thinking of getting into crocheting hyperbolic planes
it’s probably a great way to develop intuition for the weirdness of hyperbolic geometry, feeling the way the surface needs to fold in on itself to push all its internal connections out into 3D space
“As illustrated in the book, there is actually negative curvature and hyperbolic geometry all around us, but people generally see it without seeing it. You will develop an entirely new understanding by actually following the simple instructions and crocheting!“
SO COOL
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Christopher Alexander’s “fifteen properties” of lifelike beautiful geometry is so extremely relevant to my current research of trying to understand why typical computer-generated “mind maps” feel too slick, skeletal, soulless to really do justice to minds
I think you can simply go through the properties and ask if each one is present in a typical tree-structured "mind map” like this one.
“Levels of Scale,” yes, although not as vibrant as in nature.
"Proofs are programs" as in Curry-Howard seems to mostly make sense if you think of programs as having an input and an output like "A to B" which in logic corresponds to having one premise and one goal conclusion
But it might also make sense to think of programs as proof assistants that are open-ended so the user is playing around with rules and resources without aiming for one particular conclusion
Of course you can model this with co-functions and keep the Curry-Howard equivalence, but somehow this seems to be related to a divide in programming culture between interactive dynamic systems and static determinate functions