Algebraic Semantics for Machine Knitting

Braid groups are really interesting, and they also come up in fluid mixing: https://people.math.wisc.edu/~thiffeault/talks/gordon2022.pd...

I've been hoping for a nice concrete example of braided monoidal categories for ages, who knew that the best one was string diagrams that represent actual string! Great post!

@the author - I assume you're aware that morphisms in symmetric monoidal categories can be represented using cospans of hypergraphs - do you know if there's a similar combinatorial representation for braided monoidal categories?

Back in the 1980s I was taking a foundational computer science course in which we derived Goedel's result using Cantor diagonalization. Excellent course. We were watching the TV version of Hitchhiker's Guide to the Galaxy at the time, too. One day I had the realization that since any recursively enumerable function could be interpreted as a computer program (given the right interpreter), that the sweater I was wearing was in fact possibly a computer program, and that all knitting (and some crocheting) was in fact just a manifestation of code in another language.

I then went on to realize any enumerable set could be similarly interpreted, including the entire countable population of Earth. And we already had the answer (42), but what was the question?

Reminds me of the work in the Carnegie Melon Textile Lab on the semantics and scheduling for knitting machine compilers (https://textiles-lab.github.io/publications/2023-knitout-sem...)

Does anyone know a good emulator for knitting machines? I'd love to play with these programs, but I'd like to get some practice before I start messing with real wool.

Still kicking myself for not buying a "3D Knitted Chisel Roll" back when Lee Valley had them --- last I checked it might have been possible to import one from Europe, but having a hard time justifying that.....

Speaking of computational knitting, I recently learned about "solid knitting" [1] which is awesome.

https://www.cs.cmu.edu/news/2024/solid-knitting

the formalization of textile programming really brings computer science full-circle. as a neoluddite i approve