For example, large parts of quantum theory, quantum computing and quantum information have been reduced to this diagramatic approach to such a degree that novel research insights are emerging from these techniques. A good introduction is Picturing Quantum Processes [1].
[1] https://www.cambridge.org/gb/universitypress/subjects/physic...
https://arxiv.org/abs/1510.05468
The (much older) paper Kindergarten Quantum Mechanics is probably the classic in this field
> If you translated the two diagrams into classical notation, you’d get the two terms at the top of that page.
So the vertical height is meaningful? Not just the arrangement of nodes on the string?
It seems like an ambiguous grammar (the two topologically equivalent diagrams) gives rise to two different parse trees (the two terms at the top of the page) which nevertheless have the same meaning?
Sorry if I'm being dense. I spent a couple of hours last night trying to understand the paper and it was pretty frustrating.
[1] http://brendanfong.com/programmingcats.html
[2] https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
[3] https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI...
Sure, the best ideas are already lurking into mainstream languages, but noone is building Monads and Functors. Implementations used in practice are not pure (flatMap on List accepts Sets/Options...).
These days I would probably jump on the Rust hype train and learned more about memory management and safety instead.
