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It's interesting to contrast this to the approach for developing style which Hamming recommends in The Art of Doing Science and Engineering—analytical, reflective, retrospective. But maybe this is a kind of "play," too.
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This made me wonder where the use of "taste" to mean the sense of aesthetics (rather than the tonguesense) came from. Etymonline gives this: (The word in the plain meaning dates to the early 1300s)
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Something I hadn't noticed before: in the "tonguesense" meaning, it can be either a verb or a noun. In the "aesthetics" meaning it can only be a noun (although, as a verb, "taste" also has the secondary meaning of "experience", as in "to taste victory")
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Taste is intuition and intuition is how our minds handle problems too complex to pick apart and handle analytically. Most of life. Following what seems fun and interesting seems a pretty good growth path IMO
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Following as 'aesthetic feel', i.e. doing what you 'like', is practically the defining characteristic of modern decadence. Instant gratification, binging shows, video games, junk/fast food, etc. Play is important, but IMO the reasoning here is off. Better explanations elsewhere.
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This is really interesting. I agree with your suggestion that what Hamming describes is a form of play. I think that sort of imaginative thinking is inherently rewarding. Sure it may not be easy and require self control but I imagine it’s like deliberate practice but for thought