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?
I suppose if nothing else, you could encode Wang tiles (https://en.wikipedia.org/wiki/Wang_tile) into knitting and then that's Turing-complete? Or would there be some better CA to encode?
42 is a stand in for 41 and 43 which are some twin prime
for me to further elaborate on this crazy idea that haunts me (I must admit I also haunt these ideas) requires a twin prime theorem which we are still waiting for in 2025....
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?
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.
Someone else mentioned the acrylic, I'm going to mention Scarlett Sparks' Open Source Knitting Machine if part of the fear is actually investing in the machine
https://github.com/ScarlettSparks/KnittingMachine
Possibly off-topic, but if you're looking to reduce your costs you should look at acrylic yarn. There's also cotton yarn if you're looking for something less scratchy :)
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.....
That also links to an older piece about a software project for knitting machines that's really neat. I've been wondering for a while how difficult it would be to build a primitive one at home.
If out are willing to move the carriage back and forth manually, and transfer yarn manually (for increases and decreases, etc.), the route to go is buy an electronic Brother machine and replace the electronics. The old standard was the AYAB board that you constructed yourself. (the evilmadscientist.com version is no longer in production) https://www.ravelry.com/groups/ayab for help and to meet fellow travelers. (circuit board and components: https://www.etsy.com/shop/redpinkgreen)
The less DIY more professional looking way is the recently released eKnitter, which replaces the electronics, but in a manner that more closely resembles the original form factor of the machine. https://eknitter.com/produkt/eknitter/
Okay, one last project to share. If you are more a start from zero sort of person, see this wonderful set of videos on designing a 3d printable manual knitting machine. Realistically, more of a wonderful educational process you should see, than an economically viable one. (Meaning you can buy used mass produced hardware for cheaper.)
...as demonstrated by the analogy in the original post here, where he explains the concrete concept of knitting stitches by reference to the much more abstract concept of garbage collection in computer programming!
Braid groups are really interesting, and they also come up in fluid mixing: https://people.math.wisc.edu/~thiffeault/talks/gordon2022.pd...
The slides are a blast, thanks
Classic mathematicians!
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?
I suppose if nothing else, you could encode Wang tiles (https://en.wikipedia.org/wiki/Wang_tile) into knitting and then that's Turing-complete? Or would there be some better CA to encode?
sorry, 42 is not gonna take us much farther
42 is a stand in for 41 and 43 which are some twin prime
for me to further elaborate on this crazy idea that haunts me (I must admit I also haunt these ideas) requires a twin prime theorem which we are still waiting for in 2025....
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?
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.
Someone else mentioned the acrylic, I'm going to mention Scarlett Sparks' Open Source Knitting Machine if part of the fear is actually investing in the machine https://github.com/ScarlettSparks/KnittingMachine
Possibly off-topic, but if you're looking to reduce your costs you should look at acrylic yarn. There's also cotton yarn if you're looking for something less scratchy :)
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...)
"This work is in part a collaboration with folks currently and previously at CMU, including Jenny Lin, Tom Price, Jim McCann, and Hannah Fechtner."
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
That also links to an older piece about a software project for knitting machines that's really neat. I've been wondering for a while how difficult it would be to build a primitive one at home.
https://www.cs.cmu.edu/news/2018/software-automatically-gene...
If out are willing to move the carriage back and forth manually, and transfer yarn manually (for increases and decreases, etc.), the route to go is buy an electronic Brother machine and replace the electronics. The old standard was the AYAB board that you constructed yourself. (the evilmadscientist.com version is no longer in production) https://www.ravelry.com/groups/ayab for help and to meet fellow travelers. (circuit board and components: https://www.etsy.com/shop/redpinkgreen)
The less DIY more professional looking way is the recently released eKnitter, which replaces the electronics, but in a manner that more closely resembles the original form factor of the machine. https://eknitter.com/produkt/eknitter/
Okay, one last project to share. If you are more a start from zero sort of person, see this wonderful set of videos on designing a 3d printable manual knitting machine. Realistically, more of a wonderful educational process you should see, than an economically viable one. (Meaning you can buy used mass produced hardware for cheaper.)
https://www.youtube.com/watch?v=kUKiXIdw2pI&list=PLWDnfcUpk7...
As for build a primitive one at home, (assuming one == machine controlled knitting machine) see the journey of Gerard Rubio from OpenKnit to Kniterate
https://www.labonthecheap.com/the-openknit-machine/ https://www.kniterate.com
the formalization of textile programming really brings computer science full-circle. as a neoluddite i approve
...as demonstrated by the analogy in the original post here, where he explains the concrete concept of knitting stitches by reference to the much more abstract concept of garbage collection in computer programming!