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loqi comments on Bizarre Illusions - Less Wrong
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Category theory doesn't take 10 years to explain. You should be able to explain to a willing, intelligent friend in two full days, and get them to a point where they see the beauty.
I've done similar things, like explaining the elegant beauty of aircraft component structural analysis -- got a decent appreciation across in 10 minutes. ("You know how a chain is as strong as its weakest link? A component is as strong as its weakest failure mode...")
The point is, you can explain it. That's a lot more than you can do for (much of) art, it seems.
Art can be explained. There just aren't that many people capable of explaining it; explaining things is a difficult skill.
If you know that art can be explained, then presumably you've encountered an explanation of it. Any chance you could point us in the direction of it?
See my other comment.