Very easy in math to get lost in misapprehended abstractions that turn out to be meaningless when you try a numeric example. Consider Abel trying to solve quintics, or anyone learning algebra in 19th C, or Haskell programmers today. So quite surprised by Weinstein's comment.
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I’m not very good at math, so I don’t have much sense of that. His experience there was quite different from mine.
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Reminds me of a piece from Our Own Metaphor, about "the people who can learn from books—those given to testing generalizations against examples they themselves construct and thus experiencing their truth at a deeper level instead of accepting it on authority"pic.twitter.com/EN3vnqNsna
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Interesting, thanks! I think I’ve automatically asked “well, is this actually true or coherent, since much of what I read or get told isn’t” about everything since I was maybe 10 or so. Including probably my own thoughts, although that’s still work in progress
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Heh, I'm pretty much solidly in the normie camp of start with the concrete. I rarely ever even get to the abstract versions of things. I tend to go sideways into metaphor and narrative at most.
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What I find is that before I can learn something complicated from the ground up, I need to have properly-calibrated feelings about it. The subject needs to have some kind of emotional landscape or narrative into which all the facts fit in a memorable way.
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I too like to learn broad propositions first and then fill in examples; I think it's the curse of the intellectual, to be dissatisfied with the concrete ("if this isn't true in all possible worlds, why both learning it?") But to be fair, there are different levels of abstraction.
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The curse of the high iq... I feel it too
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"abstraction" seems like a very fickle concept and "be less/more abstract" are not very good advice because the way they're applied is heavily dependent on the interpretation of this concept.
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I've noticed a contrast between the way mathematicians talk about math in general where they emphasize the deductive and formalized aspects of it and the way they talk about their own work, often much more informal and inductive.
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