maybe "learning" math is not the right name for what i have in mind; being taught math would probably be worse than Civ/AOE/etc played "seriously for fun" (like, serious AOE people actually do math and experiments and theory to get good build orders, tactics, etc).
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Odgovor korisnicima @argletargle @alexeyguzey
"teaching" real math probably looks somewhat like being a good meditation teacher, at least relative to how math is usually taught; you're more trying to get the student to be "turing complete" ASAP, rather than imparting some specific info / understanding, though info also good
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Odgovor korisnicima @argletargle @alexeyguzey
but anyway. why math? because what i'm calling "real math" is about seeing all the way into the core of the structure of things. playing AOE really well... it has way more virtue of empiricism than tasteless math.
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Odgovor korisnicima @argletargle @alexeyguzey
but, you aren't by default led to think about things **more deeply in some general sense** than you've ever thought about things before. (i'm groping for my point here...) in other words: math is about investing heavily in generalization.
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Odgovor korisnicima @argletargle @alexeyguzey
not talking about the often-bad kind of generalization, where you drop important aspects of some phenomenon and then call it "more general" because your thoughts depend on less detail. talking about the good kind.
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Odgovor korisnicima @argletargle @alexeyguzey
the good kind is where you explain all the data better / unify all the skills more elegantly. real math is about doing that iteratively, each time re-including your new understanding into the pool of data to be explained / understood.
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Odgovor korisnicima @argletargle @alexeyguzey
maybe at the most basic it's just: learn to stick with looking at something that you have no idea how to go about understanding, until your brain invents new understandamathings. difficult but trainable skill, better feedback in math.
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Odgovor korisnicima @argletargle @alexeyguzey
though, the better feedback in math is also easily goodhartable. (i personally do not understand number theory or the appeal of number theory, and always have a slight sneaking suspicion that a lot of it is sort of just noticing that simple questions can be super hard to answer
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Odgovor korisnicima @argletargle @alexeyguzey
... and then not getting bored with trying really hard to answer the questions, even though they're not otherwise interesting)
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Odgovor korisnicima @argletargle @alexeyguzey
all this about math being about "seeing into the core of things" cashes out in many ways, but for example, you have lots of physics insights coming along seemingly necessarily with tough math, eg electromagnetism (field theory), GR (riemannian geometry), QM (hilbert spaces)
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like, only doing math when you're led to it directly by something else you were doing... is actually a cool thing people should try; but i think even better is accounting for the straightforward induction saying that that strategy doesn't shave the yak enough.
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