf/1111.2374
John Baez (Jun 01 2020 at 22:04):Then I guess it helps to know how a chain complex is a special kind of n-category; that's still somewhat esoteric knowledge.